CA1138073A - Tension control of fasteners - Google Patents

Abstract

ABSTRACT OF THE DISCLOSURE
There is disclosed a technique for tightening threaded fasteners in which values of offset torque, initial tension rate relative to angle advance, final tension rate relative to angle advance and other joint related factors are empirically determined by instrumenting a plurality of fasteners of the type ultimately to be tightened. In one embodiment, torque and angle of advance are monitored during the tightening of production fasteners.
Calculations are conducted, while tightening, of the ratio of the torque and the torque rate of the fastener being tightened to determine the tension prevailing in the bolt at a particular angle of advance. By using the calculated tension value and the particular angle of advance, an instantaneous position of thread-ing advance on the tension-angle curve of the fasteners is established. From this instantaneous position, it is determined how much greater angle of advance or how much torque is required to tighten the fasteners to a final desired tension value. The same technique is also used merely to monitor tightening which is terminated by a different tightening strategy. In another embodiment, analog devices are utilized to convert sensed values of torque and the rate of threading advance into parameters which control tool shut off.

Description

This application is a divisional of copending Canadian patent application serial No. 284,293 filed on August 8, 1977 by Rockwell International Corporation.
This invention relates to a technique for tightening threaded fasteners. The func~ion of threaded fasteners is, of course, to unite two or more pieces into a typically rigid part called a joint. For purposes of convenience, the term fastener pair may be used to designate male and female threaded members, e.g. a nut and bolt, bolt and internally threaded hole oE a joint part, threaded stud and nut, and the likeO The connected pieces of a joint should be so tightened as to remain in contact during vibration, static and/or dynamic loading of the part. In many applications where several threaded fasteners are used, it may be of substantial importance to assure that the contact pressure between the pieces created by the ~asteners is uniform since non-uniform deflection of the pieces may create unacceptable joint conditions. Proper assembly should produce uniform contact pressures from joint to joint in accordance with design require-ments. This can be achieved only by assembly procedures that produce uniform joint preload or clamping load. Although it is conceivable to determine join~ preload or clamping load in terms of compression of a nut, it is more practical to deal in terms of bolt tension. There is, unfortunately, no direct technique for measuring bolt load externally without instrumenting the bolt or using a load washer which are either impractical or uneconomic for assembly line production. Accordingly, all practical techniques of bolt tension control in production quantities ar~
inferential.

~1 3t~3 There are a number of well known techniques for tiyhtening threaded fasteners based on information available from external instruments such as torque and angle sensors as contrasted to specially designed fasteners or load washers. Included in these techniques are torque control, turn-of-the-nut method, the yield point method, acoustic measuring, overrunning schemes and torque rate methods.
One of the present techniques in wide use is torque control in which a constant final torque is applied to the fasteners. Final torque is typically produced by a stall air tool and the degree of torque control depends on the uniformity of air pressure, motor performance and the hardness of the joint.
The intention is to achieve tension scatters in the range of +
10-20~ about the mean. The actual scatter limits can only be verified by instrumenting the bolts in a laboratory environment.
Opinions vary on what tension scatters are actually present in large quantities of fasteners tightened with torque control methods. It would not be surprising to learn that total tension scatter in production quantities are on the order of 100% of mean which can be caused by a + 41% scatter in friction alone.
Torque is, of course, related to tension but the relation-ship is subject to large uncertainties resulting from a first order dependence on thread and head friction. In the simplest theoretical consideration, the following equation describes the relation of torque and tension:
T = (fhrh + fthrth) (1) where T is torque, fh is the coefficlent of friction between the ~ 3~

fastener head and the abutting piece, rh is the effective radius of head friction, fth is the coefficient o friction between the threads of the fastener, rth is the effective radius of thread friction and F is bolt tension. Although the mean value of the coefficients of friction can be substantially reduced by lubricants and coatings, the relative scatter about the mean value cannot be substantially affected. Combining the friction uncertainties with the variations in applied torque, the tension control actually achieved in practice is quite poor.
Accordingly, in order to minimize fastener failures during assembly, the mean torque must be designed at unreasonably low levels as co~pared with the strength of the bolt. Even with unreasonably low mean torque values, a significant proportion of the fasteners are woefully understressed while many have been stressed past the elastic limit.
Discussion of torque control methods of tightening threaded fasteners are found in Assembl~ Engineering, Octoher 1966, pages 24-29; Hydrocarbon Processiny, January 1973, pages 89-91; Machine Design, March 6, 1975, pages 78-82; The Engineer, London, May 26, 1967, pages 770-71; The Iron Age, February 24, 1966r page 66; Machine Design, February 13, 1964, pages 180-35;
Power Engineerillg, October 1963, page 58; and United States patents 3,555,938 and 3,851,386.
Another widely used technique for tightening threaded fasteners is called the turn-of-the-nut method which makes use of the applied torque as well as the angle of threadiny advance. In its simplest form, the technique is to advance the fasteners ~;3~

until a predetermined torque value is reached, for example snug torque, and then turn -the nut an additional constant predetermined angle. The concept is that the relation of -the turn of the fastener to the strain of the bolt will eliminate the influence of friction on the final deslred tension value.
If the clamped pieces were purely elastic and contact between them were immediate and perfect, one would expect the bolt tension to increase linearly with unit angle of advance starting with the value of zero at the onset of contact. In theoryl tension control would be as accurate as the uniformity of the joint tension rate which is the slope of the curve obtained by plotting tension against angle of advance.
In practice, the tension rate is not exactly a constant from joint to joint nor is it uniform as a function of angle for any single joint. The reasons are related to microplasticity which is the yield o~ surface irregularities in the moving fastener components, lubricant squeeze film, and the fact that contact is gradual rather than immediate. The turn-of-the-nut method is customarily considered to be substantially superior to the torque control technique although data developed during the investigation of this invention suggests that this method is substantially overrated, at least at low to moderate tension values~ The turn-of-the-nut method does have the di~advantage of partly relying on torque which is subject to the large uncertainties previously discussed. The selection of the threshold torque is a critical decision. If threshold torque is too high, the theoretical advantage over the torque control method is substantially reducedO If threshold torque is too low, final bolt tension will fluctua-te greatly from joint to joint, since at low torque values, both the torque-angle and tension~
angle curves have varying curvature. The comb.ination of uncertain tension at the threshold torque and nonuniformity of tension rate in a large angle span will more than offset the theoretical advantage gained. The turn-of-the nut method, being essentially a strain approach to tightening has the advantage of reducing substantially the rate of bolt failure during assembly hecause very large strains can be sustained by the bolt material in the plastic zone. During the investigation of this invention it has been learned that the difference between low torque rate fasteners and high torque rate fasteners from the same sample can develop a scatter in the final desired tension value of + 50% at tension values in the range of 3000 pounds for a ~/16 " - 24, grade 8 bolt using the turn-of-the-nut method. As the final tension value .increases, the scatter reduces as a percentage of final tension.
Another difficulty wi~h turn-of-the-nut methods is that recalibration is required when the final desired tension value is changed. This is in contrast to this invention where the final desired tension value can be changed at will so long as this value is in the second tension rate range and is sufficiently far from the break in the tension curve so that the tool will not~
run past the desired value because of tool overrun.
Discussion of turn-of-the-nut methods of tightening threaded fasteners are found in Hydrocarbon Processing, January 1973, pages 89-91; Machine Design, March ~, 1975, pages 78-82;

'73 Journal of the Structural Division, Proceedings of the American Society of Civil Engineers, April 1966, pages 20-40; Machine Design, February 13, 1964, pages 180-85; and United States patent 3,851,386.
As pointed out in some detail in United States patents 3,643,501 and 3,693,7~6, and Design Engineering (London), January 1975, pages 21-23, 25, 27, 29, another approach ~or tightening threaded fasteners is known as the yield point method.
In this approach, an attempt is made during tightening to sense the onset of plastic elongation of the bolt and terminate tightening in response thereto. The yield point, which is the boundary between the elastic and plastic deformation zones of a metal in a uniaxial state of stress, is quite difficult to determine precisely. Accordingly, the yield point is customarily defined in terms of an offset strain, typically ol - .2~, which is arbitrarily chosen.
It is apparent that a point is made up of the clamped piece~ as well as the fasteners. The design is usually such that yielding occurs in the bolt although it could conceivably occur in the bolt head or nut. The bolt is also subject to shear as a result of torsion created by the turning moment or torque.
Accordingly, the bolt is in a combined state of stress. Thus, at high torque values, the stress in the bolt is due to both torque , and tension and can substantially alter the tensile strength of a particular specimen. Additional errors may be introduced when the goal is bolt tension control due to natural scatters in the material yield point. Other errors involved in yield point " .

methods are the result of noise and other uncertainkies in consistently sensing the yield point. The main objection to the yield point method is the concern over the fatigue strength and reusability of the bolt. Although the matter is subject to some controversy, it appears clear that one time application and release of an external load will cause relaxation of ~he joint and accordingly reduce -the clamping for_e applied by the bolt below the original clamping force. In extreme cases, the bolt may lose all tension and be loose.
An overrunning approach which may be used to detect galled threads or cross threaded members is disclosed in United States patents 3,368,396 and 3,745,820. In this technique, a warning signal is produced when a predetermined torque is developed before a given number of turns has been effected which may be indicative of galled threads. A different warning signal is produced when a larger num~er of turns are effected before the development o~ a desired higher torque is obtained which is suggestive of cross threading. It will be apparent that these approaches are not designed to control bolt tension.
Another approach for controlling bolt tension involves acoustic devices which attempt to measure the elongation in a bolt caused by tension. Such devices are discussed and illustrated in United States patents 3,306,100; 3,307,393;
3,650,016; 3,759,090 and 3,822,587.
Another technigue related to yield poin-t methods is found in United States patent 3,939,920. This technique basically is to measure a tightening parameter, e.g. torque, at the yield '7~

point, conduct certain calculations and back off the nut until the final desired axial stress is achieved and terminate tighten-ing. There are several defects to such a technique: (]) yield point is not a closely reproducible characteristic of most production fasteners, (2) the yield point is difficult to consistently sense by the disclosed technique, (3) the joint properties, i.e. tension rate and torque rate, are not the same during the first advance toward the yield point as during a subsequent advance toward the yield pointt and (4) the properties o~ the fastener pair, particularly adjacent the threads, have been permanently altered at the yield point.
Another group of prior art techniques which have been suggested involve a consideration o-E the rate o~ torque increase relative to the angle of threading advance as disclosed in Assembly Engineering, September 1974l pages 42-45; Design Engineering (London), January 1975, pages 21-23, 25, 27, 29; Iron Age, April 28, 1975, page 44; and Machine Design, Vol. 47, January 23, 1975~ page 44. These techniques monitor the torque-angle curve during the tightening process in order to terminate tightening in response to conclusions derived from the torque-angle relationship. In the Design Engineering disclosure, tightening is terminated upon sensing a significant drop in th~
torque rate, which occurs at the yield point. In the remaining articles, tightening is apparently terminated when a predetermined torque range is attained within a ~airly narrow angle range.
These disclosures are thus similar to the overrunning schemes mentioned above.

