CA1184991A - Grinding control methods and apparatus - Google Patents

Abstract

Abstract of Disclosure Grinding control methods and apparatus pertaining generally to maintaining the shape and sharpness of a grinding wheel, despite the tendency of the wheel face to deteriorate from the desired shape and sharpness, as grinding of a given workpiece or a succession of workpieces proceeds. Generally, as a common denominator of the novel features disclosed, a "conditioning element" is brought into rubbing contact with the face of the grinding element under specially controlled and unique conditions to (i) restore the desired shape (conventionally called truing), or (ii) to establish the desired degree of sharpness (conventionally called "dressing"), or to accomplish both (i) and (ii) simultaneously.
The methods and apparatus disclosed include creating the aforesaid controlled rubbing contact either while the grinding wheel is free of grinding contact with a workpiece or simultaneously while grinding is occurring, and then either continuously or intermittently. The methods and apparatus in many of their various embodiments involve use of a "truing element" or a "conditioning element" which may be a generally homogeneous metal, and in many cases the same metal as that of the workpieces being ground. This advantageously results in lower costs as well as greater productivity and workpiece quality (both size tolerance and surface finish). In their different facets, the disclosed inventive features involve truing of wheel faces in a fast, economical fashion by controlling relative surface speeds and feeds of the wheel and the conditioning element; conditioning wheel faces to be sharp or dull to provide efficient rough grinding or precise finish grinding with a desired surface finish; and workpiece size control (despite wheel wear reduction in wheel radius) by either no gage at all or a simple gage sensing the conditioning element rather than the workpiece.

Description

Field OI In.venti~n and Objects .
The present invention relates in general to methods and apparatus for grinding workpieces with rotationally driven grinding wheels of known types which structurally comprise abrasive grits bonded in a supporting ma-trix. In use, the grits become flattened and dulled under certain conditions, and they fracture or break out OI the supporting matrix so that the wheel wears down uncler otheY con~litions--not only causing reduction in the wheel radius but also deterioration vf the wheel face from the desired "form" or shapeO More particularly, the present invention relates to methods and apparatus fo:r conditioning a grinding wheel, iD e., restoring or maintaining a desired degree of wheel face sharpness and/or shape, as grinding of workpieces progresses~
It is the general aim of the invention to vastly enhance the speed, ef:eiciency and accuracy with which workpieces are ground to a desired size, shape and surface finish --relative to the speed, efficiency and accuracy ob-tainable through known and conventional practices of the grinding art.
More particularly, it is an object of the invention to control the condition, io e., sharpness and/or the shape of a grinding wheel face, despite the normal tendency for the wheel to become dull and lose its desired shape-- by methods and apparatus which not only depart radically from known and conventional practices :in the art but which yield greater economy and higher productivity for the grinding procedure O
:~ this latter aspect, it is an object of the invention to so control the interaction between a "conditioning element~ for example, a truing roll) and the face of a grinding wheel to bring or maintain the latter to the desired sharpness and desired shape --ancl with a less expensive conditioning ele-ment being re(~uired, \,vith r~elatlvely long life for the s~onditioning element, with little expenditure of time, and -thus with little or no robbing of time devoted to the grinding of workpiecesO
A related object of the invention is to achieve the grinding of workpieces through the use of a single grinding wheel which, during all different stages of action on a workpiece, is controlled to have the desired sharpness and form (wheel face shape~.
Specifically, it :Ls an object to t:rue (rnaintain shape) a grinding wheel face rapidly while leaving the whee:l. face gr its sharpO
Speci~ically, it is an object to true (.maintain shape) a grinding wheel face rapidly through the use OI a conditioning element which is low in cost (especially compared to the common diamond truing roll), lasts reasonably long, and is easily replaceable~
Specifically, it is an object to true (maintain shape) a grinding wheel face rapidly through the use of a conditioning element which is the same in material and shape as the workpieces being ground by the wheel, ancl which indeed ma.y be one of those workpiecesO
Specifically, it is an object of the invention to extend the useful life of a diamond truing element by a :~actor presently unknown but which appears to be at least ten or twenty times the use:Eul life presently obtained in the grinding art for a diamond chip truing element or roll.
A further object of the invention is to condition a grinding wheel face ~or sharpness and/or form in a reproducible fashion so that the grinding action is predetermined and known as the wheel continues in or is returned to its grinding con-tact with the work~piece.
Another object is to provide methods and apparatus by which a grinding wheel ~ace is readily made sharp during or for rough grinding, thus to promote efficiency o:E grinding action; and by which the wheel face is readily made smooth du.rillg or fo:r ~inal, .t`inisll grinding --thus to achieve a low microinch (smooth) surface firlish on the workpiece Still ano$her object of the invention is lo d~tain the foregoing advantages by wheel conditionîng action which transpires, either intermittently or continuously, while the wheel is grinding on a workpiece --thereby saving time and increasing pr oductivity of a given grlnding machineO
~ n important object of the invention is to achieve control of the "specific grinding energy" (SGE)J between a workpiece and a grinding wheel, by controlling the conditions of rubbing contact between the wheel and a conditioning element, A related object is to successfully grind thin or flexible workpieces without surface burn or other metalurgical injury and despite the fact that the grinding wheel being employed otherwise could only be infed to the workpiece with such small force and rate that the wheel would tend to rapidly dullo It is also an object of the invention to achieve the results of an in-process workpiece-sensing size gage in the grinding o:E
workpieces --and thus to obtain workpiece size control despite wheel wear-- by methods and apparatus which (a~ involve no sensing gage at all in some cases, or (b) l,vhich involve a conditioning element-sensing gage which may be much less e}~pensive and complex and operate over a lesser range of distances as cor.npared to a conve.ntional workpiece sensing gage.
These and other objects and advantages will become apparent as the following detailed clescription proceeds, taken in conjunction with the accompanying drawings, Identification of Drawing Figures FIGURE 1 is a diagrammatic illustration of an exemplary grinding machine with rotational and feed drives for the various relatively movable components, ancl with sensors for signaling the values o different physical parameters such as speeds, feed rates~
positions and torques.
FIG. lA is a generalized representation of a control system to be associated with the apparatus of FIG. 1 in the practice of the present invention according to any of ~everal embodime~ts.
FIGo 2 is a fragmentary, diagrammatic representation of a surface grinding machine (as contrasted to the cylindrical grinding machine represented in FIG. 1 ) and which as a matter of background illustrates the various relative motions for surface grinding and truing of the grinding wheeL
FIG. 3 is a fragmentary, diagrammatic illustration of a surface grinding machine having wheel feed motions different from those shown in FIG. 2.
FIG. 4 is a fragmentary, diagrammatic representation OI
a roll grinding machine to illustrate the various motions there involved FIG. 5 is a fragmentary, diagrammatic representation of a cylindrical grinding machine and corresponds, in simplified form, to FIGo lo FIG. 6 is a plan view, taken generally along line 6-6 in FIG. 5, and showing the face of a cylindrical grinding wheel which has deteriorated from the desired shape and requires restoration by truingO
FIG. 6A is similar l;o FIGo 6 but shows a grinding wheel having a "formed" face associated with a workpiece and a truing element having correspondingly shaped work surfaces and operative surfaces~

FIGo 7 is a vertical section, taken substantially along the line 7~7 in FIG. 2, and intendecl to show a grinding wheel having a cylindrical face acting on a generally flat workpiece in a surface grinder.
FIGo 7A is similar to lE~IG. 7 but illustrates a formed grind.ing wheel having a face other than one which is purely cylindrical in shape, and which grinds a formed surface on an associated workp.iece.
FIGo 8 is a simplified counterpar-t of E~'IG. 1 and shows a grinding wheel being conditioned by relative :rubbing ancl feeding contact with a truing element, the wheel being :Eree of gr.inding engagement with any workpiece O
FIG~ 9 is an electrical block diagram, to be taken with FIGo 8~ o~E apparatus constituting one embodiment of -the system shown generally in I?IG~ lA" for controlling the truing ratio T:R with which a grinding wheel is trued to restore its face to a desired shape~
FIG~ 10 is an electrical block diagram, to be taken in conjunction with FIG. 8, illustrating another embodiment of a control s~stem for maintaining the ratio TR at a desired value when truing action is occurring in accordance with the principles of the invention to be described.
FIGo 11 is an electrical block diagram, constituting another form of the control system of FIGo lA, and illustrating --together with FIGo 8-- the control of parameters to carry out truing in accordance with the invention when the truing element and the grinding wheel fall in Class III (to be defined).
FIG. 12 is to be taken with FIGo 8 and iLlustrates still another specific embodiment of control apparatus for effecting truing OI
a grinding wheel in accordance with principles of the present inventionO
FIGo 13 is an elect.rical hlock diagram, to be taken with FIGo 8, of still another control apparatus embotliment us,lble in the practice OI the present invention in maintaining the ST:E ratio (to be defined) within a predetermined range during truing of a gr inding wheel.
FIG. 14 is an electrical block diagram which, with FIG.
8, depicts a control me~od and apparatus embodiment for maintaining the STE ratio at a desired value.
FIG. 15 is similar to FIGS. 13 and 14 but relates to still another speciEic embodiment of a control system for carrying out wheel truing in accordance with one aspect of the invention.
FIG. 16 is a generalized graphical repre~entation of the 10 relationships between grinding wheel material removal rate and the STE
ratio, as well as the general relationship between STE and the resulting smoothness of workpiece surface finish obtained by grinding with the wheel after the wheel has been trued at various STE ratios.
FIG~ 17 is a simplified counterpart of FIG. 1 and illustrates the relative positioning of the different components when a grinding wheel is acting to grind a workpiece and is being simultaneously trued or conditioned by the action of a truing element~
FIG~ 18~ taken with FIG. 17~ is an electrical block diagram of one embodiment of the control system of FIG. lA, and by ZO which the STE ratio of truing action is controlled while grinding and truing are taking place simultaneously.
FIGSo 19~ ~O.and 21 are simplified diagrams illustrating the relative positions of a grinding wheel, a workpiece, and a truing or conditioning element at different stages within operations by which a truing element "follows with the gap" the wheel eace and periodically engages the wheel face while the wheel continues grinding of a workpiece.
FIGS~ 22A and 22B, when joined, constitute an electrical block diagram to be taken with FIGS. 17 and 19-21 for illustrating the manner in which periodic truing may be eEfected and with the truing 0 element "following with the gap".
~6--t.~l FIG. 23 illustrates diagrammatically one arrangement for periodically initiating the -truing operations in the apparatus of FIGSo 22~1 B.
FIG~ 24 illustrates an alternative embodirnent of apparatus for initiating the intermittent truing pr ocedures carried out by the system o:E FIGSo 22A, 22B at spaced instants which are deterrnined by the radius reduction or wear o the grinding wheel.
FIG~ 25 is a diagram.matic plan view of a grinding wheel, workpiece and truing element for form grinding, and indicates one manner of sensing that the wheel face has deteriorated or lost its desired shape.
FIGo 26~ taken with FIGo 25~ illustrates still another arrangement for initiating periodic truing procedures carried out by the apparatus of FI~GSo 22A, B at those successive instants in time when loss of shape by the wheel :face is detectedO
FIGo 27J taken with FIGo 17~ illustra-tes still another embodiment of control methods and apparatus, and in this case for controlling the SGE of grinding action by automatic adjustment of the parameters with which truing or conditioning action is simultaneously created O
:FIG, 28 is a simplified counterpart of FlGo 1 and shows the relative positions of grinding machine components while grinding and truing are occurring simultaneously with controls effected simply from a probe or gage sensing the truing elementO
FIG~ 29, taken with FIG. 28, illustrates another e.mbodiment of control methods and apparatus for effecting truing or wheel conditioning operations while grinding is occurring and with the STE ratio maintained at a desired value.
:FIG. 30, taken with !FIGo 28, is a block diagram of electrical apparatus for controlling the STE ratio at the grinding interface while grinding action and trwing action are occurring simultaneously~ -FIGo 31~ taken with FIG. 28, is a block diagram of electrical apparatus for controlling grinding of a part at a desired rate and to a desired size with continued conditioning of the wheel :Eace while grinding and truing are occuring simultaneously, and without the need for any in-process sizing gage.

Typical Grinding Machine Configuration and Components _. ~
FIC:URE 1 diagrammatically shows a typical grinding machine with its various relatively movable component~, together wi-l;h various sensors and driving motors or actuators. Not all of the sensors and actuators are required in certain ones of the nlethod and apparatus embodiments to be described, but FIGo 1 may be taken as an "overall" figure illustrating all o:f the various machine-mounted components which are employed in one embodiment or anol;her, so long as it is understood that certain ones of such components are to be omitted in some casesO
The grinding machine is here illustrated by way of example as a cylindrical grinder but the invention to be disclosed below is equally app~icable to all other types of grinding machines such as surface grinders, roll grinders, etc. The machine includes a grinding wheel 20 journaled for rotation about an axis 20a and rotationally driven (here, counterclockwise) by a wheel motor WM. The wheel 20 and its spindle or axis 20a are bodily carried on a wheel slide WS slidable along ways of the machine bed 22. As shown, the face 20b of the wheel is brought into relative rubbing contact with the work surface 24b of a part or workpiece 24, and the wheel face is fed relatively into the workpiece by movement of the carriage WS toward the left, to create abrasive grinding action at the work/wheel interfaceO
In the exemplary arrangement shownJ the workpiece 24 is generally cylindrical in shape ~or its outer surface is a surface of revolution) and supported on fixed portions o:E the machine bed 22 but journaled for rotation about an axis 2'LaO The workpiece is rotationally driven (here, counterclockwise) by a part motor PM rnounted on the bed 220 Since the workpiece and wheel surfaces rmove in opposite directions at their interface, the relative surface speed of their rubbing 3 ~

contact is equal to the sum of the peripheral surface speeds of the two cylindrical elements.
Any appropriate controllable means may be employed to move the slide WS left or right along the bed 22, including hydrawlic cylinders or hydraulic rotary motors. ~s here shown, however, the slide WS mounts a nut 25 engaged with a lead screw 26 connected to be reversibly driven at controllable speeds by a wheel feed rmotor WF'M
fixed Otl the bed. It may be as,sumed for purposes of discussion that the motor WFM moves the slide WS, and thus the wheel 20, to the left or the righ-t, according to the polarity of an energizing voltage Vwfm applied to the motor~ and at a rate proportional to the magnitude of such voltage.
To sense and signal the actual rate at which the wheel 20 is being fed, a dc. tachometer 28 is mechanically coupled to the lead screw 26 or the shaft of the motor WFM, the tachometer producing a signal in the form of a dc. voltage FWs which is proportional to the bodily feed rate of the slide WS and the wheel 20. Of course, any of a variety of alternative feed rate sensors or signaling means may be employed .
Also, any suitable means are employed as a position sensor 29 coupled to the slide WS or the lead screw 26 to produce a signal PWs which varies to represent the position of the wheel as it moves back or forth. In the present instance, the position of the wheel is measured along a scale 30 (fixed to the bed) as the distance behveen a zero reference point 31 and an index point 32 on the slide. 'rhe refererlce and index points 31 and 32 are for convenience of discussion here shown as vertically alined with the axes '~4a and 20a and the signal PWs represents the position or horizontal distance of the wheel axis 20a relative to the workpiece axis 2~a. C)ne suitable position sensor 29 - .lO ~

may comprise a bi-directional pulse generator feerling pul~es into a reversible counter whose digital count contents are applied to a digital-to-analog converter which produces the signal ~ws as a variable dc. voltageO Many other known forms of position signaling devices farniliar to those skil]ed in the art may be used as a matter of choice.
In the practice of the invention in certain o its ernbodiments, it is desirable (for a purpose to be explained) to sense and signal the power which is being applied for rotational drive of the grinding wheel 20, and also to sense and signal the rotational speed of the wheel. While power may be sensed and signaled in a variety of ways, FIG. 1 illustrates ~or purposes of power computation a torque transducer 35 associated with the shaft which couples the wheel motor WM to the wheel 20. The torque sensor 35 produces a dc. voltage TORW
which is proportional to the torque exerted indriving the wheel to produce the rubbing contact described above at the interface of the wheel 20 and the workpiece 2a~. The wheel motor WM is one which is controllable in speed, and while that motor may take a variety of forms such as an hydraulic motorJ it is here assumed to be a dco motor which operates at a rotational speed (')w which is proportional to an applied energizing voltage Vwm. As a convenient but exemplary device for sensing and signaling the actual rotational speed of the wheel 20, a tachometer 36 is here shown as coupled to the shaft oE the motor WM
and producing a dco voltage G )w proportional to the rotational speed (eO g., in units of r. p. rn. ) of the wheel 20.
In similar fashion, it is desirable in the practice of the invention according to certain ones of the embodiments to be described that the power and rotational speed of the workpiece or part 2~ he signaled directly or indirectly. For this purpose, and as e~plained further below~, a torque transducer 38 is associa-ted with the shat`t 3~
which drivingly couples the part motor PM to drive the workpiece 24.
The latter torque transducer may take any suitable known form and it will here be assumed that it produces, as an out;put signal, a dco voltage TORp proportional to the torque which is exerted by the motor PM in rotationally driving the part 24 counterclockwise during grinding action. The rotational speed of the part 24 is contr ollable, and in the present instance it is assumed that the rnotor PM ~rives the part 24 at an angular velocity ~)p proportional to the magnitude ot a dco energizing voltage Vpm applied to that motor. Further, to sense the actual angular velocity of the rotationally driven part 24, a tachometer 39 is coupled to the shaft of the motor 39 and produces a dco signal G~p proportional to the workpiec e speed O
AgainJ although not essential to the practice of the invention in all of its embodimerlts, FIGI~E 1 illustrates a typical and suitable arrangement for continuously sensing and signaling the size (i~ eO, radius) of the workpiece 24 as the latter is reduced in diameter due to the effects of grinding actionO Such workpiece sensing devices are often called "in-process part gagesl' and one known type of such gage operates on the principle of variable inductive coupling between a probe and the metallic workpiece surface as the gap between those two components changesD While the invention is not limited to the specific in-process work gaging arrangement here illustrated, FIG. 1 shows a work-sensing gage 40 carried on a probe slide PS disposed to the left of the workpiece 24 and mo~able horizontally along the ways oE the bed 22. The gage 40 includes a probe 41 extending along a horizontal line extending through the axes 24a and 20aO It includes known circuitry by which a probe signal PSIG is produced so as always to be proportional to the gap or clearance CL bet~veen the tip of the probe 41 and the adjacent surface ot`-the workpiecc. Because the 3~1 workpiece in many instances will be ground down to re~luce its radius considerably during the course of a given grinding operation, the gage 40 is associated with a positioning servomechanism which acts always to keep the clearance CL substantially equal to a constant but selectable valueO As here shown, the probe slide PS carries a nut 42 engaged with a lead screw ~3 reversibly driven by a probe feed motor PFM
having its stator rigidly :Eixed to -the bed 2~o The motor P:~'M is here assumed to be a dc. motor wh.ich rotates in a direction according to the polarity of, and at a speed proportional to the magnitude of, the energizing voltage Vpfm applied thereto from a suitable driver amplifier 44 whose input signal comes from the output of an algebraic summing circuit 45. The latter circuit receives, as a positive input, the signal PSIG which is proportional to the physical clearance CL; and it receives as its negative input voltage CLd created at the wiper of a potentiometer 47 energized from a suitable constant dc~ voltage source.
Whenever the actual clearance CL is larger or smaller than the desired clearance CLd, the output of the summing circuit 45 is positive or negative in polarity and proportional to the errorO Thus, the motor PFM is energized to turn the lead screw 43 in a direction to shift the slide PS right or left until the actual clearance CL is restored to the set point value CLd. As the workpiece 24 is gradually reduced in diameter, therefore, the probe slide will follow toward the right to maintain the gap CL constant.
In order to produce a signal which always represents the radius Rp f the workpiece, a position sensor and signaling device 48 is suitably coupled to the probe slide PS, or as here shown, to the lead screw 43. The position sensor 4$ may take a variety OI forms and may be similar to the sensor 29; it need only be understood that it produces an output signal Pps here assumed to he a clcO voltage which in magnitude is proportiorlal to the r~dius of the worL-~piece 24 measured from the reference point 31 on the scale 30. That is, the position sensor 48 is initially adjusted such that when the probe 41 is spaced from the workpiece 24 by a distance CL~ then the signal Pps in its magnitude corresponds to the abscissa Pp~3 labeled on the scale 30 in FIG. lo As the workpiece 24 reduces in diameter, the probe sl.ide PS will rnove to the right to keep the clearance CL constant, and the signal Pps will :l~all in value so that its :magnitude is continuously proportional to the radius Rp of -the workpiece or part 24.
It may also be desirable in carrying out certain aspects of the present invention to create a signal which represents the rate at which the probe slide PS is being moved and which thus represents the rate R' at which the radius of the workpiece 24 is being reducedD For this purpose, a tachometer 49 is coupled to the lead screw 43 and produces a signal Fps in the forrn of a dco voltage proportional to the linear velocity at which the slide PS is movingO
As will be treated more fully below, as grinding o:E the part 24 by the wheel 20 proceeds, the wheel may not only becorne dull but its ~ace may deteriorate from the desired shape. AccordinglyJ it has been the practice in the prior art to periodically "dress" the grinding wheel to restore sharpness and/or periodically "true" the grinding wheel face in order to restore its shape or geometric form to the desired shape. These related procedures o:E dressing and truing will here be generically called "conditioning" the wheel face, and the invention to be described in some detail below deals primarily with procedures for conditioning a grinding wheel :face in novel and advantageous fashions.
For future reference, it may be noted here that the grinding rnachine of FIG. 1 includes a coriditioning element or truing roll 50 having an operative surface 50b which conforms to the desired 3~
wheel face shape. Whenever truing or dressing is required or desired, the operative surface of the truing roll 50 may be relatively fed into relative rubbing contact with the wheel face 20b in order to either wear away that wheel face so it is restored to the desired shape, or to affect the sharpness of the abrasive grits carried at the wheel face Thus, FIGo 1 shows the truing roll 50 as being mounted fc)r rotation about its axis 50a on a spindle supported by a t:ruing slide TS movable to the left or right relative to the wheel slide WSO That is, the truing slide TS is slidable along the ways formed on the wheel slide WS and it may be shifted or fed to the left or the right relative to the index mark 32 by a truing feed motor TFM mechanically coupled to a lead screw 51 engaged with a nut 52 in the slide TS. The motor TFM has its stator rigidly mounted on the wheel slide WS so that as the lead screw 51 turns in one direction or the other, the slide TS is fed to the left or right relative to the wheel slide WSO The motor TFM is here assumed, :Eor simplicity, to be a dc. motor which drives the lead screw in a direction which corresponds to, and at a speed which is proportional to, the polarity and magnitude of an energizing voltage Vtfm The position of the truing roll 50 and the truing slide TS
is measured, for convenience, relative to the index mark 32 on the wheel slide WSO As here shown, an index mark 54 vertically alined with the axis 50a indicates the position PtS of the wheel 50 along a scale 55 on the wheel slide, such scale having its zero reference location alined vertically with the axis 20a and the index mark 320 In order that the position of the truing roll 50 may at all times be known, a suitable position signaling device 58 is coupled to the lead screw 51.
The device 58 may take any one of a variety of known forms and may be similar to the position sensor 29 previously described; in any event, it produces a signal Pt~ which in magnitude is proportional to the physical position PtS along the scale 55, i~ e., proportional to the distance between the axes 20a and 50a as the slide TS moves to the leIt or to the right~
For reasons to be explained 'below, it is desirable that the rate of feed or translation of the slide TS be signaled and known~
For this purpose a tachometer 59 is couplecl to the lead screw 51 and produces a dc. voltage FtS which in magnitude and poLlrity corr esponds to the velocity and direction with which the truing slide is at any instant 'being moved.
When the conditioning element 50 is employed in a cylindrical grinding machine, it will usually take the form of a cylindrical roll having an operative surface which conforms to the desired shape of the wheel faceO Jn order to produce the relative rub'bing of the wheel and truing roll 50, the latter is rotationally driven or braked at controllable ,speeds by a truing motor TM which is mounted upon, and moves with, the truing slide TS. Merely for simplicity in the description which ensues, it is assumed that the motor TM is a dc. motor which may act bi-directionally, i. e, either as a source which drives the roll 50 in a clockwise direction or which affirmatively brakes the roll 50 (when the latter is driven cO w~ by the wheel 20 in contact therewith) by torque acting in a c. cO wO direction. It is known in the motor art that a dc. motor may be controlled to act as a variable brake by regenerative action. ~ssuming that the grinding wheel 20 has been brought into peripheral contact with the roll 50, the motor TM may thus serve as a controllable brake producing a retarding effect proportional to an energizing voltage Vtm applied thereto. E desired, one m~y view the m~tor as an electromagnetic brake creating a variable torque `by which the rotational speed ~te of -the truing roll 50 is controlled by variation of the applied voltage Vtm- In this fashion, the relative rubbing 3~
surface speed between the wheel face and the truing roll 50 may be controlled by controlling the braking effort exerted by the motor TM
through a shaft coupled to the roll 50.
Also for a purpose which will become clear, it is desired to sense or control the power expendecl in either driving or braking the truing roll 50 by the ac-tion of the motor TM during the r e~lative rubbing con-tact~ While a variety of known power sensing devices may be utilized~ the arrangement illustrate(l by way of cxample in F'IG. 1 includes a torque transducer 60 associatecl with the shaft which couples ~0 the motor TM to the truing roll 50~ That transducer produces a signal in the form of a dc. voltage Tt~Rte which is proportional to the torque transmitted ~either by motoring or braking action, but usually the latter30 Also, the rotational velocity of the truing roll 50 is desirably sensed and signaled ior reasons to be made clearO Fs~r this purpose, a tachometer 61 is coupled to the roll 50 or to the shaft of the motor/brake TM and it produces a dc. voltage G.);e which is proportional to -the speed (expressible in r. pO mO ) with which the roll 50 is turning at any instantO
During the course OI rubbing co~act be-tween the conditioning element 50 and the grinding wheel 20J the former may wear down somewhat and thus be reduced in radius. It is desirable to sense and signal the radius of the truing roll 50 in order to practic the present invention in certain ones oi` its embodimentsO While a variety of dimension-sensing gages may be used for this purpose~
FIGo 1 shows an inductively-coupled gage 65 which is generally similar to the gage 40 previously described but acting to sense the surface of the roll 500 ~s here shown, the gage 65 is rigidly mountecl on the slide TS sc that its probe 66 is spaced by a gap ~Ra i`t`On-l the operntive surface 50b oi` the roll 50~ The inilial distarlce t`L~om the~ a~is 5Qa - L7~

to the tip OI the probe 66 is rneaswrecl ancl kno-wn; it is here labeled Rio This distance will remain constant even though the radiws of the truing roll 50 is reducedO The gage 65 includes known circuits for producing an output signal AR proportional to the physical gap ~\RGo As the radius nf the roll 50 reduces so that the gap ~RG increases, the signal ~R
will correspondingly increase. The initial distance Ri is represented by a voltage P~iV obtained from the acljustable wiper of a potentiometer 68 and Eed to the positive input of an algebraic summing circuit 69 The latter receives the signal ~R as its negative inputO The OUtpllt of the summing circuit 69 is equal to the difference Ri ~ ~ ~nd thus at all times represents the radius ~te OI the truing roll 50. In other words, the signal Rte produced by the summing circuit 69 in FIG, 1 is proportional to and repr esents the physical distance labeled Rte immediately above the scale 55O Still further, it may be desirable to sense and signal the rate at which the radius of the truing roll 50 is being reduced while truing or dressing action is taking place. For this purpose, the signal ~R is fed through a known electronic differentiating circuit 70 which is shown as producing an output signal QR~o Thus, when the raclius E~te of the roll 50 is being reduced at a rate R'te (expressible in inches per minute, f~ example) and the signal ~R
is increasing as the radius Rte decreases, the signal '~R' is proportional to the rate of change ot` ~R and therefore represents the radius reduction rate R' te FIGo lA is a generic block representation of a control system 71 employed in the various embodiments of the invention to be described and which operates to carry out the inventive methodsO In its most detailed form, the control system r eceives as inputs the signals PPs~ ~S PWS~FW~PtS~l~t~ te~R't~ TORp, ~Vp, TORW, W~, TO~eJ
and Wte produced as shown in FIG. 1~ and it provides as output signals 3~

th motor energizing signals Vpm, Vwm, Vtm rotational speeds of the workpiece 24, wheel 50 and truing roll 50 --as well as the signals Vwfm and Vtf which determine the feed rates of the slide WS and the slide TS. Yet, it will become apparent that not all Of the sensors, and signals representing sensed physical variables, need be used in the practice of all embodiments of the invention.
Several typical but different embodirnents will be clescr ibed in some detail, both as to apparatus and methocl, in the following portions of the present specification.

10 Prior Art Practices In Truing and Dressing _ ., . , , _ When a grinding wheel is actively grinding a workpiece, two things usually occur. At the commonly accepted ranges of feed rates and speeds used with a given wheel acting on a given workpiece rnaterial, the wheel becomes progressively duller; the torque required to drive the wheel increases, and if the speed OI the wheel rotation is maintained, the wheel driving power increases until it reaches or exceeds the maximum, safe power at which the wheel-driving motor is rated. More heat is generated at the workpiece sur~ace and the 20 possibility of "burn" or metallurgical damage at the work surface increases as the wheel becomes duller and duller.
As a second e~ect, however, the wheel face may wear down (reduce in radius) unevenly so that its original, desired shape will deteriorate. This is especially troublesome when "formed" wheels (having wheel faces which are not purely cylindrical in their desired shape) are being used. To grind the desired shape on a work surface rubbed by the wheel, the wheel face must conform rigorously to that desired shape.

9~

It has been the prior practice in the industry, therefore, to periodically "dress'l a wheel face, i. eO, to "sharpen" its grits, as it becomes dull. In simple systems the wheel is 'Idressed'' after each of successive predetermined time periods of grinding have elapsed or a certain number of workpieces have been groundO In these situations~
the grinding is carried out with a fi~ed feed rate and the operating wheel speed is made high in the hope that wheel wear rate will be low--in order to get longer life out of a given wheelO lhe "dressirlg" is commonly accomplished by causing a single point diamon~ tool to trace along the wheel face so it in effect cutæ away a small layer and exposes fresh grits whose edges and corners are sharp.
When loss of form or shape occurs, the wheel must be "trued" -to restore its shapeD Again, the single point diamond tool may be used to trace along the face and cut away the high spots until the whole face takes on the desired shape. Truing has also been accomplished through the use of "truing rolls" which are almost universally manufactured to consist of small diamond (synthetic or natural) chips bonded in a matrix of hard material. The operative surface of the truing roll is shaped to conform to the desired shape for the wheel face (cylindrical or otherwise) and it is fed into relative rubbing engagement with the wheel face to purposely wear of f the high spots.
All other conditions remaining constant, a dull wheel requires more energy to remove a given volume of metal from a workpiece, than does a sharp wheel. k one defines "Specific Grinding Energy" (SGE) as the ratio of (i) the power applied -to effect grinding to (ii) the volumetric rate of removal of material from the workpiece, then a wheel when dull will operate with a higher SGE than the same wheel when sharpO

Applicant's earlier United States Patents 3, 653, 855 and 3, 798, 846 teach that a wheel may be kept at and returned to a desired degree of sharpness or dullness by maintaining the SGE with which it operates at a predetermined set point value. If the actual SGE (i) increases above or (ii) falls below the set point, then (i) relative rubbing surface speed is decreased or feed rate is increased, or (ii) relative rubbing surface speed is increased or feed rate is clecreased. Such corrective actions either change the "velocity impact strength" of the wheel grits or the feeding forces on the grits so that fracturing of the 10 grits (which sharpens them) is changed, and the operation of the wheel thus restores automatically to the set point value of SGE. To a major extent, the need for wheel "dressing" is eliminated if the methods and apparatus of applicant's earlier patents are employed.
Those methods and apparatus, when used to their best, do result in the grinding wheel wearing away faster than experienced in conventional industry practice under which wheel speed is maintained high to lessen wheel wear rate and reduce the expense OI shortened wheel life. Yet, the SGE method and apparatus provide an overall benefit in cost and efficacy of grinding parts since any increased 20 expense of buying more grindi~g wheels is more tha~ offset by the saving in time and labor which flows from ~i) eliminating "dressing"
tools and "dressing" time and (ii) grinding of required amounts of metal from workpieces at higher rates in a machine OI a given wheel motor power rating.
Nevertheless, with either conventional grinding procedures or the SGE method~ the grinding wheel will lose shape or form. It mU~t be trued. Indeed, since wheel wear rate will be greater with the preferred practice of the SGE method, loss of wheel face shape may be accelerated.
Thus, there is a need to see that the wheel face is "trued" and restored ~"

3~

to its desired shape; and this need is especially critical when "formed"wheels are used under conditions which aim to increase the grincling rate by accepting increased wheel wear ratesO
"Truing" as carried out in prior art, industry practice with diamond chip truing rolls has been, to the extent of applicant's knowledge, conducted at relative surface speeds and infeed rates which are not chosen on a basis which has any rekltion to the abracling action which the truing roll creates on the grinding wheelO In a conventional cylindrical grinding machine, for example, the truing roll is often rotationally driven at about 17~5 r.p. m., regarclless of its diameter, simply because that rotational speed is the one produced by a standard, low cost, four pole induction motor directly coupled to the truing rolL
The grinding wheel is rotationally driven at its normal grinding speed (typically in the range of about 4000 to 12, 000 peripheral surface feet per :minute), and infeeding of the wheel relative to the diamond truing roll is arbitrarily conducted in steps of O 001" followed by pauses of 3 or 4 secondsO Such inEeeding is that recommended by the manufacturers OI diamond truing rolls based upon experience as to how fast a diamond roll can be "pushed" into a grinding wheel without causing chatter or undue wear and damage to the diamond rolL Generally, a grinding wheel which has been trued with a diamond truing roll is "dull" because the diamond chips (the hardest material known) smooth o~ the sharp corners and edges of the grits exposed at the wheel face, The grinding industry has also used what is known as "crush truing"O In crush truing, there is no relative rubbing contact between the wheel ~ace and the operative sur~ace of a very hard (e~ g~, tungsten carbide) truing roll. Rather, that truing roll is simply journaled with freedom to rotate about its axis and brought with ver~r high pressures into contact with the rotationally driven grillding ~,vheel. The wheel face thus rotationally drives the truing roll to make their surface speeds equal and without rubbing or abrading action, and the truing roll "crushes" off high spots on the wheel face until the latter reasonably conforms to the shape o~ the operative surface of the crush truing roll. Crush truing requires a machine of unusual strength and stiffness to create the high forces required; it o-ften does not precisely shape the wheel face because chunks of the wheel material may "cru.sh" out unevenly and in a Eashion which cannot be known in advance. The very high Iorces involved result in a relatively short useful life of a "crush 10 truing roll" even though the latter is rnade of a very hard steel or metal alloy~ It has been observed, however, that a grinding whee~l, immediately after a crush truing operation, is very sharp. This comes about, it is believed, hecause crushing produces fracturing of the bonds between the wheel grits and their supporting matrix so that "fresh" grits are exposed which, due to the lack OI previous rubbing, are not worn or flattened ofI.
So far as applicant is aware, those skilled in the art have not suggested systematic, varied control of, or actually systernatically controlled, relative surIace speed of rubbing contact and relative infeed 20 at the interface between a grinding wheel and a conditioning element (e.g., truing roll) during the truing procedure. Nor has the art r ecognized that conditioning elements may advantageously be made of various available hard metal alloys (incl-lding the same material as that of the workpieces being ground)~ as contrasted with expensive diamond rolls, while still obtaining the desired truing and/or wheel sharpening action.
DeIinitions and Symbols _ _ _ _ As noted above, during the use of a grinding wheel, it needs to be "dressed" to increase or dccrease the sharpness of grits which are exposed at the wheel face, a nd it neecls to be 'Itr~lec~" to restore ` '~.4 the wheel face shapeO ~s generic to dressing and/or truingJ I have chosen the term "conditioning". Thus I define:
Wheel ~onditioning: The modification of the face of a grinding .
wheel (i) to affect its sharpness (making it either duller or sharper); or (ii) to affect its shape, essentially to restore it to the desired shape; or (iii) to carry out both fwnctions (i) and (ii).
Wheel Conditioning Element: Any member havin~, an operative surface conforming to the desired shape of a grinding wheel to be conditioned, and which can be brought into contact with the face of the wheel to create both relative rubbing and feeding which causes material to be remov~d from the wheel ~and in some cases undesirably causes material to be removed from the conditioning element)O Throughout this specification the term "truing element"
will be used as synonymous wi-th "conditioning element" merely for convenience.
Relative Surface Speed: The relative surface velocity with which .
rubbing contact occurs at the wheel face/operative surface interface. E the wheel surface is moving in one direction at 3000 feet per minute and the operative surface is moving at 1000 feet per minute in the opposite direction, the relative surface speed is 4000 feet per minuteO If the operative surface is not movingl then the relative speed of rubbing is equal to the surface speed of the wheel face due to wheel rotationO If the operative surface is moving in the same direction as the wheel face, the relative surace speed is the difference between the surface velocity of the wheel face and the surface velocity of the operative surfaceO
:CE those two individual surface velocities are equal, the relative surface speed is zero, there is no relative rubbing of the wheel face and operative surface, even though they are in contact.

Thiæ latter situation exists duxing crush truirlg.

