US1705887A - Method of generating hypoid gears - Google Patents

Description

' March '19, 1929. E. WILDHABER METHOD OF GENERATING HYPOID GEARS Filed Mar'oh 1, 1927 a SheetsSheet 1 INVENTOR Ernest Wltdhaber ATTORNj 7 March 19, 1929. E. WILDHABER METHOD OF GENERATING HYPOID GEARS Filed March 1-. 1927 5 Sheets-Sheet 2 I I INVENTOR ATTORINKL/ E. WILDHABER METHOD OF GENERATING HYPOID GEARS March 19, 1929.

a Sheets-Shei a 5 Filed March 192'? Y mvNToR Emest Wildbaber mange Patented Mar. 19, 1929.

UNITED STATES AT T o FIcE,

ERNEST WILDHABER; 0E BnoOKLYN, NEW Yonxgass eNon "Iro GLEAsoN noonnscnnn, NEW YORK, A CORPORATION OF NEW YoEfx;

WORKS, )0}? METHOD OF GENERATING HYPOfD. GEARS. i

Applicatiqn filed March1l1927. i Serial' NoQ171Q773i' The present invention relates to, hypoid gears and to a methodoi"producing such gears and particularlyto a method of producing hypoid gears which have longitudinally inclined teeth;

The primary objectof this invention is to provide a method whereby the side tooth sur-- faces of each memberofapair of hypoid gears, having longitudinally inclined teeth,

emay he cut'two sides simultaneously in agenerating operation in such manner-that the gears themselves will mesh-With theoretical accuracy. The primary aim of thisin'vention, is therefore, to speed up the product on of hypoid gears Without in any way affecting their running qualities. I i The present invention is particularly plieable to the production of hypoid gears having longitudinally curved teethf l-Vith the present invention the tooth surfaces of each member of such a pair may beicut two side taces'simultaneously on existing machines and ithout requiring any additional adjustment or added motion. v

' In the accompanying drawings, I have illustrated two different embodiments of my invention. It Will be understood, however,

that this invention is not restricted to the,

forms shown but is capable of further m0dilication Withinits scope and the l mitsot the appended claims.

In the draw ngs: Figure 1 is a plan tudinally curved may be produced 1n aeco view oi a pair of longirdance With the present invention; V l ,1

Figure 2 is a front elevation, partly inisection, of the gears shown in Figurel; r

Fl gure 3 is a diagrammatic vieiv oi the itch surfaces of the gears shoiv n in Figuresjl and 2, the plane of the drawing being a plane tangent to the pitch surfacesof thet-Wo gears;

Figures 4 and 5 are a front elevation, part,

ly in section and a plan view, respectively,

of a pair of hypoid gears, constructed according to this invention, whose tooth surtacesare according to another embodiment oi. this inderived from straight tooth basic members;

' Figure 6 is a diagrammatic view showing and 10 and ,jugate toan ofi'set cro'v'vh gear or basic gear,

tooth-hypoid gears; such as Figures 9 and 1 0 are aside elevation, partv gear or larger member oi a pair of longitudinallycurved tooth hypoid gears;

Figure 11 is. a plan View illustrating diagrammatically the preferred method of generating the pinion to mesh with the gear prov ducedaccording to, the process ot Figu'res 9 Figure12 is a plan View illustrating diagrammatically the preferred method of pro ducing, vjvith this invention, gears such as the gears shown in Figures 4' and. 5 which are conjugzlite' to a basic gear having straight inclined teet 1. I i

With the present invention each member of apair of hypoid gea'r'sis generated conthatis",,is produced in a generating operation in hich inaddltion tothe cutting motion ot the tool an additional relative mo-tion is imparted between the tool and hlanlccorre- [spondmg to that of. agear meshing with a crown gear or basic gear Whose. axis is offset from the axis of the blank. A principal-advantage of the present'inventionis that it enablesboth members of a pair of hypoid gears to be out two side faces simultaneously .in such manner that the gears Will run together Without bias hearing or artootli surlaeecontact which extends diagonally across a the races of the matlng teeth. This invention a is particularly applicable to the production of'hypoid gears in which both members of the pair. have longitudinally curvedjteeth "inthe generation 'ofhypoid gears conjugate and ingen'eralis especially adapted toruse 'clined' longitudinally tothe' straight ge-neratriee's oftheir pitch surfaces.