,. ~ , 1~l.3&1~'73 The goal of inferential tightening techniques is not merely to achieve a predetermined clamping load on one set of fasteners, since this can be readily done in the laboratory by instrumenting the bolt. The goal is to achieve consistent and reproducible clamping loads or final tension values in large lots of fasteners at a low cost per fastener. Thus, the major fallacy in prior art inferential tightening techniques has been to select a fixed tightening parameter, such as torque or angle in the torque control and turn~to-the-nut methods respectively, or a fixed range of a particular tightening parameter and terminate tightening in response to the attainment of the fixed tightening parameter or the range thereof. This broad approach of the prior art has several major difficulties. First, the critical item in tightening is clamping load as may be measured ~y final bolt tension. With the possible exception of some o the acoustic methods, no one has apparently heretofore been able to inferentially determine final bolt tension in production quantities. Second, because of the selection of some parameter other than tension, there is introduced such widely variable factors as friction coefficients, speed related losses, and the like which grossly affect the relationship between the fixed tightening parameter or the fixed range thereof and the only important result in tightening, which is clamping load or bolt tension.

_ g _ ~ 3~

It is an o~ject of the presen-t invention to provide an improved method and apparatus for tightening threaded fasteners.
According to one aspect of the present invention, there is provided a method of tightening seriatim a multiplici-ty of substantially identical pairs of threaded fasteners comprising tightening the fastener pairs with a powered tool; establishing a final tightening parameter; predicting an amount of tool overrun, variable from one fastener pair to the next, at the termination of tightening; and instructing the tool to terminate tightening of each fastener pair in response to the difference between the final tightening parame-ter value and the amount of predicted tool overrun.
According to another aspect, there is provided apparatus for tightening seriatim a multiplicity of substantially identical pairs of threaded fasteners toward a final tightening parameter comprising a powered tool for tightening each fastener pair;
means for predicting an amount of tool overrun, variable from one fastener pair to the next, at the termination of tightening; and ~.31~3 means for instructing the tool to terminate tightening of each fastener pair in response to the difference between the final tightening parameter value and the amount of predicted tool overrun.
According to a further aspect, there is provided a method for monitoring the tightening of a joint including at least one threaded fastener pair, comprising tightening the fas-tener pair beyond the yield point thereof; sensing torque and not load applied to the fastener pair at various angles of advance;
determining, from the sensed values, the stress appearing in one of the fasteners at the termination of tightening at a stress value adjacent the fastener yield poin-t which stress differs from ~he nominal strength of the one fastener and which varies from joint to joint.
The invention will now be described in greater detail with reference to the accompanying drawings, in which:

Figure 1 is an .illustration of typical torque-angle and tension-angle curves generated during the continuous tightening of a fastener pair far beyond the elastic limit;
Figure 2 is an enlarged illustration of the low end of a typical torque-angle curve where tightening is temporarily suspended at the upper end thereof;
- Figure 3 is an illustration of a typical torque-speed relationship of an air powered tool;
Figure 4 is an illustration of a tension-angle curve representative of the relaxation of a typical joint at the termination of continuous tightening;
Figure 5 is an illustration of typical tension-angle curve representative of the relaxation of the joint at a mid-point stop during tightening to a higher tension value;

Figure 6 is an illustration similar to Figure 1 graphically explaining another facet of the invention;
Figure 7 is an enlarged illustration of torque and tension curves graphically explaining another facet of the invention;
Figure 8 is a schematic view of the mechanism of this inventlon;
Figure 9 is a side view of a component of the mechanism of Figure 8;
Figures lOA and lOB are circuit diagrams of another component of Figure 8;
Figure 11 is a front view of a typical operator's console;
and Figure 12 is a block diagram of another mechanism of this invention .
Referring to Figure 1, there is illustrated a typical torque-angle curve 10 and its corresponding tension-angle curve 12 which are developed during the continuous threading of a fastener pair to a point far beyond the elastic limit of the bolt, as may be measured in the laboratory from suitable equipment. In the torque curve 10, there is typically a free running region or period 14 where only a small torque is required to advance the nut and no appreciable bolt tension exists. This is followed by an engagement period or region 16 where the contact between the surfaces of the fastener and the clamped pieces are being established while the rate of angle advance is gradually being reduced according to the torque-speed characteristics of the tool employed. The tension rate FRl in the region 16 is less than the ultimate tension rate FR2 but is rather well defined.
The engagement region 16 appears to cover an approximate tension range of about ten percent to about Eifty percent of the elastic limit of the bolt. Above the enyagement region is a final tensioniny region or period 18 which exhibits the increased tension rate FR2. Fortunately, FRl, FR2 and the location of the bend therebetween are well defined and reproducible properties of the joint and are not related to friction or other variable factors which may develope in the course of tightening.
The torque rate TR is initially quite low in the free running region 14 and begins to rise substantially during the engagement period 16. Due to the existence of speed-dependent losses such as lubricant squeeze film and microplasticity of the surface irregularies between the fastener parts and clamped pieces, a linear approximation TR of the torque curve 10 in the region 16 does not intersect the angle axis at the point of origin of the tension curve 12. An offset angle ~os exists which is proportional to such speed-dependent losses. Because of the torque-speed curve of the tool employed, it can be shown that ~os is torque rate dependent so that the offset torque ToS is the appropria~e joint property and Tos is the product of the offset angle ~O$ and the torque rate TR.
The elastic limit 20 occurs at a polnt beyond which strain is not recoverable upon unloading and appears toward the upper end of the final tightening region 18 as is well known in classical mechanics. Somewhere in the yield region 22, the bolt commences to deform plastically rather than elastically. As all~lded to previously, the normal definition of the yield point is in the range oE .1-.2~ strain which is somewhat arbitrary.
The proportional limit occurs substantially below the yield point 20 and occurs where the stress/strain ratio is no longer constant.
In order to implement the hereinafter disclosed method of torque control, one needs to determine FRl, FR2, ToS and other parameters as discussed more fully hereinafter. This i5 conveniently accomplished by selecting a reasonably large sample of the fasteners that ultimately will be tightened by the technique of this invention and empirically determining the values in the laboratory. It will normally be experienced that scatters in FRl, and either FR2 or r, the ratio of FR2/FRl, will be quite small~ In new bolts, FR2 is normally 5-15% higher than FRl. In fasteners that have been tightened previGusly, FR2 is normally quite close to FRl. The conclusion is that the differ~
ence between FRl and FR2 is related to the microplasticity of surface irregularities hetween the mating faces of the joint.
As is true in all torque measurements, Tos will have much larger scatters. Fortunately, the offset torque correction is normally quite small so that its lack of consistency has a quite minimal effect on the final tension values. One exception is in the use of so-called "prevailing-torque" fasteners which usually comprise a bolt or nut having the threads intentionally deformed for various reasons. Another exception involves the use of a bolt or nut in which the threads are unintentionally deformed.
In such situations, the normal value of ~os should be increased by the addition of the measured "free-running" torque.
~ roadly, the technique of this invention is to periodically or continuously sense the torque applied to the fastener pair and the angle of advance corresponding to the sensed torque, determine the -tension appearing at least at one point 24, calculate a value of a tightening parameter sufficient to achieve a final desired tension value FD and instruct a tool to advance the fastener pair until the attainment of the tightening para-meter.
During a study of torque-tension-angle relationship~, it was discovered that the inverse of the rate with respect to angle of the logarithm of torque is theoretically a measure of bolt tension irrespectlve of joint friction. Defining, P da LOG T, (2) F p ,~>ap ~3) ap is the angle where P achieves a maximum value and conceivably could be used as the origin for the turn-of the-nut method thereby totally eliminating the influence of joint friction. In practice, it is difficult to detect a single meaningful peak which can be labelled ap because of the noise inherent in the ~0 actual torque-angle signal. Although the concept expressed in equation (2) is valid, it requires a different procedure for processing the torque-angle data to achieve a practical solution.
As will be apparent to those skilled in the art, the solution may be analog, rather than digital, as hereinafter disclosed~ The theoretical basis for equation (2) can be derived from equation (1), as follows:

a~ i 3 T = (fhrh ~~ f~hrth) (1) differentiating equation (1) relative to angle, da (fhrh + fthrth) da (4) dividing equation (4) by equation (1), dT/da dF/da ~5) T F
Since dT/T is the definition of d log T, dF/d~ = d LOG T t6) if ddF, the joint tension rate, is a constant, then:
F = (d ) (d- LOG T) 1 = FR/P (7) Equation (7) shows that the constant of proportionality in equation (3) is the tension rate FR.
Several assumptions have been made in the above derivation:
1~ The tension rate is a constant. This is not precisely true throughout the tightening range. The more preclse assumption would have been that tension at any angle of advance aftPr the angle of origin ! where the tension rate commences, is a unique function of the joint and therefore that the tension rate at any, angle after the angle of origin is a unique function of the joint.

2) Torque is not a function of the turning speed. This is not strictly true and for accurate application, it should be accounted for.

3) Joint ~riction (fhfth) is not load depende~t for any one sample. This is a good assumption except when non-metallic (molybdenum disulfide, Teflon*, etc.) coatings are utilized.
Even in the case of non-metallic coatings, any changes in a finite tenslon range should be small.
For purposes of convenience, the tightening technique of this invention may be referred to as the logarithmic rate method.
The importance of equations (5) and ~7) should now be appreciated. It has been demonstrated in the laboratory that the value of tension rate dF/d is a function of the joint having small scatters and is independent of friction. The torque rate dT/d~ can be determined from torque and angle measurements taken during the tightening of each fastener pair by suitable torque and angle sensors on the tightening toolO The torque value T is, of course, measured by the same torque transducer. It will accordingly be apparent that the friction dependent parameters, i.e. torque ra'ce and torquej are determined for each fastener while tightening, which is here defined as the time frame commencing with the onset of threading and stopping at the termination of tightening. Since tension rate dF/d is a function of the joint which is determined empirically prior to the tightening of production fasteners, it is a simple matter to solve equation (5) for tension.
Referring to Figure 1, it may be assumed that the fasteners are -threaded together with measurements being taken of both torque *Trade Mark '7~

and angle with tightening being advanced to the point 24. The average torque rate T~ is ca]culated, as by the use of the least squares method. 5ince the tension rate FRl is known from empirical measurements of the joint in question. the tension in the joint can be calculated at the point 24 from equation (5~.
Graphically, the angle required to advance the fasteners from the tension value calculated at the point 24 to the final desired tension value FD can be easily done since the tension rate FR2 has likewise heen determined empirically. After determining the additional angle afinal, the tool may be instructed to so advance the fasteners thereby attaining the desired final tension value FD. In a similar fashion, the additional torque ~T or the final desired torque TD can be calculated.
There are substantial difficulties in applying these principles to production line operations. It will be apparent that the calculations being made are being done while tightening.
It will be apparent that the duration of tightening should be minimized so far as practicable commensurate with the attainmen-t of consistent results. In any event, it will be apparent that long tightening times, for example two minutes, would render the technique unsuitable for many production line operations although some suitability may remain for special purpose applications such as in the fabrication of reactor vessels, aircraft and the like where precision is paramount. Xt is accordingly evident that the use of electronic computation techniques is highly desirable for processing the data obtained from measurements taken during tightening. Even with the use of electronic computation ~.3~ '3 techniques, it is desirable to advance the fasteners for some initial distance, suspend tightening momentarily and then resume tightening to the final desired tension value. The momentary stop allows time to complete lengthy calculations and has the additional benefit of allo~ins the joint to relax at this point rather than at the final tension value attained. As will be more fully apparent hereinafter, many of the calculations are done while the tool is running as well as when the tool i5 momentarily stopped. It will, however, be evident that simplified computations may be utilized thereby eliminating the necessity for a momentary pause in the tightening operation.
More specifically, the following steps may be taken to attain a consistent bolt tension utilizing an instructable tool equipped to measure torque and angle information only, after the acquisition of certain empirical information:

.. .
1. Engage the fasteners, start the tool and record torque at equal angle increments.
2. Shut the tool off in a tension range of .4-.5 of elastic limit. Although a turn-of-the-nut approach may be used to estimate the initial tool shut off, a simplified logarithmic rate method in accordance with this invention provides more consistent results.
3. Calculate the torque rate from the torque and angle measurements by a suitable smoothing technique, e.g. least squares. Calculate the torque at the mid-point of the range from which the torque rate was calculated, by averaging the torque value along this range. Accordingly, the intersection of the 8~'7~

average torque .rate with the angle axis is established~ Since the offs~t torque ToS is largely a function of the joint, the intersection of the tension curve with the angle axis is established.

4. The tension curve is then a straight line emerging from the origin or intersection determined in 3. above with the initial slope FRl. This is valid up to about .5 of elastic limit at which point the tension curve has a slope of FR~. The location of the bend in the tension-angle curve is determined empirically when determining the values of FRl, FR2, and Tos.

5. Calculate the tension value appearing in the fasteners at some location, for example, point 24. Given the tension value at point 24, calculate the additional angle afinal or the additional torque ~T necessary to tighten the fasteners to the final desired tension value FD.

6. Instruct the tool to resume tightening and advance the fasteners through the angle final or for the increased torque QT.
For purposes of discussion, the implem~ntation of the technique of this invention may be broken down into four segments: (1) determining the mid-point stop, (2) calculating the torque rate and the angle of tension origin, (3) calculating the final shut off parameter including a prediction of tool overrun, and (4) determining the occurrence of yield and calculating the final attained tension value in the event yield , ~, occurs prior to the attainment of the final shut off parameter.

The intent of the mid~point stop determination is for the join-~ to be tightened to an angular location corresponding to the break in the tension-angle curve for reasons pointed out more fully hereinafter. Although a turn-of-the-nut method can be used to determine the mid-point stop, it is preferred to use a simplified logarithmic rate method in accordance with this invention. Referring to Figure 2, the tool i5 turned on with torque values being recorded and stored at fairly small equal angle increments ~a which may be, for example, in the range of 1-5. With fasteners of the type studied, a selection in the range of 2-3 seems preferable. In getting to the mid-point, torque and angle measurements obtained in the lower part of range 16 are used. The torque value Tl is an empirically determined value and is the first torque value utilized to calculate a preliminary torque rate. Tl is on the order of about 20% of the average final torque value obtained in running the samples to empirically determine FRl, FR2 and Tos. When running torque is first sensed to be equal to or greater than Tl, such as at the location 26, the angular position of the location 26 is noted and stored. When the tool passes the point 28 which is one ~k degrees beyond the location 26, the torque value T2 is sensed and stored. The value of ~k is preferably large enough to give a rough approximation for a preliminary torque rate, which is calculated as (T2 - T~ k. If ~k were very large, e.g. 20 , the tool would not be stopped until late, leaving little or no additional room to resume tightening. If k were very small, e.g. 3 , the value of torque rate calculated from (T2 ~ Tl)~k ~.3~ 3 would be so influenced by noise in the torque sensings that i-t would be unreliable. A compromise of 9 for ak has proved acceptable although other compromise values are obviously accept-able.
The data processor then calculates 1~ in accordance with the following equations:

1 = c + aT2 (8) aor T To~
c = ~d{l-(~ )} - (~or (1- - ) ~k T To (9) Tl-Tos Tl ~ - 2 - (2Ko ~ Nk -Ko ~k 1 ~or~d Tl - Tos a = - { ~ N - 2 - } (10 ak To Ko ad is the desired angle from tension origin to mid~point and is FM or slightly greater where FM is the tensio~ value at the junction of the two tension regions indicated by FRl, and FR2, aor is the tool overrun at idle due to actuation delay, To is th~
stall torque of the tool, Ko is a typical -torque rate for the particular fasteners involved and is determined empirically, and Nk is a correction factor necessi-tated by the inaccurate algebraic expansion of a more precise equation, which expansion substantially reduces calculation time for equation (8)~ It will be apparent that~ in a production line situation involving the same size bolts and the same size tools, every value in these equations, except T2, can be reduced to numbers before starting.

Thus, the computations are actually easier and quicker than appears.
It might be questioned why the value of ~k is of any importance since neither equation (8), (9~, or (10) appear to contain a value for preliminary torque rate. Equations (8), (9), and (10) constitute an application of the logarithmic rate method to achieve a mid-point tension value of FRl ~d with provisions made for tool overrun due solely to the time delay between the shut off command and exhaustion of air from the tool. The mathematical complexities have, by design, been transferred from equations (8) to equations (9) and (10) so that computation of equation (8) during tightening requires the least possible elapsed time. Equations (9) and (10) can be computed manually either prior to system installation or computed by the microprocessor when in a dormant portion of the tightening cycle, for example, prior to the initiation of tightening. Although the preliminary torque rate 2 1 does not appear in equations (8), k (9), or (10) as written, if one were to substitute the equations fsr a and c into equation (8~, one would find that the preliminary torque rate appears. Accordingly, the reasons why ~k should not be too large or too sma]l are as previously discussed.
As will be recognized by those skilled in the art, equations (9) and (10) do not include a tool overrun prediction due solely ~o the inertia of the rotating parts of the tool. For moderate and high torque rate bolts, the amount of angular overrun due solely to inertia is rather insignificant. The reason, of course, is that the tool is not rotating very fast.

~L~3~C~'7~

With low torque rate bolts, which the tool is able to turn faster, the amount of overrun due solely to inertia is still modest. For applications where maximum accuracy is desirable, equations (9) and/or (10) may be modified to incorporate a measure of overrun prediction based on inertia.
The determination of the mid-point stop is of some import-ance as may be visualized from an appreciation of Figure 1. It will be recollected that it is desired to calculate the av~rage torque rate TR. If the mid point stop occurs, for example, in the lower part of the region 16, the average torque rate will be substantially too low. If the mid-point stop is too late and well into the region 18, two difficulties are presented: (1) the calculated average torque rate TR may be substantially too high although some calculations can be done to disregard some of the later data in order to shift the range where torque rate calculations are actually being conducted, and (2) there may be little or no additional room available to resume tightening to the final desired tension value considering allowance for tool overrun.
Referring to Figure 2, the tool is commanded to shut off at a point 30 which is ~1 degrees beyond point 26 which was where the torqu~ value Tl was first equalled or exceeded. Because of the time delay in the tool from the shut off command until the tool actually stops, which is represented by the point 32, the tool has overrun by an angle ~. The mid-point stop 32, typically falls in the range of about .4-.6 of the elastic limit. For any given application, the empirically determined ~L~3~73 values act to establish the mid-point stop 32 at a given fraction of the elastic limit which is not changed until new empirical data is developed, as for example, may occur when a diferent type fastener is selected.
In order to calculate the average torque rate TR, a decision must be made of which torque and angle measurements are to be used. It has been learned that the torque value at the stopping point 32 is somewhat unreliablebecauseof speed dependent variables. Accordingly, the highest torque value used in the torque rate calculations is at a location 34 which is one Q~
backward from the point 32. The torque value at the point 34 is T3. The total number of values used in torque rate calculations, designated n for more general purposes, may vary widely and is subject to considerable compromise~ A total of ourteen consecutive data points with the point 34 being the highest torque value has proved quite acceptable. The mean torque Tm and the adverage torque rate TR are then calculated using the following summations where i is a designation for each point selected for the torque rate calculations and Ti is the torque value there sensed:

T n Ti: (11) i=l TR = -6 ~ (n+1-2i)Ti (12) (Q~)n(n+l)(n-1) Equation (11) will be recognized as merely adding the -torque values occurring at each o the points i and dividing this sum '3~

~.3~

by the total number of data points n. Equation (12) will be recognized as a least squares fit for the data points i.
It is desirable to assure that the mean torque Tm and the average torque rate TR are taken over substantially the same tension range during the tightening of each fastener pair. This may be accomplished by checking to determine how close the angular position of the stopping point 32 is to the break in the tension angle curve 12~ The angular position of the mean torque Tm along an abcissa To5 may be calculated from the equation:

aF = -TRTS where aF > (13) The angular distance from the point of origin of the tension curve 12 to the stopping point 32 may be calculated from actual data derived from the fastener being tightened from the equation:

origin 2 aa(n~ F where ~ (14) For calculation purposes, it is desirable that aOrigin be negative. From empirically determined information done prior to the tightening of production fasteners, the start of the second tension region may be calculated from the equation:

FM
aF ~ FR where aF > (15) where Fm is the tension value at the break. The difference ~ 27 ~

~.3~;3~

between aO i in and aF may be obtained from the equation:

origin FM (16) If X ~, O! this means that the midpoint stop 32 is too late and consequently that the largest torque value T3 in the torque rate calculations is too large. Without revising the value for ~R, TR will tend to be too high as previously discussed. Accordingly, one needs to shift the range of torque rate calculations down-wardly on the torque-angle curve presented in Figure 2~ Thus, n = ~( x ) + 1 (17) nl - n (18) From the stopping point 32, one moves downwardly along the torque-angle curve by nH angle increments of ~a to define a new point 35 as the upper limit of the range through which torque rate will be calculated. The-symbol ~ means that any fractional value is dropped so that the number used is the next lowest integer ~rom the calculated value. The total number of data points n remains the same.
If X ~ O, this means that the stopping point 32 occurred too soon which would tend to give a value for torque rate that is too low. Since one cannot move upwardly on the torque-angle curve to obtain an additional area of measurement, the practical solution is to accept fewer data points for torque rate calcula-tions thereby, in effect, lopping off the lower end of the range.