-2~L -

3~

elative Feed: The relative bodily movement Or a grinding wheel and conditioning element which causes progressive interference as the relative rubbing contact continues and by which the material of the wheel is progressively removedO It is of no consequence whether the wheel is moved bodily with the conditioning element stationary (although perhaps rotating abou-t an axis) or vice versa, or if both -the wheel and elemen-t are movecl bodily, ~eeding is e~pressible in units of velocity, e. g., inches per minute.
Rate of Material Removal: This refers to the volume of material , = . .. _ . , . _ . .
removed from a grinding wheel (or some other component) per unit time. It has dimensional units such as cubic centimeters per second or cubic inches per minute. In the present application alphabetical symbols with a prime symbol added designate first derivatives with respect to time, and thus the symbol W' represents volumetric rate of removal of material from a grinding wheel.
~ similar fashions, the symbols P' and TE' respectively represent volumetric rates OI removal OI material from a part (workpiece) and a truing element.
From the introductory treatment of FIG, 1, it will also be apparent that the following symbols designate di~erent physical variables as summarized below:
PWR = powerJ io e., energy expended per unit time PWi~W = power devoted by the wheel motor to rotationally drive a grinding wheel PWR = power devoted by the part motor to drive or brake the part (workpiece) to create, in partJ the rubbing contact with the wheel PWRte = power devoted by the truing elemen-t motor to drive or brake a truing element to crea-te, in part, rubbing contact with wheel PWRWt = that portion oE PWRW d~votecl to truirlg actior PWRWg = that portion of PWRW ~evoted to grinding action PWRt = total power devoted to truing action PWRg = total power devoted to grinding action TORW = torque exerted to drive the wheel TORp = torque exerted to drive or brake the workpiece TOR~ = torque exerted to drive or brake -the truing element TORWg = -that portion of total wheel torque TORW applied to rubbing action at the grinding interface, when truing and grinclin~ are occurri.ng simultaneously TORWt = similar to TORWg, but that portion oX TORW applied to rubbing action at the truing interface FOR = the force, in a direction tangential to a grinding wheel periphery, on a grinding wheel, a truing roll5 or a workpiece due to rubbing action (~)w = rctational speed of grinding wheel ~typically in units of rO pO mO ) (~)p = rotational speed of workpiece, io eO, the part to be ground C~)t = rotational speed of the truing element Sw = the surface speed of the grinding wheel (typically in feet per minute) Sp = the surface speed of the workpiece or part Ste = the surface speed of the truing element Sr = the relative surface speed OI rubbing contact Rw = radius of grinding wheel Rp = radius of workpiece or par-t Rte = radius of truing element p = position of wheel slide ws Pps = position of probe slide Pts position of truing slide (relative to wheel axis) Fws feed rate (velocity) of wheel slide Fps = feecl rate (velocity) of p:robe slide -2~; ~

Fts = feed rate (velocity) of truing slide R'w = rate of radius reduction of wheel R'p = rate of radius reduction of part being ground R te rate of radius reduction of truing element L = axial length of wheel face or region of grinding or truing contact Ri = initial radial distance (as measured) from truing element axis to prohe tip ~R = spacing from probe tip to truing element sur~ace M' = the volumetric rate of removal cf rnaterial (metal) from the part being ground. Exemplary units: cubic inches per minO
W' = the volumetric rate of removal of material from $he wheel.
Exemplary units: cubic inches per minO
TE' = the volumetric rate of rernoval of rnaterial from the truing elementO Exemplary units: cubic inches per min.
NOTE: Any of the foregoing symbols with an added "d" subscript represents a "desired" or set point value for $he corresponding variable For example, ~vd represents a commanded or set point value for the rotational speed of the wheel.
Certain ones of the foregoing symbols will be explained more fully as the description proceedsO
There has already been mentioned ~as disclosed in the above-identified patents) the concept or variable called "Specific Grinding Energy" (herein designated by the symbol SGE). .It is the raffo c f energy used to the volume of material removed from a workpiece being groundO It might be expressed in numerical units of Ioot-pounds per cubic inch or watt-minutes per cubic centimeter, for exampleO If both the numerator and denominator are divided by the time which 3q~

elapses to remove the material, then that ratio becomes energy per unit time to material volume removed per unit time. The ratio is thus expressible as the ratio of two rates, i. e., rate of energy expended and volumetric rate of material removal, and thus it can be determined at any given instant while grinding is in progress. Energy per unit time is the classical expression of power (e.g., power is expressible as foot-pounds per minute, one horsepower being 33, 000 foot-pounds per minute). Volume removed per unit time is simply volwrnetric rate of removal, e.g., cubic inches per minute. [n summary:
10 SGE = Specific Grinding Energy; the ratio of (i) energy consumed in removing workpiece material to (ii) the volume of material removed. The same ratio is represented by the ratio of (i) power ~energy per unit time) to (ii) rate of material removal (volume of material removed per unit time) --i. e., PWR/M ' .
Exemplary units: Horsepower per cubic inch per minute, or gram--centimeters per second per cubic centimeter per second.
The present invention introduces a variable called "Specific Truing Energy" (herein designated STE). It will be described more fully below, but for ready reference, its definition is set out here:
20 STE = Specific Truing Energy; the ratio oE (i) energy consumed in r emoving wheel material to (ii) the volume of such material removed. The same ratio is represented by the ratio OI (i) power expended (energy per unit time) to (ii) rate oE material removal (volume of material removed per unit time) --i. e., PWR/W'. Exemplaryunits:Horsepowerper cubic inchper minute, or gram-centimeters per second per cubic centimeter per second.
Asnoted above, feeding motion requires only relative bodily movement of one component in relation to another. There are ,~

-2~3-z~-several different types of relative mvtions which occur in the cliffer-ent categories or types of grinding. These same different types of relative motions may also occur between a grinding- wheel and a truing element in order to create the wheel conditioning action to be descr ibed. It will be helpful to consider these various motions in order to understand that the present invention may be practiced to advantage in all types or categories of grinding, and that the appended claims are to be construed as generically embracing such various types of motion.
With the wheel 20 grinding on the part 24, as shown in FIG. 1J the wheel is driven by the motor ~TM and the part is driven by the motor PM in order to create the relative rubbing contact of face 20b and work surface 24b. The wheel slide WS is moved to the left by the motor WFM at a ~Ifeed rate" FWs proportional to the voltage Vwfm to advance th heel 20 steadily into the part 24 as the radius of the latter is progressively reduced. When this is occurring, the feed rate FWS
of the slide is equal to the sum of the rates R'p and R' at which the part and wheel radii are being reduced. In prior industrial practice, conditions are established which hopefully make R'w quite low in order to lengthen the useful life of the wheel 20 and reduce the expense of 20 frequently replacing the worn out (and expensive~ wheel with a new one.
It is apparent that in a cylindrical grinding rnachine (FIG. 1) the feeding motion of the wheel is along a horizontal path parallel to a radius of the wheel extending through the region of rubbing contact. This is here called "infeeding". It is the only relative feed which is required for cylindrical grinding (although as an obvious equivalent the rotating wheel could be bodily stationary and the part 24 then bodily fed to the right) and it results in material being removed by abrasive action from the workpiece (as well as rnaterial being removecl from the wheel due to whecl wear).

.~ "
~"
-2')-q~

But other relative feecling motions are crea,ted in other types of grinding machinesO Consider ~IG. 2 which generally illustrates a surface grinder wherein a grinding wheel 75 rotationa~ly driven about its axis 75a is supported on a wheel slide 76 horizontally translatable along path PA1 relative to a stationary workpiece 78 supported on the machine bed 79, In this case, the wheel slide is also vertically translatable along a path P~20 When the wheel periphery is positioned at a distance DEP below -the unground surface of the workpiece, and the slide moved toward the le~t, a thin layer of the workpiece will be ground o~f during each cross-feeding pass. The "down feed" is employed to determine the depth DEP of each horizontal feed "pass"
and to compensate for the reduction in wheel radius as wheel wear occurs. The term "feed" as used herein thus means any relative bodily movement of a grinding wheel and workpiece or truing element which causes physical interference to occur at the region of their relative rubbing contact, The more specific term "infeeding" is here used to designate relative motion between a wheel and workpiece along a line extending radially of the wheel axis and which has the effect of compensating fs~r wheel radius reduction (and whether or not it also produces the interference which resul~s in workpiece material removal3" Thus, in FIG. 1, the "feeding" and "infeeding" are the same; in FIGo 2, the "feeding" is the cross-feed motion along path PA1~ and the "infeeding" is along path P~20 Of course, it makes no difference whether any sort of feeding is created by keeping the wheel bodily stationary (although rotating~ and moving the workpiece or vice versa; it is the relative bodily movement of the two components which is necessary.
FIG. 3 i~lustrates a modified form of surface grinderO
EIere the workpiece 80 is stationary on a bed 81 and the rotationally ~9t9S~
driven grinding wheel 82 is journaled in a wheel slide 84 translatable along a horizontal path PA3 which lies parallel to the wheel axis 82a (as contrasted to the path P~l lying normal to the wheel axis 75a in FIG~ 2 ). The wheel slide 8~L is also translatable vertically along a path PA4 to adjust the depth DEP of each cross-feed pass and to compensate for wheel wear, and this constitutes "inEeed"O
Of course, in either FIGo 2 or FIG. 3~ it the wheel slide is not moved horizontally but is simply moved vertically downward to "plunge grind" an arcuate slot in the workpiece, that infeed motion would constitute the total feeding action, FIG. 4 diagrammatica~ly illustrates a roll grinderO
Here the wheel slide 83 is movable hori~ontally along a path PA5 and vertica~ly along path PA6 (the motions being similar to those of FIG. 3) but the workpiece is a roll 86 which is rotationa~ly driven about its axis 85~ Thus the rotational speeds and radii of the wheel 87 and the roll 86 jointly determine the relative rubbing surface speed, The "infeeding" occurs along path PA6 to control the depth of cut and compensate for wheel radius reduction due to wheel wear.
FIG. 5 is similar to FIGSo 2-4 except it illustrates a cylindrical grinding machine comiguration like that already treated in FIGo 1~
In summary:
(a) "Feeding" means relative motion which produces interference (and may or may not be infeeding).
(b) "~lfeeding" means relative motion of a wheel and workpiece along a path r~dial of the wheel axis.
The directions of feeding motion may be different in various types of grinding machines, as indicated above, but the grinding is always characterized by (i) rotation OI a grinding wheel about its a~is, (ii) relative rubbing contact at the wheel face and the work surface of a workpiece, whether or not motion of the workpiece contribwtes to such rubbing, (iii) relative infeeding of the wheel and workpiece at least to compensate for wheel wear and consequently wheel radius reduction, and (iv) relative feeding of the wheel and workpiece to produce interference and removal of workpiece m~terial (such feeding in some cases being in the same direction as infeeding)~
Exemplary Types of Tr~ung Elements As explained earlier, in the practice of the present invention the conditioning element (shown in exemplary form as a truing rol.l 50 in FIGo 13 has its operative surface 50b brought into contact (see FIGo 8~ with the :Eace 20b of the wheel 20 under certain circumstances and with certain control of variables to be described.
The objective of such contact is to wear off material from the wheel face, either for restoring the wheel face shape or for determining the sharpness of the exposed gritsO Analogously to "grinding contact", the conditioning element contact involves (i) rotation of the grinding wheel about its axis, (ii) relative rubbing contact of the wheel face 20h and the operative surface 50b whether or not motion of the conditioning element contributes to such rubbing, (iii) relative "infeeding" of the wheel 20 and element 50 to compensate for truing elemlent wear (if any) and (iv~ relative feeding of the wheel 20 and element 50 to produce interference and removal of wheel material (such feeding in some cases being in the same direction as infeeding).
In FIGo 2~ the conditioning element may take the :form of a block-shaped member 90 into rubbing contact with which the wheel 75 is fed, as illustrated by the wheel in the dashed line position 75c~
Motions of the wheel slide 76 along paths PAl and P~2 determine t.he relative feeding, while rotation of the wheel 75 crea-tes the ~elative rubbing contactO ~lternatively, the wheel 75 rnay be brought to the elevation shown at the dashed line position 75d and fecl to the right along path PAl to establish rubbing contact with a conditioning element in the Eorm of a roll 91 rotationally driven (or braked) about it~ axis.
this case, the wheel conditioning element and infeeding are es~entially similar to those created in the arrangements oE' FIGS~ 1 and 8.
In FI(~S. 3 and 4J the conditioning elernent 93 is shown as a cylindrical member 93 rotatable about i-ts axis. That member may'be moved down, or the wheel slide 84 may be moved up (or 'both), to establish the relative feeding and rubbing contact which will condition the wheel face. 1~ FIG. 5 (corresponding to FIGo 1) the conditioning element 50 is moved to the left, or the wheel 20 is moved to the right, or both, to establish the same sort of relative feeding and rubbing contactO
In summary, it is to be understood that a "conditioning element" may take various specific forms and shapes, and the contact between a wheel and a conditioning element may involve different types of specific feeding motions, although relative rubbing of the operative surface of the element and the wheel face is always involvedO
The conditioning element may have, but need not necessarily have, a shape or si~e which is the same as or similar to the workpieces to be ground, but its operative surface will always have a form or shape corresponding to the desired form or shape of the wheel face and the workpieces to be ground through the use of the wheel~
To pictorially confirm the difference between "~ormed"
grinding wheels and ordinary grinding wheels, brief reference may be made to FIG. 6 which is a diagrammatic plan view taken along line 6-6 in FIG~ 5~ Here the grinding wheel is intended to have a desired, purely cylindrical face 20b, io e,, a surface of revolution de~ined by -3~ -rotating a straight line, lying parallel to the axis 20a, about that axisO
The workpiece 24 is to be ground down to a perfectly cylindrical shape.
L.oosely speaking, the desired shape of the wheel face is Elat and straight along one axial element of the grinding wheel cylinder. But as shown to an exaggerated degree in FIG. 6, the wheel face will become rough and uneven ("lose Eorm") when the wheel has been used for a relatively short interval, especially at a high ra-te of rou~h grinding. Such loss of form may make the rough grinding of the part inefficient; certainly it will create a drastically unacceptable final surface finish on the workpiece if uncorrected prior to finish grinding and sparkoutO The "truing" operation involves bringing the conditioning elemen~ 50 into rubbing contact with the face 20b to wear off the wheel face down to the straight line 20d. Thus, truing to restore the wheel face to the desired shape involves purposely removing material from the wheel.
FIG~ 6A, by contrast to FIGo 6~ illustrates an example of a formed grinding wheel 20A rotatable about an axis 20Aa, It is to be used to grind a "V" notch in the periphery of an otherwise cylindrical workpiece 24A rotatable about an axis 24Aa, the work surface being at 24Abo FIG. 6A shows the wheel 20A with the ideal~, desired shape at its face 20Ab, while the face in a typically deteriorated condition is shown, purposely with exaggeration, at 20Abbo Observe that the sharp nose at the point of maximum radius is blunted and rounded off, and the sides of the "V" are irregular. To restore the wheel to the desired shape, the wheel face is brought into rubbing contact with a truing roll having an operative surface 50Ab which accurately conforms to the desired shape of the wheel face 20Abg thereby to wear down the deteriorated wheel face to the correct contour represented by lines 95. When a "formed" wheel (one having other thatl a purely -3~L -cylindrical face) is to be used in order to grind a work surface to some special shapeg the problem of loss of shape is accentuated~ and the need for truing becomes even more critical than in the case of a cylindrical wheel faceO
One normally tends to think of a cylindrical wheel in connection with surface grinding. This is illustr ated by FI~. 7 whiah is a diagrammatic view ta.ken along the line 77 in Flao 2. Here the loss of form from the desired cylindrical face shape creates the same problems explained with reference to FIG~ 6~ E~IGo 7A indicates, however, that the wheel 75A may have a Iormed face 75Ab in the configuration of two rounded ridges (merely as an example) intended to grind side-b~-side rounded grooves eætending across the slab-like workpiece 78A~ This simply confirms that form grinding with specially shaped grinding wheel faces may exist in all the various categories of grinding machines; and the need to efficiently true wheel faces to their desired shapes creates a major challenge in industrial grinding operationsO

A New and Basic Approach to Wheel Conditioning I ha~e discovered that the procedure of conditioning a gri.nding wheel, especially for purposes of truing the wheel :Eace, may be vastly impro~Ted (in terms o:E less time required, better accuracy of wheel face shape, lower cost OI the truing elements employed, and enhanced sharpness s~f the wheel a-t the termination of truing) by controlling the physical ~ariables of the wheel face/truing element engagement in a particular fashion.
First, I have recognized that when one wishes to true a grinding wheel, the objective is to remove material from the wheelO
My invention does not embrace procedures employing a single point diamond cutter used somewhat like a lathe tool to sllave of the ~,~rirlding ;~ rj wheel; on the contrary, my invention will find application and advantage in those cases where a conditioning element has an operative surface conforming to the desirecl shape of the wheel face --and wherein wheel material is removed by infeeding the wheel face and the element's operative surface into rubbing contact with one anotherO
Secondly, I initially recognized that because the objective is to remove .material from the whee]., a guiding principle lies in the fac$ that, when truing is occurring, the truing element rnay be viewed, in effect; as "grinding" material off the wheel as a consequence of the relative rubbing and infeeding of the two, Indeed, when a diamond chip truing roll is employed, it is plain that because diamond is vastly harder than the grits (for example, aluminum oxide or silicon carbide) in the grinding wheelg the diamond chips "grind down" the wheel face and the grits therein. That principle, I learned, is not sufficient as a guide in all cases because I later discovered that I can accomplish truing of a wheel with a truing element made o~ a material (metal alloy or other substantially homogenous material) which is of lesser hardness than the material OI the wheel grits. This is a startling discovery inasmuch as it bears little or no similarity to ordinary grinding action on a ~0 worl~piece because rarelyJ if ever" does one grind a workpiece of a first material with a grinding wheel having grits of a second material where the first material is harder than the second. ~ such a situation, the wheel wear rate will almost certainly exceed the workpiece wear ra.te --and grinding will proceed very slowly and at h:igh expense for replacing worn-out wheelsO
My invention was conceived fully by observing that a grinding wheel is not a substantially homogeneous body af materialO
Its "material" is a physical mixture of discrete, albiet sxnall, grits of a first hard material which are bound (bonded) in a supporting rnatrix of a second strong (in a tensile or compression sense) but perceptibl;y softer material. And from this I continued my thoughts to perceive that I could accomplish truing of a wheel in a controlled fashion if I
would establish relative rubbing speeds and feeds of a grinding wheel and truing element which (i) promote wheel wear and (ii) reduce or tend to minimize truing element wear.
To true a wheel, I create relative rubbing speeds and feeds of the wheel and truing element which --if one viewed the wheel a~
grinding on the element--would create very poor grindi.ng performanceO
That is~ the wheel wear rate is high and the truing element wear rate is low.
To do thi~ in accordance with my invention, (i) the relative surface speed o:E the rubbing contact between the wheel face and operative surface of the conditioning element and tii) the relative feeding of the wheel face and operative surface are conjointly established to make the ratio of (a) wheel material volumetric rate of removal to (b) element material volumetric rate of removal extremely high --and higher than anyone (to the extent OI my knowledge of the art) has ever achieved in practice or suggested in the literature. That ratio is symbolically expressible as W'/TE', and the control OI variables (as explained below) according to my invention involves making W' very high for a given level of TE'" or making TE' very low for a given level of W'O Ideally, for fastest and yet mos-t economical trulng action, W' is maximized within the capability and stiffness of the grinding machine being used, while TE' is minimizedO But to obtain significant benefits of the invention, it is not real.ly required that such maximum W' and minimum TE' actually be rea~ized"
There are, of course, many different specific materials which have been used to serve as (i) grits in a grinding~ ~,vheel alld (ii) -37 ~-$33~

workpieces which are to be groundO Just a few typical materials are listed below in ascending order of hardness, with those used for grits identified by an asterisk:
lo Aluminum 2D Cast Iron M:ild, low carbon steels, hardened by heat treating e.g~, 10!20steel

4. 1050 steel 1090 steel M Series Cutting Tool SteelsJ hardened by heat treat M 1 steel 7. M 2 steel etcO
80 Aluminum Oxide*
9O Tungsten Carbide lOo Silicon Carbide~'~
llo soFon Nitride* (known by trademark BOROZON) 12O Di~mond*
The foregoing list is not complete by any sense; it is intended only to indicate that the higher the number in the list, the harder is the materialO The list obviously could be expanded to include many other materials in the order of relative hardnessO
Now, for the purpose of grinding workpieces of a given m~terial, it is the logical practice o~ industry to procure and use grinding wheels having grits that are harder than the workpiece material, and yet which are near the lowest cost of the several grit materials which wil:l do the jobO For example, cast iron workpieces could be ground with grinding wheels having diamond or silicon carbide grits;
but since aluminum oxide grits do the job adequately and are less -3~3 -costly, they would be the choice, Similarly, 1020 steel will be ground with a wheel having aluminum oxide grits, but the more expensive silicon carbide or diamond grits could in theory be used to advantage if cost were no factor~ On the other hand, M2 steel 90 closely approaches aluminum oxide in hardness that wheels having bororl nitricle grits are usually chosen to grind hardened M2 steel partsO ~nd to grind tungsten carbide (a very hard and difficult-to-grind matex ial), silicon carbide or diamond grits will be the choiceO Diamond grits ar e used in grinding wheels only when there is no viable alternative, clue to their high costO
The foregoing "relative hardness ranking" of a limited number of materials illustrates an important, known axiom: In order to grind workpieces, the grinding wheel is chosen to contain grits which are relatively harder than the workpiece material. This is so because the abrading action of grits requires that they gouge or scoop out minute pieces OI the workpiece as they "rub through" the region of contact between the wheel face and work surface. If the grits are soEter than the workpiece material, the result woulcl be simply that the grits would wear down and flatten, or they would fracture and break off --so that wheel wear rate or dulling would detract from the overall success of 2 0 grindingO
~ second axiom becomes apparent: Because grinding wheels inevitably will wear to some extent (with truing and dressing contributing) and will sooner or later wear out to require replacement, the cost of the wheel grit chosen bears heavily on the choice of wheel grit material employed in the grinding of any given workpiece materialO
It should be noted here that diamond tsynthetic or natural) is the hardest material known to man. I estimate that its hardness, relative to silicon carbide or boron nitride, is greater by a factor oE at least twenty. But its price is likewise e~tremely hig~h --and this $3~

has limited the use of diamond grits in grinding wheels~ Diamond chip truing elements or rolls are used - almost exclusively for truing in those instances where single point ~liamond tools with path control are not emplo~ed --with their very high cost reluctantly accepted, because they have been perceived by those skilled in the art as the only implements which could true a grinding wheel wi-thout su.~fering rapid and intolerable wear and loss of fo:rmO .If the element used to true a formed grinding wheel wears and loses its shape (and unless it is replaceable at very low cost), it is essentially useless in a practical, economic senseO
In any event, when speaking of diamond grits or chips carried in a grinding wheel or truing element, one must recognize that diamond stands as a class by itself in terms OI hardness and costO
Because my invention may be practiced by controlling the physical parameters of rubbing contact between a grinding wheel and a truing element, and where (i) the truing element material is softer than the wheel grit material, or (ii) the truing element material is of equal or greater hardness than the hardness of the wheel grit material9 or (iii) the truing element material is diamond chips in a supporting matrix and therefore vastly harder than the wheel grit material, it is dif`Iicult to characterize or define the invention in terms which are both precise and generic to all such c~ases. Therefore, my invention is to be considered in three distinct classes according to the materials involved, with a common thread or physical parameter control being present in all classes but with different boundary limits for each classO
For this purpose, I have defined three classes of h~uing contact between a wheel face and a truing element, as follows:

CLA~S I: The truing element hardness is less than the hardness of the grit material of the wheel.
CL~SS II: The truing element hardness is equal to or greater than the hardness oE the grit material in the wheel, but not by such a degree that CLASS III applies.
CLASS III: The truing element material so vastly harder than the wheel grit material that attrition type wear (defined below) of the truing element material does not perceptibly occur, Examples of CIl~SS I: The truing element is made of 1020 steel and the wheel grits are aluminum oxide; or the truing element material is M2 steel and the wheel grits are silicon carbideO
Example of CLASS II: The truing element material is tungsten carbide and the wheel grits are aluminum oxide.
Example of CL~SS l:[I: The truing element material is diamond chips bonded in a matrix and the wheel grits are silicon carbide.
A word OI explanation is in order with respect to CL~ASS IIIo It is known in the art that when a grinding wheel is employed to grind a rnetal workpiece, three types of "wear" occur on the wheel.
These are:
(a) Attritious Wear: Due simply to the rubbing of the grits through the workpiece material, and the heat and oxygen present, the sharp corners and edges of individual grits are flattened off and made smoothO They tend to become flush with the support matrix in which they are bondedO To some extent, attritious wear involves chemical reaction of the grit material with the workpiece m2terial. Attritious wear per se results in a relative low rate in the reduction oE wheel radiusO

~b) Grit Facturing: At the relative surface speeds between a wheel face and a work surface, the individual wheel grits impact into the work. If the work is hard and the grits less hard, the irnpact breaks and fractures off small pieces of the grits. This results in the wheel "wearing away", but it has the advantage of exposing i`resh, sharp corners or edges of a given grit until the latter is totally consumed or rernoved. As attritious wear rounding occurs>
it tends to lessen the grit I'racturing because impact forces become of lesser intensity.
lû (c) Bond ~racture: Here the infeed forces are sufficiently great, andthe impact forces are high enough, that entire grits are bodily knocked out of the bonding "sockets" in the supporting matrix, which then wears away and exposes fresh grits which in turn get knocked out. If this type of wheel wear predominates, it eats up wheels fast. The degree of bond fracture depends, of course, in part upon the substance chosen for the matrix and for grit bonds, but it is in part determined by the sharpness of the grits and their hardness which enables them to go through the workpiece without creating high reactive forces which impose breaking stress on the bonds.
No doubt all three types of wear, each to a greater or lesser degree, occur simultaneously when grinding of a part is in progress. The first type dulls the wheel but results in relatively low wheel radius reduction.
The second type reduces the wheel radius considerably but tends to keep the wheel from becoming progressively duller. The third type tends to wear down the wheel radius; but certainly the freshly exposed grits should be in a sharp condition.
In the case of a diamond grit wheel, the grits are so hard that they experience very little attritio~s weat~. [)l~lling~ is IIOt a ~~L~-¢~

serious problem unless friction-generated heat at the interface leads to heat-generated fracture of the cliamond materialO l'he same relationship exists if'J say, boron ni-tride is used as a wheel grit material to grind a very soft material.
My new method for conditionirlg (tr uing) of grinding wheels includes the steps of 1. ~otating the grinding wheel and f'eeding -the wheel face into relative rubbing contact with the operative surface of a truing element, such surrace conforming to the desired shape for the wheel face;
2. S~onjointly establishing (i) the relative surface velocity of the rubbing contact and (ii) the relative feed rate of such rubbing contact in such fashion that 3a. For CLASS I, the r atio W' /TE~ is greater than lo O and prefera'bly much higher in the range of 10 to 100;
3b~ For CL~SS II, the ratio W'/TE' is greater than 10 and pre:Eerably much higher in the range of 100 to 1000; and 3c. For CLASS III, the wearing off of the wheel is promoted in the grit and bond frac-turing modes as contrasted with attrition rounding or smoothing of the wheel grits, and particularly by making the relative surface speed less than 30ûO ~eet per minute;
wher-e W' and TE' are the volumetric rates of removal of materials from the grinding wheel and the truing element, respectivelyO The ratio W'/TE' may be called the truing ratio TR.
The conjoint control of relative sur~ce speed ancl relative feed, in general terms, is carried out by (a~ rnaliing the relative sur:Eace speed much lower -than the relative sur~.lce spee(ls heretofoL~e employed in either the grincling of worl~pieces o~ ttle tl~ling ot` wt~eels by . . ~

3~

rubbing action, or ~b) making the relative feed rate much hi~her than feed rates l~eretofore employed in either the grinding of workpieces or the truing of wheels by rubbing action, or (c) a combination of low relati~e surface speed and high relative Leed rate My experience has confirmed that the ratio W'/TE' varies as an inverse generally monotorLic function of relative surface speed and as a direct generally monotonic function oi feed rate.
Assuming that the relationships ar e linear, although that is not necessarily true, this may be expressed:
TR = TW I _ ka s~ (a) where F is feed rate, Sr is relative surface speed and k is a factor of proportionalityO ~n order to keep the W' /TE' ratio abo~e the lower limits defined at 3a and 3b above, it is only necessary to keep the ratio F/Sr above some value which can be readily ascertained by simple tests with grinding wheels of a given type ~grits and matrix) while being acted upon by a truing elernent of a given material. It makes no difference whether one chooses to employ (a) a high feed rate and a rmore or less conventional surface speed, (b) a low surface speed and a more or less conventional feed rate, or (c) a feed rate which is reasonably higher than, and a surface speed which is reasonably lower than~ the feed and speeds which would normally be used iP the wheel were to be employed in grinding a workpiece made of the same material as the truing elementO
With respect to CLASS III and the requirement 3c set out above, I am presently aware of only one truing element material which falls in this class. Such material is diamond chips carried in a matrix to form the truing element. Such chips are of strength and hardness that they can fracture and knock out the grits of a ~,vheel (if the relative surface speed is low~ wi-thout smoothing and roullding tllose grits and without the chips themselves being attritiously worrl OL` ractureclO

I acknowledge that cliamond chip truing rolls have been used in the prior art to true grinding wheels, but such prior practices have usually involved driving the grinding wheel at about 6, 000 to 12, 000 surface feet per minute and with little significance being given to (i) the relative surface speed of rubbing contact which is affected by both the direction of rotation of the truing element and its surface speed, or (ii) the rate of relative infeeding. Indeed, infeeding by increments rather than at a selected rate has been the usual prior practice. PriOr practices of truing a grinding wheel by use of a diamond truing roll are known to leave the wheel dull.
10 Undoubtedly this undesired result of the prior practices flows from the use of high relative speed (4~ û00 s.f.m. or more) and feed rates so modest that attritious flattening of the wheel grits takes place. The prior art did not (a) remove grinding wheel material as fast as my invention in CLASS
III and 3c achieves, or (b) reduce wear of the diamond roll to extend its life as much as my invention achieves.
The method set out above in sub-paragraphs 19 2, 3a, 3b, 3c produces a high wheel wear rate W ' (and therefore rapid truing of a deteriorated wheel face to the desired shape) by creatingfracture of grits and bond fractures in the wheel. It does so by creating high effective 20 forces on the wheel grits by the joint effects OI (i) making the "velocity factor" of strength for the grits and their bonds low and¦or ~ii) imposing relatively high forces due to a high feed rate and which tend to fracture the grits or their bonds.
It is known that any solid object has greater hardness and strength against breakage or deformation when it moves relati~ely into another body at high velocity, as contrasted to low velocity. This is the "velocity factor" phenomenon to which I have referred above. It is readily understood from the example: If a lead bullet is slowly pushed into a wood plank by an hydraulic press, the bullet will det`o~LIl and ti 3~ crumble; but if the same bullet is t`ire(l witll lligll veloeity t`roln rit`lt~
cL5 at the plank, it will penetrate through and with very little de~ormation or crumblingO The same effect applies to wheel grits and grit bonds;
by my method of making the ratio F/Sr high through the avenue of making relative surface speed low, I lessen the "velocity factor" with which the wheel grits and their bonùs would otherwise resist fractureO
Further, by making the ratio :Ei'/Sr high through the avenue OI making the feed rate F high, I increase the physical force which is irnparted upon the wheel grits anà their boncls, so that grit and bond fracture is promoted.
Both factors F and Sr bear upon the ratio W'/TE' but I
prefer to use relative surface speed as the major controlling influenceO
For this reason, and as explained below, I prefer to use an "up cut"
for the rubbing contact vf a wheel and truing cylinder in order to effect truing at relative surface speeds much lower than the art has heretofore used for either ~a) grinding of workpieces or (b) truing of wheels by the rubbing action of a truing roll.
My invention greatly extends the useful life of the truing element. This is important in dealing with formed wheels where the truing element must be manufactured with an operative surface of 2û complex shapeO The truing element life is extended because the wear rate on its operative surface is reduced to a very low (and in some cases, negligible~ valueO This flows from the fact that at the high ratio of W'/TE' employed in the method of 3a and 3b (and the lo~,v surface speed of less than 3000 feet per minute in the method category 3c) the I'velvcity ~actor" of the wheel grits rnakes them have insufficient strength to gouge through the surface layer of the truing element without fracturing. The material of the truing element is not eroded or worn away at an appreciable rate and the shape of the opercltive surface is retained as the wheel face is vrorn OIt` to a m~lrll greclter e.~terlt.

-~LG -The truing method here disclosed may be practiced in a wide variety of speci~ic procedures which all lie within the generic boundaries in one of the classes set out in sub-paragraphs l to 3c, supraO That is:

____ (a) The truing element operative surface may or may not itself have surface velocity which in part cont:ributes to the relative r ubbing speed Sr; compare the truing element,~ 90 and ~?l in :F'IG. 2 .
(b) The eed rate o:f the truing ele:ment relative to the wheel may result from bodily movement of the wheel, bodily movement of the truing element, or both.
~'c) The relative surface speed and relative Xeed rate of the rubbing contact may be established by open loop or closed loop actionO
It is not necessary for the CLl~SS I or C.1ASS II categories that the ratio W'/TE' be kept constant; on the contrary, the relative speed Sr and the relative feed rate F may be permitted to vary widely so long as the ratio W'/TE' is kept above l, 0 (Cl:.ASS I), lO. 0 (CLASS II3 or so long as speed Sr is kept lower than 3, 000 feet per minute ('CL~SS III)o In all such cases the benefits and advantages over the prior art will, at least to a significant extent9 be obtainedO
(d) The contact between a wheel to be trued and the truing element may be created intermittently or continuously; while the grinding wheel is or is not in grinding contact with a workpiece;
and either when the wheel is opera-tively mounted in a grinding machine used to grind workpieces or when such wlleel has been removed to a separate machlne in which the t.ruing operation is performedO Indeed, t~e i.nventiorl nlay be practiced with the truing element moullted i~l the place oX a worli~)iec~e ~~'7 -within the machine by which the wheel is employed to grind workpieces, and in fact (as notecl below) the truing element rnay be one of the workpieces~
(e) Further, if the truing operation is performed intermittently by the method here disclosed, the methocl may be practiced li) aIter each of successive predetermined time intervals OI grinding action performed by the urheel, (ii) each time after a cer-tain number of workpieces have been grouncl by the wheel or after a predetermined thickness or volume has been ground o~ of a workpiece, or (iii) each time after an appropriate sensing and signaling device has indicated that the wheel face has lost its desired shape or has worn down a predetermined amount.
FIGS. 1, 8 and 9 - --- . ... _ _ Reference may be made to FIGS. 8 and 9 for one embodiment OI apparatus suitable for carrying out the method explained aboveO FIG. 8 corresponds to FIG. 1 except some of the components OI the latter figure have been omitted, the slide WS has been moved to the right to retract the wheel 20 clear of the workpiece 24, and the slide TS has been moved to the left (on the slide WS) to bring the truing roll 50 into rubbing contact with the wheel face.
In the control system 71A, motors WM, TM and TFM
are each controlled in speed by connection through respective manually adjustable rheostats 100, lVl, 102 to a dco source voltage E (FIG. 9~O
It is to be observed that the motor WM acts as a motor and drives the wheel 20 counterclockwise. The wheel in rubbing against element 50 drives the latter clockvrise~ but the motor TM when rotating in that direction acts as a controllable regenerative brake whose current is fed back into the source Eo Motor TFM acts as a motor which drives - the lead screw 51 to move the slide TS towarcl the left at a Eeed ratc ~ts which is adjustable by se-tting the rheostat 102~

.t'~
The manual adjustment of the rheostat 100 is made to create a preselected surface speed S for the wheel 20. The wheel radius 1~ having been previously measured, it is easy to adjust the rheostat 100 to make the surface speed Sw, say, about 2500 feet per minute (f.p.m.) bearing in mind the relationship:

SW = 2i~R,.W ~W ( 1 ) If Rw is expressed in feet and G~JW in r.p .m. then Sw is in feet per minute (f.p.m.). To make Sw 2500 E.p.m., a human operator simply adjusts the rheostat 100 until an appropriately calibrated meter Ml 10 indicates that ~w is equal to _2500 in r.p.m. Further, the rheostat 101 is adjusted to make the relative surface speed S of rubbing contact have a very low value (compared to relative surface speeds employed in grinding) such for example as 400 f.p.m. Bearing in mind the relation:

Ste = 2~Rte- ~Jte (2) and the radius Rte having been previously measured (in feet) so it is known, the rheostat 101 is adjusted until the angular velocity Jte makes the truing roll surface speed Ste approximately equal, for example, to 2100 f.p.m. I'hat is, the rheostat 101 is adjusted until a meter M2 indicates that ~Jte is equal to ~ in r.p.m.
The relative surface speed Sr is in this case expressible:

Sr Sw ~ Ste (3) and accordi~ to the values given by way of example:
Sr = 2500 - 2100 = ~00 f.p.m. (4) The rheostat 102 is adjusted to make the feed rate FtS
have a high value (relative to feed rates employed in grinding of workpieces with the particular wheel 20 here involved) such as .040"/min.
If desired, a meter M3 coupled to the tachometer 59 and calibratecl in mils per minute may be used to ~cilitate such ~-ld;justmellt~

_~9_ As the feeding of the slide TS oecurs, the radius P~A~
of the wheel will be reduced at a rate R'w and the radius Rte Of the element 50 will (in most cases) reduce at a rate R'teo Simply from inspection of FIGD 8 FtS = R w + R te; R'w = E~tS - R'te (5) Tnis means that if the feed rate FtS is constant, as the wheel wear rate R'w increases, the element wear rate R'te will clecrease.
If the rheostat 100 is adjustecl to decrease its resistance value, the surface speed Sw will increase, and the relative speed Sr will increase~ as made clear by Equation (3)O Conversely, if the rheostat 101 is decreased in resistance value and the speed Ste increases, the relative sur~ace speed Sr will decreaseO As the surface speed Sr is decreased or increased, the lowering or raising of the "velocity factor" strength of the wheel grits will make the wheel wear rate R'w increase or decrease. Assuming that the feed rate FtS remains constant, the element wear rate R'te will correspondingly decrease or increase in accordance with Equation (5).
To an approximation (see the exact relation in Equation 11, nfra) which is s~ficiently close~, the volumetric material removal rates W' and TE' are proportional to the radius reduction ratesO This approximation may be expressed:
TRUING R~TIO = TR = TlE' k R~te (6) where k is the ratio of the starting radii RWlRteo By substitution from :Equation (5) this becomes TR =TE' --k---R' te (6a~
Thus~ by adjusting either the rheostat 100 or 101, the truing ra-tio TR
may be brought to approximatel;y a desired value, such as 20 or 50.
The key is to establish a lower and lower relative sut~face speecl Sr when it is desired to make the ratio TE~ llighe~r and highe~`~

