CA1103460A

CA1103460A - Method of and means for grinding pairs of gear wheels as spiral or curved toothed bevel gear wheels

Info

Publication number: CA1103460A
Application number: CA303,053A
Authority: CA
Inventors: Dieter Wiener
Original assignee: Individual
Current assignee: Individual
Priority date: 1977-05-11
Filing date: 1978-05-10
Publication date: 1981-06-23
Also published as: SE434807B; BE866882A; SU1075954A3; FR2390233A1; CH628271A5; IT1094826B; BR7802973A; IT7823284A0; GB1593225A; ATA319078A; LU79639A1; DE2721164B2; JPS549090A; DE2721164A1; FR2390233B1; NL7804959A; AT354885B; DE2721164C3; SE7805312L

Abstract

ABSTRACT OF THE DISCLOSURE

A method of grinding pairs of spiral or curved tooth gear wheels is proposed wherein the teeth of one of the mating gears are formed by grinding the opposed flanks of a gap between successive teeth in one operation by a tool having outwardly facing grinding flanks, whilst the teeth of the other mating gear are formed by grinding the opposed flanks of a given tooth in one operation by a tool having inwardly facing grinding flanks.

Description

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The invention is concerned with a method of and a means for grinding pairs of spiral or curved tooth bevel gears in the gear generating process, in which the teeth of one of the gears are produced by grinding the flanks at the two sides 5. of a tooth gap by a cup wheel having two mutually outwardly facing grinding flanks and which form a bevelled outer ring.
During the grinding of gear wheels by the gear generation-procedure, the gear wheel to be ground, on the one hand, and the grinding disc, on the other hand, describe synchronized 10. movements with respect to each other, the movements being coupled together through the driving train of the gear grinding machine. After each gear generating procedure, in which one or two tooth flanks are ground, the gear wheel is indexed forward, and a further gear generating procedure is 15. carried out, un-til all tooth flanks have been machined.
Whilst grinding flnds widesplead use for spur gears, grinding of bevel gears has hitherto been used only to a small extent. This is mainly due to the high cost of grinding and to the lack of a suitable grinding procedure. It is true 20. that bevel gears with straight and oblique teeth can be ground, but no grinding procedure is known by which spiral-toothed bevel gears can be satisfactorily ground. Many applications of spiral-toothed bevel gears are particularly desirable, since they have a large jump overlap and can be manufactured 25. by suitable design in such a manner that under load the bearing surface wanders only s1ightly, whilst with single sided positioned straight- and oblique-toothed bevel gears the bearing surface under load wanders from the inner to the ' --outer end of the tooth. As a result of their low sensitivity to displacement and the favourable jump overlap, spiral-toothed bevel gears have especially favourable noise properties.
`~ In procedures of the type described, which have become 5. known in practice, both wheels of each gear-wheel pair (wheel and counter wheel) are machined with cup wheels which have two conical grinding flanks and which are located in one tooth gap during grinding. The grinding flanks are thus turned away from each other and form a conical outer ringj which 10. projects concentrically to the axis of rotation of the grinding disc from a plane which is orthogonal to the axis of rotation.
It is true that accurately meshing pairs of gears can be produced by this method, but only after considerable expenditure of time, because expensive and complicated control procedures 15. are necessary. Both flanks of each tooth gap of a wheel can be ground in one operation by means o~ this known procedure.
But for the counter wheel each flank must be matched to the corresponding flank of the wheel. This necessitates the carrying out of two operations under expensive control with a corres-- 20. pondingly high expenditure for measuring and control equipment.
~ If, on the other hand, both toothed wheels of a pair are - ground in one operation, then on at least one tooth flank the ~earing region (known as contact surface) does not lie in the centre of the tooth flank, but at the edge of the 25. tooth (known as edge contact).
The object of the invention is to provide a method of and means for grinding the tooth flanks of the counter wheel (to a prevlously ground gear wheel) in one operatlon and without 6C~