Figures 1' and 2 show a-pair 0t hypoid gears such as might be producedaccording to one embodiment of this invention and Figures l and 5 show a pair of hypoid geaii's' produced vention, In each case, both members of the {pair a1 provided with teeth which are lonl 'itudin llfinelined that isiiielined a ainstv ca 7 k:

of the gears. The g T Figuies 1 and 2 are provided with longitudinally @curved teeth and are, d'emved from ba 'ie g'ears hav ng longitudinally "curved teeth I gears er- -r with rotary annular face mills.

Figures 4 and 5 are derived from basic gears having teeth which are straight, but nonradial or skew.

In Figures 1 and 2, indicates the gear or larger member of the pair and 11 the pinion or smaller member of the pair. These two gears mesh together with axes non-intersecting and non-parallel, the axis 13 of the gear being offset from the axis 14 of the pin ion. In the shown embodiment, the axes 13 and 14 ot' the gears are disposed at right angles to each other. The gears mesh together witha combined rolling and sliding action. The gears are provided with conical pitch surfaces, the pitch cone apexes of gear and. pinion being at 15 and 16, respectively. Each member of the pair has, as stated, longitudinally curved teeth. In the preferred construction, the spiral angle or tooth inclination angle or the teeth 19 of the pinion will be larger than the spiral angle or tooth inclination angle of the teeth 18 of the gear, as with this construction it has been iound that the pinion can be made larger and stronger than bevel pinions 01" corresponding ratios. The tooth surfaces of each member of this pair are derived from, that is, generated conjugate to basic crown gears having longitudinally curved teeth. The tooth surfaces of each member of the pair are cut preferably two sides simultaneously being conjugate, thus, to basic gears whose adjacent tooth surfaces are concentric surfaces of revolution.

In Figures 4 and 5, 20 indicates the gear or larger member of the pair and 21 the pinion. The gear axis is at 22'oifset from the pinion axis 43. In the shown embodiment, the two axes are arranged at right angles. The pitch cone apex of the gear is at 24 and the pitch cone apex of the pinion is at 25. Each member of the pair is provided with teeth hich are longitudinally inclined to the straight generatrices of its pitch surface, the teeth 27 oi the pinion being, preferably, more inclined than the 'teethQS of the gear. Each member or the pair is generated from an oil'setv basic gear having teeth whichare non-radial or skew. I

Figures 9, 10 and 11 illustrate diagramiuatically themethod of producing longitu dinally curved tooth gear pairs such as shown in Figures 1 andQ and Figure 12 shows how the members of the pair shown in Figures '4 and 5 may be generated according to this invention.