On the other hand, if the rheostat 102 is increased or decreasecl in resistance, the feed rate FtS will be decreased or increased. Increasing Ft will cause both of the wear rates E~'w and R'te to increase, but not equally. Since the wheel is composed of discrete grits in a supporting softer matrix, an increase in the feecl rate will increase the infeed force at the wheel-element interface, and this will cause the whecl wear rate R'w to increase more than the elemcnt wear rate R'te increases. This, in turn, will make the TR ratio W'/TE' increase; see Equation (6).
:For the specific, exemplary relative surface speed of 1000 f.p.m. and a feed rate FtS of 0040"/min., the radius reduction rates might typically be R 'w = . 038"imin. and R'te = . 002"/min., so that the truing ratio T~ according to approximation (6) would be 19 when a truing element and grinding wheel falling in CLASS I are involved. Although it is not essential, instrumentation may be included in the apparatus to permit observation of the actual truing ratio TR so that manual adjustments may be made on the rheostats 100, 101, 102 to obtain a desired value or range of values of TR.
For this purpose, the signals FtS and ~Ite (from FIG. 1) are fed 20 respectively to voltmeters M4 and M5 appropriately calibrated so that a human operator may read the truing slide feed rate and the truing roll radius reduction rate. These same signals are applied to a suitable known type of summing circuit 103 whose output is fed to a known type of dividing circuit 104. The second input to the latter is the signal R't from FIG. l, so that its output varies as the value of Fts ~ R te 1~ te That output is fed to an adjustable gain amplifier 105 which is set by a resistor 106 to have a gain of k, where k is equal to the ratio RWtRte of the initially measurecl radii. The amplifie~ 105 t`e~ds an 3~

appropriately calibrated meter M6 which displays the value OI TR
according to the relation of Equation (6a), supraO ~or the CL~SS I
example here given, adjustments at 100, 101 and 102 may be macle until the meter M6 gives a reading oE 19 or 20 --or TR Of whatever value may be desired, For a grinding wheel and truing element falling in CLASS II, the radius reduction rates might typica]ly be E~'w =, 0195"/min.
and R'te = . 0005"/min., the TR, ratio thus being 39. 0O
If the grinding wheel and truing element are in CLASS
III, then the rheostats 100, 101 are simply adjusted to make the relative surface speed Sr less than 3000 ft. /minD, such as in the given numerical example where Sr is abo~ 400 fO p. mO as~cording to Equation (4)O The truing element will not wear a perceptible amount (i. eO, no wear is discernible by micrometer measurement) over hours of truing operationO I have been unable to obtain a finite number for the truing ratio TRJ and I can only state with certainty that it will lie well above 1000 and approaches infinity in the CLASS III practice of my invention.
The truing ratio W'/TE~' is, in a precise sense, a ratio of volumetric rates OI material removedO In FIG. 8, the volume W oE the cylindrical wheel 50 is the area of an end face times the axial length L of truing contact, viz.:
W =T7R~2-L (7) By di~Eerentiating, it is seen that when the wheel radius is reducing at a rate R'w, the material removal rate becomes:
dt = W' = 277 RW 9 dtW . L = 2 77 LR,1,oR'~ (~) Of course, the wheel face may be slightly jagged or uneven (as sho~,vn with exaggeration at 20b in FIG~ 6) so that the volllmetr.ic removal rate W' is not represented by Equation (~) with e~treme precisio~l~

`~

It is, rlevertheless, sufficien-tly accura-te to assurne that the wheel face is purely cylindrical in computing the rate W'.
Similar expressions apply to the truing element 50 here shown as cylindrical in shape:
TE = 7~R2te o L (9 ) TE' = 277LRtef~ le (10) The truing ratio TR more accurately e~pressecl --in contrast to approximation (6)-- thus becomes:
_ W' 2~LRW~R'W _ Rw R'w TR --- ~ i'7'~ P' ~ R -- ~ ' (11) Assuming as an illustrative example that the grinding wheel and the truing element are initially 10" and 5" in radius, the ratio RW/Rte will be 2. 0 and will not change appreciably as several thousandths are taken off of the wheel radiws and a few thousandths a:re taken off OI the truing roll radius. Thus, approximation ~6), where the factor k representing R~,,,/Rte is assumed to be constant, is sufficiently accurate as an expression of the ratio W'/TE' and may be used effectively in the practice of my invention.
FIGS. 1, 8 and 10 . . . _ ~
A second embodiment of apparatus according to my i.nvention, and which may be used to carry out my method, is constituted by FIG. 10 taken with FIGS. 1 and 8. FIGo 10 shows one form of a control system 71B accepting signals corresponding to certain sensed physical parameters to conjointly establish and control the relative surface velocity and relative feeding in a manner to keep the ratio VV'/TE~ within a desired range --and indeed at a desired set point value which satisfies the foregoing sub-paragraphs 3a and 3h with respect to CL~SS I and CI~SS II~
In FIG~ lO, the s:i.gna:Ls labe:Led at the left come rom FIGo 1 and have already been ident:ified. :lt is assulned tllat the t~ ing ~r)3 ~

roll 50 and the grinding wheel 20 are, however) in rubbing contact as shown and eYplained with reference to ~'IG. 8. To establish with reasonable precision (and this is not required in all embodiments of my invention) the surface speed Sw f the wheel 20 as the latter changes its radius over a wide range, the circuitry of FIG. 10 controls the motor WM according to the relationship o:t :Equation ~1), supra~
Thus, in FIG. lV a potentiometer 109 is adjus-ted to produce a signal Swd representing the desired or set po:int value of wheel su:rface speed.
From FIGS. 1 and 8 it is apparent tha.t, during t:ruing contact:
Rw = Pts - Rte (12) With the signals PtS and Rte applied to an algebraic summing circuit 110, the output of the latter represellts the radius Rwo A multiplier circuit 111 of known organization receives that output and a voltage (from a potentiometer 113) representing the constant 27~to feed the procluct 2J7RW to a second multiplier 112 having the signal ~w as its other input The output Sw thus varies as the actual surface speed of the grinding wheel 20 according to Equation (l )o This is applied, in bucking relation to the signal Swd9 to a summing circuit 114, the output of which therefore represen-ts the error hetween the desired and actual wheel sur:face speeds~ The error signal ERRl is applied to the input of a servo ampli.fier 115 which creates and applies the energizing voltage Vwm to the motor WM. The driv.er amplifier may include servo action stabilizing and enhancing components which, in kno~,vn fashion, provide proportional, integral and derivative (PID) action A1SOJ the ampli:fier 115 may contain a bias circuit which keeps the motor WM running at a preselected "center speed" even when the error signaled from summing circuit 114 is exactly ~ero, so that small changes in the error result in the motor speed ~)w being corrected to bring the speed -to a vallle which makes the eL~ror ret~lrrl substarltiaLly r) ,~ _ to zeroO In any event, if the surface speed Sw falls or rises from the desired value Swd for any reason, the closed loop of FIG. 10 controlling the motor WM will increase or decrease the ~oltage ~wm so as to change the angular speed ~w until the signal Sw i,s restored to approximate equality with the set point signal Swd. .~ potentiometer 109 is adjusted to make the signal Swd represent ~by an applicable scaling factor) a surface velocity of 250û f3 p, m., the wheel face will be maintained substantially at -that linear speed despite changes in loacling or changes in wheel radius Rw Throughout the drawings, the representations OI ser~o ampli.ïiers (such as 115 in FIGo 10) are intended to illustrate amplifiers with proportional plus integral action, plus derivative action if that is desired. The servo circuits may also include a constant bias signal so that the output from the final stage of the ampli~ier energizes the associated motor or brake to keep its speed as a "center" value absent any integration of the error signalO The closed servo loops may be designed through the exercise of ordinary skill by servo control engineers, and the details of the servo amplifiers thus need not be illustrated or describedO In FIGo 10 and similar figures to be discussed, it is sufficient to understand that the servo loop for the motor WM is constructed with suf:Eicient gain and integration that ~he ERRl signal will be restored essentially to zeroJ and the speed Sw will be returned essentia31y to the value represented by the signal Swd when any disturbance or change in physical parameters causes the control~ed value to tend to depart from the desired set pointO
As further shown in FI(~ lO, the motor TFM is controlled by a closed loop to maintain the :Eeed rate FtS essentially constant at a desired set point FtSd. The set point is selected by a~ljusting a potentiometer 118 to produce a signal FtSd which is hucked in a s~lrnming 55 ~

circuit 119 with the actual feecl rate signal FtS to produce an error signal ERR2 fed to a PII) servo amplifier 120 to excite the motor TFM.
The torque of the motor TM is variably controlled so as to adjust the speed ~te such that the ratio TR is ~naintained at least approximately in agreement with a desired value. That desired value is signaled as TRd by setting a potentiometer 121. 'rhe signals FtS and R'te are subtracted in a summing c:ircuit 122 to feed the difference R'W (see Equation 53 to one input of a known type of analog di~rider 123. The output of the latter feeds an amplifier 124 whose gain k is adjusted by manual setting of a rheostat 125 to equal the ratio RWlRte determined from manual measurement of the two radii and Rteo The output signal from amplifier 124 is k~ and is thus approximately equal to the actual truing ratio TP. as expressed in Equation (6), supra. That output is algebraically compared ln a summing circuit 126 wi-th the set point signal TRd to create an error voltage ERR3 forming the input to a PID servo amplifier 127 The latter produces a voltage Vtm to energize the motor TM (acting as a brake) such that the speed~te of the truing roll 50 is increased or decreased when the actual ratio TR falls below or rises above the set point TRd~ In other words, if the actual truing ratio TR is less than TRd, the error signal ~RR3 becomes positive and this increases the voltage Vtm from its mid-bias value, so less regenerative braking current flows through the motor TM, braking torque decreases, and thus the angular and surface speeds ~ te and Ste of the truing roll increase. From Equation (3), this decreases the relative speed Sr of rubbing contact That~ in turn (and for the reasons explained above), causes the radius reduction rate R'w to increase and the rate R'te to decrease-- thereby increasing the signal TR until the error ER:R3 is re9tored to ~.ero 3~33~

In selecting and setting the set point S-wd (FIGo 10) a relatively low value will ordinarily be chosen in the practice of the invention because it is preferred to operate in ranges of the speeds Sw an(~ Ste which make Sr low. Once the set point Swd is chosen, then the closed loop servo which includes the amplifier 127 will variably brake (or forwardly drive) the truing element 50 to cause the speed Ste to increase or decrease, as required9 to keep the truing ratio TR
substantially equal to the set point l~ In this aspect, the a1pparatus acts to maintain:

TR - TRd = ERR3 = 0 (13) TR = W ''~ kR w ~v kFts R te = TRd (14) It is appar ent therefore that since FtS is held essentially constant at the value FtSd, when R'te tends to rise or fall3 and the truing ratio departs from TRd, then the relative surface speed Ste is changed to correctively adjust Sr until the actual truing ratio returns to the set pointO This action flows from the ~act that grinding wheel wear rate R'w varies inversely and monotonically (but not necessarily linearly) with relative surface speed Sr, and truing roll wear rate R'te varies oppositely to R'w for a given value of the feed rate FtS (see Equation 5).
From the foregoing, it may be observed that an embodiment of apparatus alternative to that o~ FIG~ 10 may readily be constructed in which the surface speed Ste is held generally constant but the wheel surface speed Sw and angular speed ~ are correctively varied in r esponse to the difference between TR and TRdo Indeed, since it is the relative surface speed Sr vvhich makes the truing ratio change (for a given feed rate FtS), control apparatus may be constructed in the light of the foregoing teachings to keep the truing ratio TR at a desired value by variably adjusti:ng both te and G~,v in r esponse to the error TR - TRd 3~3~

Further, from Equation (14), if the feed rate FtS is increased or decreased (all other conditions remaining constant), then the truing ratio TR will increase or decrease. The truing roll wear rate R'te will in most cases change with changes in feed rate F
but not to the same extent that wheel wear rate R'w changes. Thus, if the value oE FtS is changed, the relative "weighting" of R'W and R'te in Equation (5) will changeO Therefore, as an alternative to the specific embodiment of FIGo 1 OJ the angular speeds GJ w and G)te may be controlled to keep the relative surface speed Sr at some set point valueJ and the error TR l'Rd e~nployed to cause the rnotor TFl~/I
to increase or decrease the feed rate FtS when the truing ratio TR
falls below or rises above the desired value TRd.
Generally, the preferred practice is to set the feed rate FtSd at a relatively high value and hold it generally constant~ as in E; IG. 10, with G)w or G~te being variably controlled to keep the actual ratio TR within a predetermined range or generally equal to the chosen set point TRd. The higher the feed rate the faster the removal of material from a deteriorated wheel face to restore the latter to its desired shape. Thus for truing operations, the feed rate will be chosen as high as reasonably possible for the strength and stiffness of the machine components and the performance capabilities of the servo loopO
Yet, it is to be stressed that the feed rate FtS and the relative surface speed Sr are conjointly controlled to make the ratio TR fall in a predetermined range or match a predetermined desired value. Either or both of those parameters FtS and Sr may be the controlled variable.
In the practice of the method through the use and operation of the apparatus of FIGS. 1, 8 and 10, iE the grit materials of the wheel 20 and the material of -the truing roll 50 fall in C~ L~SS 1, then the potentiometer 121 will be set to make the signal TRd represent a

-5~3 --~
.~ 3~

ratio of gre~ter than 1.0 and preferably in the range of 10 to 100.
When truing contact as shown in FIG. g occurs, the apparatus of FI~. 10 will keep the ratio TR at or near the set point value, produce grit and/or bond fracture in the wheel face, and result in the volumetric removal rate W' being much greater than the rate TE'. The truing element will thus wear down very slowly and it can be employed for many truing operations before it "wears out".

Example for Class I: ~ wheel 20 of aluminum oxide grit in a .. ..
matrix of ceramic is trued with an element 50 made of 1050 quench hardened steel, the latter having an operative surface (whether truly cylindrical or otherwise) of 3" radius conforming to the desired wheel face shape. If the measured radii Rw and ~te are respectively 5" and 3", the gain k for the amplifier 124 is set to 1.66. The truing slide feed rate FtSd is set at .062"/min., and the wheel surface velocity Swd is set at 2000 f.p.m. The set point signal TRd is adjusted to represent a desired ratio of 50. The wheel radius reduction rate R'w in these conditions may be approximately .060"/min. To "true off" the wheel by 6.0 mils only 6 seconds of rubbing contact will be required; and during this interval the truing element radius will wear down by only about 0 . 2 mils. ThusJ truing is accomplished rapidly but without appreciable wearing of the homogeneous metal truing roll 50.
If the practice of the invention by the apparatus of 1 ' '' FIGS. 8 and 10 involves Class II material relationships, the signal TRd will be set to represent a ratio greater than ten, and preferably in the range of 100 to 1000~ In this case, the feed rate FtSd may be set even higher and the wearing down of the wheel face will occur even more rapidly.

- 5 ~'3 3 ~
Example for Class II: A wheel 20 of sil:icon carbide grits in a matrix of ceramic is trued with an element 50 made of tungsten carbideO The truing slide feed rate FtSd is set at 0,100'!/minO
and the wheel surface velocity Swd is set at about 1500 fD p. r.n9 ~ the measured radii Rw and R.te are 10" and 5", respectively, the gain k for the amplifier is adjusted to 2, 0. The set point signal TRd is ad;justed to repr esent a :ratio of 2000 T:he wheel radius reduction rate R'w in these conditions :may be approximately 99. 5 mils/min. with the radius reduction rate R~te being about . 5 mils per minuteO "Truing off" 5 mils from the wheel ~ace will requir e only about three seconds, during which time the truing element radius will wear down only about . 025 mils --and the truing roll will thus retain its size and shape.
As noted above with respect to Equations (6), ~11) and (14) the actual truing ratio may be approximated because the ratio RW/Rte does not change very muchO E those radii start, for example, with values of 10" and 4" then the ratio RW/Rte will not vary appreciably over a long tirne span during which Rw decreases by 00 25" and Rte decreases by 00 û2". .If desiredg howeverg the truing ratio TR may be signaled more accurately and without the approximation, as illustrated in FIGo lOA. The latter figure shows components for replacing the amplifier 124 in FIG. lOo The signals :E~w and Rte are fed to a clivider 124a to produce an output varying as RW/Rte; the latter signal is applied to a multiplier 124b which also receives the output signal from the divider 123 of FIG, 10, thereby producing an output signal TR ~fed to summing circuit 126 in FIG~ 10) which varies according to the relation evident from Equations (11) and (12):
W' R-~V R ~,v Rw Fts~R te TR = , =~
TE Rte R te Rt~ R te Thi~ FIGo lOA modification to E~IGo lO will therefot~e Inn.illtail~ ttle act~lal ,'3~

truing ratio TR in agreement with the desired value TRd even if the radii oE the wheel and truing roll change over a wide rangeO ~ut in cases where truing action does not produce a significant percentage change in wheel or truing element radius (and there are many such cases in industrial practice), one may treat radius wear rate R'w or P~'te as representing volumetric rernoval rate W' or TE'~ thi~ being here indicated by Equation (6) and FIG. 10, FIGSo 1~ 8 and 11 If the practice of the invention by the apparatus involves Class ITI material relationships, then the truing ratio will approach infinity if the relative surface speed Sr is less than 3000 f p. mO Thus, the control system 71C of FlGo 11 (taken with FIGSo 1 and 8) may be employed. Here, the components 109a-120a are organized and operate in the same ways as the corresponding components 109-12û described with reference to FIG~ 10~ In FIG. 11, a feed rate FtS is selected and maintained, but the motor TM is controlled simply to keep the relative sur~ace speed Sr at a set point Srd which is less than 3000 f. pO m. For this purpose, the signals Rte and 2t7- are applied to a first multiplier 128 whose output, along with the signal te is fed to a second multiplier 1290 The latter produces a signal proportional to 2~Rte~e which thus represents the truing element surface speed Ste (see Equation 2).
That signal is algebraically subtracted ~rom the signal Sw in a summing circuit 130 to produce a relative speed signal Sr (see Equation 3)O
This is compared in a summing circuit 131 with the set point signal Srd from a manually adjustable potentiometer 13~ to create an error signal ERR4 fed to a servo amplifier 134~ The latter produces the voltage ~tm which determines the braldng torque on the -truing roll 50 and thus the speed (~te~ When the relative surface speed S~ di~ers from the set point Srd, the motor (brake) TM is controlled to remove the error.

q~

As statedJ when the Class III conditioning is practiced with a diamond chip truing roll, the radius reduction R'te is essentially zeroO The feed rate FtS may be set relatively high (e. g~, 40 mils/minute) and because the relative surface speed is low, the wheel grits are bodily Eractured or knocked from their bonding sockets in -the matrix material.
Example for Class III: ~ grinding wheel with siLicon carbi(le grits bonded in a matrix oE ceramic is trued with a truing roll OI diamond chips set in a matrix of tungsten carbideO The feed rate FtSd is set and maintained at approximately 40 mils/min. and the wheel and rolï speeds ~) w and ~te are controlled to make the relative surface speed Sr about 400 f. p. m. It will require only about 4~ 5 seconds to "true off" 3 mils from the wheel face;
and the diamond truing roll will not wear enough to be measuredO
That truing roll may be used for many, many such separate truing operations, and its useIul ~ife will be greatly longer than that of diamond truing rolls as used in prior, conventional procedures.
FIGSo 1~ 8 and 12 .... _ _ Another of the ~arious possible control apparatus forms for keeping the ratio TR in agreernent with a desired value is illustrated in E;~IGo 12~ In the system 71DJ two summing circuits 135, 136 respecti~Tely receive input signal pair s PtS, Rte and ~ts~ Rte to produce output sig~als varying to represent Rw and R'w in accordance with Equations (12~ and (5~O These are fed to a multiplier 137 whose output RW E~'W is applied to an amplifier 138 having its gain adjusted by setting of a rheostat 13~ to a value of 27TL~ where L is the length of the wheel ~ace being truedO The output of amplifier 13~3 therefore signals the value of volumetric wear rate W' ~see ~qllation 8). ~\
potentiometer 140 is set to prodllce a set poillt Sigtl;ll W~tl WhlCIl iS :t`e( ~(i2 -s~

along with signal W' to a surnming circuit 141 to produce an error signal applied to a servo amplifier 142 energizing the motor TFM. ~n this fashion) the feed rate FtS is automatically varied to keep the wear rate W' substantially equal to the desired ~alue Wld selected at the potentiometer 140.
The volumetric renloval rate TE' is also controlled automatically to agrec with a selected sct point TE'CI signalecl frorrl a potentiometer 143. The signals l~te and I~'t are mllltiplied at 14~1 and the signal l~te R 'te is fed to an amplifier 145 having a gain set to 2~L .
10 The output thus varies as TE' (see Equation 10) and is îed to a summing circuit 146 in opposition to the signal T:E'd, the resulting error signa:l being the input to a servo ampliEier 147 control]ing the motor WM.
The speed ~Jw is thus automatically varied to keep TE' substantially constant and equal to the set point TE'd.
The motor TM is controlled by a closed loop servo circuit 148 to keep ~)te at some selected set point value ~Jted Since the apparatus of FIG. 12 keeps W' and TE' constant at set point values, a human operator may know and determine the truing ratio TR simply by selecting those two values and thus their ratio W'/TE'.
20 The truing ratio need not be actually signaled. Merely as an optional convenience, FIG. 12 includes a divider 149 receiving the signals W' and TE' to energize a meter M7 which displays the numerical value of TR
and aids an operator in setting the potentio~leters 140~ 143 so that a truing ratio TR greater than 1.0 (Class I) or greater than 10.0 (Class II~ is obtained. The amplifiers l38, 1~5 are not strictly necessary since their effects cancel in the divider 149 ~see Equation ll), but those amplifiers are here shown for completeness. Those skilled in the art will understarld tha-t scaling factors may be introduced so that potent;omete~s 1~0 and 143 may be calibrated in cubic inches per mirlute Ol~ any Othel' Cli.mellSiOrlcl 30 units which may be desired.

~ .3q~

In the Class I and Class rl wheel truing operations described above, it is immaterial what relative surface speed value is chosen so long as the relative feed rate ~ is made sufficiently high to give the desired range oE values or value for the truing ratio TP~;
conversely it is immaterial what relative feed rate Ft is chosen (except where rapid truing is of the essence) so long as the relative surface speed Sr is made sufficiently low to give the clesired .range~ of values or value for the truing ratio TR . When holding the r ati.o ~t~R reasonably in agreement with a set point TRd, ~ pre:Ee:r to keep the ~i~olu.metric rate W' 10 constant and to automatically adjust the relative surface speed S by automatic control of the wheel motor speed ~L)w (FIG. 12~ . But in any event, for rapid wheel face shape restoration the truing procedure is in its preferred form carried out with the relative surface speed S
lying o:r varying within a range of values substantially lower than the range of relative surface speeds created when the wheel is being trued according to conventional industry practices. Likewise, the relative feed rate FtS is created to lie or vary within a range of values which is substantially higher than the range of feed rates employed when the wheel is used in conventional grinding of workpieces. Although it 20 is not essential in the broadest aspects of my invention, its preferred practice may be viewed informally as truing a wheel by rubbing contact with a truing element such that the relative surface speed and the feed rate at the truing interface are respectively much lower and much higher than the surface speed and feed rate which would be selected by a skilled artisan to be used when that same ~,vheel is conventionally employed in grinding a workpiece.
Supplemental Actions .. ... _._ The method and apparatus here described with reference to FIGS. 9, 10~ lOA, 11 and 12 will result in rapid rernoval of material from the grinding wheel face --and thus quick r estoration of the desired shape~ Not only is this main objective obtained, but in all cases there are the further benefits that (a~ the truing element wear is relatively slight so it remains usable over a long time span and (b) the wheel face is left sharp! The rapid wheel material removal and the :resulting sharpness of exposed wheel face grits both come about because the relative feeding and surface speed of -the rwbbing contact between the wheel 20 and the truing element 50 are conjointly controlled to fracture the wheel grits and indeed :~ractur e wheel grit bonds (so that fresh grits are exposed)O
I have recognized that supplemental procedures and apparatus may optionally be employed to further promote wheel grit fracture and grit bond fracture --and thereby make the noted advantages even more pronouncedO Specifically, I propose purposely to induce vibrations at the region o:f rubbing contact between the grinding wheel and a truing element9 so -that the impact forces on grits are increased, thereby promoting greater grit fracture and bond ~racture (while lessening to an even greater degree abrasion of the truing element surface)O
Thus, in the practice of the methods and apparatus already described (in any o:E Classes I, II, III)J I may induce vibrations at a rate of several cycles per revolution of the grinding wheel and in either or both (a~ a direction tangential to the region OI rubbing contact, and (b~ a direction normal to the region of rubbing contactO
For tangential vibrations, I may create "dither" in the voltage VWm or Vtm so that either or both of the wheel and -the truing element have small9 rapicl rotational vibrations while their average rotational speeds ~L) w and ~)te remain at the selected or adjusted values.
For translational vibrations along a path normal to the wheel axis and extending through the region o rubbil1g contact, I

-~;5 -3i Q ~ 3~

may create "dither" in the voltage Vtfm so that the truing element 50 in FIG. 8 vibrates left and right while continuing an average feed rate Ft toward the left.
It will be apparent to those skilled in the art how a "dither" signal may be injected ints) the one or more of the servo amplifiers 115, 120, 127 (FIG. 10) or the servo amplifiers 115a, 134, 120a in FI(; . 11 thereby to create one or more of the vibrating actions described above.
Further as a supplernental aid promoting rapid wheel 10 wear (and low rate of truing element wear), I may construct the truing element 50 with serrations or slots extending parallel to the axis of the grinding wheel --but with the operative surface otherwise corresponding to the desired shape for the wheel face. In the case of a cylindrical truing element, it would thus appear somewhat like a splined shaft.
In the use of such a "slotted" truing element, impact will be greater as the leading edge of each rib strikes the region of rubbing with the wheel face, and thus grit and bond fracture action will be enhanced.
Finally, to create vibrations for the effect here described I may purposely construct the truing element such that it is dynamically 20 unbalanced and so that it thus vibrates as a result of its rotational speed.

A Second Approach 13y Setting or Controlling STE Conditioning of Grinding Wheels . .
Thus far my invention has been shown to be practiced by methods and apparatus in which the truing ratio TR is ir~itially set or continuously controlled so that it always resides above 1.0 for Class I materials or above 10.0 for Class II materials. For Class III
materials, the relative surface speed Sr of rubbing contact between the wheel and truing element is set or continuously controlled so that it always resides below 3000 f.p.m. The relative truing feed rate FtS is chosen (whether it is variably controlled or held constant, the latter being shown in FIGS. 10 and 11) such -that the wheel raclius Rw wears down fast --this being the objective when it is clesired to "true"
or restore the shape of a deteriorated wheel face. The high truing ratios TR (above the minimums of 1. 0 for Class I ancl 10. 0 for Class II) vastly exceecl values heretofore employed or suggested, so far as I know, in the art. And the low surface spe~ds Sr (below 3000 f. p. mO for Class III) are greatly less than values employed or suggested, so far as I know, in the artq The synergistic and surprising result of the invention as thus far described is that the truing element wears down slowly --even in Class I or Class II where that element is an homogeneous crystaline material such as a 1050 steel or an M1 steel, and in Class III where it appears that the useful life of a diamond truing roll wi~l be virtually infiniteu Thus, the main objective of rapidly truing a wheel by removing material from its face may be accomplished with a low cost truing element, the operative surface thereof retaining its shape over a long span of usage; and a diamond truing roll becomes, in effect one o:E low cost because of its greatly extended useful life.
~0 My invention may be practiced, however, with all those same advantages by a second control approach which is more flexible and which yields many additional advantages to be described. The second approach may here be given the short name "STE Control"
and it is next treated herein~
The action which takes place at the rubbing interface betvreen a wheel and a conditioning element is subject to many variablesO
The best indicator of the action at that interface, and OI the degree of "sharpness" being produced at the wheel face is the energy efficiency with which material is being removed from the g~rinding wheel~ I call ~67 -q`3~

such energy efficiency "Specific Truing Encrgy" (STE) and define it as the amount of energy expended in removing a given amount (volume~
of wheel material. This is e~pressible as a ratio of an amount of energy Et expended in removing a given volume W of wheel material:

STE = Energy Expended Et (16) Wheel Volume Removed W
The dimensional units of STE are e~pressible, for example, as foot-pounds per cwbic inch" watt-minutes per cubic centimeter, or horsepower-minutes per cubic inchO
If one divides the numerator and denominator in Equation (16) by the time span during which the volume W is removed, then STE
becomes the ratio of power applied in removing wheel ~aterial to the volumetric rate of material removal~ I'his is expressed:
STE = PWRt (17 Consider that a grinding wheel 20 is rotationally driven in relative rubbing contact withJ and with infeeding relative to, a truing element 50 as shown in FIG, 8, and that certain physical variables are signaled as explained above with reference to FIGo 1~
The power (rate of energy expended) in rotationally driving the wheel 20 is expressible:
PWRW = 277 o TORW ~L) w (18) Normally that power would be expressed in dimensional units of fto -lbs./min"
but it can easily be converted to other units such as horsepower.
Likewise, the power applied in driving or braking the element (and thereby contributing to the rubbing action) is PWRte = 27To ToRte G~te (19) The total power PWRt applied to the rubbing contact at the interface between the wheel face 20b and the element's operative surface 5Ob thus becomes:
PWRt +PWRW +PWRte = 2~J(_TORW (~)W ~TORt~U C~Jte~ (20) It may be noted that Equation (3) as an expre.ssion for relative surface speed Sr may be more rigorously written:

Sr ¦ Sw + Ste ¦ (21) where Sw and Ste are taken as terms each having its own sign clesignating a positive or negative direction. If in FIG. 8, a positive direction is taken as vertically upward at the rubbing contact region, and with the wheel 20 driven c.c.w. and the element 50 turning c.w. (but being braked), then Equation (3) becomes a specîfic ancl correct reflection of Equation (21) with direction signs applied. In order tc create rubbing at the 10 region of contact, however, it is only necessary that the surface speed Sw and Ste have different ~alues regardless of their directions. Thus, one may state the several cases:
Case 1: ~JW is c,c.w,; Sw is positive, C~Jte is c.w.; Ste is positive; Sw~Ste Case la: Same as 1 but Ste~S
Case 2: ~J~ is c.c.w.; Sw is positive;
C~Jte is c.c.w., Ste is negative; SW~Ste Case 2a: Same as 2 but Ste~Sw Case 3: ~Jw is c.w.; Sw is negative G~Jte is c.c.w.; Ste is negative; Sw~ Ste Case 3a: Same as 3 but Ste~ Sw Case 4: ~/w is c.w.; S is negative ~ e is c.w.; St is positive; Sw~ Ste Case 4a: Same as 4, but Ste~ Sw In all such cases, the relative surface speed Sr is finite (other than zero) --and the only requirement for this is that Sw and Ste be unequal~
The sign or direction of Sr is immaterial. Further, in Cases l, la, 3 and 3a, the magnitude or Sr is determined by subtracting the magnitucle of Ste from that of Sw; and in cases 2, 2a, 4 and 4a the magnitude of S

~69-J~

is determined by adding the magnitude of Ste to tha-t oX Sw.

F'urther, it is apparent that in Cases 2, 2a, 4 and 4a the motors WM and T.M both act affirmatively as motors to produce torques in the direction of their rotations. Both motors thus contribute :.............. ene:rgy to the rubbing action at the wheel element lnter.face, such ~; energy creating in part work that removes material and creating in part heat due to frictionO In these cases the PWRt in Eqwation (20) is arrived at by taking the _ symbols as +.

But in Case 1 (see :Ei'IG. 8) power PWRW from motor WM
goes in part to drive the element l'ED and the motor TM acts as a brake because its -torque is in a direction opposite to its rotation.
Thus, the power PWRt (producing work to remove material and heat at the interface) is found in Equation (20) by taking the PWRW sign as +
and the PWRte sign as -. Conversely, in Case la the motor TM drives the element 50 by acting as a motor, and to control the speed ~ v~
the motor WM will act as a brake which absorbs some OI the power produced by the motor TM. Thus~ Equation (20~ for Case la will be used with a + sign for PWRte and a - sign for PWRWo From what has been said, it will be seen that for Case 3, the sign of PWRw will be + and the sign of PW~te will be - in Equation (20) and the motor TM will act as a brake; furtherJ for Case 3ag the sign of PWRW will be taken as - and the sign OI PWRte as +, because the motor WM acts as a brakeO
These several cases are mentioned here ~or the sa~e of completeness because it is purely a matter of choice as to which case is used to create the rubbing relative surface velocity Sr. Indeed, in a surface grinding machine i~ the conditioning element is a stationary member (see 90 in FIG. 2) then the sur:Eace speed Ste and the power PWRte are both zeroO But for a cylindrical grinding machine and a 3~

mov.ing ~rotating) conditioning element 50 as exemp]ified in FIGo ~ I
prefer to employ Case l because it permi~:s relative speeds Sr less than wheel surface speeds Sw --and thus lower values of Sr even if the motor WM is not controllable down to low values Of ~.)w- ~nd Case l (like all except Cases la and 3a) does not requix e that the motor WM have the capability of acting also as a b:rake~
For the balance of -this specificatîon, therefore, I will assume that the rotational directions and surface speec1s Sw ancl Ste fall into Case l as illustrated in FIGn 8~ Equation (3) may be taken as a specifical:ly applicable form OI Equation (21). Also, a.s a specifically applicable form of Equation (20), I shall use for purposes OI discussion:
PWPlt = PWRW - PWRte = 27T(TORW ~)W - TRte ~)te) (22) Those skilled in the art may choose to use any case other than Case l;
but in any event they will be able to apply the teachings which :~ollow by using the correct signs in the equations which reflect physical r elationships, Considering the volumetric wheel wear rate W', one may first note that the truing element 50 is being fed toward the left (FIGo 8) and toward the wheel at a rate FtS ~expressible, for example, in inches per minute). The wheel radius Rw will be wearing down at a rate E~'w and -the element radius ~te wi.U be wearing down at a rate R'te~ The latter two values are signaled :from the probe 65 (FIGo 1) but neither Rw or R'w are directly known from the sensors employed in FIGo lo Yet~
as noted by equations set out above, Rw may be found from the relationship Rw = PtS - Rte (12) and R'w may be found from the relationship l~ts = R'w + R'te; R'w = FtS - R te The volumetric wheel removal rate is thus determinable from W' = 27T- LRWR~

and by substitution from Equations (12~ and (5) this is rewritable W ' = 2 7~ L (Pt~ ~Rte )(Fts -R te ~ (8~ ) The STE ratio from Equation (17) becomes by substitution from Equations (22) and ~8a):
PWRt (T03~WG~)W - TORte G~te) (IORW~G)W ~ T~Rte ~te) STE = = ~ 23 W' L-RWoE~w L(PtS - Rte)(Fts ~ R te) The numerator and denominator are respectively proportional to PVVRt and W'O
In accordance with an important aspect of my invention, I have discovered that rapid trui.ng of a grinding wheel and low wear rates on the truing element are obtained when the relative rubbing and feeding action of the wheel and element are set up or controlled to make the STE ratio lie always within a low rangeO By "low", I mean at least an order of magnitude less than -the SGE ratio which has been used or suggested in the art when the same grinding wheel involved is employed in grinding of a workpieceO If the STE ratio is expressed in dimensional units of horsepower per cubic inch per minute, the "low range" here referred to denotes a value of ûO 5 or lessO At any STE
of 0O 5 or below --and irrespective of whether the wheel and element materials fa~l in Class I, II or III --the truing action will be rapid (assuming that FtS is chosen or controlled to be sufficiently high), the wear rate R1te and volume rate TE' will be low, and the wheel face will be made sharp (or left sharp after a truing opera$ion ends)O
FIGS. 1~ 8 and 13 . . .
To achieve these results it is not necessary that the STE
ratio be accurately known or controlled. Indeed, it may vary widely, and approximai:ions may be usedJ so long as STE rernains low for rapid truing action~ A simple and lovv cost method and apparatus system 71E is illustrated in FIGo 13 taken with F`IGS~ 1 and 8, In FIG~ 13 a closed loop servo circuit 150 is associated with a set point -72 ~

potentiometer 151 to control the wheel motor WM and the speed ~-3w to agree with a set point signal G ) wd By manually acljusting the potentiometer 151 the speed ~ w may be changedO The servo circuit 150 includes a summing device 152 and a PID servo amplifier 154, and it operates in the same way explained above with :reference -to the control of the motor TFM in FIG, 11.
In FIG. 13 two identical servo ci:rcuit~ 155 and 15B are associated with the motors TFM and TM so that the truing slicle feed rate FtS and the truing element speed G-~te are held in agreement with set points selected by adjusting respective potentiometers 158 and 159.
although not essential9 apparatus in FIG. 13 serves as an aid in making manual adjustments to keep the STE ratio within a desired range or near, if not equal, to a desired valueO For this purpose, the signals TORW and~L)w from FIG. 1 are applied to a multiplier circuit 160 driving an amplifier 161 having a gain of K1 and an oul;put coupled to a meter M8. The amplifier output varies as Kl TORW' ~7 w where K1 is a proportionaLity factor chosen to permit the meter M8 to be calibrated directly in horsepower (see EqO 18)o The signals p~ 'te and FtS are bucked in a summing circuit 162 which drives an ampli.fier 164 having a gain of LR~j,K2, the output of the latter thus being K2 L Rw (~ts - R te) where K2 is a constant o:f proportionality which, taken with the previousl~ measured values of truing interface length L and radius Rw~
permits a meter M9 to be calibrated in cubic inches per minuteO
The outputs of the two amplifiers 161 and 164 are fed to a dividing circuit 165 the output of which is appLied to a meter MlO.
The input signal to that meter va:ries accord.ing to the value n~`