expensive control procedures, so as to be an exact fit with the teeth of the wheel.
This object is attained in accordance with the invention, by the formation of the teeth of the other bevel gear (counter 5. wheel) by the simultaneous grinding of the flanks on the two sides of one tooth by means of a cup wheel having two grinding flanks which are inclined towards each other and form a conical inner ring. Thus, as hereinproposed the wheel and the counter wheel are machined by different cup wheels. Whilst one of 10. the cup wheels has, as explained, grinding flanks which are inclined away from each other, (that is to say mutually outwardly facing), and form a conical outer ring, the counter wheel is machined by a cup wheel of which the grinding flanks are inclined towards each other, (that is to say mutually 15. inwardly facing)~ and in effect form a hollowed-out conical inner ring concentric with the axis of rotation of the grinding disc, in a plane orthogonal to the axis of rotation. The invention is based on the appreciation that when grinding the gear teeth by reference to the tooth gap as in the prior art, 20. due to the geometry of the tooth arrangement, during grinding of the counter wheel in one operation only one of the two tooth flanks of each tooth gap (therefore only the left or only the right hand flank) can be so ground that the direction of its flank agrees with that of the corresponding flank of 25. the wheel which has already been ground, and therefore meshes accurately with it. The solution of the problem in accordance with the invention consists essentially of carrying out the grinding procedure accurately symmetrically for wheel and counter wheel, in that the counter wheel is ground by a ' , .
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cup wheel of which the contour is complementary to that of the cup wheel which is grinding the wheel itself. The axes of the two cup wheels naturally coincide in their position with respect to the teeth to be ground.
Accoxding to a preferred feature, the cup wheel is sub~ected to an additional motion, cyclic in nature and of small eccentricity, during grinding. Such an additional motion can be effected, for example, by moving the axis of rotation of the grinding disc parallel to itself in a circular orbit, lO. by means of an eccentric bearing box, for example. An analysis of the conditions shows that the additional eccentric motion influences the curvature of the concave tooth flanks differently from the curvature of the convex tooth flan~s.
In consequence of this a wide convexity is produced, which 15. leads in an advantageous manner to a limited lateral bearing surface with the consequence that within certain limits displacements of the~axes of the gear wheels meshing with each other can be permitted.
During rotation of the grinding disc under simultaneous 20. cyclic motlon, the outer flank is ground during the outwards part of this additional cyclic motion, and the inner flank of a tooth gap is ground during the inwards part, so that the .
corresponding flanks of the counter wheel can be machined in the same manner in one grinding procedure. By corresponding 25. choice of the diameter of the grinding disc on the one hand, and of the diameter of the cyclic curve followed by the grinding disc on the other hand, the wheel and the counter wheel can be ground so as to give optimum fit together. In - 5 ~

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particularl there is also the advantageous possibility of machining one of the wheels of a pair, in general the one with the larger number of teeth (i~e. the so-called rim gear) bv form-grinding, but machining the pinion in accordance 5. with the above-named procedure.
-An advantage arising from the additional motion is that the danger of grinding burns is greatly reduced. During grinding without additional motion the grinding flanks of the aup wheel remain in the direction of the circumference 10. along a line, known as the generator, so that one grinding stroke can move over the whole width of the tooth in one - engagement, with the workpiece held in position. This leads to a considerable danger of burning and ripping during the grinding, so that grinding can be carried out only at a 15. low rate of feed. If, on the other hand, grinding is carried out with the cyclic additional motion as explained, then the contact between gear wheel and grinding disc is reduced from a contact line to a closely localised contact region, so that the danger of grinding burns and grinding rippin~ is reduced, 20. i.e~ work can be carried out at a higher rate of feed.
Diferent methods are available for production of the additional motion. The additional motion can be a circular motion about the a~is of the grinding disc, as already described.
In many cases it is advantageous for the additional motion 25. of the grinding disc to be over a varying path, made up from two paths in the same direction with different radii of curvature. By this means, shorter down times are obtainable, during which the grinding disc is in contact with neither -;: ` `"