Longitudinally curved tooth gears will be out according to this invention preferably Each member of the pair is generated conjugate to an offset crown gear. Figures 9 and lO illustrate the generation of the gear or larger member of the pair. Here, the gear blank is indicated at 30. Its axis is at 31 and its apex at 32. The toolused, a rotary annular face mill, is shown at 34. It is provided with a plurality of cutting blades which represent a tooth surface or tooth surfaces of av basic gear, such as indicated in dotted lines at 35, whose axis 36 is oii set from the axis 31 of the gear blank during generation. In the form shown, the basic gear 35 is a true crown gear, that is, has a plane pitch surface 37. Preierably,two side tooth. faces of theblank will be cut simultaneously and for this pur-- pose the tool 34 will be arovided with cutting blades 38 havino cuttin ed 'es which are C C) C! adapted. to finish cut adjacent side tooth iaces of a blank. The blades 38 may be so arranged that alternrte blades will finish cut opposite side faces of the tooth or the blank, or each blade may be provided with a pair of finish cutting edges so that each blade finish cuts simultaneously on two adjacent side tooth faces of the blank. T he tool 34 will be so positioned relative to the blank that it rep resents adjacenttooth surfaces of the basic gear In the generating 01 oration, the tool 34 is'rotated on its axis 39 in engagement with the blank, while simultaneously a relative motion is produced between tool and blank corresponding to that of a gear meshing with the basic gear 35 with its axis oti'set from the axis of the basic 35. in this relative motion, theblank will pi terably be rotated on its axis 31 while a relative move ment is produced between the tool and blank about the axis 36 of the basic gear 35, which axis is offset from the 310i the blank. The apex ot the basic gear is indicated at 40. After b o adjacent tooth surfaces of the blank have been completely generated the manner described, the tool and blank are withdrawn relatively to each other and the blank indexed, then the tool and blank are retin'ned into engagement and another pair of tooth surfaces ol the blank generated. The

llil) alternate cuttingand indexing will continue r until the blank is completed.

The pinion which 1S to mesh with a gear generated in themanner just desci I a will be out in asimilar fashion. Figure '11 illustrates (ihagrammatically the method of producingthepinion. 42 designates the pinion blank, whose axis is at 43 and whose apex s at 44. A rotaryannular :t'ace mill is anal preferably employed and tlllo race mill again preferably provided with cui blades 46 which are provided with cutting edges adapted to finish cut adjacent s de tooth faces of a blanln- As before, alter ate blades may be provided with finish cut" edges for finish cutting adiace t side laces; of the teeth of the blank, or each. blade may have two side finishcuttingi edges and at cut simultaneously the'two adja nt tooth faces of the blank. The finish cutting edges of the tool againrepresent coaxial longitudinally curved tooth surfaces of a basic gear such as indicated in ClO'tQBCl lines a 48 whose from the axis 57 of the basic gear axis 49 is olfset from the axis of the blank. The tooth surfaces of the blank are. generated by rotating the tool on its axis in on gagement with the blank, while sin'iulta neously producing a relative motion between the tool and blank corresponding to that oi a gear meshing with a basic gear whose axis is oll'set from the axis of the blank. This relative motion will preferably beel'lected by rotating the blank on its axi l?) and simultaneously moving the tool and blank tively to each other about an axis ell) representing the axis of thebasic 1' 48. After two tooth surfaces of the blank have been completely genera-tedit will be indexed and alternate cutting and indexing will proce d until the blank is finished. The relationship between the basic gears and 4r8rrom which gear and pinion are generated, respectively, can be determined. as described her inafter.

V] hen the gear and pinion are out n the manner just described, each of them may be generated upon a machine such as de: ibcd in my'copending application No; 77,310, filed December 23,1925. In this machine, the

of the cradle or carrier will represent the axis of the basic gear to which the gear being cut is generated conjugate and the blank axis may be otl set any desired distance from the axis of the cradle.

Both members of the pair, shown in Fig ures 4 and 5 may be generated according to the method illustrated diagrammati'cally Figure 12. Here, a pair. of planing tools 52 and 53 are employed, representing side tooth" surfaces oi the basic gear 54. 'lhe teeth oi this basic "car are strai 'lihani'l inclined to the generatrices of its pitch surfaceflhat is, they are non-radial or skew. The blank 55 tobe cut is positionedwith its 56 ollset V In the generating operetio the tools-52 and 53 are reciprocated across the face of the blank 55 in paths converging-in a point 58, representing the point of convergence oi. the side tootl'i faces of the teeth of the basic gear fi l, which point 58 lies on acircle circumscribed about the basic gear center or apex as a center,