., '`'' .

Accordingly, nHl (19) n ~ F~ a ) ( 2 0 ) where nHl indicates the point or location where the largest torque value used in the torque rate calculations occurs. Since the largest tor~ue value will remain the same, nHl = 1 so tha~
the torque T3, being one ~a removed from the stopping point 32, is the largest torque value used. The new value for nl, which is the total number of data points used, is based on the assump-tion that the tension rate in the first region is substantially linear above a minimum tension value FL, determined empirically, and ~hat the tension Fo in the joint at the stopping point 32 lies in the first tension range. The symbol ~F is the additional tension in the first tension range per angle increment Aa and may be expressed mathematically as:
~F = FRl~a (21) The tension Fo in the joint at the stopping point 32 is Fo - -FRl ~origin (22) It is conceivable that nl may be too small, e.g. two or three points, to give good results with the least squares equation (12). Accordingly, a check is made to determine if n is less than one half of n. In this event, Fo - F
~2 = ~( ~F ) (23) and n2 is used as the total number of data pointsO

~a~

Accordingly, a new summation is performed for mean torque Tm and torque rate TR in accordance with equations (ll) and (12) utilizing the new starting place in the event that X ~ o or starting with the same highest torque value but using fewer number of data points in the event that X ~ O.
With revised values for mean torque Tm and torque rate TR, a revised value may be obtained for the angle of origin of the torque-angle curve using equation (13) and a revised value may be obtained for the origin of the tension-angle curve using equation (14). A calculation is again made to determine whether the tool has overshot or undershot the break in -the tension curve in accordance with equations (15) and (16). If X > O, the tension appearing in the joint a-t the stopping poin~ 32 is calculated to be:
Fo -- FM + rFRlx (24) where FM is the empirically determined tension value of the break in the tension curve and r is the ratio of FR2/FRl. If X ~ O, the tension appearing in the joint at the stopping point 32 is obtained from equation (22).
It will be apparent that the values of mean torque Tm, F origin and the like may be revised a times as deemed desirable.
One of the defects in the technique heretofore described is the assumption that the empirically determined tension rate FRl correctly describes the elastic properties of the fastener actually being tightened. For good quality joints, the tension rate FRl does not vary widely. There are, however, a number of ~3~ 3 relatively common situations, e.g. yalled threads, misaligned fasteners, poor contact surfaces, dirt or other foreign particles between the contact surfaces, and the like, where the actual tension rate for the fasteners being tightened is significantly below the empirically determined tension rate FRl. In such poor quality joints, the actual final tension value will be signifi-cantly below the desired tension value FD and significantly below the final calculated tension value Ffinal. To determine the significance of such poor quality joints, two 5/16" - 24, SAE
grade 8 nuts and bolts were tightened with a shim, .015 inches in thickness inserted from one end in order to simulate poor contact due to misalignment. The final desired tension value FD
was 5500 pounds. The actual measured final tension value was 2400 pounds and 1700 pounds for the two fasteners~ a percentage variation of -56~ and -69% from desired. It will accordingly be apparent that the occurrence of such poor quali-ty joints can have a major effect on -the scatter seen in fasteners tightened by the technique of this invention. It will also be evident, upon reflection, that such poor quality joints will have a like effect on the scatter in fasteners tightened by a turn-of-the-nut method.
It has been learned that poor quality joints of the type exhibiting abnormally low tension rates can readily be detected by the data developed during the course of tightening a fastener' pair with this invention. In such poor quallty joints, the torque rate is not constant in the upper part of the region 15 where the average torque rate TR is calculated, as contrasted to the showing in Figure 2. Instead, the torque is arcuate and, if 3~ '7~

plotted, is upwardly concave. Thus, it is a relatively simple matter to measure or calculate and then compare the average torque rates in the upper and lower parts of the range where the torque rate TR is calculated. For example, in a situation where thirteen data points are being used to calculate TR, wikh the point 34 being the highest torque value used, the torque rate TRa over an angle of six ~ increments backward from the point 34 would be calculated. The calculations may, of course, be a two point or a least squares technique. Mext, the torque rate T ~
over an angle commencing with six ~a increments backward from the point 34 and ending twelve increments backward from the point 34 is calculated by a two point or least squares technique. Then, the ratio of TRa/T ~ is computed. If the ratio of TRa/TRb is near unity, e~g. 1 ~ .I0, the conclusion is that the joint has an acceptable tension rate. If the ratio of TRa/TRb diverges significantly from unity, e.g. TRa/TRb ~ 1.10, t~e conclusion is that the joint has an abnormally low tension rate FR1 and, if tightened by the technique of this invention or by a turn~o-the- -nut method, will result in a fastener stressed substantially below the desired tension value FD. A suitable signal may be displayed at the operator's station and the joint rejected and the parts replaced.
Ik will now be appreciated that the location 32 of calculated tension Fo appearing in the joint corresponds to the point 24 illustrated in the more general showing of Figure 1.
The only determination yet to be made is the additional angle inal or the additional torque ~T required to achieve the final ~ 32 -desired tension value FD. Compared to the manipulations used to assure consistently reliable values for torque rate TR and the angle of tension origin, these calculations are relatively straight forward.
One tightening parameter that may be selected to attain the final desired tension value FD is the additional angle a F -Fo If x ~ afinal rF~1 ~25) ' final -x + rFR (FD - F ) (26) Fo is, of course, obtained from equation (22) or (24) while FM
is the tension value at the break in the tension-angle curve and is determined empirically.
It will be appreciated that the tool overran an angle ~
when stopping at the point 32. It is equally apparent that some amount of tool overrun will occur approaching the final desired tension value FD. A typical torque-speed curve for an air powered tool is shown in Figure 3. Since the tool will be slow-ing down during tightening, it will be apparent that the tool overrun approaching the final desired tension value FD will be less than the overrun approaching the point 32. Defining, To~T
~a TR (27) where T4 is the torque value at the point 30 where the initial shut off command was given prior to reaching the stopping point 32~ To is the stall torque o the tool, TR is the calculated . .

torque rate and ~a is the measured angle overrun approaching the point 32. The expected tool overrun approaching the final desired tension value FD is:
d~ = ~ (1- final) (28) It has become apparent that a typical joint will relax, i.e. lose tension without unthreading of the fasteners, at the mid-point stop 32 and/or at the termination of tightening. If the fasteners were continuously tightened, i.e. without a mid~
point stop, the relaxation at termination of tightening can be rather significant while, with a mid-point stop, the relaxation at termination of tightening is qui~e modest. By stopping at the mid-point 32, the bulk of joint relaxation occurs prior to the resumption of tightening. Thus, the stopping at the mid-point 32 provides greater consistency in final joint tension although this phenomenon complicates the determination of:a final angle shut off parameter.
If the joint did not relax at the mid-point stop 32, the tool would be instructed to go an additional angle ~inal -d~
beyond the mid-point stop 32 where the final shut off command is given. As shown in Figure 1, the final shut off command would occur at about the point 36 whereby the tool overruns to tighten the fastener pair through an angle d~ until stopping at the final desired tension value FD.
The phenomenon of joint relaxation is illustrated in Figure 4 where the curve 38 represents the tension-angle relation-ship during continuous tightening -to a location 40 below the , ~1 3~ '3 elastic limit of the fastener. When tightening stops, the joint relaxes as suggested by the tailing off of tension along a constant angle line 42. The final tension appearing in the fastener is accordingly at the point 44. A typical value for joint relaxation along the line 42 is 7~ of joint tension within twenty one hours.
Referring to Figure 5, the curve 46 represents the tension-angle relationship during tightening to the mid-point stop 32. Because the joint relaxes, tension in the fasteners tails off along a constant angle line 48 to a tension value at the point 50.
Instead of instructing the tool to go an additional angle ~final -d~ from the mid-point stop 32, the instruction is to advance the fasteners an additional angle ~final -da after the running torque equals or exceeds Tsp where Tsp = T3 + TR (Q~) (29) It will be recollected that the torque value T3 is located at the point 34, which is one ~a backward from the mid-point stop 32. By advancing the tool until running torque equals or exceeds Tsp, the torque and tension values at the mid-point stop 32, before relaxation occurs, are essentially reproduced. This is indicated in Figure 5 where the point 52 designates the location where running torque is equal to or greater than Tsp. Tightening will then be done correctly, regardless of prevailing tension in the bolt at the time the tool resumes tightening. As shown in Figure 5, the final shut off command occurs at the point 54 whereby the tool overruns to tighten the fastener pair through an cg~

angle d~ until stopping at the final desired tension value FD.
In order to shift the bulk of joint relaxation from the ~inal stopping point to the mid-point stop 32, the mid-point stop 32 is at least .4 of yield strength and conveniently is in the range of .4 - .6 of yield strength. ~ith the mid-point stop 32 so located, typical joint relaxation at the final stopping point is on the order of 1/2 - 2% of final bolt tension within one hour.
It should be clear that this amount of joint relaxation i5 the relaxation of a good quality joint rather than a joint suffering from misaligned parts, compressed gaskets and the like.
Another tightening parameter that may be selected to attain the final desired tension value FD is the additional torque or the final torque TD (Figure 1). The final torque TD
is preferred since the joint may relax at the mid-point stop 32.
Because the tool instruction is to achieve an absolute torque value TD, any relaxation in the joint is automatically accommodated. In using a torque-governed shut off parameter, even a possible tightening of the joint at the mid-point stop will also be automatically compensated for.
In using a torque-governed shut off, an interesting phenomenon has been noted for which no simple explanation appears.
Referring to Pigure 1, it will be noted, as previously mentioned~
that the tension rate FR2 is greater than the tension rate FRl, typlcally by 5-15~ depending mainly on the value selected for FM.
This would lead one to believe that the torque rate in the region 18 would be greater by a similar amount than the torqùe rate in the region 16. Laboratory investigations indicate that the .~

torque rate in the reglon 18 typlcally exhlbits a slightly smaller increase over torque rate in the reglon 16. Fortunately, the ratio of the torque rates in the regions 16, 18 to ~he ra-tio of the tension rates FRl, FR2 is more nearly constant for a single type fastener pair. In calculations for a final torque shut off command~ this factor is taken into account.

TMC = Tos + TFR FM ( 30 ) TD = TMC + FRl (FD M) ( 31) where TMC is a calculated value for the torque at the break in the tension curve, R is defined as TR2/rTR, TR2 is the torque rate in the region 18, TR is the torque rate in the region 16, r is the ratio of FR2/FRl.
As is the case in the angle governed final shut off calculations, the tool will overrun after the final shut off command is given. Defining, ~T _ TR (~) (32) Ta To-T4-~T, then (33) To-T
dT = ~T( Ta ) (34~

After tightening is resumed, the final shut off command is given when running torque T ~ TD ~ dT. As shown in Figure 1, the final shut off command will occur at about the point 36 whereby the tool overrun continues to tighten the fastener pair for an additional torque dT until stopping at the final desired tension value FD.