flank. This also permits a larger variation in the convexity available. In addition, it is possible, between the curved sections of the path, to provide a section in which the motion is approximately perpendicular to the flank of the 5. tooth, whereby the play between the profile strength of the grinding disc and the width of the tooth gap of the bevel gear can be equalised by a simple means Finally, the mid-points of the two curved sections of the path can be located at different points, wherehy the position of the bearing surface 10. on one tooth flank can be varied with regard to the other tooth flank.
`- In each case the additional cyclic motion, combined with - the method of working as explained in accordance with the invention, leads not only to a suhstantial improvement of 15. the meshing of the toothed wheels, but also to a favourable in~luence on grinding burns by means of the corresponding variation in closeness of fit between tooth flanks and grinding flanks especially also o~ the sunken bevel inner ring. In addition, the convexity, and with it the bearing 20. area, can be changed in an advantageous malmer in that the grinding disc is disposed so as to be movable in the direction of its axis, so that it grlnds on a diameter which can be selectedO
The ratio between cutting speed and feed speed of the 25. grinding disc lies preferably between 30:1 and 60:1, where the feed is defined as the motion of the contact point of grinding disc and wheel in the direction along the tooth.
Further, it has shown itself to be advantageous for the cutting ., `-~

motion and the additional motion of the grinding disc to be arranged in directions opposite to each other, thus grinding in contrary motion. Grinding in contrary motion is known in itself, but has no advantage in current grinding 5. procedures. On the other hand, within the framework of the invention, there is the advantage that higher feed quantities (rate of removal of material) are possible than with grinding with the same path.
With regard to the equipment for carrying out the 10. procedure described, the invention is based on a current equipment for gear generation in the form of bevel gear ~ wheels, which includes a cup wheel which can be driven about ; a grinding axis and which has two conical grinding flanks.
In accordance with the invention such a device is characterised 15. in that the grinding flanks are inclined towards each other and form a conical inner ring. ~ ~
The invention will now be described further, by way of example only, with reference to the accompanying drawings in which:-20. Fig. 1 is a schematic illustration of the interlocking relatlonships of a pair of wheels, and the interlocking relationships between the grinding disc and the wheel;
Fig. 2 shows a bevel wheel in the idealised form of a 25. crown wheel;
Fig. 3 is a perspective view of the bevel wheel to be ground with the grinding disc shown in`partial section;

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Fig. 4 shows a bevel wheel in the idealised form of a crown wheel, showing the geometry and kinematics : of the grinding wheel; and Fig. 5 illustrates a number of examples for the path 5. followed by the cyclic motion.
Referring now to the drawings, Fig. 1 shows a pair of gear wheels with two lntermeshing bevel gears 1 and 2 having spiral teeth. Each wheel 1, 2 has the same constant .. :
length R for the bevel, whilst the angles of bevel of the ~; 10. two wheels are denoted byJ Ol and ~02~ respectively. Finally, both wheels have an outer;bevel length Ra. In addition, in the example illustrated the tooth height is independent of the bevel;length R.~ ~
The outer peripheries of clrcles Ra are shown projected 15. onto the plane of the drawing to the right of the pair of gear wheels, and are consequently shown as ellipses, (in~
dotted lines on the~drawlng). One tooth 10 of wheel l and one tooth gap 20 of gear~wheel 2 are shown. If the two wheels mesh with each other, an ideallsed plan may~be imagined, i~

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20. which the teeth have straight flank lines, which mesh ~; simultaneously wlth both wheels and whose points o~ contact in all posltions of generation with the two wheels l, 2 :
are also simultaneously the points of contact of~the two wheeIs one with another. This form of tooth arrangement -25. known as the ideal crown wheel - is developed as tooth pro-jection 3 between the two wheels l, 2. This ldeal tooth arrangement of the bevel gear has an outer radius equal to the outer bevel length ~ and an angle of bevel of 90 - and :~ , g _ ~3~