Simultaneously, a relative movement is imparted between the tools and blank in the manner of a gear meshing with the basic gear 54- With its axis 56 o: roni the i 57 of the basic gear. This adt itii'inal motion is preferably effected by rotating the blank on its axis and by simultaneously moving" the tools and blank relatively to each other about an axis 57 representing the 'aXsolijthe basic gear. After two side faces of the blank have been cut in the manner described-the tools and blank are withdrawn relatively to each other and the blanl': indexed. The alternate cutting and indexing will proceednntil the blank has been completed. The mating gear ISCUQt con ugate to an offset basic gear in a similar manner. The relationship :be- I plane pitch surfaces.

is described more completely hereinafter;

Preferably, the basic gears to which the two members of a hypoid pair are generated conjugate, by the process of this invention, are true crown gears, that is, gears having Usually, the crown gear to which the gear or larger member of the pair isgenerated conjugate is different from the crown gear from which thepinion or smaller member of the pair is derived. Preferably, however, both crown gears have the same tooth inclination or spiral. angle at x a mean point of contact between the crown gear and the respective gears which are gencrate-d there-from. v V

Figures 8- and 6 are diagrammatic views showing the pitch surfaces of the gears of Figures 1 and 2 and-oi Figures 4 and 5, re-

spectively, in relation to the planes 60 and 61 respectively, tangent to the pitch surfaces of the respective pairs at the respective mean points of contact 62 and. G3 between the gears ot the respective pairs. The planes (50 and 61 may also be considered the pitchplanes of crown gearsll rom which the members of the respective pairs are generated and (SQhnd 63 would be mean'points of contactbetween the crown gears and the respectivem'embers of the respective pairs. 13 and 14 arethe projections ott the axes of the gear lO-and pinion 11, respectively, to the plane 60 and 22 and 23 are the projections of the axes of the gear 20 and the plane 61.

As stated, preferably, the crown gears or basic gears from which the two members of a pair are derivedhave the same tooth inclination or spiral angle. at the mean'point of Contact. In otherwords. the centers ol the twocrown gears from which the two members of a pair are derived are located on the same line which passes through the mean point of contact. Thus the centers 65 and 66 pinion 21, respectively, to

of the crown gears'lrom which the gear '10 and pinion 11 are he rived respectively, ar located on the line 67 passing through the nieanpoint of contact 62 (Figure 3). Like wise, also, the centers 68 and 69 ot' the crown to which the gear. 20 and pinion 2l are a;eneraled conjuga respectively, are locate-(l on the same line. 70 'iassingr I through the mean point of contact Fl gear pairs of tllOPl'OPOI'tlUHS shown, thelines 67 or 7O, as the case may-be, are situated between the projected gear and pinion axes andnearer to l be projected gear axis. The location of the lines 67 vand 70 can'be determined as de-' scribedbel'ow. i i i The basic crown gears contain tooth sides which preferably are surfaces of revolution in the case of longitudinally curved tooth gearsorplanes where the teeth of the crown gears arestriarght, In Figure 3, 72 indicates in v) I termination o'l the tooth direction of the teeth of the crown gears from wnich the gears and 11 are derived. The tooth direction of the crown gears from which the gears and 21 are derived is indicated at 73 in Figure 6. 'lhe lines 72 and 73 are pitch lines of the crown gears, that is, the lines formed by the intersection of the tooth surfaces of the crown gears with their pitch planes.

The principl on which are based the dee crown gear centers "for a hypoid pair constructed accord ng to this invention, are the same whether the crown gears have circular arcuate teeth or straight inclin d teeth. lvlatheinatically considered, the loneitudinally curvul tooth gears reprei sent the b 'oader or more general case and in what follows the method of determining the crown. gear centers tor such will be specifically considered, it being understood that the same method may be applied to the determination of the crown gear centers for the crown gears which have straight teeth.