Kl TORW ~, .PWR~
K2-L-RW(Fts-R te) W' (24) The numerator PWR in that expression may be reacl from meter M8 as an indication of the horsepower being cle:l.iverecl by the wheel motor WM . The clenominator W ' may be read from meter M9 and r epresents the wheel material removal rate in cubi.c inches per minute. The ratio displayed on the meter M10 represents, to an approxirnation, STE.
It is to be noted that Ecluation (24) omi.ts the truing element power term TORte- GJte which appears in Equation (23).
This omission may be made because the wheel motor power PWRW
is in most cases very large relative to the truing element motor (braking) power PWRte and sufficient accuracy is obtained despite the omission.
.Also, Equation t24) employs a constan-t factor Rw rather than the variable factor (PtS - Rte) in Equation (23), thus treating the ~,vheel radius as constant even though that is not in fact the case. Yet, if the wheel radius is initially 10" and represented by the constant factor Rw in Equation (24), then as the wheel wears by several tenths of an inch the approximation will still be sufficient.
In the use of the FIG. 13 apparatus, a human operator brings the truing element 50 into contact with the wheel 20 ~FIG. 8) and then sets the potentiometers 158 and 159 to produce desired values OI
FtS and ~iJt . Ee reads the meter M10 to observe the STE value and then adjusts the potentiometer until he obtains an indicated ratio OI, say~ 0.25 horsepower per cubic inch per minute, This ~,vill not be a truly accurate indication of STE, due to the approximations e~plained, but it will not be off by more than about 25%. If the Ineter M10 first reads higher or lower than 0 . 25, the operator may adjust the pote.ntiometer 151 to decrease or increase hJw and thus to bring the mete:r readillg to that value. Such adjustment has the et`fect of clec~easillg~ Ol` inc~easing~
the value of PWRW and there~ore PW~ in l~ uc~tiotl (2 3~l ~ lternatively, th~ operator may adJu~t the potentiometer ~ 58 to change FtS. If FtS is increased or clecreased, the wheel radius reduction rate will increase or decrease, 90 W1 will increase or decrease, and ST:E will tend to decrease or increase~ Torque TORW
will tend to increase or decrease and make the numera-tor in Eqwation (24) in part cancel such change in ST:~, but -ther e will not be to-tal cancellation~ The adjustment of ~lts :may the:re:Eore alsv be used to adjust ST~ Likewise~ the operator may adjust the potentiorneter 159 to change ~te ~and therefore relative sur:Eace speed Sr.) which due to changes at the interiace will cause the wheel power PWRw to change and thereby cause the STE (as indicated on meter M10) to change~
Once the initial reading OI 00 25, or thereabout~ has been established on meter M10, the truing may continue --and even though the STE value so indicated rises or :~alls by 30 to 40 percentg it will be known that the STE ratio is somewhere below 0. 50~ Truing wiLI be accomplished by rapid wear of the wh.eel; the wear on the truing element will be slight; and when truing action is terminated the wheel face will be sharp.
FIGSo lg 8 and 14 .. _ _ ... . ._ FIGO 14 urhen taken with FIGSo 1 and 8 illustrates another embodiment of the present method and apparatus for controlling the STE
ratio without the approximations mentioned above with :respect to FIGO
13. In the system 71F OI FIGO 14J the truing feed motor TFM and the truing slide rate :FtS are controlled by a servo circuit 155 identical to that pre~riously described with reference to FIG~ 130 Similarly~ a servo circuit 156 is employed to control the truing element speed ~)te such that it is kept substantially equal to a set point v~lue C) ted as established by adjustment of the potentiomete:r 159, Thus, ln the operation of the apparatus showr:l in F~ O 1~:L the .t`eecl rate :E~'t~; nd the _ 7 r) ~

elementis rotational speed G ~te are both maintained essentially constant ancl equal to preselected set point valuesO
In order to sense ancl signal the value of the STE ratio actually e~isting in the machine while truing is occurring, first ancl second multip~iers 170 and 171 feed thei:r output signals to a summing circuit 1720 The first multiplier r eceives the s:ignals rr0RW and C~) while the second multiplier recei~es the signals rrOP~,te ancl (~)te The output of the summing circuit 172 varies as the total power PWRt and represents the numerator in Equation (23).
Further a multiplier 174 receives as its inputs a signal L rom an adjusted potentiometer 175 ~representing the axial length of the truing inter:face) and the output OI a ~umming circuit 176. The latter receives the signals PtS and Rte so that its output varies in accordlance with the wheel radius Rw in accordance with E~uation (12~o Another summing circuit 178 receives the input signals FtS and R'te to produce an output signal vrhich varies as the wheel radius reduction rate R'w in accordance with Equation (5). The outputs Irom the summing circuit 178 and the multiplier 174 are applied to a multiplier 179 which produces an output signal here labeled W'. This latter signal thus varies in accordance with the denominator in Equation (23) and is fed to a divider circuit 180 along with the signal PWRt from the summing circuit 172.
The output from the divider 18() varies in accordance with the actual value OI ST:E~ existing in the machine while truing is in progress (:FIG~
8). That signal is fed subtractively to a summing circuit 181 which also receives additively a set point signal STEd from ~n adjusted potentiometer 1820 The operator of the system may set up on the potentiometer a desired value oI the STE: ratio which he wislles to have automatically maintained during t;he course of the trlling proceclure, ~f the actual value of ST~: cliers rortl tll~ set UOillt, tl~e ~ tl~ming, circ~

181 produces an error signal ERR7 fed to a PID servo amplifier 183 which supplies the energizing voltage Vwm to the wheel motor WM.
~ this fashion" if an error exists, the motor WM adjwsts the speed ~ w until the signaled value of the actual STE agrees with the set point ~alue ancl the error ERR7 is restored to zero.
1~ rapid truing O:e a deteriorate d wheel ~ac~ is desireci and with relatively small wear on the truing element being employed, the operator of the system will set the potentiometer to call for an STE
ratio of 0~ 5 HP/in. 3/min. J or lessD Wheel speed (~w will then be adjusted to maintain the STE ratio and the system wiU operate with a combined truing Eeed rate and relative surface speed such that the wheel wcar occurs mainly by grit fracture and grit bond fracture. When the truing operation is terminated, the wheel face will be sharpO
In FIGo 14 the correctively adjusted value is )w ~E STE becomes greater or less than STEd, the wheel speed G)yv is decreased or increased; and thus the surface speed Sw is decreased or increased ~see Equation 1~; and the relative rubbing surface speed Sr is decreased or increased (see Equation 3) because G ~te is held constant by the servo loop 1560 As noted above, iI Sr is decreased, impact strength of wheel grits and grit bonds is decreased so that wheel radius reduction ra$e E~'~ increases (and R'te decreases with FtS
remaining constant~. Alternatively, i Sr is increased, the wheel radius reduction rate R'w decreases and R'te increases, while, in this embodiment, the feed rate FtS is held constantO Thereforel by selecting a set point STEd and keeping the actual STE equal to it, the apparatus ancl method depicted by E~ So 1~ 8 and 14 will vary the relative surEace speed Sr to change the truing ratio TR.
It should be understoocl that ottler variahles besiclesG_)~
may be adjusted automatically in otcler to keep STF ~otl~tant and eclual to a selected set point value, The STF. ratio \,viLl ctlat~ it` eit~ler t~le -'77 truing element speed ~)te or the truing feed rate F.tS is changed, and either o:E these qua,ntities may be controlled auto.matically to provide corrective acljustments whenever an error arises between the actual value and the se-t point value of ST~.
FIGS~ 1~ 8 and 15 It is not essential that the value of ,S'rl!' actually be computed ancl signaled in order to keep the ST E ratio w:ithin a desi:red range or at a desired set point, An alter native forrn of control apparatus is shown in FIGo 15 (taken with FIGSD 1 and 8) to confirm thiso In the system 71G of FIG~ 15~ the wheel material removal rate Wl is controlled to agree with a desired set point W'd by the components 1~5 to 142 which are identical in organization and operation to those cot~ponents identified by the sarne reference characters in FIGo 12~ In addition the total truing power PWRt is, in FIG~ 15~ controlled to agree with a set point P'WRtd selected by an operator who adjusts a potentiometer 185~ For this purpose, two multipliers 170, 171 and a summing circuit 172 (organizecl and operating as previousl~ explainecl relative to FIGo 14) produce a signal proportional to ~TRw ~w~ ~ (TRte ~te) :Fed through an a.mpli~ier 186 ha~ing a gain OI 277~o The ampli:Eier output varies as PWR,t (see Equation 22) and is fed in bucking relation to a sum.ming circuit 187 to create an error signal applied to a PID servo ampli:fier 188 controlling the motor WM. The speed ~,v is thus automatically varied to keep PWRt substantially constant and equal to the set point PWRtd In FIG. 15, the motor TM is controlled by- a closed loop se:rvo circuit :L48 to keepCOte at some selected set point value~)ted (in the same fashion previously show:n by FTG~ 12)~
Since the app. ratus of F:~G. 15 l;eeps W~ d l''W~t constant at set poin-t values, a humall oper.ltot~ nl ~y kl~ow al~cl clel;e~nitle the STE ratio simply by selecting those values and thus their ratio PWRt/W~o The STE ratio need not be actually signaled~ Merely as an optional convenience, FIG. 15 includes a divider circuit 189 receiving the signals PWRt and W' to energize a meter Mll which displays the numerical value of STE ~see Equation 23) a~ld aids an operator in setting the potentiometers 140, 185 so that ~m STE ratio of less than 0.5 (or some other va:lue) is obtainecl. r~lhe amplifiers 138 and 186 ar e here shown for the sake of completeness with gains conforming to Equations (22) and (8). Such gains are not strictly necessaryJ however, iE scaling factoxs are otherwise provided so that potentiometers 14Q and 185 are calibrated respectively in (a) cubic inches per minute and (b) horsepower --or any other dimensional units which may be desired.
Methods Yielding Marked Economies and Advantages . . ~ .
While the controlling of STE so that it resides within a range of preselected values, or so that it is maintained substantially equal to a selected set point value, may be applied to effect rapid and efficient truing with the advantages heretofore noted when the ratio is kept below 0.5, and preferably at about 0.05 to 0.03, there are other advantages to be gained from controlling STE at different set points and in different ranges in a fashion to be made clear hereafter.
Thus far I have described t~,vo approaches for obtaining fast wheel truing -while leaving the wheel sharp. One may keep the truing ratio TR above a value of 1. O for Class I, or 10 . O for Class II~
or keep S below 3000 f.p.m. for Class III. One may accomplish these same results by controlling the ratio STE ~,vithin a range or at a set point which is below 0.5 horsepower per cubic inch per minute.
In all such procedures it is a startling fact that the w~lr on the operative --7~)~

face of the truing element will be quite small over a considerable time and as a considerable amount is trued off of the wheel (whether in time-spaced truing operations or one long one) --and even if the truing elernent is a grindable, substantially homogeneous material such as hardened Ml steel (as contrastecl to a discrete particle material such as diamond chips set in a matrix).
My methods for truing with Class I or ~lass ll materials thus include the procedure of forming a truing element of an homogeneous ! crystaline metal such as 1020 or M2 steel so that it has an operative 10 surface which conforms to the desired shape of the wheel face to be trued. The truing element may be one of many materials which heretofore those skilled in the art would not have dreamed to be feasible. The truing element and its operative surface may be created in the first instance by machining the steel to approximately the desired size and shape, heat treating to harden it~ and then hand finishing to exactly the desired shape. Alternatively, the final shaping of the operative surface may be performed by grinding with a wheel known to have almost perfectly the desired face shape, so the truing element operative surface ends up in the correct configuration. Merely as an example, 20 if a grinding wheel of aluminum oxide grits is to be employed to grind workpieces of cast iron, the truing element is made of M2 steel and its operati~e surface is initially shaped by grinding the truing element with a second wheel of boron nitride grits having a face known to be accurately shaped. When the first wheel (of aluminum o~ide) is later trued by rubbing contact with that M2 steel truing element, the truing operation will ~all in Class II and the TR ratio will be held above lO.0 or the STE will be held below 0 5.
Another example: ~ wheel of silicon carbide g`I`itS iS to be used in pr oduction gr inding oL` l\I l ~I.IL`delled ~;teel p.l~`tS . l\ tl`Ui~

f~ 3~

element of M2 steel is formed by hand finishing the operative surface to have the desired shape. Thereafter, as production grinding of successi~e Ml steel parts proceeds, the wheel is periodically trued by rubbing contact with the M2 steel element, and with relative surface speeds and infeed rates conjointly controllect, for Class I, to give a ratio TR greater than 1.0 and preferably ahout 30 (or to provide an STE les s than 0 . 5 and prefer ably about 0 . 3 ) . If and when the truing element itself ceases to have a sufficiently accurate shape (possibly after 20 or 30 wheel truing operations) it is again restored by hand finishing.
Workpiece Substitution These considerations have led me to a further subclass of my truing methodsO I call it 'Iworkpiece substitution". I~l that procedure the truing element employed to restore the shape of a given grinding wheel is made of the same material as the workpieces which are to be ground by that wheel when the latter is employed in the production grinding of parts~ And~ indeed, the truing element itself may be a workpiece whose operative surface has been shaped earlier by grinding action of the wheel to be trued.
Example I
More specifically, to carry out the "substitution"
method (a~ Obtain, in any suitable way, a first workpiece of a given material and shape --ancl which is identical to the desired finished shape of a second workpiece which has not yet been ground;
(b) Obtain a grinding wheel ha~Ting a face which at least approximately, if not e~actly, cont`orms to tlle ctesil~ed shape ~- of the work surface OI cl ~,vorkpiece to l)(? ~ `OUII~t;
s~

(c) Utllize the grinding wheel to grind the second workpiece; and (d) Prior to, during or at intermittent stages in the course of grinding the second workpiece, true the wheel by rotationally driving it and relatively feeding it into rubbing contact with the work surface of the fir st workpiecc, the :Latter serving as a truing element, while conjointly establishing the relative surface speed Sr and the .relative infeed rate ko :make the truing ratio T:R grea ter than l o ~
In that method, it is likely that the wheel grits will be harder than -the truing element (first workpiece) material because the wheel grits will be chosen for good grinding action on -the second workpieceO The truing will probably (but need not inevitably) be C:iass Io It will be preferred, nevertheless~ to make the truing ratio TR fall in the general range of 20 to 50O And, of course, this may also be accomplished by holding the STE rati~ below 00 5 and pre~erably about 0O 3 during the truing procedure (d).
Example II
.
As a further version and example of my substitution method as applied to production grinding of a series of identical workpieces to a deslred size and final shape, despite progressive cleterioration in the shape of a gi~en grinding wheel employed:
(a~ Create, by any suitable procedure, a first ~f said workpieces with a work surface having the desired shape (its size is not important ~;
(b) Obtain a grinding wheel having a face which at least approximately, if not exactly, confor:ms to said desired final shape;
(c) Utilize said wheel to grinct -the seconcl a~lct successive ol~es of the workpieces to the desit t~d .f:illal s.i%e atld Sllape; allct (d~ From time-to-time during the course of procedure (c) (when the wheel face no longer suf-ficiently conforms to the desired shape) create relative rubbing and infeeding of the wheel face and the worl~ surface of the first workpiece (which serves as a truing element) to true the wheel by (dl) Conjointly establishing the relative surface speed S~r and infeed rate to make the truing ratio greater than 1 . O (and pr ef erably much higher than 1. 0 ) .
In E~ample II, if the wheel face initially does not conform 10 to the desired shape, a truing procedure (d) may of course be performed before grinding of the second workpiece begins. And, as indicated above, procedure (d) may be carried out by selecting a truing feed rate and controlling the STE ratio such that it is 0.5 or substantially less. It may be noted that in some specific applications, the truing procedure might be performed several times during the course of grinding each of the second and successive w~orkpieces, or it might be performed once after each workpiece has been ground, or it might be performed once after each five or six workpieces have been ground.
This all depends on how often the wheel face loses shape to the extent 20 it is no lo~ger acceptable and re-shaping by truing is desired.
As a variant of Example [I, if the wheel to be used is known at the beginning to have precisely the desired face shape, then the creating of the first workpiece, according to procedure (a), may be accomplished by taking one of the workpiece blanks and grinding it with the wheel to create the proper shape on the operative surface of the workpiece which is subsequently used as a truing element.
Still further, if as a res~llt of a considerable mlmber of truing procedures, the operative surface of Ihe t`irst workpiece (that is, tlle :~ truirle element) terde to lose the dcsil od eh:lp-~, thr~ IIC oi th~ p~ viollely finished workpieces may be substituted as the truing element employed :From that point forward. Such substitution may be rnade r epeatedly; the method therefore perpetuates its own succession of truing elements as they wear outO Even if, in high quantity production of say, two thousand workpieces, fifty are pulled out ancl used as truing elements, the cost :Eor the truing function becomes very low in relation to prior art methodsO
In review, the methods and apparatus here disclosed permit the truing operation, which is vital in the grinding art, to be effected by the use of truing elements made of ordinary metals or steels and, indeed, of the same metals or steels which ar e in the workpieces to be ground. The economics of this, compared to special costly, wear resistant material truing elements which are di~ficult to produce with the desired shape (and especially in the case of form grinding) are self-evident.
This is not to say, however, that the present invention will not be without marked advantages even if one chooses to use truing elements of special wear-resistant materials~ For example, in the truing of wheels having aluminum oxide grits, a truing element of the desired shape may be made of tungsten carbide or boron carbide The time and cost of making such a truing element (especially for use in form grinding) may be high. But when employed in the fashion here taught, truing ratios of 2000 or 3000 are possibly to be obtained" and thus the cost of the element spread over its extremely long useful life becomes very reasonableO
In that sense, my invention may turn out to promote widespread use of diamond chip truing elements to an almost unbelievable advantage in the grinding industry. When operated at a rela-tive surface speed Sr below 3000 fO p~ m. (a range not heretofore used or suggested, -~3~L -so far as I know) and preferably at about 300 or 400 f. p. m~, a cliamond chip truing roll will quickly reduce a wheel of almost any grit rnaterial (eO g., aluminum oxide or silicon carbide). The infeecl rate may be as high as desired~ subject only to the strength ancl stift'ness of the grinding machine itse~f. Yet, the diamond -truing ro]l will show almost no perceptible wear or loss of shape as it is usecl repeateclly to -tr ue wheels (even as successive wheels wear out) employecl to grincl thousanc-ls of workpiecesO I have been unable to measure wear on a diamoncl truing roll which I have used at relative surface speeds of about 400 f~ pO m. and with significantly high infeed rates (about 60 mils per minute), I estimate conservatively that the useful life of a diamond truing roll employed according to the present invention will be extended by a factor of at least twenty compared to prior art procedures. And therefore, in high volume industrial grinding of the future it seems likely that expensive diamond truing rolls may become extremely low in effective cost if employed in the manner here explained.
Determination of Sharpness ___ ._____ ___ It is known in the art that a sharp wheel cuts fast in grinding of a workpiece; feed rates may be high, and power to produce the rubbing, abrading action is relatively low comp~red to a dull wheelO
A sharp wheel generally has jagged corner grits exposed to bite through the workpie(~e. It is known that final surface finish when grinding ends with a sharp wheel is poor (microinches of roughness is high)~
A dull wheel (where grits have been flattened) used for grinding cuts the workpiece material slowly. A-t a given, high wheel slide feed rateg the duller the wheel hecomes, the greater the proportion of wheel-c-lriving power which is conver-ted to heat by ft`iCtiOIl ~instead o~ creating workpiece removal)~ Thus, if a wheel is in:t`ecl at a constant rate and r elative surface spe~d at the work S~lt~lCC ls kept a,~pro~imately constant~ as the wheel dulls due to att:ritious wear, the wheel driving motor WM takes more power, and heat at the interface may create "metalurgical burn'l of the workpieceO .~e burn is avoided by a low feed rate, a dul;L wheel will, however, leave a smoo-ther (less .microinches of roughness) surface finish on the workpiece.
Generally stated, it is desi:rable to rough grinct a part with a sharp wheel for faster removal o:t workpiece material, anct to finish grind a part with a dull wheel for smoother final surface finish~
The grinding art has l,vrestlect with the problems of truing (shaping~ and sharpening (dressing~ a wheel :tace wi-thout much attention to interrelations between the twoO As an example, it is recognized in the literature that truing of a wheel with a diamond truing roll leaves the wheel face dull --and this is accepted as a burdensome fact of life, with those skilled in the art often truing (shaping) a wheel with a diamond roll and thereafter "dressing" it in a separate operation to sharpen the face. From the teachings in this application, however, it will now be understood that diamond roll truing (shaping) in the fashion set out abs~ve will leave the wheel face sharpO And the grinding art has tended to consider "dressing" OI a ~heel as "s.harpening", recognizing that it rnay sometimes be desired purposely to produce duLlingO
I have explained above methods for truing a vvheel face which not only reduce the wheel raclius fast, but also leave the wheel face sharp and produce li-ttle wear or shape deterioration of the operative surface on the truirlg element --e~en when the truing element is made of steelO In one aspect, that is accomplished by rubbing actio.n at the interface such that the ST:E~ ratio is low (e. g., iess than 0~ 5 HP/in. /minO )~ This results in the trlling elerlletlt producing very :Little attritious wear on the wheel gritsJ but ttle \,vlleel is re(tuced :itl radius by g:rit fracture an~l boncl eract~re.

q~

My work has resulted in a related and startling discovery.
I a.m able to determine the degree of wheel sharpness which exists after or because OI a l'truing operationl' by adjusting or setting the conditions under which the rubbing contact occursn More particularly, I have discovered tha.t there is an inverse, monotonic (but non linear) relation between the STE ratio and the resulting condition or sharpness of the wheel~
Sharpness Degree Method P~
= ~
In accordance with my invention in this aspect, a grinding wheel is restored to or main$ained at a desired degree of sharpness by (a) rotating the wheel and relatively feeding its :face into relative rubbing contact with the operative sur:tace of a truing element, and (b) controlling such relative rubbing speed and feeding rate to make the STE ratio fall within a preselected rangeO
Implicit in the foregoing are the facts that in executing Method A
(i) The STE ratio need not be precisely known~, measured or compu-ted so long as conditions are maintained which assure with reasonable con~idence that, if measured, the STE ratio would fall within the preselected range~
(ii) the ST:E ratio may be determined by single settings and open loop action so long as it is within the preselected range, or it may be held at a set poin$ value (which is changeable) by closed loop action, (iii) the rubbing contact with the STE range may be created in$ermittently during time spaced i.ntervals or contimlously over a long time span, and with the preselec-ted rang~e changed or smoothly varied :Erom one value to anot~ler at d:i:t`erellt - points in time, (iv3 the rubbing contact of the wheel and truing element (conditioning element) may take place while the wheel is or is not also in contact with a workpiece to be ground; ancl indeed it may be created in a machine separate and apart from the machine in which the wheel is used to grind workpieces, and (v) truing (shaping) of the wheel face may or :may not be an objective or synergistic incidental benefi-t of the procedur e which af:Eects (increases, decreases or m.aintains) the desirecl degree o:E
wheel sharpness, Method A will generally be utilized by (1) making the preselected range for STE lower when a greater wheel sharpness is desired and (2) making the preselected range for STE higher when a duller wheel is desiredO For exampleJ if a wheel face has deterioratecl in shape and needs truing~ but the wheel is next to be employed in rough grinding a part, the preselected range for STE will be made low (eO g., 0~ 5 to ûO 02 or even less)D As explained above, the wheel w~ll not only be "trued" but will also be made sharp --so that rough grinding of a workpiece may thexeafter proceed at a high work removal rate M' and without likelihood of metallurgical burnO But if a wheel is next to be employed for finish grinding of a workpiece to a smooth (low microinch~ surface finish, the preselected range for STE will be made high ~eO g., 3O 0 to 7. Q), the wheel thereby being left dull. Gr inding OI a wo:rkpiece thereafter will be carried out at a finishing feed rate and the workpiece surface finish will have low microinch roughness ~a high degree of smoothness)O
. Sharpness Degree Method B
Method A embraces but may be re-expressed as a narrower Method B for rough grinding and inishing grinding a workpiece with a single grinding wheel by (a) establishing :relative rubbing and imeed:irlg of a wheel face and truing elernent operative surface swch that the STE ratio falls within a :first precletermined range~
(b) subsequent to procedure (a), estab~ishing a relative rwbbing and infeeding such that the STE ratio falls within a seconcl predetermin.ed range, said second range being higher than the first, (c) feeding the wheel face relatively into rubbing contact with the workpiece to grind the Lltter, such gr:incling being carr.ied out either during or after performance of said proceclure (a) and during or after performance of said procedure (b)o The performance of the grinding procedure (c) su~sequent to procedure (a) is best suited to rapid rough grindingO Performance of the grinding procedure (c) subsequen$ to procedure (b) is best suited to finish grinding to yield a good (smooth) surface finishO Indeed, it is preferable ~hat the feed rate for grinding which follows procedure (a) be higher than the grinding feed rate which follows procedure (b)o If truing contact is not created while grinding of the workpiece is ta.king place, the sequence of the three procedures, with respect to a single workpiece will ordinarily be (a3, (c), (b), (c) --thereby to produce one rough grind and one finish grind stage~ ~ the workpiece is one on which a great deal of rough grinding must be performed (during which the ~,vheel for any reason loses shape or sharpness) then the sequence OI procedures might pre:Eerably be (a), (c), ~a), (c~, (a) (c), ~b~ (c~.
The same apparatus and truing element may be used to carry out procedures (a) and (b); to change from one to -the other requir es only resetting the value of ~Jw- ~.)te or Fts- ~s e~plained previously, with reference to li'IG. 8, if ~ w is increased, STE will be increased; and if FtS or~ tc is inc:~eased, STE will be decreased.

For reasons and with added advantages to be explained more fully below, the procedure (c) may wholly or partly overlap in time the procedures (a) and (b). Thus [i] Procedure (c) may be performed continuously over a span of time and procedur es (a) and (b) performed cluring r-elatively earlier and later portions of that time spanO
[iil Procedure ~c) may be perforrned continuously over a span of timeg procedure (a) is performecl substantially continuously over a first portion of the span, and procedu:re (b) is carried out substantially continuously during a later portion of the span which immediately follows the first portionO
[iii] The timing of ~i] but with procedure (a) carried out intermittently during time spaced intervals within the earlier portion of the time spanO
[iv] The timing of [i]~ Eii] or [iii] and wherein procedure (c) is carried out with first and second grinding feed rates during the earlier and later portions of the time span, the first feed rate being greater than the secondO
Of course, in all of these methods for determining wheel sharpness, the truing element may be one falling in Class I~ II or III
with respect to the material of the grinding wheelO The truing element may be a substituted workpiece. ~nd with respect to procedure (a), the first STE range of values may or may no-t be chosen to give TR
ratios of greater than 1. 0 for Class I, greater than 10. 0 for Class II
or a rela~ive surface speed of less than 3000 fO p. mO fo:r Class IIIo If so, then rapid truing and high wheel sharpness will be obtained, but it may not be desired in all situations to produce such a high degree of`
sharpness O

--'3 (J--'3~3~L

Typical Apparatus for Executing the Sharpness Degree Methods A or B
FIGS~ 1, 8 and 13 depict exemplary apparatus which may be employed to carry out Method A in a broad sense and with STE
controlled to fall within a preselected rangeO As noted ear~ier, FIG. 8 shows the wheel 20 and truing element 50 in rubbing corltact, the relative surface speed Sr being determined by the set points L.) wd ~d C;~) ted chosen by setting or adjusting the potentiometers 151 and 1590 The relative infeed rate is chosen by set-ting or adjusting potentiometer 15U
to determine the feed set point FtSd. Given the fact that the radii of the wheel 20 and element 50 have certain values, the truing action will occur with some STE value which is expressed by Equation (23) but which will not necessarily be accurately known by $he operator~
:1~ the human operator makes several measurements and co~nputes STE
for different values of G ) w~ C~ te and FtSl acquire a sufficient "feel" so that he can make set point adjustments to create an STE falling within a preselected range which he desiresO
The optional meters M8, M9, M10 and associated components may assist the operator in making STE fall within a desired preselected rangeO To an approximationJ as noted earlier, the rneter M8 indicates truing power PWRt by displaying wheel power PWRw and neglecting the relatively smaller truing element power PWRte (compare Equations 23 and 24). To an approximation, the meter M9 indicates volumetric wheel removal rate W'O Thus, the reading on meter M10 .indicates to an operator at least a reasonable approximation of the STE value.
In carrying out Method ~, therefore, the operator need only manually adjuStc~wd~ CL) ted or Ftsd reading on rneter M10 in the mid-region OI the preselected STE range which he desiresO Increasing C~)wd will increase STE; decreasingC)te or FtS will increase STE~ If the operator desires to rnake the wheel sharp, he makes adjustments which result in a low STE initial reading;
if he desires to make the wheel dull, he makes adjustments which result in a higher initial STE reading. Thereafter, changing conditions may cause the STE reading to vary from the initial value but this is tolerable so long as the reading stays within the preselected range~ And if STE
should depart from that range the oper ator may bring it back into the range by .readjusting one or more of the potentiometers 151, 1$8~ 159 To carry out Method B in one specific for.m with the apparatus of FIGS. 1, 8 and 13, after an unground workpiece has been placed in the machine (:FIG. 1) with clea:rance from the wheel 20, the truing element 50 may he brought into contact with the wheel (FIGo 8) and then adjustments made in FIG~ 13 sO that a low STE reading (on the order of 0~ :10) is obtained, and such that STE will vary over a pr eselected range of, say9 0O 12 to 0. 080 The wheel will be trued and le:Et x elatively sharp. Then the element 50 is backed away from the wheel 20 (FIGo 1 ) and the wheel moved into grinding contact with the workpiece 24 to rough grind the latter at a relatively high wheel slide :Eeed rate FWs chosen by open or closed loop setting of the voltage Vw~m ~fter the part has been reduced to a certain radius (indicated by the voltage Pps) the operator may manually control the motor WFM to back the wheel free of the part 24, and may manually control the motor TFM to move the element 50 again into rubbing contact with the wheel (as shown in FIGo 8)o The operator might then adjust the potentiometers of FIG~
13 to obtain a low STE reading --solely to restore the wheel face shape by rapid truing --inasmuch as the wheel may have lost :Eorm during the rough grindingO Then, however, the operator will adjust the potentiometers of FIGo 13 to obtain a much higher S~reading on meter M8 (say, about 7. 0) and such that the STE value will therea:Eter vary w.ithiQ a preselected 3t~l range (say, 9~ 0 to 5. 0)O This will not rapidly recluce the wheel radius but it will dull the wheel face grits so that they are con,clitioned to create a fine (low rnicroinch) surface finish on the part~ Next, the operator backs the element 50 clear of the wheel 20 and advances the wheel slide until the wheel again makes grinding contact with the part 24 (FIG. l)o The vol.tage Vwfm is manually adjusted to create a relatively low eed rate FWS~ so that finish grincling occur~O When the part has reached the desired final radius, the whee:l slide is retracted and the finished part is removed from the machineu That finished part will have a fine surface finish clue to final grinding with a dull wheel, the surIace fineness being directly and monotonically related to the STE range preselected for the last truing or conditioning procedure .
Of course, many variations of the last-described example may be practiced within the scope of Methods A and Bo A truing procedure may be carried out several times over the course of rough grinding, and the sharpness left at the wheel face after each procedure may be less if one chooses a higher STE range for each successive procedure.
And, as will become apparent below, it is not neces~ary that the grinding action on the workpiece be interrupted each time the truing element is brought into contact with the wheel.
FIGS. 1, 8 and 14 may be utilized to carry out Methods ~ and B in a different specific fashionO When a fresh workpiece is placed in the machine3 a truing procedure is conducted by locating the wheel and element as shown in :F'IG. 8; the potentiometers 158 and 159 in FIG~ 14 ar e set to produce desired values of FtS and ~)te; and the potentiometer 182 is set to ca~l for a relatively low set point STEd (sayJ 0. 07). Now~ as already explained, wheel speed G)w will automatically change to keep STE equal to the set po:int STh'd (and -~ ~ ~3'~,~,3~ ~

therefore within a very narrow preselected range of values). The wheel will be trued and left sharpO Next, the truing element is backed away from the wheel and the wheel is advanced in-to contact with the part 24 (FIG. 1~ so grinding at a rough grind feed rate occursO Thereafter, the wheel is backed free of the part 24 and the element 50 moved into wheel contact (FIG. 8)o Now, however, the potentiometer 182 is adjusted to call for a set point STEd which is higher (~ay, 8~ O) than before. The wheel will now be "trued" in the sense that its face will be conditioned to dull (the greater the set point STE`d, the duller the wheel will be made). Then, the element will be backed away from the wheel and the latter brought into contact with the part 24 with a finish grind feed rateO
When finish grinding is completed the part will have a surface finish which in fineness (smoothness) has been determined by the set point value o~ STEd chosen for the second conditioning procedure.
~gainJ the apparatus of FIGSo 1~ B and 14 may be used to carry out methods having many variations of the last-described example, and all within the broad definition of Method ~ and/or B.
Merely as an example, the control circuitry of FIGo 14 may be supplemented such that the first truing procedure is terminated automatically after a certain time duration or a certain reduction in wheel radius, with the rough grinding then initiated automatically.
The rough grinding may be terminated when the part 24 is reduced to a predetermined first radius and the voltage Pps has fallen to a corresponding value, whereupon the second '~truing" procedure is automatically initiated with automatic switching of the set point signal to a second higher value. The second "truing" procedure may then be terminated automatically after a certain time lapse, and finish grinding initiated automatically with switching of the motor WFM to produce a low wheel feed rate. And the finish grinding may be eilded automatically - 'J~L -.a ~ ~9'~.`3q~ ~

when the signal Pps falls to a predetermined value generally related to final part radius. These sorts of automatic sequence controls are optional and within the skill of those work.ing in the art.

Pre-Establishing ~fter-Grind Workpiece Sur.ïace Smoothness It may be noted here that Methods A and :B permit direct selection of the surface finish which a given grinding whe~el will produce on a workpiece if the latter is ground a small amount immediately after a "truing" operation~ I have ascertained from test data that STE varies as a non-linear, inverse monotonic function of wheel removal rate W', as illustrated by curve 200 in FIGo 160 That curve represents in a general way, for a wheel and a truing element of given respective materials, the relationship of STE ancl W'~ assuming that relative surface speed Sr- is held constant at a given value Srl and FtS
is varied to create changes in W'. The curve 200 represents a family of curves each one corr esponding to a different constant relative surface speed Sro For example, curve 200a corresponds to a surface speed Sr2 which is less than the Sr1 applicable to curve ~00; and this confirms that as surface speed decreases but W' remains constant, STE decreases in a monotonic fashion~
With respect to curve 200, STE values are to be read as ordinates on the left scale 201.
Surface finish smoothness (here called S~ll) is here de:Eined as the opposite of roughness hecause the higher the degree of smoothness (and the lower the microinches of roughness) the higher the quality of a ground part. One cannot predict the after-grind smoothness of a workpiece surface which will be produced by a given wheel on a given part ground with a wheel just after the wheel face has been trued or conditioned at a given removal rate W', Thc reclsQn is -~)5 -thal; the sharpness of the wheel grits left after contact with a truing element depends on both the removal rate W ' and the relative rubbing speed Sr, the latter being unknown. If speed Sr is known, but W' of the "truing" contact is not known, the wheel face sharpness, and thus part smoothness which will result from the next use of the wheel, cannot be predicted.
I have found that STE reflects both relative surface speed and wheel wear rate and that I can tie the after -grind surface finish, produced on a part by a given wheel, to the STE with which the 10 wheel was "trued" (by a given truing e]ernent) just prior to the grinding.
I am thus able to plot a curve 202 in FIG. 16 to indicate the value SM
on a scale 204 at the right versus the value of STE (on the scale 20 at the left) . The curve 2û2 is very nearly but not necessarily linear as shown; it indicates in any event that after-grind smoothness SM
decreases monotonically with reduction of the STE ratio.
Thus, in FIG. 16 if curve 200 is applicable because truing is carried out at a surface speed Sr Or S~l, and if the rate W' is W'l, the STE value will be STEl and the after-grind smoothness will have a corresponding value SMl . If now the truing procedure is carried out at a higher removal rate W'2, the STE value of that procedure will be lower at STE2 and the smoothness SM will have a lower value SM2.
On the other hand, if the truing procedure is conducted with the original rate W'l, but the surface speed and power is reduced to Sr~, curve 200a becomes applicable. The result is that STE falls from STEl to STE3 and the after-grind smoothness SM falls from SMl to SM3.
I am thus able to reveal a method of forecasting and actually establishing (within limits, of course, for a grinding wheel, workpiece and truing element of given materials) the after-~rind surface ~; smoothness created on a workpiece grourld briefly and immediatel~y e -~)6-r3~

after that wheel has been "conditioned" by truing. The method comprises "truing" the wheel with a selected STE~ value (by using the methods and apparatus of FIG. 14 or FIG. 15, for example) and thereafter finish grinding the workpiece; and in making the STE value so selected higher or lower when the smoothness SM is to be made higher or lower. The two values, STE and SM, will monotonically correlate arld fvr any given wheel material, truing element mater ial and wor kpiece mater lal. Ther e are some constraints to be observecl if such correlation is relied upon to obtain reproduceable results. After a wheel has been conditioned at 10 a given STE ratio (and the conditioning action is terminated), the very act of grindirlg a workpiece may change the wheel sharpness, usually making it duller. The degree of further dulling is dependent upon the finish grinding feed rate, relative surface speed and time duration of the finish grinding procedure --and the finish surface finish SM depends upon the wheel dullness just prior to the termination of finish grinding.
Therefore, the correlation of after-grind work surEace smoothness SM
to the STE of a previous wheel conditioning procedure has best precision when the finish grinding is conducted for only a very short time interval and at grinding speeds and feeds which do not tend to change the wheel 20 sharpness. Subject to such constraints, if data are taken with a wheel, workpiece and truing element of given materials by conditioning procedures at several STE values, each procedure being followed by finish grinding at a given grinding feed rate and relative speed for the same given time interval after which surface smoothness SM is measured and logged in a table OI SM v. STE --then that table may be used in later predeterminations of SM to be obtained on subsequent workpieces of the same material. The inish grinding on such subsequent workpieces should be conducted al the same grind~ng feeds and spe~d~
and for the same time intervals, as were useà in loggillg the data.