~1.3~ 3 It lS apparent that tigh~ening of the fas-tener pair can be terminated in response to calculated tension which is derived by the techniques of this inven-tion. Upon analysis, it will be evident that terminating tightening in response to calculated tension is in reality the same as terminating tightening in response to either angle or torque, depending on how the calcula-tions of tension are conducted.
It will also be apparent that tightening ma~ be terminated in response to a combination of torque and angle, for example, a linear combination of torque and angle~ Assuming that one wished to equally weigh the calculated advance derived from the torque and angle computations, the appropriate equation is generically:

(TD-Tsp) FD = Fo + ~rFRl [~final + TR2 (35) where Fo is the calculated tension value at the mid-point stop 32 as may be calculated from equa~ion (22) or (24) depending on whether X s O or X > O, and Tsp is the calculated torque value at the mid-point stop 32 as may be calculated from equation (29).
The calculations for afinal will depend on whether X ~ O or X ~ O
as pointed out in equations (25) and (26). Calculations for TD
are made using equations (30) and (31).
As with the use of other tightening parameters, it is desirable to provide an overrun correction. It is apparen~ that the angle overrun correction of equation (28) may be incorporated as an overrun prediction, as follows:

For = r(FRl)d~ (36) where For is the increase in tension due to overrun. It may also be desirable to use an equally weighted linear combination of torque and angle in determining the predicted tool overrun. The tension produced in the bolt during overrun may be calculated as For = ~XFRl(d~ ~ TR ~ (37~

It will be apparent that one cannot merely instruct the tool to proceed an additional angle or until a desired torque level is reached in order to stress the bolt to the desired tension value FD when using a mixed parameter of torque and angle.
Instead, one may calculate the tension appearing at any angular position ~3 beyond the point 32 as If x ~ O, F~3 = Fo + ~rFRl ~3 + TR P~ (38) , 3 FM + ~rFP~, [a3 ~ x -~ 3 ] (39) where Ta3 is the sensed torque value at -the angular position ~3~
Tsp is the calculated torque value at the mid-point stop 32, and TMC is the calculated torque value at the location of FM
according to equation (30).
The calculated tension value at the point of shut off is:
F = F - F (40) whexe FD is from equation (35) and For is from equation (36) or (37). By comparing the value of Fa3 at angle increments, such as ~, 1 or the like, with Fso, as soon as F3 ~ Fso, the shut off command is given. In this fashion, tightening may be ~erminated in response to a linear combination of torque and angle.
Referring to Figure 6, another feature of the invention is illustrated. When tightening to the final desired tension value, it is highly desirable to assure that the yield point is not reached or is at least not substantially exceeded. This may be done graphically as shown in Figure 6 by drawing a line 56 parallel to the torque curve 10 in the region 18 or parallel to the tension curve 12 and spaced therefrom by an angle ~y. The value oE ~y can be correlated with an acceptable amount of strai in the bolt since the amount of nut rotation in this region of the torque curve can be calculated into a percentage of bolt elongation because of the known pitch of the threads. When the running torque value T intersects the line 56 at the point 5~
the tool is given a shut off command and ultimately comes to rest at a point 60 because of tool overrun.
In order to implement this technique, the torque value sensed by the tool is monitored after the tool is turned on again after the mid-point stop 32. One difficulty arises since the restarting torque applied to the fastener in order to resume tightening typically is relatively substantially larger than the running torque immediately prior to the mid-point stop 32 as is caused by ~he difference between the static and dynamic coefficients of friction and com licated dynamic factorsO When the sensed value of running torque T first equals or exceeds the value of TM where:
TM = T3 ~ TR (~-x) (42) this location is marked and two ~a increments beyond this location, which is location 62, the running torque value T is sensed and stored as T5. TM will be recognized as a calculated torque value which appears at the location on the torque-angle curve corresponding to the break in the tension curve.
As is apparent from Figure 6, the calculations being done to detect yield or non-linear strain occur in the region 18 where the value of torque rate is somewhat different than the torque rate value calculated in the region 16. The torque rate in the region 18 can be expressed:
u - rR(TR) ~42) Since R has been defined as TR2/rTR, it will be apparent that equation (42) reduces to the proposition that u = TR2.
Yield or non-linear strain calculations can be conducted periodically during tightening in the region 18 as often as is deemed desirable. Although the calculations can be done at every angle increment a~, results are quite satisfactory if done every other angle increment ~. Accordingly, ~ Tl = 2u (~a) ~43) QTy -- u~y (44) where ay is the angle corresponding to a desired strain level which can either be elastic but non-linear or plastic, ~Tl is the incremental torque over the incremental angle 2~a and ~Ty is the incremental torque over the incremental angle ay. By selecting small values for ~y, the shut off command will tend to be in the elastic but non-linear ranye. If ay is selected to be a large value, the shut off point will appear in the yield range.

~ ~3~

It is thus apparent that the detection of non-linear strain can encompass both elastic and plastic strain. The only difficulty in selecting very small values for ~y is that noise in the torque curve 10 in the range 18 might create a premature and false yield signal. At a point 64, which is two ~ degrees after the occurrence of T5, the value of running torque T is compared with Tyl = Ts - ~Ty ~ ~Tl It is apparent that Ty1 is a torque value on the curve 10 at the point 64. If T>Tyl, tightening continues. At a point 66, which is two Qa degrees beyond the point 64, the value o running torque T is compared with Ty2 = Tyl + ~Tl (46) = (T5 - ~Ty ~~ ~Tl) + ~ 1 If T ~ Ty2, tightening continues~ This procedure continues by adding an additional torque value ~Tl to the preceding value of Ty at angle increments of two Q~. In the event that T ~ Ty before the occurrence of the shut off command derived from the normal tightening parameter of torque or angle, a shut off command is given to the tool. It will be apparent that the actual shut off command from detection of non-linear strain or the actual detection of non-linear strain will not occur at exactly the point 58 since comparisons are being made every two ~a . Thus, the actual yield detection will probably occur later, e.g. at the point 68 as shown in Figure 6.

Thusr tightening is normally terminated in response to a

7~

torque-governed, an angle-governed or a mixed shut off command, but in the case of yield detection, a premature shut off command is given It will accordingly be apparent that the upper end of the scatter band is eliminated by a secondary yield point shut off. Thus, the total scatter will be reduced. It will also be apparent that the danger of bolt failure during assembly is eliminated. It will also be apparent that the detection of non-linear strain may be conducted as disclosed in United States patents 3,643,501 or 3,693,726, although the technique herein disclosed is deem~d preferableO
It is preferred that the selection of FD will be low enough so that the cutoff due to detection of non-linear strain will be rare, e.g. .1%. In the event that the percentage of non-linear strain detection rises substantially during a production run, this indicates that the fasteners, i.e. bolts or/and threaded parts, employed do not meet design specifications. Thus, a high percentage of non-linear strain detections is a signal that quality control investigations need to be conducted on the fasteners employed. For example, if the normal occurrence of non-linear strain is on the order of .1%, and a running average of non-linear strain detections is 10%, it is likely that the fasteners being run do not meet specifications.
To this end, a running count of the number of joints tightened is maintained and a running count of the number of joints exhibiting non-linear strain is detected. When Cy ~
C A (48) ~l.31~07~

where CJ is the number of joints tightened, Cy is the number of yielded joints and A is some fraction acceptable to the user.
From present information, it appears that the value of A should be in the range of .10 - .20, e.g. .15. The ratio of Cy/CJ is preferably a running ratio, rather than a cumulative ratio, as by storing, on a first-in, first-out basis, a finite number of joints tightened CJ, e.g. 30, and any instances of yield detection Cy~
When the running ratio of Cy/CJ exceeds the selected value A, a suitable signal may be provided indicating that the frequency of non-linear strain is much too high. The investigations to be conducted normally include analysis of the strength and material composition of -the fasteners, a technique well known in the prior art.
It is highly desirable to calculate and store the final tension appearing in a fastener which has been stopped prematurely because of non-linear strain detection. It may be that the final tension value achieved is well within an acceptable range. In this event, it would be disadvantageous to require removal of the fastener pair and replacement with a new pair if the problems associated with marginally yielded fasteners are not material if the fasteners are sufficiently stressed to assure acceptable joint conditions.
Accordingly, when using an angle approach, the value of final tension may be calculated as follows:

final FD rFRl(~final + ~Y ~ ~2) (49~
where a2 is the angle from the stopping point 32 to the location where yield detection is sensed. It will be appreciated that any ~ 3~37~

calculated value of Ffinal is somewhat of an approximation since the tension rate well above the proportional limit is unknown and perhaps unknowable with any degree of accuracy. Figure 7 graphically illustrates the diffi.culty. If the final tension value were calculated:
Ffinal = FD rFRl(~final ~2) (52) the tension actually being calculated would be at the point 70 which is at the same angular position a2 from the stopping point 32 as the yield detection point 68~ It will be appreciated that the difference in tension values between the points 68, 70 may be significant in some circumstances. Since it is known that the tension rate falls off substantially immediately prior to the point 58, it is safe to calculate the tension value at the point 72 which is spaced downwardly along the slope FR2 by an angular distance ~y. Thus, the rationale for the equat~on (50) is apparent. It will be appreciated that the actua~ final tension appearing in the joint is that at the point 68 which difers from the calculated tension value appearing at the point 72. It will be seen, however, that the tension value at the point 72 is a substantially better estimation of actual final tension than is the tension that would be calculated at the point 70. Th.is is particularly true since the tension rate in the range 74 is known to be quite low. The final tension value Ffinal along with a notation that the bol-t has yielded may be displayed at the tool location, printed or otherwise recorded for further use or analysis.
In the event the torque-governed final shut off parameter is being used, when T ~ Ty, non-linear strain is detected and a shut off command is given -the tool~ The final tension value may be calcula-ted from a torque approach~ as follows:

final = FD - 1 ( D f) (51) where Tf is the highest value of torque sensed within one or two ~a increments before the final stopping point 60. This is likewise illustrated in Figure 7. The detection of yield occurs at point 68 on the torque curve 10 with the point 60 being the final stopping point~ The torque at the point 60 is unreliable for the same reasons that the torque reading at the mid-point stop 32 is unreliable. Accordingly, the torque value Tf is taken as the peak within one or two ~a increments backward from the point 60, such as at the point 76. The effect of this, graphically, is shown by the horizontal line 78 terminating on the torque slope TR2 at the point 80 and the vertical line 82 terminating at the point 34 on the tension slope FR2. Thus, the final tension value Ffinal is the calculated tension at the point 84.
It is also desirahle to calculate and store the final tension appearing in a fastener, the tightening of which is terminated normally, i.e. in response to torque and/or angle rather than yield. When using a torque approach, equation (51) gives the value for Ffinal reyardless of whether yield has occurred or not. When using an angle approach, the final achieved tension value may be calculated from:

Ffi 1 = FD ~ rFRl (afinal aactual (52) where aactual is the actual angle increment between the mid-point - 4~ -~q.3~

stop 32 and the final stopping point.
It may also be desirable to calculate and store final tension appearing in a Eastener in other unusual circumstances, such as when the tool stalls. Tool stall may occur before the mid-point stop 32 or after the mid-point stop 32. Before the mid-point stop 32, final Fo (53) After the mid-point stop 32, the final achieved tension value Ffina1 may be calculated, using a torque approach, as:

FRl 10 Ffinal Fo + R(TR) (Tf ~ Tsp) (54) where Tsp is the calculated tor~ue at the mid-point stop by equation (29).
After the mid-point stop 32, the final desired tension value Ffinal may be calculated, using an angle approach, as; for instance F . = F + rFR a ,X>O (55) flnal o 1 actual where actual is the actual measured angle from the mid-point stop 32 to the final stopping point.
In the event the tool continues to run far beyond any reasonable angle of advance, the conclusion is ~hat the tool was never coupled to the fastener or that the bolt has failed withou~
yield detection, as may occur before the mid-point stop 32. Thus, no appreciable tension appears in the bolt and final (56) Another approach of this invention is to normally terminate tightening in response to one parameter~ e.g. torque, and check this shut off parameter against another shut off parametor, e.g. angle. If the results compare closely, -this is an indication that the assumptions made, the empirically deter-min~Gd joint paralrlete-rs an~ tl~e 1 .~e a-e re~svr~ ccrrec~ If the comparisons are significantly different, this is an indication that something is amiss and that the operation should be stopped or investigations instituted to determine the cause.
When using torque as the tightening parameter, FD has been placed in the calculations for the final torque value TD by equation (30) or (31) depending on whether X ~ O or X < O~ The calculated value of final tension Ffinal using an angle approach at a final stopping angle of is: -final D 1( final actual) (5 )where aactual is the angle of advance from the m~d-point stop 32 to the final stopping point. If the difference between FD and Ffinal is small, e.g. + 5-10%, it is apparent that substantial confidence may be placed in the technique. If the difference between FD and Ffinal is larger, e.g. + 29%, it is apparent that something is amiss and that the tightening operation should be stopped or investigations instituted to determine the cause.
In any circumstance where Ffinal is calculated, it may be desirable to compare it with the final desired tension value FD. In this event, if final ~ ~ -B (58) 7~3 where B is a fraction deemed acceptable to the u~er, a suitable signal may be displayed to indicate that calculated tension is substantially below desired tension. From present information, it appears that the magnitude of B sho~lld be greater than the expected scatter from use of this invention and preferably should be 3-4 normal deviations. Thus, an exemplary value of B is .17. It will be seen that only when B is negative is there a difficulty with the joint because if Ffinal is too high and the bolt has not yielded, there is obviously nothing wrong with ~he joint in a normal situation~ One very useful advantage of this technique is to detect cross-threaded fasteners.
~ nother feature of this invention resides in the use of the tool overrun prediction to indicate tool malfunction.
Although the tool overrun at the termination of tightening may be used to determine tool malfunction, this operation is more conveniently and accurately monitored during overrun adjacent the mid-point stop 32. Let Tl + alTR
(59) To Ca Z = - (60) 2aor y+2z-1 E + 100 % (61) 1--z It will be apparent that Y iS a dimensionless number and basically is the ratio of T4/To. As shown in Figure 2, T4 is the existing torque value at the mid-point shut off command location 30 while To is the normal stall torque. It will be seen from Figure 3 that Y is an inverse function of ~ool ~peed. If ~he time delay bekween the giving of the shut off command and the closing of the valve remains constant, Y is a prediction of tool overrun. Since ~
is the measured tool overrun, it will be seen that Z is a function of measured tool overrun while ~or is the normal angular overrun of the tool under no torque conditions. E will be recognized as a percentage change in tool and control performance.
If E is low, for example ~ -10%, the deduction is that actual stall torque has decreased significantly, such as from a loss or decline in air pressure, lack of lubrication, worn or broken parts, or the like. In such an event, a signal may be displayed at the tool location to indicate that the tool requires inspection, maintenance, repair or replacement. It is conceivable, but quite unlikely, that a significant decrease in E could be caused by a decrease in the time delay between the shut off command and the air valve closing.
If E is positive, i.e. greater than zero, complications arise. It appears that Z, which is a simplication of a more complex equation, loses accuracy. The more complex equation indicates that if E is positive, Z should be reevaluated as Zl = (62) ~or Accordingly, E should be reevaluated for greater accuracy, when positive, as:

E -- 100 ~ (63) 1 l-Y

~l 3~

If El is high, for example ~ + 10%, the deduction is that the -time delay between the shut off command and the air valve closing has increased significantly or that air pressure supplied to the tool has increased. This normally indicates that the valve control solenoid is beginning to stick or that air pressure is too high. In such event, a signal may be displayed at the tool location to indicate that ~the air control system requires inspection, maintenance, repair or replacement. It is conceivable, but quite unlikely, that a significant increase in E1 could be caused by increased tool efficiency.
As will be apparent to those skilled in the art, the prediction of tool overrun embodied in equation tS9) does not include a measure of overrun based on inertia, but instead is based solely on time delay. As mentioned previously, inertial overrun is rather insignificant with moderate to high torque rate fasteners although accuracy can be improved somewhat for low tension rate fasteners. In the event that is desirable, a measure of inertial overrun can be incorporated into equation (61) through one or both of equations (59) or (60).
It is apparent that a single indication of tool malfunction is probably not siynificant but that an abnormal frequency of tool malfunction is significant. Thus, a running ratio of CT~/CJ ~ C (64) is maintained where CTL is the number of times that E ~ -10%, CJ
is the number of joints tightened and C is a fraction acceptable to the user. As with the ratio Cy/CJ, of equation (50), a running ~ .^' ~, , ratio is preferable to a cumulative ratio. From present in~orma-tion, it appears that C should be in the range of .1 - .~, for example .15.
Similarly, a running ratio of CTc/CJ ~ D (65) is maintained where CTc is the number of times that E ~ +10% and D is a fraction acceptable to the user, for example, .15.
Another approach for predicting tool overrun and thereby detecting tool malfunction is pointed out by:
~ap = (1 ~ To)~or (66) where ~ap is the predicted tool overrun from the shut off command point 30 where the torque value T4 appears. The measured value of overrun from the point 30, which has been previously designea ~a, can be compared against ~ap, as follows:

~a F ~ - ~ G (67) ~c~p where F and G are values acceptable to the user, such as .85 and l.lS respectively. When measured overrun ~ is too small, this indicates a motor malfunction while if ~a is too large, it indicates a control system malfunction.
When tightening seriatim a multiplicity of fasteners comprising part of a single joint using a conventional technique, it is well known that the first tightened fasteners will lose at least some tension by the time the last fasteners are tightened.
This is, of course, related to joint relaxation and aliynment of ~L~ 3~

the joint parts. In accordance with this invention, one powered instructable tool as disclosed more fully hereinafter may be used for each fastener and used in the following manner.
The tools are started simultaneously. When all of the tools have stopped at the mid-point 32, all the tools are restarted simultaneously to accomplish the final advance. In this manner, the alignment of all the fasteners and all joint relaxation occurs at the mid-point 32. Each tool would then compensate for any relaxation that may have occurred adjacent the fastener coupled thereto. It will be apparent that the control mechanism for the tools would be interconnected electronically in a fashion that will be apparent to those skilled in the art following the more complete description of the tool hereinafter.
Referring to Figure 8, there is illustrated a schematic showing of a mechanism 86 for performing the previously described technique. The mechanism 86 includes an air toQl 88 connected to an air supply 90 and comprising an air valve 92, an air motor 94 having an output 96 coupled to the fastener pair comprising part of the joint 98, a torque transducer 100 and an angle transducer 102. The torque transducer 100 is connected to a signal conditioner 104 of a data processing unit 106 by a suitable electrical lead 108.
The signal conditioner 104 is designed to receive electrical signals from the transducers 100, 102 and modify the voltage and/or amperage thereof into a form acceptable by an analog-to-digital converter 112 through a suitable connector 114.
The converter 112 changes the signal received from the conditioner ~ 3~

104 into digi-tal form for delivery to an interface logic unit 116 through a suitable connection 118. The angle transducer 102 is connected to the interface logic unit 116 by a suitable electrical lead 110.
The interface logic unit 116 comprises an interface logic section 120 designed to handle information and is connected through suitable connections 122, 124 to a microprocessor unit 126 which is in turn connected to a data memory unit 128 and an instruction memory and program unit 130 through suitable connections 132, 134, 136, 138. The interface logic section 120 is also designed to receive input parameters such as Tos, FRl, r, FD and the like.
The interface logic unit 116 also comprises an amplifier section 140 controlling a solenoid (not shown) in the air valve 92 through a suitable electrical connection 142. The amplifier section 140 also controls a display panel 144 having suitable signal lights through an electrical connection 146 as will be more fully explained hereinafter.
The air tool 88 may be of any type desired but is conveniently a Rockwell model 63W which has been modified to reduce the amount of overrun. It has been surprising to learn that the bulk of the tool overrun occurs between the time the shut off command is given through the electrical connection 142 ' and the time that high pressure air downstream of the valve 92 is exhausted through the motor 94 while the amount of overrun attributable to inertia of the air tool 88 is rather insignificant at high running torque values because tool speed is rather slow.