lChe center of tooth ciuvature of the crown gear tooth 72 is at 75, Figure 3. The tooth surfaces of gear and pinion and of their respective crown gears will contact in the mean pointo'lt contact To avoid bias bearing, that is a tooth surface contact which enter diagonally of "he tooth surfaces oi the mating; gears, the sting gears should be so constructed the the points of conta t betwee; mating toohi so tacos will move straight up the tooth profiles from the bottom to the top of the same during the mesh of the 'earsQ l-lc 'erence is now made particularly to l i gill) s 4 which is an emerged diagrammatic view or he parts about the mean contact point (39. of

l igure 3, and to Figure 8 which is a diagrammatic side elevation looking in the di rection of the arrow shown in Figure 7. Let us now consider a point 'I (S on the side of the crown gear teeth, soown in liull at 7T. in Figure 8, which point 76 lies directly above or below the mean point oi? contact 62. The point 76, in other words, lies in a plane v-sliich passes thr ugh the mean point et contact and ,is perpendioulm' to the itch li..e Depending); on the side ot th crown gear tooth considered, the point- 76 is tn: v l above or below the pitchplane of the crown gear by a distance s.

fatter the cr wu and blank, say, the gear blanighave rolled tog ther a certain disice the point 76 will bec'nie coni'u lretv-reen the cutting er of the tool,

rraco surface inv i 1,705,eer

some point 79. nine 76-79 is actually a circular are about the crown gear center, but in the relatively infinite enlargement of Figures 7 and 8 this line appears as a straight line.

.ln uniiiorin motion gears, in general, a force extending in the direction of the tooth normal at any point of tooth contact produces moments on either gear of a pair'which are in the proportion oi their respective numbers of teem. l t e will now consider a force e2:-

1 the direction 015 the tooth normal at the mean noint of contact 62 and a force extendingii the direction of the tooth normal Ltorees acting 6:2 and 76 are equal, or, in

other words, the increment in moment between the points 62 and "6 is Zero. The increment in inoinent exerted upon the crown grjear at (32 and 79 is,-therelfore, also zero. Hence, the increment in moment exerted upon the gear being out by forcesextending in the direction of the tooth normal at62 and 79 must be zero, in order that gear and crown ,o ear roll together with uniform motion. This fact makes it possible to readily determine the distr Z between the points 76 and 2 9, that is, the distance which the crown gear must roll before the point 76 becomes a point contact at T9 with the blank being cut.

For convenience the tollowin s unbols are employed e -the distance oi? the considered point 76 7 A. Zl the cone distances of gear andv pinion, rcsl'icctiv ly, the distancesl562 and.

16-62, respectively, in Figure the cone distances of the crown gears underlying; the generation of the gear and pinion respec .el the distances65+62 and 66-62. respec 'vely,-in Figure 3.

7a,, ll the spiral angles of pinion and gear respectively.

7z,. the spiral angle of the basic crown 1' p th pinion reps "h cone ang'gles of gear and s v. o==tho i. oruial pressure angle.

Fl'Olll the consideration of uniform motion gearing outlined above, andby app ying the known rules of mathematics, the lollowing equation can be derived:

cos E In this equation, the upper sign refers to the tooth side of the gear Whic'h'faces the pinion apex during the mesh and to the mating tooth side of the pinion. The lower sign refers to 1 the other tooth side.

Generally, the point 79, which-is a point of contact between the crown gear and gear" points 62 and 80 are equal.

It is understood "that the forces here considered are always in a direction perpendicular to the tooth surface and considering the points'GQ and 76 are of such magnitude that their projection to the pitch plane are alike. If the profile of't'he crown gear tooth is straight, this results in the normal forces being equal also.