--.') 7--t3~

I'he after-grind surface smoothness SM is more directly predeterminable, and not subject to -the cautions or restraints here no^ted, iI the wheel is conditioned by a truing element which acts simultaneously on the wheel during intervals when finish grin~ing takes place, as described later in the present specification.

Truing or Wheel Conditioning hile Grinding With STE Control As seen from the foregoing, by keeping the Sl'E ratio within a predetermined range or at a predetermined value, I am able not only to keep the wheel face in a desired shape but also to establish its degree of sharpness~ and, if desired, the smoothness OI the work surface left after a workpiece is ground by the wheelO In accordance with another aspect of the present invention, I am able to obtain these results while the physical grinding of a workpiece is in progress and thereby to save time and increase economy and productivity~ Truing or dressing of a grinding wheel sirnultaneously with grinding OI a workpiece has been broadly practiced in the prior art, but it has not been suggested that this be carried out while controlling the STE ratio so as to determine, with quantitative predictability, the wheel face condition and the consequences OI that condition on the workpiece.
For simultaneous truing (wheel conditioning) and grinding, the wheel 20 and workpiece 24 are in rubbing, grinding contact while the wheel 20 and element 50 are also in rubbing contact, as shown diagrammatically in FIG. 170 The latter figure is thus merely a specific repetition OI FIGo 1 illustrating that the truing slide TS has been moved inwardly ~left) to contact the wheel face while the wheel is grinding on the workpiece. The part 24;, wheel 20 and element 50 are all r otating (the first two being driven and -the latter being braked) by their respective motors PM, WM, TM; the wheel slide WS is being _9~

3~

fed (left) toward the work at a rate F and the truing slide TS is being ws fed (left) toward the wheel at a rate Fte, so that both the grinding and truing involve relative rubbing contact and relative infeeding.
For the exemplary method embodiments next to be described, the apparatus does not require (in FIG. 17) the truing element probe 65 which appears in FIG. 1 and thus some economies are achieved, as in FIG. 8 where the work probe 40 is not required. This is not to say that a truing element probe may not be used in other specific forms of the apparatus.
From inspection of FIGS. 1 and 17, the following relations may be expressed:

Rp Pps (25) R~p = Fps (26) ~w PwsRp Pws Pps (27) R' = F- R' - F - F (28) w ws P ws ps Rte Pts Rw Pts Pws ~ Pps (29) R'te = FtS - R w FtS Fws ps In the arrangement OI FIGS. 1 and 17 it is possible to determine the total power PWRw applied to the wheel 20 by the motor WM according to Equation (18). In FIG. 17, unlike FIG. 8, a portion of the total wheel driving power PWR is taken up at the grinding region between the wheel 20 and workpiece 24, and another portion is e.Ypended at the truing region between the wheel and the element 50. In FIG. 17, unlike FIG. 8, the signals TORW and~)w cannot be used to determine the power (here called PWRWt) applied by the motor WM to the truing interface. But one may note that at the truing interface the tangential force FOR1 which is transferred from the wheel face to the truing element operative surface is equal and opposite (absent acceleration effects) to the tangential force FOR2 which, in effect, is appliecl to the ~39-truing element by the motor T~ acting as a brakeO Since the torque TORte is signaled by the transducer 60 (FIG. 1 ) and the radii Rw and Rte are ascertainable from Equations (27) and (29), it is possible to express the torque TORWt which is being applied by the motor WM
via the wheel to the truing interface even -though a portion of that motor's total torque is applied to the grinding interLaceO Thus, it may be written:
FORl = FOR2 (31~
FORl-RW = IE~wt (32) FOR2 Rte = TRte Combining (31 ) to (33 ) yields ToRwt TRte Rt (34 ) Now, the total power PW:RWt applied by the motor WM via the wheel into the truing interface rnay be written PWRWt = 2no TRWt G~w and by substitution from (34) .PWRWt = 2~To TORte~Rte ~)w (36) Further, the power expended as work and friction-generated heat due to the rubbing contact at the truing interface is the input power less that removed to the motor TM acting as a brake, as explained previouslyO
Thus, by analogy to Equation (21), but as applicable to FIG~ 17 taken with FIG. 1, one must write PWRt = PWRwt - PWRte Substituting from Equations (36) and (19), Equation (37) becomes PWRt 2 T~ TORte [( )w ~ ~ t~ (38 ) To determine the Sl'E ratio produced under various circumstances, it is to be recalled:
STE = W' t (17) And the removal rate W' may be determinecl in the FIG. 17 apparatus in a slight:Ly different fashion from that of FIGS. 8 and 14. Recalling that W ' = 2 ~L R R ' (8) and putting (8) and (38) into 117) results in:
STE = Rt = TORte ¦llJw R-- ~ te¦ (3 L R`~w Rw ' If Rw, Rte and R'w from (27), (29) ancl (28) are substituted, the expression, applicable to FIG. 17, becomes STE = PWRt = RtG~(p p s ~ pps ) ~ ~)te]
W L (PWS ~ Pps~(Fws Fps) In carrying out the method of wheel conditioning while grinding, a control system 71H as shown in FIG. 18, taken with FIGS.
1 and 17, may be employed. It is assumed that the wheel is in rubbing contact with both the workpiece 24 and the element 50, with the slide WS
feeding toward the left relative to the machine base and the slide TS
feeding tward the left relative to the sl-ide WS. To create these relative motions, three closed loop PID servo circuits 220~ 221, 222 control the motors PM, WM and TFM in order to maintain the variables ~)p, ~-)w and FtS in close agreement with set point values l~pd~ ~)wd and FtSd obtained, for example, by adjusting potentiometers 223, 224, 225.
In addition, the wheel slide feed rate FWs is controlled such that the radius reduction rate :E~'p of the part 24 (also here called the grind rate GR) is maintained at a desired value. It will be recalled that the probe slide servo causes the clearance CL to be kept constant as the radius Rp reduces, so the eed rate Fps at which the probe slide moves to the right is equal to the grind rate or radius reduction rate R'p of the worl;piece (and the signal Pps equals the radius :E~p).
Thus, in FIG. 18 a desired probe slide feed rate FpSd is signaled hy ;~ adjusting a potentionmeter 230. That signal is buckecl in a SU.Inming 3~

circuit 231 to create an error signal El~Rlo applied to a PID ,servo amplifier 232 which energizes the wheel feed motor WF~. ~ consequence if the actual part radius reduction rate R'p ~which is equal to Fps~
increases or decreases above or below the desired value :E~pSd~ the motor WFM decreases or increases the wheel slide feed rate F'Ws~
Therefore, despite any wheel radius wear rate R'w that m.ay occur, the part radius reduction rate R~p is .maintained at a clesired vaïueO
In reviewJ FIGo 18 shows apparatus hy which values of (~L)p~ ~WL~ FtS and R'p (that is, :E~ps) are selected and then :maintained, with FWS taking on whatever value is necessary.
Further in FIG. 18 (taken with FIGS. 1 and 17), provision is made to automatically vary the truing element speed ~)$e so as to keep the actual STE ratio within a predetermined range or in agreement with a predetermined set point STEdo The set point version is here shown only because it is the more rigorous; those skilled in the art wi:Ll understand how to "degrade" the apparatus of FIG. 18 if only a loose control OI STE within a certain range is deemed sufficient in particular circumstancesO ~s illustrated, the signals PWS and Pps are applied to a summing circuit 235 whose output signal is Rw (see :L~quation 27)o The latter signal is sent to a summing circuit 236 and buc.ked with the signal PtS to produce a signal Rte (see Equation 29)o The signals Rw and Rte are divided in a circuit 238 whose output RW/R~e corresponds to the fraction in the numerator of Equation (39). That signal is, in turn, applied to a multiplier 23g along with the signalG)w and the resultant signal is fed to a summing circuit 240 along with the signal ~te taken subtractively. The output from 240 thus varies as the bracketed expression in Equation (39); and it is multiplied by TORte a circuit 241 to produce a product signal varying as the numerator of Equation (39).

To produce a signal varying in proportion to W' and corresponding to the denominator of Equation (39), the signals ~w~;
and Fps are bucked in a summing circuit 244, the difference signal R'w being applied with the signal Rw (from 235) to a multiplier 245 whose output is further multiplied by an amplifier 246 adjusted (by a rheostat 247) to have a gain of L. The output from 246 is fed to a clivider circuit 249 which receives the product signal from 241. The 0l1tput from 249 is thus a signal which varies as the actual STE according to Equation ~39)~ assuming that all wheel material is being removed from the whe~l face by action of the elernent 50~
The desired value STEd is signaled by adjusting a potentiometer 250. That is bucked with the signal STE in a summing circuit 251 to send an error signal to the input of a PID arnplifier 252 which energizes the motor TM. Thus~ if the STE value rises above the set point STEd, the motor voltage Vtm is increased~ the armature and braking torque of the motor TM decrease, the speed 4-)te increases and the value of STE is reduced (see Equation 39) until STE restores to equality with STEd. When this occurs, the relative surface speed Sr at the truing interface decreases (see Equation 3) so that the wheel grits fracture more easily, the wheel becomes sharper, and the truing power PWRt decreases, thereby to restore the STE ratio to the set point value.
In the operation of the apparatus of FIGS. 17 and 18~ the wheel radius Rw wlll reduce at a rate R'w in part due to wheel wear at the grinding interface and in part due to wheel wear at the truing interface. It has been assumed above that the former effect is so smaLI
in relation to the latter effect that sufficient accuracy is achieved by treating all OI the wheel material removal rate as occurring at the truing interface. This approxirmation is tolerable because ~vheel radius .;~ ~ ;, - 10:3 -3~3~

reduction rate due to grinding will amost always be much less than that due to truing. But if the former effect is greater than the latter effect --and because the truing infeed rate F in this embodiment maintained constant-- then the wheel face might retreat from rubbing contact with the element 50. Thus, one should choose a truing slide rate Ft d ~at potentiometer 225) comfortably greater than the wheel radius reduction rate which will occur due to grinding action, and then the servo action by amplifier 232 on the motor W~M will adjust the wheel slide feed rate FWs to maintain grinding contact and part radius reduction R~ 'p at the desired grind rate C~. Alternatively, control components may be added to automatically adjust the truing infeed rate F~tS if the error signal f.rom circuit 251 becomes excessively negative ind.icating that STE has fallen to an extent that changes .in ~)te will not r estore STE
to agreement with the set point STEdo As still another alternative, the truing element speed ~-)te may be maintained constant at a set point value (by a servo circuit similar to but replacing the circuit 222 in FIG. 18), and the STE error from the sumrming circuit 251 ~FIGo 18) applied to correctively energize the motor TFMo :In that way, and as an incident to keeping STE at the set point STEd, the truing element will always be infed sufficiently fast to maintain rubbing contact with the wheel face regardless of the wheel radius reduction rate caused by the grinding actionO
In the use of the method and apparatus shown by FIGSo 1, 17 and 18, once grinding and simultaneous truing have been startedJ
if the set point signal STEd is made :I.ow (say, equivalent to 0O 8 :HP/in, 3/rnin. or less~ then the wheel face will be maintained sharp and true in shape over a long interval of rough grinding at a relatively high grind rate GR. But the set point signal STEd may be readjusted, either manually or automatically, from time to time so as to change the sharpness of the wheel faceO In accordance with the "sharpness degree" rnethod described above, such set point changing may involve a smooth, gradual (or a step) change from an initially low STEd value or range to a higher one (accompanied preferably by a reduction in the grind rate GR on potentiometer 230) so that the wheel is dulled and -lO~L

finish grinding leaves the work surface with a desired smoothness.
That is, for rough grinding, STEd is initially set to STE1 and the grind rate GR = R~p is initia~y set to R~pl; and for subsequent fini~h grinding, these settings are ehanged to STE2 and R'p2, where STE
and R p2GR pl C)f course, it is not essentia] to the method that the element 50 contact the wheel 20 during the entire span of time in which the whee3 is grinding on a given workpiece. There may be some applications in whic}l, as grinding of the workpiece is continued, the e]ement 50 is, in effect, withdrawn from wheel contact and then restor ed to contact.
This might be desirable if grinding is controlled according to the SGE
method taught in my above-identified prior patents so that wheel sharpness is maintained automatically; but in such cases the wheel will lose shape, and the element 50 may be brought into contact to produce r e-shaping according to the above-described STE approach (with low wear on the truing element) as spaced time intervals. In such cases it may be advantageous to make the truing element OI a common hard steel as its material, or of the same material as that in the workpieces being ground, but the material chosen ;Eor the truing element is not criti- al to a realization of benefits from the method here described with reference to FIGSn 1~ 17 and 18.
Certainly, it will now be understood that the "STE control"
method, as set out above, may in part include truing or conditioning a wheel with controlled STE at least during some time intervals when the wheel is actively grinding a workpiece.
Finally, it is to be noted that speciic control apparatus other than that exemplified in FIG~ 18 may be utilized to keep STE in a predetermined range or at a set point valueO Apparatus and steps by which G_~w or Fte are correctively adjusted (rather t~lan CL)te) may be 3~
used; and approximations which ignore certain variables or assume them to be constant may be adopted without departing fro~n the novel methodO For example, as explained previouslyJ the radii Rw and Rte may be initially measured manually and assumed to be constant over a long time spanJ since significant radius reduction rate~ R'w and R'te will still not produce great percentage changes in Rw and Rte.

~termittent Wheel Conditioning While Grinding ~ . ..
The generic method oE controlling the STE r atio of truing (conditioning) action while grinding of a workpiece is on-going includes intermittently producing the truing action. But I have discovered that intermittent truing steps can lag behind those points in time when they are desired, unless some special provisions are made. Accordingly, I have conceived a method for intermittently truing a wheel, with control of STE, by which the truing element sur~ace is caused to "follow with a gap" (and usually a small gap) the wheel face, but is moved into truing contact at spaced instants in time. The spacing of those instants in time may be determined (i) merely at equal time spacings, (ii) when wheel radius reduction of a certain amount has occurred, or (iii) when loss of wheel face shape is detected by appropriate sensors.
~l general, FIGS, 1 and 17 will be helpful to an understanding of the "intermittent truing by following with a gap" method and apparatus9 but FIGSo 19~ 20 and 21 will be of Iurther aid. ~ the exemplary embodiment to be described, the wheel ~0 is Iirst brought by manual control into kissing contact with the workpiece and the truing element 50 brought into kissing contact with the wheel (FIG, l9)o The feeds FtS
and FWS are at this instant zero, `but it is possible now to determine the element radius Rte and store it, Next, the apparatus may be initiated into automatic sequencingr by which (i) the workp:iece is continuously ground at a grind rate GR, and (ii) the slide TS is controLled in its feeding such that a predetermined small gap GAP (FIGo 20) is maintained between it and the workpiece-- even as the wheel radius Rw reduces due to wheel wearO When truing of the wheel is required or desired and a "start truing procedure" signal STP is generated ~in any of several ways to be described~, the truing slide is moved rapidly inward (le~) to make the elerment "l~iss" the wheel again (I~IG. 19), and then is further fed inwardly to true o:E:f the wheel by a pr edetermined increment, io e~,, to reduce the wheel :radius by an amount .D~C (compare FIGS. 19 and 21~ --and while the wheel continues grinding action at the workpiece. This truing occurs with the STE controlled to be within a predetermined range or at a desired set point value, so wheel sharpness as well as shape may be predeterminedO But after the increment INC
has been removed from the wheel radius, the truing slide is again controlled to make the element 50 follow the wheel face with a gap (FIGo 20)~ while grinding continues, until the next "start truing" signal STP is created, whereupon the sequence or cycle is started againO
Several of these intermittent truing cycles may be executed autornatically during the total span O:e time over which a workpiece is being continuously ground and during which the wheel face otherwise would seriously deteriorate from the desired shape.
Turning next to FIGSo 22A~ 22B, a system 71I for carrying out this method includes servo circuits ~20, 221 (identical to those in FIGo 18) for controlling the workpiece and wheel rotational speeds GL)P and G )W at selected set point ~aluesO Also, the wheel slide ~:eed rate FWS is controlled by components 230, 231, 232, WFM to produce a desired grind rate (~R (as described above with reference to FIG~ 18) when the arm SSa of a :multiple pole, double-throw selector switch SS is in its lower "run" positionO

) 7 -I:E the switch arm SSa is in its upper or "set up" position, the wheel slide may be moved to di.fferent positions by motion in a direction and at a rate manually determined by adjusting a potentiometer 280. The potentiometer 280 is grounded at the center and connected between positive and negative voltage sources so that a set up voltage FWSS can be either positive or negative to make the slide WS move left or right ~FIG~ 1 or 17). It is here assumed that motor WFM drives the wheel slide WS to the right when the voltage Vw~m is positiveJ and vice versaD The signal FWSS is applied to a summing circuit 281 with the feedback signal FWS sO that with arm SSa in the position shown the slide moves in a selected direction at a selected rate.
For controlling STE during those inter~als when truing action takes place, the components 235 through 252 (FIGo 22A~ are iden-tical to, and operate in the same wayJ as the correspondingly identified components appearing in FIGo 18~ described above. There is added, in FIG~ 22A~ an analog gate 282 through which the STE error signal passes to the servo amplifier 252 whenever that gate is enabled by a signal Q2 (described below~ at a logic high levelO In that case, a second gate 283 controlled by the complement signal Q2 produced by an inverter 284 is disabled and the STE control apparatus of FI(~;~
22A operates in the same fashion already described with reference to FIG~ 18, --the motor TM acting as a brake to adjust ~)te as necessary to keep STE equal to ST~d9 When the signal Q2 is low, however, the gates 282 and 283 are respectively disabled and enabled, and thus the motor TM is controlled to drive the truing element in a clockwise direction at a "standby" speed in agreement with a standby set point .signal G.) teds whichJ to a rough approximation, will be close to that which will exist during truing contact. This avoids abrupt acceleratior of the truing element 50O

~ 10 ~3 ~

As explained below, the automatic, intermittent truing with controlled STE (within the time span in which the workpiece is being continuously ground) involves three conditions or states; these states are signaled by a three-stage ring counter 290 (FIC~. 22B) producing output signals QO, Ql, Q2 which individua~ly go to loglc hi.gh in succession as it executes successive counting cycles~ P"esetting the counter makes signal QO high. The three states, as notecl below, are QO high: The truing element follows the wheel face with a preselected gap or spacing (FIG. 20).
Ql high: The truing ele nent is moved rapidly in (left in FIG. 20) to close the gap and until the element just touches the wheel face (FIG. l9)o Q2 high: The truing action occurs at the wheel/element interface until the wheel radius has been reduced by a preselected increment INC (FIG~ 21~
When the truing during state Q2 is completed, state QO is resumed and continued until a l'start truing procedure" signal STP is received (for e~ample9 in response to detection that the grinding action has reduced the wheel radius by a further predetermined amount).
When a selector switch arm SSb (ganged to SSa~ is in its ~Iset up" position (FIGo 22B~, the motor T:F'M is controlled manually by adjusting a potentiometer 291 which produces a signal FtSS for initial set up. This latter signal, which may be zero or positive or negativeJ is applied to a summing circuit 292 which receives the feedback signal FtS and feeds an error signal to a PID servo amplifier 294 controlling the motor TFMo Thus, the truing slide WS may be moved to different positions by manual control and will remain in any given position when the sig.nal FtSS is .rnade zero.

-:lO')-3~

The remainder of FIGS. 22A, B may best be described by a narrative of the sequential operations which are carried outO
Initial Set Up Wi-th the motors PM and WM active and producing the desired rotational speeds ~)p and G )w (by operation of servo circuits 220 and 221, ~IG. 22A), it is desirable first to obtain a reading~ or signal indicative of the truing element radius RteO rhe switch ar~ s SSa and SSb are initially in their set up positions and the part 24 and element 50 are both iree of contact with the wheel 50O First, a reset switch RE is momentarily closed so that a differentiating circuit 296 applies a resetting pulse to the counter 290, thereby assuring that the latter is lnitialized to state ~0~ This means that gates 282 and 283 are respectively disabled and enabled, so motor TM is controlled to make ~ te equal to the standby set point speed ~ teds. Now a human operator manipulates the potentiometer 280 to move the wheel slide le:Et until the wheel Eace just contacts or kisses the workpiece 24; and then he manipulates the potentiometer 291 to move the truing slide WS
left until the truing element just contacts or kisses the wheel face. The two slides are stopped in these positions (by centering potentiometers 280 and 291) so that no slide feeding is taking place, this positional relationship of the components being illustrated in FIGS~ 17 and 19.
Thereupon, the human operator may momentarily close a switch INIT (FIG. 22B~ so that an input pulse passes through an OR
circuit 298 to actuate a one~shot multivibrator ~,vhich p:roduces a "store enable" pulse to a sample-and-hold amplifierO The latter thus accepts the signal Rte at its input, and its output Rteh thus becomes equal to Rte and is "held" at that valueO The storing or holding OI Rte as the signal :Rteh is desirable because Equation (29) is valid, and the output from summing circuit 236 is accurate, only wllel~ the wo.rkpiece 2 3-~.

and element 50 are both in contact with the wheel 50, as illustrated in FIGSo 17 and 19. If the element's radius Rte does not change (and it can change only while truing action is in progress), then the signal Rteh remains accurate even after the components are positioned as shown in FIG~ 20~
Following With a Gap ~ fter such initialization, and with the components located in kissing contact (FIC;S~ 17 and 19)~ the operator shifts switch arms SSa and SSb to -their run positions. This s-tarts inEeed of the wheel sl;de and grinding of -the workpiece by action of the motor WFM
to produce a grind rate GR selected on the potentiometer 230. Such grinding will continue during the remainder of the operational procedures to be described for FIGSo 22~ and 22B~
Recalling that counter 290 was previously reset to the Q0 state, analog gates 300 and 301 (FIG~ 22B) are now enabled. rhus, shifting switch arm SSb to its lower position results in the servo amp~ifier 294 receiving an input signal via the gate 300 and an ampliier 302 from the out?ut of a position servo loop summing circuit 3040 The latter receives a truing slide position set point signal PtSd and the actual position signal PtS to produce a position error signal PtSERRo Because a positive or negative polarity input at ampli~ier 294 is assumed to create truing slide motion toward the left or right respectively, and motion toward the left decreases the numerical ~ralue of the position PtS
(FIGo 1)~ the signals PtSd and PtS are Eed respectively to subt~active and additive inputs of the summing circuit 304O When the signal PtSERR
is finite and positive, the truing slide moves toward the left,, The amplifier 302 establishes the position loop gain, and the motor TFM
will thus drive the slide TS to keep the actual position PtS in agreement with $he set point PtSd. Some following error will develop while 3 ~

movement is occurring but those skilled in the art may add kn~Nn expedients which reduce following error and which virtually eliminate overshoot and hunting about a desired end point, where stopping is to occur if the signal PtSd remains constant.
The signal PtSd during the Q0 state does not, however, remain constant because grinding action will be causing the wheel radius Rw to decrease, and it is desiredtokeepthe truing element constantly spaced from the wheel Eace by a small, predetermined distance or gap.
That distance is repre~;ented by a signal GAP obtained ~rom a manually preset potentiometer 305 and applied through the enabled gate 301 to the input of summing circuit 309. From inspection of FIG. 22B (and recognizing that another analog gate 308 is disabled so that its output is ~ero because signal Q2 is low), it will be seen that the signal PtSd produced by the summing circuit 309 varies according to the relation:
PtSdo Rw + GAP + Rteh [when Q0 is high] ~41) From FIG. 20, one sees that if PtS is kept equal to PtSd, then the spacing GAP will be maintained~ even as Rw decreases. This is precisely the result of the summing circuits 309 and 304 acting through enahled gate 300 in FIG. 22B. Immediately after switch arm SSb is moved down and with 20 counter 290 in state QOJ the truing slide TS will actually move right (FIG.
17) relative to the wheel 20 until the gap GAP is opened, and thereafter will feed left to keep the gap constant as the wheel radius Rw decreases.
Thus, while grinding is taking place and the control system 71I is in state Q0, the operative surface of the truing element "follows with a gap" the wheel face.
Closing the Gap When state Q0 c~ists, there will appear from time to time a "start truing procedure" signal STP (the generation of this signal being explained below). In response to that sig~nal, the next procedure - 1 :l 2 -is to move the truing element into contact with the wh~el face, i.e., to close the gap.
The signal STP passes through an OR circuit 310 (FIG.
22B) to advance the counter 290 to state Ql. This disables the gates 300 and 301; it enables an analog g~ate 312 so that the latter feeds (via switch SSb) to the amplifier 294 the error signal from a summing circuit 314 whose inputs are the actual truing slide feed rate signal Ft~; and a set point signal FtSdl from a previously adjusted potentiometer 315. In consequence, motor TFM now moves the truing slide ancl element 50 10 toward the left ~from the location shown in FIG. 20) at a rate agreeing with the set point FtSdl which is selected to be relatively large.
That motion is continued until the control components detect that the gap has been closed. With the gates 301 and 308 disabled because the Q0 and Q2 signals are both at logic low) the signal PtSd from circuit 309 varies as Ptsdl Rw ~ Rteh [with Ql high] (42) Initially after state Ql begins, thereIore, PtSdl (then equal to Rw plus Rteh) will be less than PtS (then equal to Rw + GAP + Rt h)~ and the signal PtSERR will be large and positive (equal to GAP). As the 20 truing slide moves left and starts closing the gap, the signal Pts will decrease, and the signal PtSERR will decrease. By the time the slide has traveled a distance equal to the original gap (from the position of FIG. 20 to that of FIG. 19), the element 50 will just touch the wheel 20 and the signal PtSERR will have fallen to zero. This zero PtSERR value is sensed by a zero detector 320 whose output swings high and passes through an AND gate 321 and the C)R circuit 310 to step the counter 290.
This action can only happen when the counter is in states Ql (as it is here) or Q2 because the AND gate 321 is disabled ~,vhen the sigrlal Q0 '~ is high.

ThusJ after the gap has been closed by slide feeding at the :~ast rate FtSdl. the counter 290 advances .Erom state Ql to state Q2 .

Truing Off an Increment of the Wheel Radius_ __ When the state advances from Ql to Q2, the gate 312 is disabled, the gate 308 is enabled, and a lurther ana].og gate 322 is enabled. Moreo~er, the gates 282 and 283 are respectively enabled and disabled so the speed ~L)te begins to be controlled in order to make STE equal to the set point STEd-With gate 322 enabledJ the servo amplifier 294 receives the output of a summing circuit 324 whose inputs are the actual feed rate signal ~ts and a second feed rate set point signal FtSd2 obtained from a manually adjusted potentiometer 325. The truing element 50 in contact with the wheel is now fed to the left to produce truing action--in the sa.me fashion as described for FIG. 18. That is, the set point signal FtSd2 of FIG. 22B corresponds to the set point signal FtSd in the servo circuit 222 of FIG. 18. And with the gate 282 of FIG. 22B
enabled, the STE value is controlled in the same fashion as set out above relative to FIG. 18.
The wheel is now grinding on the workpiece at a radius reduction rate of GR = FpSd because the wheel slide WS is being fed left at a rate FWS. The truing slide is being fed left at a rate F-tS
equal to FtSd2, whlle the speed C;~te is being automatically adjusted to maintain the desired STE ratio. The desired ratio STEd may be set to any desired value. If it is chosen to be 0. 5 HP/in. 3/min. or preferably much lower, then the radius reduction rate R~e will be quite low (as explained above) and the wheel reduction rate R'w will be quite high in relation to the selected feed rate FtSd2 --and the wheel Eace grits will be - 1 1 '~ -left quite sharp. This is the choice when the wheel is rough grinding a workpiece.
To terminate the truing action after a predetermined increment has been ground off, the summing circuit~ 309 and 304 are again active. With the gate 308 enabled, the signal PtS,~ will vary according to the expression PtSd2 = Rw ~ .teh - INC [ with Q2 high~ (43~
where INC is a signal from a pre-adjusted potentiometer 328 representing the radius increment to be taken off the wheel (to restore wheel face shape) during each truing procedur-e. When the state Q2 initially begins, the actual position PtS (equal to E~w -~ Rteh; see FIG. 19) is greater than the set point position PtSd (equal to Rw + Rteh - INC) and the signal PtSERR is therefore positive and equal to INC. As the truing slide moves to the left, the error signal PtSERR becomes progressively smaller and reaches zero when the slide TS has moved the element 50 from the relative position of FIG. 19 to the relative position of FIG. 21. It is assumed as a reasonable approximation that the radius Rte of the truing element does not change during one truing procedure, and even if it does reduce slightly, this only serves to make the incremental wheel radius reduction slightly less than the desired value INC set on the potentiometer 328.
When the signal PtSERR reaches zero, the output of;
the zero detector 320 again swings high. This is transmitted through the AND and OR circuits 321, 310 to create a positive-going wa~e front at the count input of the counter 290 --so the latter rolls over from count state Q2 to Q0. At this instant, the signal Q2 swings from high to low, so the complemental effect at OR circuit 298 is to produce a positive pulse edge a-t the input of one-shot 299, whereupon the current value of Rte is stored in the sample-and-hold amplifier 299 as a new value ~`or R

- l l 5 -3~

In this way any wear which has occurred on the element 50 is taken into .account for the next cycle. The freshly stored value of Rteh is accurate because the components at this instant are relatively positioned as shown in FIC~S. 17 and l9.
Repetitive Truing Cycles With the state change :Erom Q2 to Q0, conditions revert to the same as those described above under the heading~ "following with a gap" (i. e., just after initial set up). The wheel continues to be fed left and to grind the workpiece. The analog gates 300, 301 and 283 are again enabled and all other analog gates are disabled. Thus, element 50 is again caused to "follow with a gap" (FIG. 20) --and will do so until the ne:xt "start truing procedure" signal arrives to advance counter 290 from state Q0 to Ql.
In state Ql for the counter, the system again closes the gap, as described above, and the counter advances from state Ql and Q2. In state Q2, the truing action with controlled STE again takes place until another increment INC is trued off of the wheel face. This cycle repeats automatically for as many times as may be desired during the overall time span in which the workpiece is being continuously ground.
The repetitive truing cycle sequence may be ended in any of a variety of ways, as s~ne example, when the operator sees or notes from a meter (not shown) displaying Rp that the workpiece has been ground to a desired radius, he may move the switch a:rms SSa, SSb to their "set up " positions and manipulate potentiometers 291 and 281 to re-tract -the element 50 back from the wheel and to retract the wheel back from the workpiece.
Thus, it will he understood that while a workpiece is being ground continuously over a span of time, the grinding wheel may be simultaneously trued during eacll of several spaced time intervals within that span, the truing action occurrillg Wittl an STE ratio selectecl - ll6~

and controlled in the manner ancl with the advantages rnentioned hereinabove. Therefore, despite the fact that the wheel may lose shape (or sharpness) as workpiece grinding proceeds, the grincling is not interrupted to true or dress the wheel. ~nd this is greatly facilitated because the element 50 follows the wheel face with a small, predetermined gap ~e. g., 3 mils) when inactive, and it can be advanced into truing contact with little delay each time one ol the truing interva:Ls is to begin.
Startin~ the Truin~ Procedure The signal STP which starts one truing proceclure may be created in a variety of ways.
As a :~irst example, in rough grinding a workpiece over a span known to require about three minutes, it may be known from experience that the wheel will need re-shaping or sharpening every 15 seconds. In this simple case, a timer 340 may be used as shown in :E~IG. 23. The timer is started initially when a switch arm SSc ~ganged to arms SSa, b) is moved to its lower posi.tion so its start terminal ST
receives a positive-going voltage transition from the high voltage at Q0.
I'hereafter the timer start terminal ST receives a rising voltage pulse edge each time the counter 290 (F'IG. 22B) reverts from state Q2 to state Q0. This starts the timer (the time-out interval of which is adjustable) on a fifteen second timing interval, at the end of which an output pulse appears to reset the timerO That pulse may be fed as the signal STP to the counter 290 in FIG. 22B --thereby advancing the counter to state Ql a~d initiating a truing procedure. I-r the timer 3~0 is set to measure off :~fteen second intervals, the wheel will be trued a:~ter every fifteen seconds of "followillg with a gap".
The time duration of the truing action, i. e., how lon~
the counter resides in s-tate Q2 within each truill~ cycLe is indeterminate;
it continues for wh~tever tiLne is rt?quirecl to reduc~ the wheel ~adlus ~ 1 17 ~

.6~

by the amount INC, as explainedD Of course, it is within the scope of the invention to simply let the truing action, within each cycle, continue for a preselected time period, rather than detecting the movement of the slide TS through the distance INC as shown in FIG~ 22e~
As an alternative to initiating a truing cycle each time the "following with a gap" has been carried out for a predetermined time interval (FIGo 23)J it may be preferable to assume that when one interval of truing has been completedJ the whee]. will n.eed truing or sharpening agai.n when the grinding action has caused a certain amount of wheel wear, io e., a certain reduction in Rw~ Thus, the -wheel radius reduction may be continuously sensed while the element is "following with a gap" and a start signal STP produced at that instant when Rw has decreased a certain amount. Apparatus for this purpose is shown in FIG. 24 where the signal ~w = PWS ~ Pps is fed both to a sample-and-hold amplifier 345 and a summing circuit 3460 The signal Q0 is fed to a one-shot multi~ibrator 347 which thus app~les an "enable store" signal to the amplifier 345 at each instant when the signal Q0 swings higho The value of Rw at the start of the Q0 state, io eO i at the start of "following with a gap" is $hus held in the amplifier 345 and signaled as its output R.Wh which is fed subtractively to the summing circuit 346.
The output ~Ryv is the wheel radius reduction (due to grinding) which has occurred since the last tru.ing procedureO This is compared with an incremental threshold signal ARWth, obtained from an adjusted potentiometer 348, in a high gain open loop operational amplifier 349.
The output from that amplifier 349 will swing from low to high when wheel wear ~:Rw slightly exceeds the preselected threshold value RWth~
thereb~ to trigger a one-shot multivibrator 3500 The short output pulse from the latter forms the signal STP to be fed to the counter ~9û in FIGo 22Bo 3~

FIG. 24 thus illustrates an arrangement in which wheel truing is initiated at spaced time instants while a workpiece is being ground, but the start of each such truing interval is dependent upon the wheel wearing down by a predetermined amount after the preceding interval has ended.
As a further alternative, particularly when loss of wheel face shape is the prirnary problem, each truing interval may be initiatecl when loss of form is in one way or another detected. Consider F[GS.
25 and 26 where the wheel 20 is shown in plan view as having a "formed"
10 face to grind a correspondingly shaped surface on the workpiece 24, the truing element 50 having an operative surface correspondingly shaped. The probe slide PS is shown (as in FIG. 1) carrying the probe 41 and the associated circuits which produce the probe signal PSIG.
Since the desired wheel face shape, here chosen merely as one example, in plan view includes a concave central arcuate por-tion 360 bounded by two cylindrical but ~Lat portions 361, it is likely that the wheel will most rapidly break down and lose form at the sharp corner regions or junctions 362 of those two portions. When this occurs, the desired sharp interior corners 363 at the corresponding locations on the workpiece will become 20 undesirably rounded and will not be ground clean. Thus, to sense when this condition has arisen while grinding is in progress, an auxiliary work sensing probe 41a (like probe 41) is mounted on the slide PS with its associated circuits 40a. The probe 41a is "aimed" at the corner 363 and disposed with slight clearance. If during grinding, the interior corner 363 is cleanly ground, the signal PSI GA from the au~iliary probe circuits will remain essentially constant since (as explained relative to FIG. 1) the probe slide PS moves to keep the clearance CL essentially constant. If, however, the wheel's exterior corners 362 ~reak or round off, the gap between the probe 41a and the interior corner~ 363 will c~ec~ea9e in ~,c.

-l;L~)-St~
effective length and the prohe signal PSIGA will decrease --even though the signal PSI~ remains essentially constant. If the signal PSIGA
decreases by more than a threshold arnount, it may be considered that the wheel face has lost its shape to an unacceptable degree and that one of the intermittent truing operations should be initiated.
Fc>r this purpose, the signal PSIGA is fed to the inverting input of a high gain operational amplifier 365 (FIG. 26) which acts as a comparator. A threshold signal TH is applied from an adjustecl potentiometer 366 to the non-inverting input. Thus, while the wheel 20 is grinding the part 24 and the truing element 50 is "following with a gap" (FIGS. 20 and 25) the arnplifier output will be at a logic low level because PSIG~ will be greater than THo Butif and when the interior corner 363 becomes rounded and the signal PSIG~ falls below TH, the output of the ampliPier 365 will swing high, thereby producing a logic high output from an AND gate 368 which is enabled by the Q0 signal from FlGo 22Bo The positive-going voltage edge from gate 368 triggers a one-shot 369 which then produces a short pulse Eorming the signal STP applied to the counter 290 in FIGo 22B~
In the FIG~ 26 arrangement (cooperating with FIGo 22B)J
therefore, one of the time spaced truing procedures is initiated each time that the wheel loses form to some predetermined degree. This may occur three or four times, for example, over a long time span during which rough grinding proceeds continuously on the workpieceO
OI course, instead of sensing the workpiece with an electromagnetic probe 40a, 41a (FIGo 25) and using its signal as an indicator that the wheel face has lost the desired shape, a pneumatic or other type of gage may be employed directly to sense the wheel face itself~ Such a gage should be located to respond to that portion OI the wheel face which will rnost quickly break away or lose shape as a consequence o;t` the grinding action~
-1~0-Control OI SGE for Grinding by Varying the Parameters of Simultaneous Truing ~ction :~ my earlier-issued patents, identi~ied above, it is explained -that the degree of sharpness of a grinding wheel --over a long interval of grinding-- may be maintained by selï-correcting action if the grinding ratio SGE (defined above) is maintained w.ithin a predetermined range OI values or at a desired set point value. .Incleecl, by adjusting the SGE ratio to be relatively low for rough grinding~ the wheel may be kept very sh~Grp (at the expense of a higher wheel wear rate W' which in most cases is more than offset by increased productivity). ~nd by adjusting to SG:E~ ratio to be relatively high, the wheel will be dulled for Iinish grinding to obtain a smoother final surface finish with the same wheelO l'he earlier patents teach that the relative surface speed Sr of grinding or the relative feed rate of the wheel and part may be corr ectively adjusted to keep SGE at a desired value~
The control of SGE does not, however, avoid the problem of the wheel face losing form or shape; and thus grinding by the advantageous SGE method OI my earlier patents still entails the need to periodically (or continuously) restore (or maintain) the desired shape of the wheel face. This need is especially critical just prior to the start of finish grinding and spark out because an out-of-shape wheel will leave the finished part out of shapeO
~ccording to one i.mportant aspect of my inve.ntion, I
am able to control the SGE of grinding action at the wheel/work interface (such that SGE falls within a preselected range or is matched to a predetermined but changeable set point) by controlling the parameters or conditions by which truing or wheel conditioning action takes place simultaneously at a wheel/element interfaceO

-:121 -To describe in specific detail one example of the many possible embodiments of this method and apparatus, reference is :made to ~ . 17 taken with FIG. 27. As noted earlier, FIG. 17 is to be taken in conjunction with FIG. 1. The former is a diagrammatic view of grinding machine components when (i) the wheel 20 is being fed left into rubbing contact with the workpiece 24 to produce grinding action at the wheel/work interface, and (ii~ simultaneously the ttuing or conditioning element 50 is being fed left into rubbing contact with the wheel to produce truing or conditioning action at the wheel/element interface.
It is to be noted first t:hat no truing elernent gage (like that of 65, 66 in FIG. l) is required in FIG. 17. Equations (25) through (30) are applicable and the workpiece sensing gage 5û, 41 is employed.
Now, the SGE ratio for grinding action at the workpiece interface is the ratio of (i) power PWRg applied to such action, to (ii) the volumetric rate M' of material removal from the workpiece 24.