- 5~ -'7~

The data processor 106 is shown in greater detail in Figure 9 and convenien~ly comprises a Rockwell microprocessor model PPS8~ For a more complete description of the data processor 106, attention is directed to publications of Rockwell International pertaining thereto.
The data processor 106 comprises a chassis 147 having a power source 149 mounted thereon along with the signal conditioner 104, the instruction memory and program unit 130, the data memory unit 128, the microprocessor unit 126, the interface logic section 120, the converter 112 and the logic interface amplifier section 140. The signal conditioner 104, the interface logic section 120, the microprocessor unit 126, and the data memory unit 128 are not modified in order to equip the data processor 106 to handle the calculations heretofore described.
The instruction memory and program unit 126 is physically a part of the data processor 106 and ïs physically modified to the extent that a suitable program has been placed therein.
The interface logic and amplifier circuits 116 and 140, illustrated schematically in Figures lOA and lOB, serve to provide interfacing of data and control signals between the microprocessor unit 126, a conventional teletype console (not shown), the torque and angle transducers 100, 102, and the air valve 92 controlling tool operation.
Interf~cing between the teletype console and the micro-processor 126 is necessitated by the fact that the conso]e receives and transmits data in a serial format while the micro-processor 126 receives and transmits in a parallel format. The ~ 3~ ~t~

interface loyic and amplifier circuits 116, 140 include a universal asynchronous receiver transmitter circuit 14~ w'n!~h receives input datar such as a desired torque value FD, from the teletvpe console over the lines 150 in a serial or one bit at a time format, temporarily stores the data, and then transmits the data in parallel format over the lines 152 to the microprocessor 126. Thus a teletype console or other suitable means may provide an input 154 (Figure 8) for variable empirical paramets r desired bolt tension and the likeO Likewise r data from the microprocessor 126, which is to be printed out by the teletype console, is converted from the parallel forma-t in which it is receive~ irom the microprocessor 126 over the lines 152 into the serial format for reception by the teletype console.
Timing pulses for the control of the universal asynchronous receiver transmitter 14B as well as other components of the interface logic and amplifier circuits ar.e provided from the microprocessor 126 over line 156, the pulse train being supplied to a conventional divider circuit 158 to produce a timing signal on the line 160 which is a pulse train of lesser but proportional rate to tha* supplied by the processor 126.
Timing pulses are also provided to other components of the inter-face logic and amplifier circuit over the line 162. The micro-processor 126 also provides signals over the lines 164 which - signals are generated in response to the program to control the transmission of data to and from the microprocessor 126. Thus, for example, when the microprocessor 126 is in condition to input data, such as the final desired torque value TD, a signal is transmitted Erom the microprocessor 126 over the lines 164 to a gating circuit 166 -to furnish control inputs at 168, 170 to the universal asynchronous receiver transmitter 148. Control and status indication signals for the teletype console are also provided over the lines 172 and, via signal conditioner circuits 174, over the lines 176.
Figure lOB schematically illustrates -that portion of the circuit which provides interfacing between the microprocessor 126l the torque and angle transducers 100, 102 and the air valve 92. Torque data from the torque transducer 100 (Figure 8) is converted by the analog to digital converter 112 into twelve digit binary signals transmitted on the lines 118. The particular microprocessor employed is, however, only capable of receiving an eight digit input. In order to permit transmission of torque data to the processor, a multiplexing arrangement is provided.
Thus, the twelve digit output of the analog to digital converter 112 is supplied, through logic level buffers 178, 180 to a pair of steering gates 182, 184, the first four digits being supplied to the first inputs a of the gate 182 while the second four digits are supplied to the corresponding first inputs a of the gate 184. The final four digits are supplied to the second inputs b of the gate 182. The corresponding second inputs ~ of the gate 184 are connected to ground, supplying a constant zero input.
The eight line output 186 of the steering gates 182,184 provide the torque data input to the microprocessor 126. The gates 182, 184 are controlled by signals on the lines 188, 190 to first pass the a input signals, i.e. the first eight bits of the torque , , signal, to the output lines 186 followed by the b input signals, i.e. the final four bits and ~our zeros. In addition to being supplied to the steering gates 182, 184, the torque data transmitted on lines 118 is also temporarily stored in the registers 192, 194, 196. These registers 192, 194, 196 normally store th~ current torque value received ~rom the analog to digital converter 112. A hold signal ~urnished by the microprocessor 126 over the line 198 actuates a latching circuit 20~ to temporarily freeze the registers 192, 194, 196 permitting the torque value stored therein to be read over the lines 202. This arrangement permits reading of the torque data into the microprocessor 126 while updated torque data is being supplied from the analog to digital converter 112 without the danger of inadvertently reading into storage a data value which is a mixture of old and updated values.
The analog to digital converter 112 supplies an end of conversion signal over line 204 which signal is supplied to the latching circuit 200 over the line 206 to reset the circuit 200 when transmission of a torque value has ended permitting updating of the registers 192, 194, 196. It should be noted that the analog to digital converter 112 is under the control of the microprocessor 126. Thus the microprocessor 126 provides an enable signal over the line 208 and a convert signal over the line 210 to a gate 212 which also receives, over a line 214, a tool rotation indicating signal, the origin of which will be described below. It will be understood that the enable and ~onvert signals on lines 208, 210 are generated in response to t~t~

the program controlling the microprocessor 126. The output of the gate 212 provides a start conversion signal to ~he analog to digi~al con~erter 112 over the line 216.
As mentioned previously, the steering gates 182, 184 receive control signals over the lines 188, 190. These control signals are generated by a pair of gating circuits 218, 220. The gating circuit 218 is responsive to the end of conversion signal from the analog to digital converter 112 on the line 204 and an enable signal on the line 222 which signal is derived rom the enable signal supplied by the microprocessor 126 over the line 208. The gating circuit 218 provides an input to the gating circuit 220 which also receives a signal over the line 224 from the microprocessor 126 in the form of a response back signal indicating that the previous data has been loaded into the micro-processor memoryO In addition to controlling t~e steering gates 182 r 184, the gating circuit 220 furnishes a da~.a ready signal on the line 226 to the microprocessor 126O A ~urther input 228 is provided for the logic gating circuit 218. The function of this input is to supply an event marker to memory.
The circuitry of Figure lOB also provides interfacing hetween the angle transducer 102 and the microprocessor 126. The output signals of the angle transducer 102, in the form of sine and cosine signals over the line 110 are supplied to a converting circuit 230 which, in response to the transducer signals, generates an output pulse for each degree of rotation of the tool.
This pulse signal on the line 232 provides the tool rotation indicating signal on the line 214 and also provides an input to a .~

1~ 3~ d 3 gatin~ circuit over a line 236. The gating circuit 234 also receives an input signal from the microprocessor 126 over the line 238. This latter signal is present during the tool on period and goes off simultaneously with the tool cff signal.
The output 240 of the gating circui-t 234 provides an input to the microprocessor 126 in the form of a pulse train with one pulse for each degree of tool rotation. The portion of thls signal occurring af~er the input signal on the line 238 has been removed is a measure of the degree of tool overrun.
Also included in the interface logic and amplifier circuits is a reset circuit 242 connected at 244 to a reset switch and providing output signals 246, 248 which serve to reset various of the circuit components when the system is turned on.
Signal conditioner circuits are also provided, the clrcuits 250 providing interfacing between the microprocessor 126 and ~xternal controls for reset, gain~ internal calibration and external calibration while the circuit 252 serves to interface the tool on signal from the processor 126 over the line 254 with a solid state relay controlling the air valve 92, the output signal being provided over the line 256. A further circuit 258 is connected to a single pole double throw external switch serving as an emergency or panic switch. The output 260 of the circuit 258 supplies an interrupt signal to the microprocessor 1260 The components illustrated in Figures lOA and lOB are more completely identified in Table I, below:

- 60 ~

d!~3 TAsLE I

Identification or Standard Parts No. Number SN7402L g Resistor Pack, 4.7K ohm 11 Potentiometer, lK ohm 13 72747, Texas Instruments 15 Diode, lN914 unmarked SN7404L, inverter unmarked Transistor unmarked SN74157L 182, 189 SN7496L 192, 194, 196 Resistor Pack, 15K ohm 23 Transistor 2N2905 29 Resistors 33, 620 have 1/2 watt rating unmarked The number adjacent each resistor is the resistance in ohms~ All resistors except 33, 620 have 1/4 watt ratings. The number adjacent each capacitor is the capacitance in microfarads. The symbol "v" is used to designate that the particular lead is connected to a 5 volt buss through a resistor, e.g. of 1000 ohm capacity, to prevent damage to the component. The symbol "POR"
is used to designate "power on reset" which means that power stays on about 1/2 second.
Although the computer program and the circuitry of the interface amplifier section 140, previously described, are designed to activate a conventional teletype console in order to enter different values for the empirically determined parameters and to obtain a printed readout of certain calculated values such - 61 ~

as the tension at the mid-point stop 32, it is appaxerlt that the details thereof can be adapted to manipulate a display panel 144 as shown in ~;gllre 11. The display pane' 1~ ic preferably located within view of the tool operator and comprises a base section 262 supported in any suitable fashion having a first group of signal lights 264, 266, 268, 270 indicating features of the joint 98. The signal light 264 indicates that the final desired tension value FD has been reached or that the final calculated tension value Ffina1 is within an acceptable range.
The signal light 266 indicates that the joint has experienced non-linear strain. The signal light 268 indicates that the final calculated tension value Ffinal is in an unacceptable range. With the lights 264, 266 lit, the deduction is that non-linear strain has occurred ~ut that Ffinal is acceptable. With the lights 266, 268 lit, the deduction is that non-linear strain has occurred but that Ffinal is not acceptable. The light 270 is; energized when the fastener exhibits a low tension rate as pointed out by the ratio of TRa/T ~ .
The display 144 also provides another group of lights 272, 274, 276 indicating quality control features. The light 272 is normally energized when the frequency of non-linear strain detection is minimal while the light 274 is energized when the frequency of non-linear strain detection is too high as pointed~
out in equation (48~. The light 276 is energized when the final calculated tension Ffinal differs significantly from the final desired tension value FD as pointed out by equation (58).
The display 144 also comprises a third group of lights C~ ~3 278, 280, 282 indicating tool operating features. The light 278 indicates that the tool is functioning normally. The light 280 is energized when the ratio ~a/~p is too small or when the frequency of low ratio values becomes significant. Similarly, when the ratio of ~a/~ap i5 too large, or when the frequency of high ratio values becomes significant, the light 282 is energized.
A typical fastener system for use with this invention may comprise 5/16", 24 threads/inch, SAE grade 8 nuts and bolts.
With this fastener pair and the modified Rockwell 63W air tool, the following values were found for the empirically determined parameters:
FRl = 47 lb/degree n = 14 r = 1.12 To - 54 ft-lb FM = 2900 lb a = 11.6 degrees/ft-lb FL = 1000 lb c = -52.3 degrees Tl = 5 ft-lb ~d = 68 degrees 'rOs = .4 ft-lb Nk = 0.80 aor ~ 20 degrees ~ = 0 93 ay = 12 degrees Ko = .21 ft-lb/degree aR = 9 degrees ~a = 3 degrees Using these parameters and 5/16" - 24, grade 8 fasteners, with a grip length of 2.44", and having a cadmium dichromatecoating, the following data was developed using part of the technique here disclosed. The stiffness of the load washer used to measure tension directly was a 5 x 106 lb/in and the clamped pieces were hardened steel. In running the tests reported in the following table, the angle option was used and execution was within + 2 to ~- 63 -~.3~ J~

- 1 degrees, which cor.responds to + 104 to - 52 pounds in tension.
The overall instrumentation repeatability and linearity, including the tension probe and the torque transducer, is estimated at 4~.