therefore a doubled angle of bevel of 180 . Fig. 2 is a view from above of the ideal crown wheel 4 appertaining to the two wheels, in which the flank lines which limit a tooth gap gl, in this case 42, 43, are represented by arcs 5. of circles. In the known method of grinding bevel wheels the working tool takes the form of a cup-shaped grinding disc 5, as shown at the right hand side of ~ig. l. With this grinding disc, whose grinding flanks 51, 52 form a conical outer, or "externa1'l ring, the right and the left flanks lO. of the tooth gap 20 of one gear wheel 2 are produced. If this tool is also used in the production of the tooth gap of the other gear wheel l, the right hand and left hand flanks of such gap must be produced in separate processes, otherwise the mid-points of the flank lines of the right hand and 15. left hand flanks~of the tooth gap of the wheel and counter wheel would not coincide.
Accordingly, in accordance with the invention, the counter~wheel is machined by a cup wheel 7, Fig. l, whose conical grinding flanks 71, 72 are inclined towards each other and 20. form a hollow sunken conlcal inner, or i'internall', rlng. By this means i~ is possible to machine the counter-wheel also in one operation. In addition it is shown how the grinding discs 5 and 7 have the same axis 8 with respect to the crown wheel used. While the grinding disc 5 grinds the tooth 25. gap 20 of wheel 2 by means of the grinding flanks 51, 52, the flanks of tooth lO of counter-wheel 1 which mesh with such tooth gap 20 are ground by means of the grinding disc 7, each in one operation. The grinding disc 7 with its spindle ,' -' ~, .

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can be displaced in the direc-tion of a~is 8 in accordance with arrow 81, so that the disc grinds on another diameter ~ence the convexity may be varied.
Fig. 3 shows a practical aspect of the method as applied - 5. to the grinding of wheel 2. The grinding disc 5 with the flank profile 51, 52 rests in the form of a conical outer ` ring on the spindle 53, which rotates in direction 54. This '- rotary motion is the cutting motion of the grindlng disc.
The gear wheel 2 to be ground rests on an axle 23 arranged 10. ~or this purpose, i.e. a driving shaft, and executes an oscillatory rotary motion- the gear-generating motion -, in the direction of the double arrow 24. The ~rinding disc5 executes, in addition to the cutting motion 54, a reciprocating motion 56 adapted to the ~otion 24 of the bevel gear, 15. for the production of which a component is used which moves the grinding disc in a cyclic motion about the intersection 57 of axle 23 of the wheel 2 with the centre line 58 of the tooth height. ~s shown in Fig. 3, tooth gap 20 of the bevel gear is being ground, and the flank 21 (below this in the drawing) 20. is being machined by the outex grinding flank 51, and the upper flank 22 by the inner grinding flank 52. Thls leads to machining o~ one of the flanks 21 or 22 from the outside inwards, and that of the other flank from the inside outwards, always while the wheel is reciprocating in one or other of 25. the directions of the double arrow 24.
On the rotary or cutting motion 54 of the grinding disc 5, corresponding to the grinding disc 7, there is superimposed an additional cyclic motion 55 of small eccentricity f~

which is transmitted either from the grinding disc 5 through grinding spindle 53, or directly from this latter. This is further explained b~ means of the ideal crown wheel 6 shown in Fiaure 4, in which the cutting lines of a toot~
gap are indicated by 61 and 62~ The flanks of the tooth gap are produced by a grinding disc, not shown in the drawing, of outer radius r and inner radius ri, which turns about axis Ç3. Again this rotary motion is the cutting motion.
In addition the grinding disc executes a cyclic motion, which is circular in the aspect of the invention illustrated here, whose orbit is indicated by 64 in the drawing. Both motions take place in the direction of the arrow 65.
The radius OL curvature of the concave tooth flank is - the sum of the radius r of the grlnding disc and the radius of the additional motion. The cutting line of this concave form is likewise an arc of a circle. The convex tooth flank has in this plane only approximately the form of an arc of a circle, since the two motions overlap along the radius ri and the radius of the additional motion. The curvature of this tooth flank corresponds approximately to the reciprocal of the radius ri and is larger than this reciprocal by a negligible amount. If the wheel and the counter w~eel are produced with a grinding disc, a~ described in Figs. 1 and 3, 5 to 7 as appropriate, and if either both or one only of the working tools are subjected to such an additional motion, an advantageous convexity is produced, leadin~ to a restricted lateral force and thus favourable displacement properties of the wheel.
In addition, the wheel and the counter-wheel can be pxoduced "` ~ 3 :' "
in one process. Contact between grinding disc and workpiece takes place not only along a contact line, which lies essentially in the cutting direction of the grinding disc, but, on superimposition of a reciprocating motion, theoretically 5. in a single point, but actually o~er a relatively small contact surface, on account of the cutting adjustment during grinding. The size of this contact surface depends with regarcl to the engaging surfaces on the mag~itude of the adjustment and on the ratio of the cur~atures of the grinding disc and 10. the additional motion.
A further advantage of this procedure is seen in Fig. ~.
In the arrangement of the additional motion indicated, the ~ contact zone wanders on the concave flank from the outer end - of the tooth to the inner end of the tooth. and on the convex ; 15. flank from the inner end of the tooth to the outer end of the tooth. Due to the form of the additional motion and the limited length of the contact surface between grinding disc and wheel being produced, the effect of heating on the wheel durlng grinding, and hence the risk of grinding burns, 20. is reduced.
Various different~forms of producing the additional motion are diagrammatically shown in FigO 5. 5.1 shows the circular path which has already been explained. 5.2 shows another cyclic curve, in which two sections of circular 250 arcs, of different radii, are combined. Whilst during a circular additional motion in accordance with 5.1 there is a large proximity time, this time is reduced by use of a form of additional motion in accordance with 5.2. In addition ,~