This is expressed:
SGE= PW:Rg (44) M' The power PWRg devoted to the grinding action (for the reasons explained above) is the sum of (i) the PWRp applied to rotationally 20 drive the workpiece 24 and (ii) some portion PWRWg of the PWRW
applied to the rotational drive of the wheel. That is, the aggregate wheel power PWRW may be determined according to Equation (18) from the signals TOR~ and ~~)w from the transducer 35 and the tachometer 36 (FIG. l); but the proportion of that aggregate power which goes into the grinding interface is not directly co.mputable from the torque transducer signals. C)ne may noteJ however, that at the grinding interface the tangential force FOR3 (FIG. 17) which is applied from the ~,vheel face to the part 24 is equal and opposite to the tangential fo:rce FOR4 which, in e:ffect, is applied to the wheel by the part 24 (absent accele.ration ~' effects). Since the torque TORp is signalecl by the transclucer 38 (FI~.
1), and the radii ~w and Rp are ascertainable from E~uafions t27) and (29), it is possible to express the torque TORWg which is applied by the wheel motor WM at the grinding interface (and which is only a part of the torque TORW). Thus, it may be written FOR 3 = FC)R4 (45 ) FOR3 Rw = TRwg (46) FOR4 Rp = TORp (47) Gombining (45) to (47) yields TOE~Wg= TORp Rw (48) Now, the grinding power PWRwg applied via the wheel 50 into the grinding interface may be written PWRWg = 2 ~ TRwg ~w and by substitution from (48) this becomes PWRWg = 2 ~ TORp w ~Jw (50) Because the motor PM drives the part 24, the total power PWRg consumed at the grinding interface (to produce work which removes workpiece and wheel material and to create heat due to friction) is PWRg = PWRWg + PVVRp (51) But since PWRp = 2f~- TORp ~Jp (52) then by substitution of (49) and (52) into (51), the latter becomes PWRg 2~ TRP[~Jw R + ~JP] (53) To determine the SG:E ratio, therefore, according to Equation ~44), one may first note the analogy to Equation (8) for wheel removal rate W' and write an equation for workpiece material removal rate M' = 2~- L Rp R'p (5~) And by substitution of (53) and (54) into (44), SGE is e~pressed ~ PWR TOR r~ ~W ~ ~ 1 SGE =--M' g = L ~p J (55) -1~3-3~

If Rw, Rp and R'p are replaced in (55) by substitution from (27), (25) and (26)J this be om TORp ~ (56) ~ carrying out the method of controlling SGE by adjustment of parameters at the truing inter.face3 a control system 71J shown in FIG~ 27 (ta.ken with FIGS. 1 and 17) may be employedO ~s noted before, the wheel is being fed left to create grinding action on the workpiece 24 and the element 50 is being fed left to create simultaneously truing or conditioning action on the wheel, For producing these motions and the relative rubbing contacts at the grinding and truing interfaces, three closed loop servo circuits 220, 221, 222 control the motors PM, WM and TF:M in order to maintain the variables ~p~ ~ w~ FtS in close ag:reement with preselected but adjustable set point valuesO The servo circuits 220, 221, 222 are identical to those which appear in FIG. 18 and this need not be described againO Moreover, the components 230-232 in FIGo 27 are identical to those correspondingly identified and described with reference to FIG, 18 and they serve to keep the wheel feed rate F~VS au-tomatically adjusted such that the grind rate GR

(work radius reduction rate R'p = Fps) is maintained at a selected but adjusted value, Provision is made automatically-to vary the element speed G)te so as to keep the actual SGE ratio within a predeterrnined range or in agreement with a predetermined set point SGEdc The set point version is here shown only because it is the more rigorous~ As illustrated in FIG~ 27, the signals PWS and Pps are applied to a su.mming circuit 400 to create a signal representing the radius Rw; that latter signal is divided in an appropriate circuit 401 by the signal Rp; the quotient signal RW/Rp is then multiplied at 402 by the signal G~)w to create a product corresponding to the .~irst terrm within the b:racket of - 12~-3~

Equation (55)0 To this a summing circuit 404 adds the signal ~)p and the sum is multiplied in a multiplier circuit 405 whose output signal therefore varies as the numerator of Equation (55). The signals P~ 'p and Rp are multiplied at 406 and fed to an amplifier 408 having a gain (adjusted by a rheosta~ 409) corresponding to the axial length L of the grinding interfaceO The output of amplifier 408 thus varies as the denominator in Equation (55) and :is fed to a divider 410 which also receives the output rom multiplier 9;05O The quotient is a signal SG13 which varies in accordance with the specific grinding energy ratio for the grinding action which is occurring.
The desired or set point value SGEd is represented by a signal preselected but adjustable and obtained from a potentiometer 411. The signal SGEd applied in bucking relation with the signal SGE
to a summing circuit 412 results in an error signal SGER~ forming the input to a PI:D servo amplifier 414 which variably energizes the motor TM
(acting in this example as a brake~ to control the element speed ~)te As the voltage Vtm from the amplifier increases, the regenerative braking torque of motor TM decreases so the speed CL)~e increasesO
It will be recalled from Equation (3) that this decreases the relative rubbing surface speed Sr at the truing interPaceO
E now the wheel tends tu become more dull, the power PWRg will increase because the wheel grits do not act as efficiently in abrading material from the workpiece 24. Since in this example ~: )p and C~)w are kept constant, a duller wheel requires greater torque from the motors PM and WM --so consumed grinding power PWRg rises~ This, in turn, makes SGE as signaled at ~10 (FIG. 27) increase (see Equation 44) and the error signal SGERR thus increases ~becomes more positive)~ The voltage Vtm therefore increases, the braking torque applied to the element 50 decreasesJ ancl the speed ~L)te -1~5 -increasesO From Equation (3) it is seen that this reduces the truing interface relative speed Sro A reduction in the truing SrJ for r easons given above, increases grit and bond fracturing at the wheel/element interface so the wheel re-sharpens automatically --and this reverses the changes described above until SGE is restored to substantial equality wi-th the set point SGEdo The self-correcting action will be almost imperceptible to the hurnan eye after SGE and SGEd have initially become equal ~and the amplifier 414 due to .its integrating action i6 holding Vtm at an almost constant value with the error SGERR being essentially æero)O But if now the set point SGEd is changed from its first to a second value, corrective adjustment of ~-)te will take place to make the actual SGE agreeO
~ the exemplary embodiment of FIGSo 17 and 27, the STE ratio for the truing action is not known --and its value is OI no direct concernO But it may be noted that when SG~ falls below the set point and G)te increases ~as explained above), this reduces the truing relative surface speed Sr at the truing inter~ace --and thereby decreases the STE ratio with which the truing ac-tion transpires. I have found that for a workpiece, wheel and truing element of given materials there is a general correlation between the STE and the SGE ratios --that is, as STE increases or decreases, the SGE of grinding action ~simultaneously vvith truing or immediately after truing~ will increase or decrease--even thoug:h that relation may not be linearO But in the practice of my invention a correlation table may be prepared and SGE may therefore be controlled to keep it at a desired value by adjusting the STEd set point value in an apparatus embodiment such as exemplified by :FIG~ 18.
In the organization and operation of FIGS. 17 and 27J
the actual value of SGE is signaled at the output of the divider 4100 This is not, strictly speaking, necessary; the control apparatus may be organized to adjust the feed rate FW~3 such that the workpiece removal rate M' is kept constant (making the denominator in Equation 55 constant) so that the signal from the multiplier 405 varies according to changes in PW~Rg and is proportional to SGE. That latter signal may thus be employed to vary the voltage Vtm and the speed C~)te in order to maintain SG:I~ at a desired but ad3ustable set point.
For effective operation of the apparatus shown in FIGS.
17 and 27J the truing slide feed rate ~ts (selected at potentiometer 225) should be chosen such that it is comfortably greater than the wheel radius reduction rate R'w due to grinding action, This (as mentioned with respect to FIGS~ 17 and 18) will prevent the truing element from losing contact with the wheel iace. Of course, the other procedures for such prevention, as set out relative to FIGSo 17 and 18, may also be employed in the apparatus of FIGS~ 17 and 270 In the use of the method and apparatus shown by FIGSo 1 17 and 27, once grinding and simultarleous truing have been initiated, if the set point signal SGEd is made low for rough grinding (say, about 70 0 to 40 0 HP/inO /min. ) the wheel face will be maintained both sharp and true in shape over a long interval of rough grinding at a relatively high grind rate GR. But the set point signal c,~t~d may be readjusted, either manually or automatically, from time to time so as to change the sharpness of the wheel faceO ~s noted, an increase or decrease in SGEd will result in an increase or decrease of STE. Therefore, changing SGEd will practice the "sharpness degree" method described aboveO 1~ one changes SGEd. either smoothly or by a step change, from an initial low va'ue or range to a subsequent higher value or range, the wheel face may be converted from a sharp condition during initial rough grinding to a duller condition for subsequent finish grinding --to produce a final work surface having a desired smoothness.

Of course, it is not essential to the methocl illwstratecl by FIGo 27 that the element 50 contact the wheel 20 during the entire span of time over which the wheel is grinding on a given workpiece, There may be some applications in which, as grinding of the worl~piece continues, the element 50 is, in effect, withdrawn fr om contact and then re,stored to contact so that there is intermittent trwing action which is, nevertheless, simultaneous with grinding but with SGE being controlled during each of the intermittent intervals~ The material chosen for the truing element may fall in any of Classes I, II or III Eor the application of the FIGS. 17 and 27 embodiment and thus the element may even be a previously completed workpiece identical to the one being ground.
Finally, it is to be noted that specific control apparatus other than that exemplified in FIGo 27 may be utilized to keep SGE in a predètermined range or at a set point value by varying the parameters oE the action at the truing interfaceO ~pparatus and steps by which G)w or FtS are correctively adjusted (rather than C3te) may be used and indeed two or more of such variahles may be adjusted to keep SGE
equal to SGEdo In other words~ FIGSu 17 and ~7 represent but one example of the broader method which is to be practiced by conjointly establishing the relative surface speed and feed rate of the rubbing contact at the truing element in order to maintain the SGE ratio of grinding action within a predetermined range of valuesO That conjoint control is effected by either or both of a group of two corrective actions when the SGE (i) rises above or (ii) falls below said range: The first action involves (i) decreasing or (ii) increasing the relative surface speed of the rubbing contact between the wheel 20 and element 50; and the second action involves (i) increasing or decreasing the relative feed rate of such rubbing contact. Approximations which ignore certain changeable quantities (for example Rw, R~e or PWRp --clS e~plained -1 2~3 -above) may be adopted when strictly accurate control of SGE i5 not required, and when SGE may be permitted to fall anywhere within some range to yield the desired results.

Advantages for Grinding of "Thin" Workpieces ~ . .
Consider for purposes of discussion that the workpiece 24 in FIGS. 1 and 17 is a tubular or hollow cyli.nder part having a wall of small thickness, or that it is rod-like in s.hape with a srrlall diameter and relatively great lengthO Such workpieces are here called "thin" as a shorthand designation that they lack sufficient struc$ural rigidity to withstand substantial forces, normal to the surface being ground, without bènding and permanently deforming or fracturingO At the least, deformation of a thin workpiece renders size gaging inaccurate and may cause chatter at the grinding interfaceO The grinding industry has been plagued by the costs and tediousness of grinding such thin workpieces becawse the feeding forces must be kept ~ery low in order to obtain finished pieces of desired ~inal size and free of metalurgical damageO
This means that grind rate GR must be kept low and the wheel slide feed rate must be kept low~ ~n consequence~ the industry has resorted to "soft wheels", low grinding rates and low sur:Eace speeds for grinding such thin workpiecesO This reduces productivity. ~:E higher surface - speeds are attempted, the wheel face dulls rapidly, and the energy poured into the grinding interface turns mainly to friction and heat --thereby causing metalurgical burnO ~ high scrap percentage is common in ~actories which grind these types of workpieces, Tc a great extent, the SGE control method disclosed in my above-identified patents has enabled the grinding wheel to automatically self-sharpen --so that rough grincling at high grind rates G:E~ may be continued without the wheel dulling, without grinding power increasing, .L29 and without so much energy going into friction and heat th~t rnetalur~f,ical damage (burn) occursO But in implementing the earlier patented method for grinding thin workpieces, the ranges of grinding power and metal removal rates required for self-sharpening of the wheel without excessive forces on the workpiece are sometimes not obtainable with the standard equipment available on a given grinding machine. And since truing of the wheel face must be accomplished by a truing element even when the method of my prior patents is used, the presently disclosed method permits high infeed forces at the truing interface as an expeditious way of maintaining SGE low (and the wheel sharp) even though the infeed forces at the grinding interface are kept within the bounds tolerable by a thin workpiece.
The invention disclosed and claimed in this application opens the way to grinding of thin workpieces with lower cost~ higher productivity and reduced scrappageO For employing the apparatus exemplified in FIGS. 17 and 18, or FIGS. 17 and 27 according to the methods described, I am able to rapidly rough grind large amounts of stock from thin workpieces, control and obtain a final surface finish of desired smoothness, and avoid metalurgical burn --all by the use of a single wheel for both rough and finish grinding.
These startling results flovv from the fact that in FIGS~
17 and 27, the SGE of grinding at the wheel/work interface is maintainable at a relatively low valueO SGE cannot be maintained low due to grit and bond fracture at the grinding interface because the thin workpiece will not withstand wheel feeding forces s~`ficient to create such grit and bond fractureO But in FIGo 27~ the relative surface speed and the relative infeed of the truing contact can be established (and with sufficient infeed force) such that grit and bond frac-ture are created at the truing interface --so a low set point SGEd creates a low S~E and rough grinding of the work can proceed at a relatively high grind rate GR even with low forces on the work, due to the sharpness of the wheelO
Specifically~ in FIGS. 17 and 27, the tr-uing feed rate FtS is made constant and the speed ~te is automatically adjusted to change relative surface velocity Sr --but of course the truing feed rate FtS
could be the automatically adjusted variable.
The synergistic beauty of rapidly rough grinding thin workpieces in this ashion lies in the fact that heat and :metalu:rgical burn at the workpiece is avoided --and high forces which would deform or break the workpiece are avoided-- while the conjoint con-trol of relative ~urface speed and feed rate at the truing interface (to produce low SGE) may involve a low STE created by a relatively low truing feed rate FtS --so that the volumetric and radial wear rate (TE' and R'te) on the truing element 50 are 10wn Thus, a single truing element 50 (even if made o:E steel such as M2 or 1050) may have a long life and may serve during the grinding of a large number of thin workpieces before it becomes worn out and thus needs to be replacedO
For the reasons given earlier, if in the operation of FIGSo 17 and 27 in grinding a thin workpiece, the truing element 50 is a diamond chip trwing roll, the life of the latter will be virtually infiniteO
Of course, in grinding thin workpieces with the method and apparatus of FIGS. 17 and 27J the set point SGEd may be increased at the start of a final, short ~inish grinding inter val --whereupon the wheel wil:l. be dulled and will serve the objective of producing a work surface finish whose smoothness is generally proportional to the higher value of SGEd which is selected.
The method and apparatus described with reference to FIGSo 17 and 18 may also be employed with the sam.e aclvalltages, for ~ri~dirl~ t~in~ovrkpieces~ For rough grinding at a relatively high grind q~q~

rate GRJ the set poin~ STEd will be made low, for example, in the range of 0,1 to 0. 05 HP/inO 3/rrlinq Regardless of what the grinding SG:E at the workpiece surface may actually be, the resulting low STE
value (obtained by conjoint control of truing surface speecl Sr and feed rate FtS) will make the wheel sharpO Grinding proceeds therefore without burn damage at the work surface --and -with a low volumetric and radial wear rate on the element 50 --but without high irlfeed forces on the workpiece and consequent defor mation or frac-tureO The same synergistic result is obtained.
And for finish grinding with the same wheel, the set point STEd may be increased so that the wheel dulls and the desired final surface smoothness is obtainedO
It is to be understood that the automatic adjustment of ~te as shown in FIGS. 17 and 18 is not the only way in which STE
may be controlledO Wheel speed ~w or truing feed rate FtS --or any combination of`these three variables-- may be varied to keep STE equal to STEd Indeed, for the reasons explained above, STE need not he known or actually controlled in order to rough grind a thin workpiece with the advantages here stated. While grinding is on-going at the workpiece, the truing element may be brought into rubbing contact with the wheel (FIG. 17), the relative wheel/element surface speed Sr and the truing feed rate being conjointly controlled to make the ratio W'/TE' greater than 1. 0 (for Classes I or II), or to make the speed Sr less than 3000 f. pO mO ((:~lass III). The wheel will not only be trued but kept sharp ~-and fast grinding without destructive forces on the workpiece may be obtained.

- l 3 2 -q~

Method and Apparatus for Determining Wheel Radius and Part Radius, Despite Wear, With a Simple Probe System _ __ In FIGSo 1 and 17 (taken with FIGo 18 or Z7) there has been shown an arrangement for truing or conditioning a wheel while grinding is simultaneously occurring --and with automatic controlling oE either the STE or SGE. As indicated earLierJ such procedwre~
may also be practiced, in the light of the teachings here disclosecl, by controlling the TR ratio while grinding ancl truing are taking place simultaneously. ~ FIGo 17 taken with FIG~ 18 or 27, it has been assumed that an in-process workpiece gage 40, including an electromagnetic probe 41 (oE known organization) is employed; and as noted with respect to FIGo 1~ this probe 41 is mounted on a slide PS
which is slaved by a servo loop including the motor PFM to keep the clearance CL constant as the part radius Rp changesO This is done because the sensing "range" of the electromagnetic probe 41 and its associated circuits is quite limited (e. g~, O 001 " to . 030"). ~ the workpiece is to be ground down a considerable amount in radius, the probe 41 would be unable to accurately signal the part radius Rp unless it "follows"
-the part surface~
The methods and apparatus here disclosed for simultaneous grinding and truing lead to a further surprising and advantageous discovery. It is: The radius Rw of the wheel (despite wheel wear) and the radius Rp of the part can be continuously known and determined --even though the part is ground down by a considerable amount such as one-half inch or more-- without the need for an elaborate "following"
servo associated with an in-process work-sensing gage; and this is possible with a simple, limited range truing element-sensing ga~e not requiring any following servo~ This discovery is founded in the fact that, with certain ones of the truing procedures here disclosed, the wear or radius reduction of the truing element is quite small vver an extended period of truing action, and so a limited range element-sensing gage can provide the necessary signal information, without servo following, even though the workpiece radius is reduce~l by an amount much greater than such limited rangeO
To make this more understandab].e, FIG. 28 illustrates a simplified version of FIG. 1 and characteriæed by the omission of the probe 41, gage circuits 40, the probe slide P~ and the probe servo loop components 47, 45, 44, PFM, etc. Un].ike .FIGo 17~ the ar:rangement of FIG. 28 uses the truing element gage 65 with its probe 66 fixed to the truing slide TS. That probe does not have to "follow" the surface of the truing element 50 by a servo slide action because the radius Rte will not reduce appreciably as one or more workpieces are ground to remove a considerable amount of stock therefromO For example, if the probe 66 can accurately sense and represent by the signal ~R
the gap QRG as the latter varies from . 001" to ~ 030", then the signals Rte and R'te (produced in the way previously described with respect to FIG. 1) remain valid even though the workpiece is grou~d extensively to reduce its radius and even though the wheel reduces considerably in lts radiusO If, for example, after installation of a "fresh" truing element (and perhaps mechanical setting of the probe 66~ the gap QRG

is ~ 002 ", the element 50 is measured and found to have an initial radius 3~,i7 the potentiometer 68 is then set to make the voltage RiV represent Ri + . 002"o Then the signal Rte = Ri ~ R initially represents RiJ and falls as the element radius decreases (and ~R increases) by as much as . 028". This means that if the truing ratio TR is viewed as a ratio of radius reductions and assumed, for example, to be 50, the wheel may have up to 1. 4" removed :Erom its radius before mechanical resetting and initialization need to be repeatedO

-13~L-FIGS 1, 28 and 29 .. _ . . .. ~ , _ The gage 65, 66 toge-ther with the position slgnaling sensor 29 and the signal Pts permit the wheel radius Rw (FIG. 2~3) to be determined ind:irectly at any instant, desplte the fac-t that wheel wear Rw occurs From the dimensional labels in F.[G. 2~, :it may be seen that ~w Pts ~ Rte (57) Further, the work:pi.ece radius Rp may be found indirectly at any instant from the relation :~p Pws ~ Rw Pws ~ Pts + Rte (58) Thus, the present invention rnakes it possible always to find the v~lues of the radii Rw and Rp despite the fact that these :radii changeg possibly over a wide range, a.nd are not directly sensedO
In the simultane~us truing and grinding action illustrated in FIG. 28, it is possible always to determine indirectly the rates of radius reduction R 'w and R'p. For this purpose, the truing slide feed rate FtS is chosen such that it falls above the range of wheel radius reduction rates which are likely to occur due to wheel wear at the grinding inter~ace; or stated another way, the rate FtS is made 2û sufficiently high that it is truing action, rather than grinding action, which establishes the rate R'w of wheel radius reduction. Then~ the wheel slide infeed ra-te is slaved to be equal to the desired grind rate GR = R'pd plus the wheel wear rate R'W which is caused at the truing interface. That is, the wheel slide feed rate ~ws is automatically varied and controlled such that FWS = GR + R w But if the truing slide is moving left at a feed rate FtS and the element 50 is reducing in radius at a rate R 'te (the latter being directly signaled in FIG,. ~8), then 3(~ R'w = ~ ts - R'te Putting (60) into (59), one obtains FWs = GR ~~ Fts ~ R te (61) Now, it may be :Eurther observed that if the wheel slide is moving let at a rate FWS and the wheel radius is reducing at a rate R'w, then the radius Rp must be reducing. The rate ~'p of that latte:r reduction is expressible R p ~ws ~ 1~ w (62) and from (60) this hecomes R'p = Fws ~ Fts ~ R te (63) lQ If (61~ is substituted into (63~, an identity is obtained~ namely, R'p = GR + FtS ~ R te ~ Fts + R te GR ~64) thereby confirming that grind rate GR and part radius r eduction rate are identical.
To utilize these relationships during simultaneous truing and grinding (as shown in FIG. 28), a control system 71K may be organized as shown in FIG. 2g. Servo circuits 220~ 221, 222 (identical to those o:t' FIG. 18) are employed to make the speeds ~,Jp and ~Jw~ and the feed rate FtS, agree with s~t point values signaled from potentiometers 223, 224, 225.
Further, howeverJ the wheel slide feed rate FWs is automatically controlled to make the part radius reduction rate R'p stay equal to a desired or set point value GR (the latter thus representing R 'pd) obtained f`rom an adjustable potentiometer 450. A summing circuit 451 receives the signals FtS and R'te to produce an output representing R 'w (see Equation 60) which is added to the signal G:F~ in a summing circuit 452. The latter produces an output signal FWsd which may be viewed as a variable "set point" for the wheel feed rate F~VS. ~ :~urther summing circuit 454 accepts that "set point" signal and the feedback ` 'f~, signal FWs t~ produce an error 9igna 1 ERR12 applied to a PII~ servo J)'~

amplifier 455 which energizes the motor WFM. l~hus, the fee(l rate FWs is automatically controlled so as to force the grind rate P~'p to agree with the selected set point value GR --and thus the part is ground at a desired radius reduction rate R'p because the wheel wear rate R'w has been determined by the truing action and the wheel feed rate is made equal to R'w plus the desired grind rate.
The three summing circuits 451, 452~ ~54 in FIG. 29 may, of course, be replaced by a single summing circuit having four inputs for the signals such that ERR12 = G~ + FtS ~ R te Fws ~65) Because wheel slide feed rate FWs is forced to take on a value-which makes ERR12 zero when the servo loop is in equilibrium~ that feed rate is kept and maintained as set out above, i.e., such that FWs = GR + ~ts R te (61~
This use of a simple low-range gage 65, ~6 as explained thus far may be accompanied by additional control apparatus which maintains the ratio STE at least approximately at a selected but changeable set point value. Such control of STE has the effects and the advantages already described with reference to FIG. 18, but is obtained in FIG. 29 20 by size representing signals originating from the simple gage 65, 66 (rather than from the part gage 40, 41 and its associated probe slide servoJ FIGS. 1 and 17).
It will be recalled from the discussion leading up to Equation (39) that the power fed into the truing interface, when grinding and truing are both taking place, cannot be determined directly from the signals TORW and G,~ w It will be useful to repeat Equation (39), which is applicable to FIC. 17 ancl likewise to the circumst~nces OI

FIG. 28:
STE _ PWRt _ TXteL~J ~,v R v ~ te]
~3 ~ w~~ "~ r~ - (39) - ;l 3 7 ~

This relationship is based upon the reasonable assumption that the radius reduction rate R 'w occurs wholly due to truing action. In fact, a small portion of such reduction rate, for volumetric considerations, occurs due to grinding action, but the assumption nevertheless gives sufficient accuracy in most all practical applications.

~r~

-137~\-By substituting Rw and R'w from Equations (57) and (60) and recalling that Rte is directly signaled in FIG~ 28~ then Equation (39) applied to FIGo 28 becomes TO~ [C~)~ (Pts~ R~ te]

STE = W'~~ L~PtS - Rt~Fts - ~ te~ (66) To control STE in FIGo 29 (taken with FIGS. 1 and 28)~
therefore, a summing circuit 460 receives the signals PtS and Rte to produce a signal Rw into which a divider circui.t 461 divicles the s.ignal Rte. The quotient signal from 461 is multiplied by the signal C~)w in a multiplier 462; the resulting pruduct s.ignal is fed to a summing circuit 464 where the signal ~)te is subtracted. The difference output is then multiplied ati465 to produce a signal corresponding to the numerator of Equations (39) and (66), and which is proportional to PWRto Also, in FIGo 29, the signal R'w (from 451) is multiplied at 468 by the signal Rw (from 460). The product output from 468 is further multiplied in an amplifier 469 adjusted to have a gain of L so that its output is L~RW~ R'w~ corresponding to the denominator in Equations (39~ a.nd (66~ and proportional to the material removal rate W'O A division circuit 47û receives the outputs from 465 and 469 to produce a signal ST:E which thus represents the STE ratio due to truing action taking place at the truing interface in FIG. 280 The remaining components 250, 251, 2529 TM in FIG. 28 are the same and function in the same way as previously described with reference to FIG~ 180 Thus, by using orlly a Limited range element-sensing probe 65, 66 the apparatus of FIGS. 28 and 29 enables not only the determination of the part radius :E~p and grinding at a desired, essentially cQnstant rate GR because wheel radius Rw and wear rate R'w are indirectly determined and used; but it also enables truing to take place at a {~

desired STE ratio (which may from time to tirne be changed). By choosing a low STE set point, the wheel will be kept sharp and the wear rate R'te will be suf~iciently low that a given truing element (even if made of a hard steel or of the same metal as that of the workpiece) will not fall out of the range of the gage 65, 66 during the cour,se of grinding sever~workpieces.
F`IGS. 1, 28 and 30 The control of SGE at the grinding interface may a]so be e~fected by conjointly establishing and correctively varying the relative surface speed Sr and the infeed rate at the truing interface when the simple probe 65, 66 of FIG. 28 is employedO The results will be essentially those obtained by the apparatus OI ~IGS. 17 and 27 --but the probe implementation and the control devices are much less complex and costlyO
lE;lIGo 30, taken with FIGSo 1 and 28, illustrates a system 71L for controlling SGE in that way. The servo circuits 220~ 221, 222 for establishing selected values of ~)p~ ~w and FtS
as described relative to FIGo 18; and the control of FWS to maintain a desired work grind rate GR is the same as described with reference to ~FIGo 29 and Equations (57) to (64).
For controlling SGE, Equation (55) is validly applicable not only to FIG. 17 but also to the circumstances of FIGS. 28 and 30 and for ready reference it is reproduced here:

SGE = ~ M~ = LRp-~R'p (55) Substituting for Rw, Rp and R'p from Equations (57), (58) and (63)~

this becomes ~G)w (Pts Rte) TORp L(Pws - PtS + Rte) __ PJ

M' L(PWS ~ Pts + Rte~(Fws - FtS + R'te) (67) As indicated in FIGo 30J SGE is contro~led to agree with a set point SGEd by ~ar;ying the element speed ~teo This is similar to the operation of the apparatus of FIGSo 17 ancl 27 except that di~ferent gage signals are utilizedO As shown in FIGo 30~ a summing circuit 480 produces a signal Rw (see Eq, 57)0 This is subtracted at 481 from the signal PWS to prodllce a signal Rp fed as a clivisor to a divider circuit 482 to produce a signal RW/Rp which is then mult.iplied at 484 b;y the signal ~iw~ To that product sign~l, a sum:ming circuit 485 adds -the s;gnal ~)p and the result is multiplied at 486 by the signal TORp.
The output from multiplier circuit 486 thus varies as the numerator s~f Equations (55~ and (67) and is propor-tional to PWRgo Also, in FIG~ 3û, a summing circuit 488 subtracts the signal R'w (output of circuit 451) from the signal FWS to prod~ce a signal (per Eq. 62) representing Rtp. This is multiplied at 489 by the si.gnal Rp ~produced at 481) and fed through an amplifier 490 adjusted to have a gain of L~ The amplifier output thereIore varies as the clenominator of Equations (55) and (67) and is proportional to the work :r emoval rate M~o That signal is divided at 491 into the signal :Erom 486 to pro~uce the actual SGE signal. The remaining components 411, 412, 414 and TM in FIG. 30 are the same and func-tion in the same way as previously described with reference to FIG. 270 Thus, by using only a limited-range element-sensing probe 65, 66 the apparatus of FIGS~ 28 and 30 enables not only the determination of the part radius Rp and grinding at a desired, essentially constant grind rate GR because wheel radius Rw and wear rate R'W
are indirectly determined and used; it also enables truing to take place with automatic adjustments at the truing in-terface which cause grinding to proceed at a desired SGE ratio (and which ma;y from time to time be changed)O By choosing a low SGE set point, the truing STE ratio will be low even though not necessaril;y known; and in consequence the 1~10 -3¢~

wheel will be kept sharp and the wear rate R'te will be sufficiently low -that a given truing element will not fall out of the range of the gage 65, 66 during the course of grinding several workpiecesO The apparatus and the method of FIGS. 28 and 30 (like those in FI~o 17, 18 or 17, 27) may be used to great advantage in the grinding of thin workpieces and without the need for a work-sensing gage~
In summary, FIG. 28~ taken with FIG, 29 or 30J
illustrate two OI many possible method and apparatus embodiments which invol~re simultaneous grinding and truing action car ried out by means to sense the surface or size of the truing element --and without the need to sense the workpiece surface or size. The truing element 50 may be a homogeneous body of metal or metal alloy; and even though it wears down somewhat, its radius reduction will be relatively slight over a given period of truing action so the limited range gage 65, 66 provides the needed intelligenceO
A first surprising advantage comes from thiso E~ren though the wheel radius Rw reduces unpredictably and by a large amount (say 0O 5"~ the element sensing probe 65, 66 enables the wheel radius to be determined at all timesD E3y sensing the operative surface of the element 50, a radius signal Rw is obtained as equal to the distance Pts ~ Rte. ThenJ the difference PWS ~ Rw = Pws ~ PtS + Rte can be signaled to represent the part dimension Rp, where Pws is the distance (signaled by position transducer 29) between a reference point 24a on the workpiece and the wheel axis 20aO The difference PWS ~ Rw thus represents the dimension the workpiece rom the reference point 24a $o the work surface being ground (i, e., Rp in FIG. 28)~
I~ will be apparent that to produce the radius signal Rw, the distance between a reference mark 50a on the element 50 and the wheel axis 20a (measured along or parallel to a line perpenclicular to the elemen~'s surface at the point of truing contact) is sensed and signaled by the position transducer 58 which produces the signal PtS. The gage 65, 66 produces a signal l~te representi~g the clistance (measured along or parallel to a line perpendicular to the element's operative surface) from that reference mark 50a and the element's operative surface. And the difference PtS - Rte is utilized as a representation of the wheel radius Rw ~ s~concl surprisLng advantage comes from the arrangement OI FIG. 28 taken with FIG. 29 or 30. With only the conditioning element gage 65, 66, the dimension Rp is available as an algebraic sum of other 10 signals (and is used for controlling SGE in FIG. 30). Thus, it is possible to terminate the grinding action simply by backing the wheel and the truing element to the right when the sum Pws ~ Rw Pws ~ Pts +
Rte reaches a particular value reflecting final part size. The position sensor 29 produces the signal PWs which represents the distance (measured along or parallel to a line perpendicular to the ground surface OI the workpiece at the point of grinding contact) from a refererlce point 24a on the part to the center 50a of the wheel~
Still another advantage comes from the arrangement OI
FIG. 28 taken with FIG. 29 or 30. With only the conditioning element 20 gage 65, 66, the grind rate GR (rate OI reduction OI the workpiece radius, R'p) may be controlled to be substantially equal to a desired set point. The gage 65, 66 and associated circuits signal the linear wear rate (R'te) of the conditioning element in a direction parallel to the relative infeeding of the wheel and the element, while the tachometer 59 serves to sense and signal the relative infeeding rate FtS. The relative infeeding of the wheel and the workpiece are then controlled to have a rate GR + FtS ~ R't so that the workpiece is abraded away in the direction of such infeeding at the desired linear rate GR. This results despite changes in the wheel radius R because the terms 14~ -FtS - :R'te represent and compensate for -the wheel wear rate R~w.

A Special System.for Controlling Size and Rates FIGo 17, taken with FIGo 18 or 27, relates to methods and apparatus in which an in-process workpiece sensing gage is employed .
FIGo 28 taken with FIG. 29 or 30 relates to methods and apparatus in which an in-process trwing element-sensing gage is lltilized insteadO This reduces considerably the complexity OI the apparatus O
In the light of my Class III truing method disclosed above, however, I am able to bring to the art a method and apparatus by which grinding size and grinding rate are accurately controlled --despite wheel wear and changes in wheel radius - with no in-process gage at allO ~s startling as it may seem, one may simply first manually measure the radius Rte, then proceed with confidence to perform simultaneous grinding and truing, with the grinding at a rate and to final workpiece size he may desire, while nevertheless automatically keeping the wheel sharp and a~oiding metallurgical burn at the workpiece.
For this aspect of my inven$ion, reference will be made to FIG. 28 with the assumption that the components 65, 66~ 68~ 69~
70 are totally omitted~ In other words, all gages of FIG. 1 and FIG~ 28 are omittedO Further, FIG. 28 is to be taken with the assumption that the wheel 20 and truing element 50 fall in Class III as defined above Merely as an example consider that the workpiece 24 is 1020 steel, the wheel 20 is made of aluminum oxide grits and the truing element 50 is a ro31 composed of diamond chips set in a supporti.~lg matrix o.t`

-l~L3--tungsten carbide. FIGo 28 taken with these assurrlp-tions will hereafter be called "special FIGo 28" since it see.ms totally unnecessary to repeat that figure with the gaging componer.ts omitted.
As indicated previously, FIGo 28 involves grinding action at the workpiece/wheel interface with the slide WS being ïed to the left, and simultaneous truing action at the wheel/element interface with the slide TS being f`ed to the left.

So long as the relative sur:Eace speed Sr o:~ the rubbing contact is kept below 30ûO sO :f~ m., the diamond truing roll will not perceptibly change in radius --at least it will not change over a long aggregate time of truing action. Therefore, I am able validly to assume that the radius Rte (which may be initially measured~ is constant and that the radius reduction rate Rlte of the element 50 is zeroO
A very simple and reliable control method and apparatus may be employed to advantage with the special FIGo 28~ and one suitable control system 71M for this purpose is depicted in FIGo 31~
~s there shown, servo circuits 220~ 221~ 222 operate to maintain the speeds O p and C~)w at selected set point values and to maintain the truing in:Eeed rate FtS at a selected value --all as described previously in relation to FIG. 18. The truing ineed rate may be set, for example, at about . 040"/minO

In FIG~ 31 (unlike FIG~ 29 or 30)~ the signal FtS
represents the wheel radius reduction rate R'w because the truing roll wear rate R'te is zero (see special FIGo 28)o Somewhat surprisingly, the following simple expression applies:
R' = Ft ~68) Thus, it is possible to make the part reduction rate ~ ~p equal a desired grind rate GR simply by causing the wheel slide WS to Ieed to the le~t at a rate FWs which is equal to the truing slide rate :~ts '3~
plus the deslred grind rate GRo This is expressed:
Rlp = Fws ~ R w (63) And from (68):
R p Fws - FtS = GR (70) Therefore, a summing circuit 500 in FIGo 31 adds the signals FtS
and GR (the latter being a set point selected by ad,justing a potentiometer 501) to produce a va:riab].e "set point" signal F,,~,Sd. The latte:r is compared with the actual feed rate signal ~ Ws in a summing circuit 502 which sends an error signal ERR12 to a PI:D servo amplifier 504 to variably energize the motor WFM. In this fashion, the actual slide feed rate FWS is made to take on whatever value is required to maintain the grind rate R'p of the workpiece equal to the set point signal ~R.