I ~
l o~o~o o o o o o~o o l ooooo ~oooo I ,~ ,~ ~ ~ ~ ~ ~ ~ , I
I ¢ ¢ u~ ;~; ¢ cn u~ ¢ ;~ ¢
I ,C ,~ ,~ r ,~ .~ r ,~ r ~rl~ r1~r~ r~
I 3 3 3 3: X 3 .C 3 3 O I a) a) ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~c~ i ~ ~ P ? ? ? ? ? ? ? ~ aJ aJ
I ~r~r ~ ~r ~ ~r ~ ~ ~rl- 0 ~ ~ ~ 0 ~ 0 0 ~d ~
I CJ ~ U U O Cl ~.1 U ~ U C~
I s~ ~ ~ h I ¢ ~ ¢ ¢ ¢ ¢ ¢ ¢ ~ ¢
I
~o$ I
I ~ ~ CO ~ o ~ ,~ U~ ~ ,` ~ ~ ,_ U~ ~ U) ~ ~ ~ o~
o I ~ ~ ,~ ~ ~ ~ oo ~ O ~ a~ ~ ~ ~ u~ ~ ~ ~ ~ o rl ¦ CO ~1 ~ ~D r~ O ~0 0 0~ ~0 U7 ~ ~D N U~
~ E-~ ~ ~ Ir-lr~ 1r-lr-lr-l ~0 I
d l OOOOOOOO~ C~ 3 ~ d I
~ i~ I
, _-I
~:: U ~4 1 ¢ ~ ~ ~
u~ ~0 I 00 ~ ~ 1~ U~ ~ ~ O ~D O O CO r~ ~ ~ ~1 ~1 ~1 IOOOOOOOOOO o~ or~
~1 ~ ~ ~ ~ ~ 1 ~ l I
_ _ I
I r~ ~ O ~ ~ ~ ~ I~ u~ ~ CO u~ ~ ~O ~ O ~J O ~0 `D
r I C~ t~) O ~ C~ I~ 00 0 t~ O 00 ~1 ~ O ~ C~

tl~ I 00 ~1 ~;t 1~ 00 0 0~ 0 00 r-i ~O CO ~ 1~ U') ~ ~ 10 ~ ~
E~ ¦

_ ~1 ~0 I ul ~ r~ ~ ~ I~ ~ u~ ,,~ ~ ~ ~D ~ ~ ~ O ~ r~ 00 r~
I u~ I~ ,1 U~ r~ .J ~ O U~ ~ r~ o o o ~;r ~ ~ ~ ~
~ I
_ I r~ C~l ~ ~ Ul ~D ~ 03 a~ o ~ ~ ~ ~ u~ O
Z j ~ ~ ~ ~ r~ ~ ~ ~ r~

~q,~6~

- - - - -a~ ,Q
oo o n .
~O ~rl C~
c~ +
x ~o ~
- -~1 g ~ o ~ c`J
E~ o ~ ~ u~ o ^ o ~o ~ c`l ~ ~
U ~9~rl t~ + 1 5 O
X ~ ~
_ ' ~
,_a~ ,1 U
a~ ~ ~
¢ ~ . ~ 00 ~rl U~ ~ ~ ~ C~l I
,~ U~ ~ +

,Q . . . . __~

U~
. ~ . .

E~
o .0 ~ ~ I~
O ~_ o ,J, ,~
_ _ ...
o ~U
~ â
a~ ~ ~1 o 00 P ~ ;~ U U ~0 Z
~ ~p ~p ¢
¢ 0 ~ ¢ 0 ~ 0 ~.3~

The tension value reported in the second column was recorded approximately 15 seconds after the tool stopped. This is believed to involve a relaxation in the joint amounting to 1-2% of the recorded tension value.
A statistical analysis of the data gathered on the twenty fasteners reported in Table II shows that the partial technique of this invention acts to control tension to within + 11.1% of the desired value in 99 out of 100 cases, or within 2.58 standard deviations. It should be thoroughly understood that the above data was taken with a program which does not include a number of features disclosed herein, including (1) the use of a second calculation of TR and aOrigin; (2) the provision of yield detection and shut off in response thereto; and ~3) the use of a curvature check of torque rate in the region where TR
is calculated in order to identify and reject low tension rate fasteners. The effect of these additions to the program is, of course, somewhat ~peculative. It is believed, however, that the inclusion thereof will reduce scatter still further.
With the same joint and tool, the use of a torque control method would have to produce an average final torque of 22.68 ft-lbs to achieve an average final tension value of 6267 pounds. The observed deviations from average ~ 43.0 to -45.5%.
Thus the torque control method would have produced a tension scatter of + 82.3% of the desired value in 99 out of 100 cases, assuming that the bolts would have been capable of accepting any tension. In reality, 10.4% of the bolts would have ruptured, producing no tension at the termination of tightening. Another , ~ ~.3~

14.7~ ol the bolts would terminate in the plastic zone, i.e. past the yield point.
With khe same joint and tool, the use of a turn-of-the~
nut method would have to advance the nut 96.3 from a threshold torque of S ft-lbs to achieve an average final tension value of 6267 pounds. The observed deviation is ~13.2 to -25.2~. Thus, a turn-of-the~nut me~hod would have produced a tension scatter of +21.7% of the desired value in 99 out of 100 cases. It is interesting to note that the selection of 6200 pound tension for a bolt having an elastic limit o 6950 pounds appears to be optimurn because only a~out .6~ of these bolts would end up in the plastic zone.
Referring to Figure 12, there is illustrated another device 298 for implementing the technique of this invention~ The basis of this approach is e~uation (7) where the value of dF/da indicates the tension rate. Rewriting equation (73.

da log T = dF/d~ (58) If dd log T can in some fashion ~e determinedr F in equation (68) can become the final desired tension value FD or the tension value F~o at the point of shut off command while dF/da is an empirically determined tension rate FR3 which is an appropriate average of FR
and FR2 over the angle interval in question. It will be apparent that dd log T _ dd (69) dt As suggested in Figure 12, the analog device 298 includes 6~ 3 an angular speed pickup 300 of any suitable type, such as a tachometer, for continuously sensing a value for d~Jdt, which is the speed the fast.ener is being tightened.
A torque transducer 302 continuously senses the value of running torque T. The transducer 302 may be of the same type as the transducer 100. A logarithmic amplifier 304, such as is available from Analog Devices, Inc., Norwood, Massachusetts, under the designation of Logarithmic Amplifier, Model 755, is connected to the torque transducer 302 by a suitable connection 306. The logarith~.ic amplifier 304 continuously converts the sensed value of running torque T into a continuous signal representative of log T. .
A time differentiating device 308 is connected to the logarithmic amplifier 304 by a suitable lead 310 and continuously differentiates the signal from the logarithmic amplifier with respect to time in order to obtain the differential of the logarithm of running torque ddt log T. The time differentiating device 308 may be of any suitable type, such as an operational amplifier 312 in parallel with a capacitor 314. A suitable opera~ional amplifier is available from Analog Devices, Inc~, Norwood, Massachusetts, under the designation Operational Amplifier, Model 741~
. The signal from the time differentiating device 308 is delivered through a lead 316 to a low pass filter 318 which acts to smooth out the signal from the time differentiating device 308 thereby removing some of the noise .inherent in the torque signal from the transducer 302.

C3'7~

The angular speed pickup 300 and the low fil-ter 318 are connected by suitable leads 320, 322, to an analog divide device 324 such as may be obtained from Analog Devices, Inc., Norwood, Massachusetts, under the designation Divide Module 436s. The leads 320, 322 are connected to the divide device to produce an output signal along a lead 32O consisting of the ratio dt log T
da dt As indicated in equation (69), this signal is representa-tive of d log T.
When the value of FR
da log T ~ F , when T ~ Tl t70) where Fso is the tension value in the bolt at the time of shut off, the Tl is threshold torque, e.g. about 20~ of average final torque, the tool is commanded to shut off. It will be evident that the threshold may be measured in terms of angle, where ~ ~ ~p, rather than torque.
Because the tool will overrun after shut off, the value of Fso is selected so that average tool overrun advances the fasteners to the final desired tension value FD. The average tool overrun may be determined empirically or from ~Fso = (dt) so (~t)F 3 (71) where (dd~)sO is the average speed of the tool at shut off, ~Fso is the average additional tension due to overrun, and ~t is the time delay between the giving of the shut off command and the closing of the air valve. Thus, Fso = FD ~Fso (72) Because Fso and FR3 are assumed to be a constant, the ratio of FR3/FSo is obviously constant. Thus, a constant signal representative of FR3/Fso is placed on a lead 328. The leads 326, 328 are connected to another divide device 330. When the output signal from the divide device on a lead 332 becomes unity, an amplifier 334 is triggered to energize a solenoid catch 336 to allow the solenoid spring (not shown) to close the air valve.
Although the analog device 298 of Figure 12 is not believed to have the accuracy of the digital device 86, it is apparent that it has the advantage of simplicity, both physical and operational. The analog device 298 operates Gloser to the theoretical basis of the invention and contains ,fewar assumptions and simplifications. Some of the disadvantages of a simple analog device, such as the inability to vary the overrun prediction and the noise reduction in the filter 318, are capable of being surmounted by more sophisticated analog techniques as will be apparent to those skilled in the art.
As will be apparent to those skilled in the art, the technique of this invention can be used to monitor other tighten-ing strategies thereby determining the accuracy thereof in tightening fasteners to a final desired tension value. This may ' readily be accomplished by modifying the amplifier section 144 in order not to manipulate the air valve solenoid in response to the tightening parameter.

Claims (5)

THE EMBODIMENTS OF THE INVENTION IN WHICH AN EXCLUSIVE
PROPERTY OR PRIVILEGE IS CLAIMED ARE DEFINED AS FOLLOWS:

1. A method of tightening seriatim a multiplicity of substantially identical pairs of threaded fasteners comprising tightening the fastener pairs with a powered tool; establishing a final tightening parameter; predicting an amount of tool overrun, variable from one fastener pair to the next, at the termination of tightening; and instructing the tool to terminate tightening of each fastener pair in response to the difference between the final tightening parameter value and the amount of predicted tool overrun.

2. The method of claim 1 wherein the predicting step comprises predicting tool overrun as a function of torque rate.

3. Apparatus for tightening seriatim a multiplicity of substantially identical pairs of threaded fasteners toward a final tightening parameter comprising a powered tool for tighten-ing each fastener pair; means for predicting an amount of tool overrun, variable from one fastener pair to the next, at the termination of tightening; and means for instructing the tool to terminate tightening of each fastener pair in response to the difference between the final tightening parameter value and the amount of predicted tool overrun.

4. The apparatus of claim 3 wherein the predicting means comprises means for predicting tool overrun as a function of torque rate.

5. A method for monitoring the tightening of a joint includ-ing at least one threaded fastener pair, comprising tightening the fastener pair beyond the yield point thereof; sensing torque and not load applied to the fastener pair at various angles of advance; determining, from the sensed values, the stress appear-ing in one of the fasteners at the termination of tightening at a stress value adjacent the fastener yield point which stress differs from the nominal strength of the one fastener and which varies from joint to joint.