there is a larger variation in width on selection of the desired convexity.
With the path of the motion 5.3 there is a displacement at the end positions, which has a component of motion in the 5. direction of the circumference of the wheel. By this means a balancing of the play between the thickness of the grinding disc and the width of the tooth gap can be effected.
Finally, the mid-points of the additional motion can be selected as desired as is shown in 5.4. By this means a 10. favourable influence of the position of the bearing surface on one tooth flank is possible, independent of the position of the bearing surface on the other tooth flank.
The method of working as explained is especially advantageous for grlnding precision gears, e.g. in machlne 15. tool production, press construction, fast-moving drives, and in aircraft production. The preliminary formation of the teeth is, in general, carried out by milling, after which the wheels are hardened and then ground. In mass pxoductlon, e.g. for lorries, the preliminary formation of the teeth 20. may be by precision forging, after which the wheels are hardened and then ground. Further, it is possible for one wheel - usually that with the greater number of teeth -to be produced by grinding to shape, and for the counter-wheel to be machined in accordance with the procedure explained.
25.

Claims

What is claimed is:-

1. A process for the grinding of pairs of spiral or curved tooth bevel gears using a method of gear generation in which the teeth of one of the bevel gears are produced by grinding the flanks of a tooth gap by means of a first cup wheel having two outwardly facing grinding flanks forming a conical outer ring, wherein the teeth of the other bevel wheel are produced by the simultaneous grinding of the flanks on the two sides of a tooth by means of a second cup-wheel having two inwardly facing grinding flanks forming a conical inner ring, an additional cyclic motion of small eccentricity being superimposed on the cup-wheels during grinding.

2. A process as claimed in claim 1, characterised in that the cyclic motion is a circular motion.

3. A process as claimed in claim 1, wherein the cyclic motion is the result of two differing curvatures which are concave with respect to the curvature of the flanks of the teeth.

4. A process as claimed in claim 3, wherein between the two sections of the motion consisting of arcs of circles, a straight section of the motion approximately perpendicular to the flank of the tooth is inserted.

5. A process as claimed in claim 3, wherein the two circular shaped sections of the motion have different centres of curvature.

6. A process as claimed in claim 4, wherein the two circular shaped sections of the motion have different centres of curvature.

7. Apparatus for use in grinding pairs of spiral or curved tooth bevel gears comprising a cup-wheel mounted for rotation about a grinding axis and having two conical grinding flanks formed at one face of the cup-wheel, the flanks being divergent in a direction axially away from said face and from said disc, thus forming an axially inwardly convergent annular recess, said apparatus further comprising means for selective axial displacement of said grinding disc.

8 . Apparatus as claimed in claim 7, characterised in that the ratio of cutting speed to feed speed of the cup-wheel lies between 30:1 and 60:1, where the feed is the motion of the point of contact along the tooth.

9 . Apparatus as claimed in claim 7, characterised in that the cutting motion and the feed motion of the grinding disc are in opposite direction.