That is, since ERR12 = FtS + GR - FWS but that error is kept at zero, then FWS = Fts -~ GR t71 To control the truing action and to assure that the diamond chip roll does not wear or recluce in radius, the relative surface speed Sr at the truing interface is held at a desired value Srd (obtained by setting a potentiometer 506) which is less than 3000 s. f. m~ (and preferably on the order of about 600 to 300 s. f. m. ) when rough grinding of the workpiece is taking placeO Because Rte is constant, its measured value is represented by a signal :E~te obtained simply by adjusting a potentiometer 508. That signal is subtracted from Pts in a summing circuit 509 to produce a signal representing the wheel radius Rw even as it changes due to wheel wearO The latter signal is multi~plied bY~JW
in a multiplier circuit 510. The signals Rte and CJte a:re likewise multiplied in a circuit 511~ The products Rw ~w arld Rte~ G)te are subtracted in a summing circuit 512 and the difference is fed to an operational ampli~ier 514 adjusted to have a gain of 27T. From Equations (1), (2) and (3)~ it is a.pparent that the relative surface speed Sr at the truing interface is Sr = 2~(RWo G~w - Rte ~)te ) (72) and thus the output of amplifier 514 varies as the relative surface speed at the truing interface. That signal Sr is bucked against the set point Srd in a summing circuit 515, and the resulting error signal ERR13 is fed to a PD~ servo amplifier which energizes the motor TM
(in this case acting as a brake)~ If the signal Sr exceeds Srd, the signal ERR13 b~comes more positive, the voltage Vtm increa,ses, the current and braking torque of motor TM decrease, and the speed G)te in~reases --until the signal Sr is reduced to equality with SrdO
The magic of this arrangement is that since R'te is zero, no gage is req~ured to sense and signal its value, and yet grind rate can easily be made to agree with the set point (~R despite wheel wearO
Equally important is the fact that with no gage at all, and because Rte is constant and signaled from a simple adjusted source (such as potentiometer 508), the changing wheel radius is continuously ascertainable :trom the difference ~w ~ts Rte (57) via the summing circuit 5û9. And this makes it possible, via another summing circuit 518 to continuously know the workpiece size or radius Rp from the algebraic relationship Rp = Pws ~ Rw = Pws ~ Pts Rte (58) With the ?~Faratus of the special FIGo ~8 and FIG. 31, the part may be rough ground at a desired grind ra$e (while the wheel is kept true and sharp) until the actual part si~e Rp reaches a desired final value simply by comparing the signal Rp with that final value and then hacking the wheel out. A11 of this with no in-process gage at all, and with virtually infinite life for the diamond truing roll 50O

-1~6 -Of course, i-t is not essential that a diamond chip truing element or Class III materials be employed~ In those cases, especially Class II/ where the truing ratio TR is established in excess OI 100 (for example)J a very low STE is maintained (eO gO, less than about 00 04),, the radius reduc-tion of the truing elernent, during grinding of two or three worJ~pieces, may be less than the final size tolerance acceptable for those piecesO Thus, lt is within the L)urview of -the method to employ a truing element which has some perceptible wear but to compensate for this (say, after one or more pieces have been ground) by re-measuring the element and readjusting the potentiometer 5080 This brings to light that the "special FIG~ 28" apparatus may be used to advantage in the grinding methods which involve control of STE or SGE~ as described with reference to FI(~So 29 and 30, respectivelyO No element-sensing in-process gage is required The ~ariable Rte in Equations (66) and (67) is fixed and obtained from an adjustable source (such as potentiometer 508 in FIGo 31)~ ~nd the variable ~te' in Equations (66) and (~7) is zero, thereby simplifying the apparatus of FIG. 29 or FIGo 30~ In such cases, the STE ratio will preferably be set and maintained at less than about 00 04 HP/in. /minD, or the SGE ratio would preferably be set and maintained at less than about 4. 0 --except that these set points may be increased (for the reasons explained above) during the short time periods where finish grinding is performed on a workpieceO
In a general sense, "special FIG~ 28~1 taken with FIGo 31 ~or taken with F[Go 29 or 30, modified as noted above) makes it plain how simultaneous (i~ grinding of a part by a wheel and ~ii) truing by an element acting on the wheel may be carried out with zero or negligible wearing and dimensional change of the operative su.rface of the truing element. With this, the wheel dimension Rw~ although it 7~-changes, is continuously deterrninableJ and the part dimension :Rp, although it changes, is continuously determinable~

The dimension :E~te (measured from a re:Eerence mark 50a to the operative surface of the element 50, along a line perpendicular to that surface) is known and constant. The dimension PtS (measurecl from the axis 20a to the reference mark 50a along a line perpendicular to the wheel face at its point of truing contact) is signa:Led by the position feedback device 58 --and thus the changing radius Rw is alvvays equal to the difference PtS ~ Rte. The dimension PWS (m axis 20a to the reference point 24a along a line perpendicular to the work surface at the point of grinding contact) is signaled by the position transducer 29 --and thus the changing part dimension Rp ~measured :trom the re:terence point 24a to ~e ground work surace along a line perpendicular to that surface) is always egual to the difference Pws ~ Rw which is equal to PWS ~ Fts + Rte-And further, since R'te is essentially zero, the wheel radius recluction rate R'W is known to equal the relative infeeding rate FtS of the truing element, such rate being signaled easily by means such as the tachometer 59. This permits the workpiece reduction rate R'p (in a dir ection parallel to that of the relative infeeding of the vuorkpiece and wheel) to be kept at a desired grind rate GR simply by causing the relative imeeding rate FWS to equal the desired grind rate GR plus the truing infeed rate :Fts-RESUME
~n the various figures herein showing exemplary embodiments of control apparatus for practicing specific examples of grinding or truing methods, analo~ signals created and processed by analog circuits have been describedO It is well known to those skilled in the control art that digital signals ~with appropriate ADC or D~C

-l~L8-`3~3~

converters, as needed~ may be employed to signal di~erent variables, with a programmed digital computer performing various arithmetic, gain9 derivative or integral functions with such signals, The computer iterates its operations at such short intervals that each signaled quantity, in practical e~ect, varies corltinuouslyO Because those working in the art can with routirle skill embody the control apparatus here disclosed in various forms employing digital signals and digital computers, it is to be understood that the claims which follow embrace such digital embodimentsO To illustrate and describe specific digital embodiments would unnecessarily lengthen the present specificationJ and the analog apparatus here shown and described provides to those of ordinary skill in the art all of the necessary teachings reqwred to construct digital apparatus for practicing and embodying the methods and apparatus here disclosed and claimedO On the other hand and by contrast, the methods here disclosed may in many instances be practiced by manual adjustment or control of the different variables, and the method claims which follow are to be read with a scope which includes purely manual set ups or adjustments.
In many speci~ic cases3 approximations and ranges oE
variables may be uti~ized, as contrasted with rigorous control, in practicing the invention here disclosed to obtain to a significant degree some or all of the advantages described. For example3 those skilled in the art will realize that in computing volumetric material removal rates W' or M'~ or powers PWRt or PWRg from instant to instant, the radii Rp, Rw and Rte do not change by large percentages; therefore, these radii may often be assumed constant over e~tended intervals.
The rates o~ radius changes may be taken as reElecting material removal rates~ And, in certain cases, the power involved in driving a workpiece (or driving or braking a truing element) may be such a small percentage -l'l'`

of grinding (or truing~ power applied by the wheel that the terms PWRp and PWRte mentioned above can be ignored while still obtaining sufficient accuracy.
The truing methods and apparatus here disclosed permit a grinding wheel to be restored to a desi.red shape by the action of truing elements made of any of a wide variety of materialsO Truing elements may be made of relatively low cost rnaterials, such ~s Inetal or metal alloy steels, heretofore deemed by the art to be unswitable.
Yet, the truing elements .may have an une~pectedly long ~ife --and in the case of a diamond chip truing elernent, the useful life lies beyond any rational prediction.
The truing procedure, where wheel shape restoration is the main objective, leaves the wheel sharp, and the faster the wheel is trued down to a desired shape the sharper it will be left and the less the wearing down of the truing ele~rentO Yet, by conjointly establishing the relative infeed and relative surface speed of the rubbing contact which produces truing ac$ion, the degree OI sharpness may be determined --and in turn the smootLmess of the ground final surface on the workpieceO
The truing action may be periodic or continuous and, if desired, with control OI STE or SGEo With essentially continuous truing action while a part is being ground, both wheel sharpness and shape may be maintainedO Thin workpieces may be ground down by considerable amounts and at high rates with neither workpiece deformation nor surface bux n~ Yet, by simple changes of certain set points, the wheel may be conditioned for finish grinding and in a way which determines the smoothness of the final workpiece surfaceO
While the inv~ntion in its various aspects has been shown and described in some detail with reference to different specific -l~Q -3~

method and apparatus embodimentsJ there is no intention thereby to limit the invention to such detail. On the contrary, it is intencled here to cover all alternatives, variations and equivalents which ~all within the spirit and scope OI the following claimsO

1~

Claims (213)

The embodiments of the invention in which an exclusive property or privilege is claimed are defined as follows:

1. The method of restoring the face of a grinding wheel which has deteriorated from the desired shape, said method comprising rotating the wheel and feeding the wheel face into relative rubbing contact with the operative surface of a Class I truing element, said surface conforming to the desired shape for the wheel face, and said method being characterized by and including conjointly establishing the relative surface speed of said rubbing contact and relative infeed rate of said element and wheel to make the ratio greater than 1Ø where W' and TE' are the volume per unit time rates of removal of materials from the wheel and element, respectively.

2. The method set out in claim 1 further characterized in that said grinding wheel is employed in the successive grinding of a plurality of substantially identical workpieces, and said truing element is made of the same material as such workpieces and with an operative surface which is the same shape as the finished surface of one of the workpieces.

3. The method set out in claim 1 further characterized in that said grinding wheel is employed in the grinding of successive ones of a plurality of workpieces, and said truing element is identical to one of such workpieces.

4. The method of restoring the face of a grinding wheel which has deteriorated from the desired shape, said method comprising rotating the wheel and feeding the wheel face into relative rubbing contact with the operative surface of a Class II truing element, said surface conforming to the desired shape for the wheel face, and said method being characterized by and including conjointly establishing the relative surface speed of said rubbing contact and relative infeed rate of said element and wheel to make the ratio greater than 10.0 where W' and TE' are the volume per unit time rates of removal of materials from the wheel and element.

5. The method set out in claim 1 or claim 4 further characterized in that said truing element is a body of an homogeneous material.

6. The method set out in claim 1 or claim 4 further characterized in that said truing element is an homogeneous body of a metal alloy exemplified in its crystaline, structural homogeneity by the carbon steels, M series steels and the T series steels.

7. The method set out in claim 1 or claim 4 further characterized in that said truing element is made of hard steel.

8. The method of restoring the face of a grinding wheel which has deteriorated from the desired shape, said method comprising rotating the wheel and feeding the wheel face into relative rubbing contact with the operative surface of a Class III truing element, said surface conforming to the desired shape for the wheel face, said method being characterized by and including conjointly establishing the relative surface speed of said rubbing contact and relative infeed rate of said element and wheel to promote fracturing and bond fracturing of the abrasive grits in the wheel as contrasted with attrition wearing and flatting of the points and corners of those grits, said relative surface speed for this purpose being made less than 3000 feet per minute but greater than zero.

9. The method set out in claim 8 wherein said truing element is a body having a plurality of diamond chips set in a supporting matrix of hard material.

10. The method of lengthening the service life of a truing element made of diamond chips bonded into a supporting matrix body, said method comprising relatively feeding the face of a rotating grinding wheel into relatively rubbing contact with an operative surface of said truing element, such surface having exposed edges and corners of the diamond chips, and said method being characterized by and including

Claim 10, page 2, conjointly establishing the relative surface speed of said rubbing contact and the relative infeed rate of said wheel and element to promote grit fracturing and bond fracturing in the wheel and minimize attrition flatting of the wheel grits, said relative surface speed for this purpose being made less than 3000 feet per minute but greater than zero, whereby the wheel is not only trued but also sharpened and with negligible wear of the truing element.

11. The method set out in claims 1 or 4 or 8 further including varying the conjointly established relative surface speed and relative infeed during the course of the shape restoration by either (i) increasing or decreasing said relative surface speed to decrease or increase the grit-fracturing action and thereby make the wheel duller or sharper, or (ii) increasing or decreasing said relative infeed rate to increase or decrease the grit-fracturing action and thereby make the wheel sharper or duller.

12. The method set out in claim 1 or 4 or 8 wherein said relative surface speed is established within a range of values substantially lower than the range of relative surface speeds of rubbing contact, between the wheel face and a workpiece, with which said wheel is employed in the grinding of workpieces.

13. The method set out in claim 1 or 4 or 8 wherein said relative infeed rate is established within a range of values which is substantially higher than the range of relative infeed rates with which said wheel is employed in the grinding of workpieces.

14. The method set out in claim 1 or 4 or 8 further including inducing vibrations between the wheel and element at their region of rubbing contact, thereby to promote grit fracturing and bond fracturing on the wheel.

15. The method set out in claim 1 or 4 or 8 further including inducing rotational vibrations of the wheel relative to the truing element.

16. The method set out in claim 1 or 4 or 8 further including inducing translational vibrations of the wheel relative to the truing element in a direction lying normal to the axis of the wheel and passing through the region of rubbing contact.

17. The method set out in claim 1 or 4 or 8 further characterized in that said truing element is a roll journaled for rotation about an axis and having an operative surface which is a surface of revolution in rubbing contact with said wheel face, said method including braking the rotation of said roll to make the relative surface speed of said rubbing contact equal to the difference between the surface speed of the wheel and the surface speed of the roll.

18. The method set out in claim 1 or 4 or 8 further characterized in that said rubbing contact of the wheel face and operative surface of the truing element is created while said wheel face is also in grinding rubbing contact with a workpiece.

19. The method set out in claim 1 or 4 or 8 further characterized in that said rubbing contact of said wheel face and said operative surface is created during time spaced intervals over a span of time during which the wheel face is continuously in grinding rubbing contact with a workpiece.

20. In a grinding machine, the combination comprising (a) a grinding wheel mounted for rotation about its axis and means for rotationally driving the wheel at a controllable speed, said wheel having a face engageable with a workpiece for producing grinding action, (b) a Class I truing element having an operative surface conforming to the desired shape of the wheel face, (c) means for relatively infeeding said wheel and element to bring said face and operative surface into relative rubbing contact, and (d) means for conjointly establishing the relative surface speed of said rubbing contact and the rate of said infeeding to make the ratio greater than 1.0, where W' and TE' are the volume per unit time rates of removal of materials from the wheel and element, respectively.

21. In a grinding machine, the combination comprising (a) a grinding wheel mounted for rotation about its axis and means for rotationally driving the wheel at a controllable speed, said wheel having a face engageable with a workpiece for producing grinding action, (b) a Class II truing element having an operative surface conforming to the desired shape of the wheel face, (c) means for relatively infeeding said wheel and element to bring said face and operative surface into relative rubbing contact, and (d) means for conjointly establishing the relative surface speed of said rubbing contact and the rate of said infeeding to make the ratio greater than 10.0, where W' and TE' are the volume per unit time rates of removal of materials from the wheel and element, respectively.

22. In a grinding machine, the combination comprising (a) a grinding wheel mounted for rotation about its axis and means for rotationally driving the wheel at a controllable speed, said wheel having a face engageable with a workpiece for producing grinding action.

(b) a Class III truing element having an operative surface conforming to the desired shape of the wheel face,

Claim 22, page 2, (c) means for relatively infeeding said wheel and element to bring said face on operative surface into relative rubbing contact, and (d) means for conjointly establishing the relative surface speed of said rubbing contact and the relative infeed rate to promote grit and bond fracturing of the abrasive grits in the wheel face, said relative surface speed being less than 3000 feet per minute.

23. Apparatus as set out in claim 20 or 21 wherein said means (d) includes (d1) means for controlling said relative surface speed and said infeeding rate to maintain said ratio ? within a predetermined range which lies above the specified lower limit.

24. Apparatus as set out in claim 20 or 21 wherein said means (d) includes (d1) means for controlling said relative surface speed and said infeeding rate to maintain said ratio substantially equal to a predetermined but adjustable set point value which is greater than the specified lower limit.

25. Apparatus as set out in claim 20 or 21 further characterized in that said truing element is a homogeneous material.

26. Apparatus as set out in claim 20 or 21 further characterized in that said truing element is a metal or metal alloy material exemplified by steel.

27. The method of grinding a second workpiece to conform identically to the existing desired shape of a pre-existing first workpiece of the same or a harder material than the second workpiece, said method comprising (a) obtaining a grinding wheel having a wheel face which at least approximately, if not exactly, conforms to said desired shape, (b) utilizing said wheel to grind the second workpiece, and (c) prior to or during the course of grinding said second workpiece rotationally driving said wheel and relatively infeeding its face into relative rubbing contact with the work surface of said first workpiece, while (c1) conjointly establishing the relative surface speed of said rubbing contact and said relative infeeding to make the ratio ? greater than 1.0, where W' and TE' are the volumetric rates of removal of materials from the wheel and said first workpiece, respectively, thereby to true the wheel face.

28. The method set out in claim 27 further characterized in that said procedure (c) is performed during or prior to initiation of rough grinding on said second workpiece with said ratio having a first value greater than 1.0, and when finish grinding is being or is about to be performed, on said second workpiece, said procedure (c) and (c1) is performed to make said ratio

Claim 28, page 2, ? have a second value which is less than said first value and not necessarily greater than 1.0, whereby the wheel grits are dulled to create a smoother surface finish on said second workpiece.

29. The method of grinding a series of identical workpieces to a desired size and shape despite progressive deterioration in the shape of a grinding wheel employed, said method comprising (a) by any suitable procedure creating the first of said workpieces with a work surface having the desired final shape, (b) obtaining a grinding wheel having a wheel face which at least approximately, if not exactly, conforms to said desired final shape, (c) utilizing said wheel to grind the second and successive ones of said workpieces, (d) at least from time-to-time during the course of performing of said procedure (c), rotating the wheel and relatively infeeding its face into relative rubbing contact with the work surface of said first workpiece, while (d1) conjointly establishing the relative surface speed of said rubbing contact and said relative infeeding to make the ratio ?, greater than 1.0, where W' and TE' are the volumetric rates of removal of materials from the wheel and said first workpiece, respectively, thereby to true the wheel face.

30. The method set out in claim 29 further characterized in that, whenever, during the course of grinding said series of workpieces, it is determined that the work surface of said first workpiece no longer possesses sufficiently said desired shape, substituting one of the previously ground workpieces for the first workpiece in carrying out said procedure (d) and (d1).

31. The method set out in claim 29 further characterized in that when said procedure (d) and (d1) is performed during or prior to initiation or resumption of rough grinding on a given one of said workpieces, making said ratio ? have a first value greater than 1.0, and when finish grinding begins or is about to be performed on said given workpiece, carrying out said procedure (d) and (d1) to make said ratio ? have a second value which is less than said first value and not necessarily greater than 1.0, whereby the wheel grits are dulled to create a smoother surface finish on said one workpiece.

32. The method of grinding a series of identical workpieces to a desired size and shape despite progressive deterioration in the shape of the face of a grinding wheel employed, said method comprising (a) conditioning the face of the grinding wheel initially to conform to the shape desired for the workpieces, (b) utilizing said wheel to grind a first workpiece to the desired shape,

Claim 32, page 2, (c) thereafter grinding a second and a succession of workpieces with said wheel, the shape of the wheel face deteriorating in the course of such grinding, (d) at least from time-to-time during the performance of said procedure (c), feeding said wheel face into relative rubbing contact with said first workpiece to effect truing of the wheel face while maintaining the STE ratio within a predetermined range.

33. The method set out in claim 32 wherein said procedure (d) includes (d1) maintaining the STE ratio at least approximately in agreement with a preselected set point value.

34. The method set out in claim 32 further characterized in that said procedure (d) is carried out by maintaining the STE ratio within a predetermined range which results in the ratio ? being greater than 1.0, where W' and TE' are the volumes of material removed per unit time from the wheel and the first workpiece, respectively.

35. The method set out in claim 34 further characterized in that said step (d) is carried out by making said set point value have a first value when truing is performed during or prior to initiation or resumption of rough grinding on said second or any subsequent workpiece;
said step (d) is carried out by making said set point value have a second value when truing is performed during or just prior to initiation or resumption of finish grinding on said second or any subsequent workpiece;
and said first value being less than said second value.

36. The method set out in claim 32 further characterized in that said procedure (d) is carried out while said procedure (c) is being executed and the grinding of the second or a subsequent workpiece is in progress.

37. The method set out in claim 32 further characterized in that said step (d) is carried out while step (c) is being executed and the grinding of the second or a subsequent workpiece is in progress by periodically bringing said first workpiece into truing contact with said wheel face.

38. The method set out in claim 32 further characterized in that said step (d) is carried out simultaneously when grinding of a workpiece is taking place.

39. The method set out in claim 38 further characterized in that said step (d) includes setting said set point value to a first level while rough grinding of said second or a subsequent workpiece is taking place; setting said set point value to a second level while finish grinding of said second or a subsequent workpiece is taking place; said first level being lower than said second level.

40. The method of restoring or maintaining the face of a grinding wheel in a desired shape or sharpness, said method comprising rotating the wheel and relatively feeding the wheel face into relative rubbing contact with the operative surface of a truing element, said surface conforming to said desired shape, and said method being characterized by and including controlling said relative motions of said wheel and element to make the specific truing energy ratio (STE) fall within a preselected range.

41. The method of restoring or maintaining the face of a grinding wheel in a desired shape or sharpness, said method comprising rotating the wheel and bringing the wheel face into relative rubbing contact with the operative surface of a truing element while relatively infeeding said face and surface, said surface conforming to the desired shape for the wheel face, and said method being characterized by and including controlling said relative motions of said wheel and element to maintain the specific truing energy (STE) ratio ? at least approximately in agreement with a predetermined set point value, where PWRt is the energy expended per unit time in creating said relative rubbing contact and W' is the volume of material removed from the wheel per unit time.

42. The method set forth in claim 41 wherein said ratio is controlled by respectively increasing or decreasing the relative surface speed of said rubbing contact when said ratio tends to decrease below or increase above said set point value.

43. The method set forth in claim 41 wherein said ratio is controlled by respectively increasing or decreasing the rate of said infeeding when said ratio tends to increase or decrease above or below said set point value.

44. The method set forth in claim 41 wherein said ratio is controlled by maintaining W' substantially constant, and in response to an increase or decrease in PWR respectively decreasing or increasing the relative surface speed of said rubbing contact.

45. In the known process of grinding workpieces by bringing the face of a rotating grinding wheel into relative rubbing contact with the workpiece surface, and wherein the wheel face tends to deteriorate from the desired shape therefor, the method of truing the wheel to restore its face to the desired shape, including (a) bringing the face of the grinding wheel into relative rubbing contact with the operative surface of a truing element, said surface conforming to the desired shape of the wheel face, and said method being characterized by (1) sensing at least approximately the specific truing energy (STE) with which material is removed from the wheel, (2) selecting a predetermined STE set point, and (3) adjusting at least one of (a) the relative surface speed and (b) the relative infeed rate of the wheel face and truing surface to restore the sensed STE at least approximately to said set point whenever the sensed STE tends to depart substantially from such set point.
46. The method set out in claim 45 further characterized in that said step (1) includes (a) controlling said relative infeed rate to maintain the volumetric rate of wheel material removed (W') at least approximately constant, and

Claim 46, page 2, (b) sensing, at least approximately, the power consumed in driving the wheel face rotationally relative to the truing element surface, and said step (3) is carried out by (a) decreasing or increasing the relative surface speed of the wheel face and truing surface when the sensed power tends to increase or decrease from the value which makes the actual STE
substantially equal to the set point STE.

47. The method set out in claim 45 further characterized in that said truing element is in Class I and said step (3) includes selecting an STE set point value which makes the ratio W'/TE' of said rubbing contact greater than 1.0, where W' and TE' are the volumes of materials removed per unit time from the wheel and the element, respectively.

48. The method set out in claim 45 further characterized in that said truing element is in Class II and said step (3) includes selecting an STE set point value which makes the ratio W'/TE' of said rubbing contact greater than 10.0, where W' and TE' are the volumes of materials removed per unit time from the wheel and the element, respectively.

49. The method set out in claim 45 further characterized in that said truing element is in Class III and said step (3) includes selecting an STE set point value which makes the relative surface speed of said rubbing contact less than 3000 feet per minute.

50. The method set out in claim 47 further characterized in that said grinding wheel is employed in grinding a series of identical workpieces, and said truing element is one of the finished workpieces.

51. The method set out in claim 45 further characterized in that said procedure (2) includes changing, from time to time, the selected set point downwardly or upwardly to increase or decrease the sharpness of the wheel left at the conclusion of the execution of the truing method.

52. The method set out in claim 45 further characterized in that said method is carried out while said wheel is in grinding contact with a workpiece.

53. The method of conditioning the face of a grinding wheel to a desired state of sharpness, said method comprising rotating the wheel and feeding the wheel face into relative rubbing contact with the operative surface of a truing element, said surface conforming to the desired shape for the wheel face, and said method being characterized by and including (a) controlling the relative motions of said wheel and element to maintain the specific truing energy (STE) ratio PWR/W' at least approximately in agreement with a predetermined set point value, where PWR is the energy expended per unit time in creating said relative rubbing contact and W' is the volume of material removed from the wheel per unit time, and

Claim 53, page 2, (b) adjusting said set point value upwardly or downwardly to make the wheel face having a desired lesser or greater degree of sharpness.

54. The method set out in claim 53 further characterized in that said conditioning procedure is carried out with a first set point value to condition the wheel to grind a workpiece with a first surface finish and is carried out with a second set point value to condition the wheel to grind the workpiece with a second surface finish, said first set point value being greater than the second and said first surface finish being coarser than the second,

55. In a grinding machine, apparatus for restoring or maintaining the face of a grinding wheel in a desired shape or sharpness, said apparatus comprising in combination, (a) means for supporting said wheel for rotation about its axis, (b) means for rotationally driving the wheel, (c) a truing element having an operative surface conforming to the desired shape for the wheel face, (d) means for relatively infeeding said wheel and element to bring said face and operative surface into relative rubbing contact, and (e) means for controlling said infeeding and the relative surface speed of said rubbing contact to make the STE ratio fall within a preselected range.

56. In a grinding machine, apparatus for restoring or maintaining the face of a grinding wheel in a desired shape or sharpness, said apparatus comprising in combination, (a) means for supporting said wheel for rotation about its axis, (b) means for rotationally driving the wheel, (c) a truing element having an operative surface conforming to the desired shape for the wheel face, (d) means for relatively infeeding said wheel and element to bring said face and operative surface into relative rubbing contact, and (e) means for controlling said infeeding and the relative surface speed of said rubbing contact to make the specific truing energy (STE) ratio ? at least approximately equal to a predetermined but adjustable set point value, where PWRt is the energy expended per unit time in creating said rubbing contact and W' is the volume of material removed from the wheel per unit time.

57. The combination set out in claim 56 further characterized in that said means (e) includes means for respectively increasing or decreasing the relative surface speed of said rubbing contact when the STE ratio tends to decrease below or increase above said set point value.

58. The combination set out in claim 56 further characterized in that said means (e) includes means for respectively decreasing or increasing the rate of said infeeding when the STE ratio tends to decrease below or increase above said set point value.

59. The combination set out in claim 56 further characterized in that said means (e) includes (e1) means for maintaining said material removal rate W' substantially constant, and (e2) means for respectively decreasing or increasing the relative surface speed of said rubbing contact when the STE ratio tends to increase above or decrease below said set point value.

60, In a grinding machine having a rotationally driven grinding wheel relatively feedable to bring its face into rubbing grinding contact with a workpiece, so that the face tends to deteriorate from the desired shape therefor, apparatus for truing the wheel to restore its face shape comprising, in combination, (a) a truing element having an operative surface conforming to the desired shape for the wheel face, (b) means for relatively infeeding the wheel and said element to maintain said face and said operative surface in rubbing contact, (c) means for sensing the parameters of said rubbing contact to signal at least approximately the STE ratio with which material is removed from the wheel,

Claim 60, page 2, (d) means for signaling a predetermined but set point STEd, and (e) means responsive to said means (c) and (d) for correctly adjusting at least one of (i) the relative surface speed of said rubbing contact and (ii) the rate of said infeeding to restore the STE ratio to the set point whenever it tends to depart therefrom.

61. The combination set out in claim 60 further including (f) means for adjusting said means (d) to decrease or increase the set point STEd, whereby the wheel face condition is made sharper or duller.

62. The method of rough grinding and finish grinding a workpiece with a single, rotatably driven grinding wheel, said method comprising (a) relatively feeding the operative surface of a conditioning element into rubbing contact with the face of said wheel, while establishing the relative surface speed and feed rate of such rubbing contact to make the STE ratio fall within a predetermined first range of values, (b) subsequent to said procedure (a), relatively feeding the operative surface of said conditioning element into rubbing contact with the face of said wheel, while establishing the relative surface speed and feed rate of such rubbing contact to make the STE ratio fall within a predetermined second range of values, said second range being higher than the first,

Claim 62, page 2, (c) feeding the face of said wheel relatively into grinding contact with said workpiece to grind the latter, such feeding and grinding occurring either during or after performance of said procedure (a) and during or after performance of said procedure (b).

63. The method set out in claim 62 further characterized in that said procedure (c) is performed at a first feed rate during or after performance of said procedure (a), and said procedure (c) is performed at a second feed rate during or after performance of said procedure (b); said first feed rate being greater than said second feed rate.

64. The method set out in claim 62 or 63 further characterized in that said procedure (a) is first performed, said procedure (c) is next performed, said procedure (b) is thereafter performed, and said procedure (c) is thereafter repeated.

65. The method set out in claim 62 or 63 further characterized in that said procedure (c) is performed continuously over a span of time, and said procedures (a) and (b) are performed during relatively earlier and later portions of said span of time.

66. The method set out in claim 62 or 63 further characterized in that said procedure (c) is performed continuously over a span of time, said procedure (a) is performed substantially continuously over a first portion of said span, said procedure (b) is performed substantially continuously over a second portion of said span, and said second portion substantially immediately follows said first portion.

67. The method set out in claim 62 or 63 further characterized in that said procedure (a) is carried out repetitively during spaced time intervals while said procedure (c) is in progress, but prior to execution of said procedure (b).

68. The method set out in claim 62 or 63 further characterized in that said procedure (a) is carried out while said procedure (c) is in progress.

69. The method set out in claim 62 or 63 further characterized in that said procedure (b) is carried out while said procedure (c) is in progress.

70. The method set out in claim 62 or 63 wherein said procedures (a) and (b) are respectively carried out by controlling relative surface speed and feed rate of said rubbing contact to maintain the STE ratio substantially in agreement with first and second set point values, the second being higher than the first.

71. The method of truing and conditioning the face of a grinding wheel, said method comprising (a) rotationally driving the grinding wheel and relatively feeding the operative surface of a conditioning element into rubbing contact with the wheel face,

Claim 71, page 2, (b) first conjointly establishing the relative surface speed and feed rate of said rubbing contact to make the STE ratio fall within a first predetermined range of values, and (c) thereafter conjointly establishing the relative surface speed and feed rate of said rubbing contact to make the STE ratio fall within a second predetermined range of values, said second range being higher than and non-overlapping with said first range, whereby the procedure (b) removes material from the wheel relatively rapidly for efficient shaping but leaves the wheel sharp and conducive to producing a rough surface finish on a workpiece, and said procedure (c) thereafter removes material from the wheel relatively slowly and dulls the wheel to make it conducive to producing a finer surface finish on a workpiece.

72. The method set out in claim 71 wherein said conditioning element is in Class I and said procedure (b) is carried out with the STE ratio in a first predetermined range to make the ratio W'/TE' greater than 1.0, where W' and TE' are the volumes of materials removed per unit time from said wheel and element, respectively.

73. The method set out in claim 72 further characterized in that said truing element is a part identical in material to that of a workpiece with which said wheel is to be used for grinding, and said truing element has an operative surface conforming to the desired final shape of that workpiece.

74. The method set out in claim 71 further characterized in that said conditioning element is Class II and said procedure (b) is carried out with the STE ratio in a first predetermined range to make the ratio W'/TE' greater than 10.0, where W' and TE' are the volumes of materials removed per unit time from said wheel and element, respectively.

75. The method set out in claim 71 further characterized in that said conditioning element is Class III and said procedure (b) is carried out with the said rubbing contact thereof at a relative surface speed of less than 3000 feet per minute.

76. The method set out in claim 71 wherein said procedures (b) and (c) are respectively carried out by controlling relative surface speed and feed rate of said rubbing contact to maintain the STE ratio substantially in agreement with first and second set point values, the second being higher than the first.

77. The method set out in claim 71 further characterized in that (d) said grinding wheel is fed into grinding contact with a workpiece simultaneously while said procedures (a), (b) and (c) are carried out.

78. The method of grinding a workpiece with a single, rotationally driven grinding wheel, said method comprising (a) feeding the wheel relatively to the workpiece under conditions to remove material at a first rate from the workpiece by rough grinding action, (b) contacting the wheel with a truing element and controlling the relative surface velocity and feed between the wheel and element to maintain the STE ratio in a preselected range of values, and (c) feeding the wheel relatively to and in contact with the workpiece under conditions to remove material at a second rate by finish grinding action, said second rate being lower than said first rate.

79. The method set forth in claim 78 wherein procedure (a) is first carried out, the wheel is retracted from contact with the workpiece while said procedure (b) is carried out, and procedure (c) is thereafter carried out.

80. The method set forth in claim 78 wherein said procedures (b) and (c) are carried out simultaneously with both the workpiece and the truing element in contact with the wheel.

81. The method set forth in claim 78 wherein said procedure (a) is first performed and procedures (b) and (c) are carried out simultaneously thereafter.

82. The method set forth in claim 78 wherein said procedure (a) is carried out with the truing element in rubbing contact with the wheel.

83. The method set forth in claim 82 wherein said procedure (a) includes controlling the relative surface velocity and feed between the wheel and element to create a relatively low STE ratio

84. The method set forth in claim 83 wherein said procedures (b) and (c) are carried out simultaneously after procedure (a) is completed, and procedure (b) includes controlling the relative surface speed and feed between the wheel and element to create an STE ratio which is high in relation to that created during procedure (a).

85. The method of conditioning a grinding wheel in a manner to generally determine the surface finish it will produce in the grinding of a workpiece, said method comprising (a) rotating the wheel and feeding the wheel face into relative rubbing contact with the operative surface of a conditioning element, said surface conforming to the desired shape for the wheel face, (b) rotating the wheel and feeding the wheel face into relative rubbing contact with active surface of a workpiece, said method being characterized by and including (c) during the performance of said procedure (a), controlling the STE of the wheel/element interaction to maintain it at least approximately in agreement with a desired set point value, and (d) adjusting said set point value, whereby the surface finish smoothness produced on the active surface of the workpiece as a consequence of procedure (b) is related monotonically to the adjusted set point value last-employed in the performance of said procedure (c).

86. The method defined by claim 85 further characterized in that said procedures (a) and (b) are carried out at least in part simultaneously.

87. The method defined by claim 85 further characterized in that said procedures (a), (b) and (c) are carried out simultaneously, and said procedure (d) is carried out to make the STE set point value have its greatest magnitude, within the span of time during which said procedures (a) and (b) are carried out, immediately prior to terminating said procedure (c).

88. The method defined by claim 85 further characterized in that said conditioning element is a homogeneous metal or metal alloy.

89. The method of grinding a workpiece with a rotationally driven grinding wheel, said method comprising (a) establishing operative grinding contact and relative feeding of the grinding wheel face and the workpiece to remove material from the latter, (b) relatively feeding the operative surface of a truing element into relative rubbing contact with the wheel face during at least a portion of the time said procedure (a) is being carried out, and (c) conjointly controlling the relative surface speed and feed of said relative rubbing contact to maintain the STE of such rubbing contact within a preselected range of values.

90. The method set out in claim 89 further characterized in that said procedure (c) includes controlling said relative surface speed and feed of said rubbing contact to maintain the STE at least approximately in agreement with a predetermined set point value.

91. The method set out in claim 90 further characterized in that said set point value is from time to time adjusted to a different value.

92. The method set out in claim 91 further characterized in that said set point value is made relatively low during initial rough grinding on the workpiece and relatively higher during subsequent finish grinding on the workpiece.

93. The method set out in claim 89 or 90 further characterized in that said procedures (b) and (c) are carried out during substantially the entire time span over which said procedure (a) is being carried out.

94. The method set out in claim 89 or 90 further characterized in that said procedures (b) and (e) are carried out during spaced time intervals within the time span over which said procedure (a) is being carried out.

95, The method set out in claim 89 further characterized in that said procedures (b) and (e) are carried out during spaced time intervals within the time span over which said procedure (a) is being carried out, and the said preselected range of values is adjusted upwardly for the last one of said intervals in comparison to the preselected range for the preceding intervals.

96. The method set out in claim 89 further characterized in that said procedures (b) and (c) are carried out during a time interval at or near the end of the time span over which said procedure (a) is carried out.

97. The method set out in claim 96 further characterized in that said procedures (b) and (c) are carried out during said time interval by first maintaining said STE within one preselected range of values and thereafter maintaining said STE within a higher preselected range of values.

98. The method set out in claim 89 further characterized in that said preselected range of STE values is changed to be lower or higher in order to decrease or increase the smoothness of the surface finish produced on the workpiece.

99. The method set out in claim 89 further characterized in that said preselected range of STE values is changed to be higher or lower in order to decrease or increase the sharpness of the wheel and the energy efficiency with which the workpiece is ground.

100. The method set out in claim 99 further characterized in that said preselected range of STE values is chosen to be relatively lower during rough grinding of the workpiece and relatively higher during finish grinding of the workpiece.

101. The method of conditioning the face of a rotationally driven grinding wheel while it is grinding the work surface of a workpiece, said method comprising (a) relatively feeding the wheel face into relative rubbing contact with the work surface of the workpiece while simultaneously relatively infeeding the operative surface of a truing element into relative rubbing contact with the wheel face, said method being characterized by and including (b) establishing conjointly the relative surface velocity and infeed rate of the rubbing contact between said operative surface and said wheel face to maintain the STE ratio PWRt/W' within a predetermined range, where PWRt is the rate of energy expended to produce the rubbing contact and W' is the volumetric rate of material removed from the wheel, whereby the wheel face degree of sharpness is determined by the predetermined range which is selected.

102. The method set out in claim 101 wherein said infeed rate is maintained at a value greater than the wheel radius reduction rate occurring due to wheel wear at the rubbing interface between said wheel face and said work surface.

103. The method set out in claim 101 further characterized in that said workpiece is a generally cylindrical part rotationally driven about its axis, and (a) initially for rough grinding of the workpiece, the STE ratio and the workpiece radius reduction rate R'p are maintained at first values STE1 and R'p1, and (b) subsequently for finish grinding of the workpiece the STE ratio and the radius reduction rate R'p are maintained at second values STE2 and R2'p2, where STE2 > STE1, and R'p2 < R'p1.

104. In a grinding machine having a rotationally driven grinding wheel, a workpiece to be ground, and a truing element, said grinding machine including (a) means for feeding said wheel relative to the workpiece to create relative rubbing contact and grinding action at the wheel/workpiece interface, (b) means for feeding said wheel relative to the truing element to create relative rubbing contact and truing action at the wheel/element interface, and (c) a control system characterized by (1) means for operating said means (a) and (b) to make said grinding action and truing action occur simultaneously, and (2) means for controlling the truing action to maintain the STE ratio thereof within a predetermined but adjustable range of values.

105. The apparatus defined in claim 104 further characterized in that said means (2) is constituted by means for controlling said truing action to maintain the STE ratio thereof substantially equal to predetermined but adjustable set point.

106. The apparatus defined in claim 104 or 105 further characterized in that said means (2) includes means for conjointly controlling the relative surface speed and the relative feed rate of the truing action at the wheel/element interface.

107. The apparatus defined in claim 104 or 105 further including means for making said preselected range of STE values relatively lower and higher during earlier and later portions of the time span during which said grinding action takes place.

108. The apparatus defined in claim 104 or 105 further characterized in that said truing element is a homogeneous metal or metal alloy.

109. The method of grinding a workpiece which lacks structural rigidity sufficient to withstand, without deleterious deflection, substantial forces imposed thereon by a grinding wheel, said method comprising (a) relatively feeding the workpiece and a rotationally driven grinding wheel into relative rubbing contact to create grinding action, and said method being characterized by (b) while said procedure (a) is in progress, relatively feeding the operative surface of a Class I truing element into relative rubbing contact with the face of the wheel, and (c) conjointly establishing the relative surface speed and relative feed rate of said last-named rubbing contact to make the ratio W'/TE' greater than 1.0, where W' and TE' are the volume per unit time rates of removal of materials from said wheel and element, respectively.

110. The method of grinding a workpiece which lacks structural rigidity sufficient to withstand, without deleterious deflection, substantial forces imposed thereon by a grinding wheel, said method comprising (a) relatively feeding the workpiece and a rotationally driven grinding wheel into relative rubbing contact to create grinding action, and said method being characterized by (b) while said procedure (a) is in progress, relatively feeding the operative surface of a Class II truing element into relative rubbing contact with the face of the wheel, and (c) conjointly establishing the relative surface speed and relative feed rate of said last-named rubbing contact to make the ratio W'/TE' greater than 10.0, where W' and TE' are the volume per unit time rates of removal of materials from said wheel and element, respectively.

111. The method of grinding a workpiece which lacks structural rigidity sufficient to withstand, without deleterious deflection, substantial forces imposed thereon by a grinding wheel, said method comprising (a) relatively feeding the workpiece and a rotationally driven grinding wheel into relative rubbing contact to create grinding action, and said method being characterized by (b) while said procedure (a) is in progress, relatively feeding the operative surface of a Class III truing element into relative rubbing contact with the face of the wheel, and (c) controlling the relative surface speed Sr of said last-named rubbing contact such that it is below 3000 surface feet per minute.

112. The method of grinding a workpiece which lacks structural rigidity sufficient to withstand, without deleterious deflection, substantial forces imposed thereon by a grinding wheel, said method comprising (a) relatively feeding the workpiece and a rotationally driven grinding wheel into relative rubbing contact to create grinding action, and said method being characterized by (b) while said procedure (a) is in progress, relatively feeding the operative surface of a conditioning element into relative rubbing contact with the face of the wheel, and (c) conjointly establishing the relative surface speed and feed rate of said operative surface and said wheel face to maintain the STE ratio of the last-named rubbing contact within a predetermined range of values selected to create wheel wear and sharpening, whereby the rate of grinding action may be made greater than otherwise possible without exceeding tolerable grinding forces imposed by the wheel on the workpiece.

113. The method set out in claim 112 further characterized in that said procedure (c) includes maintaining said STE
ratio at least approximately equal to a predetermined but adjustable set point.

114. The method set out in claim 113 further characterized in that said set point is adjusted to have first and second values respectively during rough and finish grinding of the workpiece, said first value being lower than the second.

115. The method set out in claim 112 further characterized in that said procedure (c) includes decreasing or increasing the relative surface speed of the rubbing contact between said operative surface and said face when said STE ratio tends to rise above or fall below said predetermined range.

116. The method of grinding the work surface of a workpiece with a rotationally driven grinding wheel, said method comprising (a) relatively feeding the wheel face into relative rubbing contact with the work surface of the workpiece, and said method being characterized by (b) while said procedure (a) is being carried out, bringing the operative surface of a truing element into relative rubbing contact with the wheel face during intermittent, spaced time periods, and (c) during such time periods, establishing conjointly the relative surface velocity and the relative infeed rate of said operative surface and wheel face to maintain the STE ratio within a predetermined range of values.

117. The method set out in claim 116 further characterized in that during each of said time periods the operative surface of said truing element is inwardly fed a predetermined distance relative to the wheel face along a path lying radially of the wheel axis.

118. The method set out in claim 116 further characterized in that during those intervals between said periods the truing element is moved bodily to maintain a predetermined gap between said wheel face and said operative surface.

119. The method set out in claim 118 further characterized in that (i) said wheel is mounted on a wheel slide which is moved bodily to infeed the wheel relative to the work surface, (ii) said truing element is mounted on a truing slide movable relative to the wheel slide, and (iii) said gap is maintained by bodily moving said truing slide relatively to the wheel slide and toward the wheel axis at a rate equal to the rate of reduction in the radius of the wheel.

120. The method set out in claim 118 further characterized in that said wheel and truing elements are bodily supported for relative motion along a common line normal to and passing through the axis of the wheel, and during said intervals said gap is maintained by continuously adjusting the bodily position of the truing element to keep Pts = Rw + Rte + GAP
as the wheel is grinding the workpiece, where Pts is the position of a reference point on the truing element, relative to the wheel axis, along said line, Rw is the wheel radius;
GAP is the length of said gap; and Rte is the distance along said line and between said reference point and a point on said operative surface.

121. The method set out in claim 118 further characterized in that prior to the start of each of said time periods, said truing element operative surface is moved bodily inwardly toward the wheel face a distance equal to the width of the gap, and during each of said periods is moved further inwardly a predetermined incremental distance.

122. The method set out in claim 121 further characterized in that said inward bodily movement prior to the start of each time period is at a first predetermined rate.

123. The method set out in claim 122 further characterized in that said further inwardly movement during each of said time periods is at a second predetermined rate which is less than said first predetermined rate.

124. The method set out in claim 116 further characterized by and including (d) producing a signal each time the wheel radius has been reduced by a predetermined amount due to grinding action of procedure (a) during an interval between two periods, and (e) in response to each appearance of said signal, initiating said procedures (b) and (c).

125. The method defined by claim 124 wherein said procedure (d) includes sensing the wheel radius at a predetermined axial location along the wheel face,, said location being that at which wheel wear and loss of form occur most rapidly.

126. The method of grinding the work surface of a workpiece with a rotationally driven grinding wheel, said method comprising (a) relatively feeding the wheel face into relative rubbing contact with the work surface of the workpiece, and said method being characterized by (b) utilizing a sensing means operatively disposed to sense the wheel face and to produce a signal when the wheel face has deteriorated a predetermined degree from the desired shape, (c) in response to each appearance of said signal and while said procedure (a) is being carried out, initiating and executing the following procedure (d) and (d1):
(d) moving the operative surface of a truing element into relative rubbing contact with the wheel face; and (d1) establishing conjointly, for a finite time period, the relative surface velocity and the relative infeed rate of said operative surface and wheel face to maintain the STE ratio within a predetermined range of values.

127. The method set out in claim 126 further characterized in that the finite time period for each execution of said procedure (d) and (d1) is ended when the truing element has been fed inwardly a predetermined increment after first making contact with the wheel face.

128. The method set out in claim 126 further characterized in that the finite time period for each execution of said procedure (d) and (d1) is ended after the lapse of a predetermined time interval from the instant at which the truing element makes contact with the wheel face.

129. The method set out in claim 126 further characterized in that after each execution of said procedure (d) and (d1), the truing element is moved to keep a gap between the wheel face and the operative surface of the truing element no greater than a predetermined distance, whereupon after the next appearance of said signal, the execution of said procedures (d) and (d1) requires that the truing element be moved relatively toward the wheel face no more than said predetermined distance to initiate said relative rubbing contact.

130. In a grinding machine having a rotationally driven grinding wheel relatively feedable into rubbing, grinding contact with a workpiece, and a truing element relatively feedable into rubbing contact with the wheel, a control system comprising, in combination (a) means for feeding the wheel relative to a workpiece to produce grinding action on the workpiece, (b) means for feeding the element relative to the wheel to produce truing action during time-spaced periods within a span of time during which said means (a) are continuously operating, and (c) means for conjointly controlling the relative surface speed and feed rate of said truing action to maintain the STE ratio of said truing action within a preselected range during each of said periods.

131. The combination set forth in claim 130 further including (d) means for controlling the feeding of said element to maintain a separating gap between said element and said wheel during the time intervals which separate said periods, said gap being no greater than a predetermined distance.

132. The combination set forth in claim 131 and further including (e) means for sequencing the feeding and positioning of said element relative to said wheel such that (i) said means (d) are active to maintain said gap while said means (a) are operating to grind the workpiece, then (ii) said element is fed into contact with the wheel, then (iii) said means (b) and (c) are active during one of said periods, and (iv) the sequence of (i), (ii) and (iii) is repeated.

133. The combination set forth in claim 130 further characterized in that said means (a) include means for terminating the truing action of each one of said periods when the wheel has been reduced in radius by a predetermined increment due to the truing action.

134. The combination set forth in claim 131 further including (e) means for closing said gap and initiating one of said truing action periods at instants equally spaced in time and demarking the ends of said intervals.

135. The combination set forth in claim 131 further including (c) means for closing said gap and initiating one of said truing action periods in response to the radius of the wheel having been reduced by a predetermined amount due to grinding action transpiring subsequent to the end of the previous one of said periods.

136. The method of grinding the work surface of a workpiece with a rotationally driven grinding wheel, said method comprising (a) feeding the grinding wheel face relative to the work surface and with relative rubbing contact to create grinding action, (b) simultaneously with procedure (a) feeding the operative surface of a conditioning element relative to the wheel face and with relative rubbing contact to create dressing/truing action which reduces the wheel radius at a rate greater than such reduction rate caused by the grinding action, and (c) conjointly controlling the relative feed rate and surface velocity of said truing/dressing action to vary and maintain the condition of the wheel face.

137. The method set out in claim 136 further characterized in that when it is desired to make the wheel face sharper or duller, either (i) the relative surface speed at the wheel face/operative surface interface is decreased or increased or (ii) the relative feed rate of said operative surface and wheel face is increased or decreased.

138. The method set out in claim 136 further characterized in that when it is desired to make the surface finish of the workpiece rougher or smoother, either (i) the relative surface speed at the wheel face/operative surface interface is respectively decreased or increased or (ii) the relative feed rate of said operative surface and wheel face is respectively increased or decreased.

139. The method set out in claim 136 further characterized in that said procedure (a) is carried out over a span of time on a given workpiece with rough and finish grinding during respectively earlier and later portions of the span, and during the later portion at least one adjusting action is taken from the following group:
(i) the relative surface speed of the truing/dressing action is increased from that created during the earlier portion of the span;
(ii) the relative infeed rate of said element and wheel is decreased from that created during the earlier portion of the span.

140. The method set out in claim 136 further characterized in that said procedure (c) includes determining the SGE
ratio of the grinding action and, in response to an increase or decrease of such ratio, performing at least one correcting action selected from the following group:
(i) decreasing or increasing, respectively, the relative surface speed of the rubbing at the wheel face and said operative surface;
(ii) increasing or decreasing, respectively, the relative feeding rate of the wheel and element.

141. The method set out in claim 136 further characterized in that said procedure (c) is carried out to maintain the STE ratio of the truing action substantially in agreement with a preselected set point value.

142. The method set out in claim 136 further characterized in that said procedure (c) is carried out to maintain the SGE ratio of the grinding action substantially in agreement with a preselected set point value.

143. The method set out in claim 141 further characterized in that said set point is adjusted to have relatively lower and higher values when said procedure (a) is creating rough and finish grinding action.

144. The method set out in claim 142 further characterized in that said set point is adjusted to have relatively lower and higher values when said procedure (a) is creating rough and finish grinding action.

145. The method of grinding the work surface of a workpiece by action of a rotationally driven grinding wheel, said method comprising (a) relatively feeding the workpiece and grinding wheel while creating relative rubbing contact between the work surface and the wheel face to effect grinding action and said method being characterized by (b) while said procedure (a) is in progress, relatively feeding the operative surface of a conditioning element into relative rubbing contact with said wheel face, and (c) conjointly establishing the relative surface speed and feed rate of said rubbing contact with said conditioning element to maintain the SGE
ratio of said grinding action within a predetermined range of values.

146. The method set out in claim 145 further characterized in that said procedure (c) is carried out by performing an action selected from the following group of actions when the SGE ratio (i) rises above or (ii) falls below said range:
ACTION 1: (i) decreasing or (ii) increasing the relative surface speed of the rubbing contact between the wheel face and said operative surface;
ACTION 2: (i) increasing or (ii) decreasing the relative feed rate of said rubbing contact between the wheel face and said operative surface.

147. The method set out in claim 145 further characterized in that said procedure (c) includes producing a signal which by direct or inverse proportionality reflects changes in the value of the SGE ratio for the grinding interaction occurring at the wheel face/work surface interface, and in response to changes in said signal adjusting the conjointly established relative surface speed and feed rate for the rubbing contact at the wheel face/operative surface interface in a direction to restore said signal to its original value.

148. The method set forth in claim 145 further characterized in that said predetermined range of values is changed from time to time.

149. The method set forth in claim 148 further characterized in that said predetermined range of values is selected to be relatively low for maintaining the wheel sharp during rough grinding of the workpiece and is changed to be relatively higher during finish grinding of the workpiece.

150. The method set forth in claim 145 further characterized in that said procedure (c) includes maintaining said SGE
ratio at least approximately equal to a predetermined but changeable set point value.

151. The method set forth in claim 150 further characterized in that when the SGE ratio of the grinding action at said wheel face/work surface interface tends to rise above or fall below the set point value, the relative surface speed of the rubbing contact between said wheel face and operative surface is respectively decreased or increased.

152. The method set forth in claim 150 further characterized in that when the SGE ratio of the grinding action at said wheel face/work surface interface tends to rise above or fall below said set point value, the relative feed rate of the rubbing contact between said wheel face and operative surface is respectively increased or decreased.

153. The method of grinding the work surface of a workpiece with a rotationally driven grinding wheel, said method comprising (a) feeding the grinding wheel face relative to the work surface and in relative rubbing contact therewith to create grinding action, and said method being characterized by (b) determining at least approximately the power PWRg applied in creating said grinding action, (c) determining at least approximately the rate M' of removal of material from the workpiece, (d) feeding the operative surface of a conditioning element relative to the wheel face and in relative rubbing contact therewith to create dressing/truing action, (e) utilizing said determined power PWRg and said determined rate M' to increase or decrease the STE ratio of said dressing/truing action when the ratio of said power to said rate rises or falls above or below a predetermined set point, thereby to maintain said last-named ratio at least approximately at said set point.

154. The method set out in claim 153 further characterized in that said set point is selected to be relatively lower and higher during rough and finish grinding of the workpiece.

155. The method set out in claim 153 further characterized in that said procedure (e) is carried out by feeding said conditioning element relative to the wheel face to make the radius reduction rate of the wheel due to dressing/truing action greater than the radius reduction rate of the wheel due to the grinding action, and said STE ratio is increased or decreased by respectively increasing or decreasing the relative surface speed of the rubbing contact between said wheel face and said operative surface.

156. The method of grinding a workpiece which lacks structural rigidity sufficient to withstand, without deleterious deflection, substantial forces imposed thereon by a grinding wheel, said method comprising (a) relatively feeding the workpiece and a rotationally driven grinding wheel into relative rubbing contact to create grinding action, and said method being characterized by (b) while said procedure (a) is in progress, relatively feeding the operative surface of a conditioning element into relative rubbing contact with the face of the wheel, and (c) conjointly establishing the relative surface speed and feed rate of said operative surface and said wheel face to maintain the SGE
ratio of said grinding action within a predetermined range of values.

157. The method set out in claim 156 further characterized in that said procedure (c) includes maintaining said SGE ratio at least approximately equal to a predetermined but adjustable set point.

158. The method set out in claim 157 further characterized in that said set point is adjusted to have first and second values respectively during rough and finish grinding of the workpiece, said first value being lower than the second.

159. The method set out in claim 156 further characterized in that said procedure (c) includes decreasing or increasing the relative surface speed of the rubbing contact between said operative surface and said face when said SGE ratio tends to rise above or fall below said predetermined range.

160. The method set out in claim 156 wherein said conditioning element is of Class I, and said predetermined range is selected to keep the ratio W'/TE' greater than 1.0, where W' and TE' are the volume per unit time rates of removal of materials from said wheel and element, respectively.

161. The method set out in claim 156 wherein said conditioning element is of Class II, and said predetermined range is selected to keep the ratio W'/TE' greater than 10.0, where W' and TE' are the volume per unit time rates of removal of materials from said wheel and element, respectively.

162. In a grinding machine having (1) a support adapted to hold a workpiece, (2) a rotatable grinding wheel with (i) means for rotationally driving the wheel, and (ii) means carrying said wheel and support to permit bodily relative motion of the two, (3) a wheel conditioning element with (i) means carrying the element and said wheel to permit bodily relative motion of the two, a control system comprising, in combination (a) means for controlling said means (2)(i) and (2)(ii) to relatively feed the wheel and the workpiece into rubbing contact to produce grinding action, (b) means, operative while said grinding action is occurring, for controlling said means (3)(i) to relatively feed the wheel and the element into rubbing contact to produce conditioning action, and (c) means for conjointly controlling the relative surface speed and the feed rate of said conditioning action to maintain the SGE of said grinding action within a preselected range of values.

163. The combination defined in claim 162 wherein said means (c) includes (c1) means for sensing physical parameters of the grinding action produced by said means (a) to create a signal which varies at least approximately in proportion to the SGE of such grinding action, and (c2) means responsive to said signal for correctively adjusting at least one of [i] the relative surface speed and [ii] the relative feed rate of the conditioning action produced by said means (b) in order to maintain said SGE within said preselected range.

164. The combination defined in claim 162 wherein said means (c) includes means for changing said preselected range from time to time.

165. The combination defined in claim 162 wherein said means (c) is constituted by means for conjointly controlling the relative surface speed and the feed rate of said conditioning action to maintain the SGE of said grinding action at least approxomately equal to a predetermined but changeable set point value.

166. The combination defined by claim 165 wherein said means (c) includes means for respectively decreasing or increasing said relative surface speed when said SGE tends to rise above or fall below said set point value.

167. The combination defined by claim 165 wherein said means (c) includes means for respectively increasing or decreasing said feed rate when said SGE tends to rise above or fall below said set point value.

168. The combination defined by claim 165 wherein said means (c) includes (c1) means for sensing physical parameters of the grinding action produced by said means (a) to produce a signal which varies in proportion to the ratio , where PWRg is the power expended to create the relative rubbing of said grinding action and M' is the rate of material removal from the workpiece as a result of the on-going grinding action, and (c2) means responsive to said signal for effecting said conjoint control.

169. The combination defined by claim 162 wherein said means (a) includes means for controlling the grind rate GR on the workpiece to maintain it substantially equal to a set point value.

170. The combination defined by claim 165 wherein said means (c) includes (c1) means for sensing physical parameters of grinding action produced by said means (a) to produce a signal which represents the actual SGE ratio of the grinding action, (c2) means for producing a set point signal SGEd, and (c3) means for effecting the control in response to the difference between said SGE and SGEd signal to return that difference substantially to zero.

171. The method of grinding a workpiece with a rotationally driven grinding wheel having an active face peripherally concentric about the axis of rotation, said method comprising (a) relatively feeding the wheel and workpiece to keep the wheel face and the work surface of the workpiece in relative rubbing contact to create grinding action, at least a part of said feeding being infeeding, and said method being characterized by (b) while said procedure (a) is taking place, relatively infeeding the operative surface of a conditioning element into relative rubbing contact with said wheel face, said operative surface conforming to the desired shape for the wheel face, (c) while said procedures (a) and (b) are taking place, sensing with a gage the operative surface of said element to develop a first signal representing the dimension (Rte) between a reference mark on the element and said operative surface, said dimension lying along or parallel to a line passing through the wheel axis and perpendicular to the operative surface at the point of wheel/element rubbing contact, (d) while said procedures (a) and (b) are taking place, sensing, and representing by a second signal, the positional distance (Pts) from said wheel axis to said reference mark, said distance lying along or parallel to said line, and (e) utilizing said first and second signals to determine the algebraic difference (Pts - Rte) between said distance and said dimension as a representation of the radius (Rw) of said wheel as the latter wears.

172. The method defined by claim 171 wherein said procedure (b) is executed to maintain the STE of the conditioning action within a predetermined range of values.

173. The method defined by claim 171 wherein said procedure (b) is executed to maintain the SGE of said grinding action within a predetermined range of values.

174. The method defined by claim 171 further characterized in that said difference is utilized in controlling said procedure (b) to maintain, by conjoint control of relative rubbing surface speed and feed rate, the STE of the conditioning action within a predetermined range of values.

175. The method defined by claim 171 further characterized in that said difference is utilized in controlling said procedure (b) to maintain, by conjoint control of relative rubbing surface speed and feed rate at the wheel/element interface, the SGE of said grinding action within a preselected range of values.

176. The method defined by claim 171 wherein said procedure (b) is executed with a Class I conditioning element and the truing ratio TR of the conditioning element is controlled to be no less than 1.0, whereby the gage employed in said procedure (c) may be one of limited range in comparison to an in-process workpiece sensing gage.

177. The method defined by claim 171 wherein said procedure (b) is executed with a Class II conditioning element and the truing ratio TR of the conditioning element is controlled to be no less than 10.0, whereby the gage employed in said procedure (c) may be one of limited range in comparison to an in-process workpiece sensing gage.

178. The method defined by claim 171 wherein said procedure (b) is executed with a conditioning element made of metal or metal alloy and with the STE of the conditioning action controlled to be less than 0.5 HP/in.3/min. during at least a major portion of the time span over which a workpiece is ground as a result of said procedure (a).

179. The method of grinding a workpiece with a rotationally driven grinding wheel having an active face peripherally concentric about the axis of rotation, said method comprising (a) relatively feeding the wheel and workpiece to keep the wheel face and the work surface of the workpiece in relative rubbing contact to create grinding action, at least a part of said feeding being infeeding, and said method being characterized by (b) while said procedure (a) is taking place, relatively infeeding the operative surface of a conditioning element into relative rubbing contact with said wheel face, said operative surface conforming to the desired shape for the wheel face,

Claim 179, page 2, (c) while said procedures (a) and (b) are taking place, sensing with a gage the operative surface of said element to develop a first signal representing the dimension (Rte) between a reference mark on the element and said operative surface, said dimension lying along or parallel to a line passing through the wheel axis and perpendicular to the operative surface at the point of wheel/element rubbing contact, (d) while said procedures (a) and (b) are taking place, sensing, and representing by a second signal, the positional distance (Pts) from said wheel axis to said reference mark, said distance lying along or parallel to said line, (e) while said procedures (a) and (b) are taking place sensing, and representing by a third signal, the positional length (Pws) from a reference mark on the workpiece to the wheel axis, said length lying along or parallel to a line passing through the wheel axis and perpendicular to the ground surface of the workpiece at the point of wheel/workpiece rubbing contact, and (f) utilizing said first, second and third signals to determine by algebraic combination (Pws - Pts + Rte) the dimensional size (Rp) of the workpiece from said reference mark to the ground surface along or parallel to said last-named line, despite wear reduction in the radius (Rw) of said wheel.

180. The method defined by claim 179 wherein said procedure (b) is executed to maintain the STE of the conditioning action within a predetermined range of values.

181. The method defined by claim 179 wherein said procedure (b) is executed to maintain the SGE of said grinding action within a predetermined range of values.

182. The method defined by claim 179 further characterized in that said dimensional size (Rp) determined from said algebraic combination is utilized in controlling said procedure (b) to maintain, by conjoint control of relative rubbing surface speed and feed rate at the wheel/element interface, the SGE of said grinding action within a preselected range of values.

183. The method defined by claim 179 wherein said procedure (b) is executed with a Class I conditioning element and the truing ratio TR of the conditioning element is controlled to be no less than 1.0, whereby the gage employed in said procedure (c) may be one of limited range in comparison to an in-process workpiece sensing gage.

184 . The method defined by claim 179 wherein said procedure (b) is executed with a Class II conditioning element and the truing ratio TR of the conditioning element is controlled to be no less than 10.0, whereby the gage employed in said procedure (c) may be one of limited range in comparison to an in-process workpiece sensing gage.

185. The method defined by claim 179 wherein said procedure (b) is executed with a conditioning element made of metal or metal alloy and with the STE of the conditioning action controlled to be less than 0.5 HP/in.3/min. during at least a major portion of the time span over which a workpiece is ground as a result of said procedure (a).

188. The method of grinding a workpiece with a rotationally driven grinding wheel having an active face peripherally concentric about the axis of rotation, said method comprising (a) relatively infeeding the wheel and the workpiece to keep the wheel face and work surface of the workpiece in relative rubbing contact to create grinding action, and said method being characterized by (b) while said procedure (a) is taking place, a relatively and bodily infeeding the wheel and a conditioning element to create relative rubbing contact of the wheel face and the operative surface of said element, said operative surface conforming to the desired shape for the wheel face, (c) while said procedures (a) and (b) are taking place, sensing with a gage the operative surface of said element to develop a first signal representing the rate of reduction (R'te) in the size of said element as measured in a direction parallel to the infeeding of the wheel and element.

Claim 186, page 2, (d) while said procedures (a) and (b) are taking place, creating a second signal to represent the bodily infeed rate (Fts) caused by said procedure (b), and (e) utilizing said first and second signals to determine the algebraic difference (Fts - R'te) between said bodily infeed rate and said reduction rate as a representation of the rate (R'w) at which the wheel radius is being reduced.

187. The method set out in claim 186 further including (g) producing a desired grind rate GR (namely, the rate at which the workpiece size is reduced in a direction parallel to the infeeding of the wheel and workpiece) by controlling the infeed rate (Fws) of procedure (a) to make it substantially GR plus said difference (Fts - R'te).

188. The method set out in claim 186 further characterized in that said difference is utilized in controlling said procedure (b) to maintain the STE ratio of the wheel/element rubbing action within a preselected range of values.

189. The method set out in claim 186 further characterized in that said conditioning element is made of a metal or metal alloy and said procedure (b) is executed to make the truing ratio TR, produced by the wheel-element rubbing contact, at least 10Ø

190. The method of grinding a workpiece with a grinding wheel rotationally driven about its axis while accurately knowing the radius of the wheel face for workpiece size control sans any in-process workpiece sensing gage, said method comprising (a) supporting the workpiece and wheel for relative infeeding motion along a First line which lies normal to the wheel rotation axis, and infeeding the rotating wheel to create grinding action, and said method being characterized by (b) supporting a cylindrical conditioning element for rotation about its axis and for infeeding motion relative to said wheel along a second line joining the wheel axis and element axis, said element having an operative surface concentric about its axis and conforming to the desired shape for the wheel face, (c) during execution of said procedure (a), rotationally driving said element and infeeding it relative to the wheel to create rubbing contact which wears the wheel face and reduces its radius, said latter radius reduction occurring at a rate greater than that arising from said grinding action, (d) employing a gage to sense the surface of said element and to produce a first signal representing the element radius Rte and (e) creating a second signal to represent the changing distance Pts between the axes of the wheel and element as they are infed relatively, and (f) utilizing the difference between said second and first signals as a representation of the radius Rw of the wheel.

191. The method set out in claim 190 further characterized in that said conditioning element is made of a metallic material and said gage is an electrical proximity gage operating on an inductive effect.

192. The method set out in claim 190 further characterized in that said procedure (c) includes conjointly controlling the relative infeed and relative surface velocity of said rubbing contact to make the ratio greater than 10.0 and the element radius Rte reduces relatively little in comparison to a given reduction in the radius Rw of the wheel, whereby said gage may function within a limited operative range without motion or readjustment relative to said element's axis of rotation.

193. The method of grinding a cylindrical work surface on a workpiece by action of a grinding wheel rotationally driven about its axis, said wheel having a face concentric about that axis, said method comprising (a) rotating the workpiece about the work surface axis, (b) relatively infeeding the wheel and workpiece along a first linear path extending through the work surface axis and the wheel axis to create relative rubbing contact of the wheel face and work surface and thus produce grinding action, said method being characterized by (c) while said procedures (a) and (b) are in progress, rotating a cylindrical conditioning element about its axis, said element having an operative surface concentric about that axis and conforming to the desired shape for the wheel face,

Claim 193, page 2, (d) relatively infeeding said element along a second linear path extending through the wheel axis and the roll axis to create relative rubbing contact which wears down the wheel face at a rate greater than wear arising from the grinding action, (e) employing a proximity gage to sense the roll surface and create a signal Rte indicative of the roll radius, (f) employing a position sensing means to create a signal PtS
representing the distance between the element axis and the wheel axis along said second path, whereby the difference Pts - Rte dynamically represents the wheel radius Rw as the latter changes, (g) employing a position sensing means to create a signal Pws representing the distance between the workpiece axis and the wheel axis along said first path, and (h) determining the apparent work surface radius Rp by using said signals Rte, Pts and Pws according to the relation Rp=Pws-Pw-Pws=Pts + Rte

194. The method set out in claim 193 further characterized in that the infeeding of procedure (b) is terminated when the determined radius Rp reduces to a predetermined value.

195. The method of grinding a workpiece with a grinding wheel rotationally driven about its axis, said wheel having a face peripherally concentric about that axis, said method comprising (a) relatively feeding the wheel and workpiece to keep the wheel face and the work surface of the workpiece in relative rubbing contact to create grinding action, at least a part of said feeding being infeeding, and said method being characterized by (b) while said procedure (a) is taking place, relatively feeding a conditioning element and the wheel to keep the wheel face and the operative surface of the element in relative rubbing contact, at least a part of said feeding being infeeding, said operative surface conforming to the desired shape for the wheel face, (b1) said conditioning element being made of a material and the surface velocity and feed rate of the element's rubbing contact being selected to result in negligible wear on said operative surface, and said element having a measured dimension (Rte) between a reference mark thereon and said operative surface, said dimension lying along or parallel to a line passing through the wheel axis and perpendicular to the operative surface at the point of wheel/element contact, (c) representing by a first signal said dimension (Rte), (d) while said procedures (a) and (b) are taking place, sensing, and representing by a signal, the positional distance (Pts) from said wheel axis to said reference mark, said distance lying along or parallel to said line, and (e) utilizing said first and second signals to determine the algebraic difference (Pts - Rte) between said distance and said dimension as a representation of the radius (Rw) of said wheel as the latter wears.

196. The method set out in claim 195 further characterized in that said conditioning element is made of natural or synthetic diamond chips set in a supporting matrix and the relative surface speed (Sr) of its rubbing contact with said wheel is less than 3000 s.f.m.

197. The method defined by claim 195 wherein said procedure (b) is executed to maintain the STE of the conditioning action within a predetermined range of values.

198. The method defined by claim 195 wherein said procedure (b) is executed to maintain the SGE of said grinding action within a predetermined range of values.

199. The method defined by claim 195 wherein said difference is utilized in controlling said procedure (b) to maintain, by conjoint control of relative rubbing surface speed and feed rate, the STE
of the conditioning action within a predetermined range of values.

200. The method defined by claim 196 further characterized in that said difference is utilized in controlling said procedure (b) to maintain, by conjoint control of relative rubbing surface speed and feed rate at the wheel/element interface, the SGE of said grinding action within a preselected range of values.

201. The method defined by claim 195 further including utilizing said representation of wheel radius to control the extent of infeeding by said procedure (a).

202. The method of grinding a workpiece with a grinding wheel rotationally driven about its axis, said wheel having a face peripherally concentric about that axis, said method comprising (a) relatively feeding the wheel and workpiece to keep the wheel face and the work surface of the workpiece in relative rubbing contact to create grinding action, at least a part of said feeding being infeeding, and said method being characterized by (b) while said procedure (a) is taking place, relatively feeding a conditioning element and the wheel to keep the wheel face and the operative surface of the element in relative rubbing contact, at least a part of said feeding being infeeding, said operative surface conforming to the desired shape for the wheel face, (b1) said conditioning element being made of a material and the surface velocity and feed rate of the element's rubbing contact being selected to result in negligible wear on said operative surface, and said element having a measured dimension (Rte) between a reference mark thereon and said operative surface, said dimension lying along or parallel to a line passing through the wheel axis and perpendicular to the operative surface at the point of wheel/element contact, (c) representing by a first signal said dimension (Rte), (d) while said procedures (a) and (b) are taking place, sensing, and representing by a signal, the positional distance (Pts) from said wheel axis to said reference mark, said distance lying along or parallel to said line, (e) while said procedures (a) and (b) are taking place, sensing and representing by a third signal the positional length (Pws) from a reference mark (24a) on the workpiece to the wheel axis (20a), said length lying along or parallel to a line passing through the

Claim 202, page 2, the wheel axis and perpendicular to the ground surface of the workpiece at the point of wheel/workpiece rubbing contact, and (f) utilizing said first, second and third signals to determine by algebraic combination (Pws - Pts + Rte) the dimensional size (Rp) of the workpiece from said reference mark to the ground surface along or parallel to said last-named line, despite wear reduction in the radius (Rw) of said wheel.

203. The method defined by claim 202 further characterized in that said conditioning element is made of natural or synthetic diamond chips set in a supporting matrix and the relative surface speed (Sr) of its rubbing contact with said wheel is less than 3000 s.f.m.

204. The method defined by claim 202 wherein said procedure (b) is executed to maintain the STE of the conditioning action within a predetermined range of values.

205. The method defined by claim 202 wherein said procedure (b) is executed to maintain the SGE of said grinding action within a predetermined range of values.

206. The method defined by claim 202 wherein said dimensional size (Rp) determined from said algebraic combination is utilized in controlling said procedure (b) to maintain, by conjoint control of relative rubbing surface speed and feed rate at the wheel/element interface, the SGE of said grinding action within a preselected range of values.

207. The method defined by claim 202 further characterized in that said procedures (a) and (b) are terminated with respect to a given workpiece when said determined dimensional size (Rp) is reduced to a predetermined value.

208. The method of grinding a workpiece with a rotationally driven grinding wheel having an active face peripherally concerntric about the axis of rotation, said method comprising (a) relatively infeeding the wheel and the workpiece to keep the wheel face and work surface of the workpiece in relative rubbing contact to create grinding action, and said method being characterized by (b) while said procedure (a) is taking place, relatively and bodily infeeding the wheel and a conditioning element to create relative rubbing contact of the wheel face and the operative surface of said element, said operative surface conforming to the desired shape for the wheel face, (b1) said element being made of a material and the surface velocity and feed rate of the element's rubbing contact being selected to result in negligible wear on said operative surface and negligible rate of change in the element's size, (c) while said procedures (a) and (b) are taking place, creating a signal to represent the bodily infeed rate (Fts) caused by said procedure (b), and (d) utilizing said signal (Fts) as a representation of the rate (R'w) at which the wheel radius is being reduced.

209. The method set out in claim 208 further characterized in that said conditioning element is made of natural or synthetic diamond chips set in a supporting matrix and the relative surface speed (Sr) of its rubbing contact with said wheel is less than 3000 s.f.m.

210. The method set out in claim 208 further including (e) controlling the infeed rate (Fws) of said procedure (a) to make it substantially equal to the rate represented by said signal (Fts) plus a desired grind rate (GR), thereby to obtain a desired grind rate (GR) at the workpiece (where grind rate means the rate at which the workpiece size is reduced in a direction parallel to the infeeding of the wheel and workpiece).

211. The method set out in claim 208 further characterized in that said difference is utilized in controlling said procedure (b) to maintain the STE ratio of the wheel/element rubbing action within a preselected range of values.

212. The method set out in claim 210 wherein said conditioning element is made of natural or synthetic diamond chips set in a supporting matrix.

213. The method set out in claim 210 wherein said conditioning element and grinding wheel fall in Class III and the relative surface speed of the rubbing contact produced by said procedure (b) is controlled to be less than 3000 s.f.m.