From what has been said, it follows that the point '79. of thegear tooth surface is turned about the gear axis to the position 80 where the moment produced on the pinion by a force extending along the tooth normal equals the moinentsproduced on the pinion the point 62. Now, the tooth normal when swung about the gear axis from 79 to 80 changes its inclination to the pitch plane. At 79, the inclination of the tooth normal equals the pressure angle of'the tool, that is, the pressure angleiof the crown gear tooth surface. At point 80, however, the incli nation of the tooth normal to the pitch plane is different. The point 80, therefore, cannot be a point of contact between the pinion and its basic crown gear. If it were, then't'he pressure angle of the pinion the point would be the pressure angle of thetool which represents the basic crown gear from which the pinion is generated, whereas, as stated above, V the pressure angle or inclination of the tooth.

normal at the point 80 should be different from the pressure angle of the tool. Point 80 of the pinion cannot, therefore, be a point g tan 7;

an will be positive if plotted in the direction" which the pinion is generated conjugate must,

its explained above, the moments, exerted (A sin h-A sin H)tanacos(h H)(1+ I cos Zr cosH tan 29(11 sin h A 'sin hg) FA tan a cos (h,jh cos a cos a tanPtA sin h 'A sin H) $11 tan a cos (h H) v of contact between the pinion and itsbasic crown gear, represented the tool. Point 80 beoomesa point of Contact between the. pinion and its basiccrown gear at someposition 81, obtained by turning the point 8Q about the axis of thepinion until thetooth normal has an inclination angle with respect to the plane of the crown gear equal to the pressure angle of the tool'or tooth of the crown gear.

The crown gear. to which the pinion is conjugate is so determined, therefore, that the tooth normal at p0int 81 when swung about the crown gearaxis to the point 76 will have the known inclination I, V ofthetoothnormal at the last named point.

, From Figure 7 it Wlll be seen that the point 81 is situated on the line 79-,76 pro-' longed. 'The spiral angleh of the crown gear is preferably selected, therefore, slightly larger than the spiralangle Hof the gear and is'such as results from the geometric addition of the distances 79 80 and 80.- 81,. In other words, thedist'anc'e 79-8l which results from'said geometric'addition, is situ ated in the direction ofthe peripheral motion of the crown gear. The crown gear axes lie on a line passing through the, point 62 which is perpendicular to line 79 8 1 V The spiral angle In, of the two crown gears, from which the gear and pinion are derived, are, therefore, alike. However, ordinarily, the cone distance A, of'the'growngear from which the gear is generated is different from the cone distance A of. the crown gear from which the pinign is. derived. 7 1 V Based on the above lconsiderationmthe following equation, from which the spiral angle 71. of the crown gears may be determined, may be derived; f i

; tan h =tan If we let the distance 79-80 eq1ial the distance 9? canbe detern i ined as follows;

be so located as to permit s'winging of the tooth normal at point 81 into its known position at the point 76,'that is, inasmuch as the crown gear axis from which the pinion is de rived must be so located that the p oin ts ,,8l

Z A. sin na 1 =-[(A, sin H-A. Sin h In this formula, it, may be determined Z a; from equation (2) and the values of E and may be introduced from equations (1) and 3) respectively. Two equations are thus obtainee, one for the upper sign or one tooth side of the crown gear and the other for the lower sign or the other tooth side of the crown gear. The cone distances A, and A of the two crown gears may be determined from these equations by the known means of mathematics.

' Gears generated according to the present invention will transmit true uniform motion and will be free from bias bearing.

The relation of the pitch cone angles of the mate gears to the respective numbers of teeth and to the lengthwise curvature of the teeth may be assumed or determined in any suitable way, for instance, in the manner described in my copending application, Serial No. 171,609 filed February 28, 1927.

In cutting longitudinally curved tooth gears with this invention, a spherical cutter, that is, a cutter having cutting edges of circular arc profile, such as shown in Figure 9, may be employed to obtain gears of theoretical accuracy and no bias, or a straight sided or conical cutter may be used. In the latter case, to avoid bias, the gears will be cut, preferably, parallel depth, that is, with teeth of uniform or constant depth along their lengths. The cutter will preferably out two side faces of the blank simultaneously and will be so positioned, as described, as to represent two adjacent tooth sides of'a crown gear tooth. If the cutter is spherical, then for the oretically correct gears, its axis should pass through the sphere centers of the tooth sides of the crown gear represented by the cutting edges.

Preferably the crown gears will have teeth which taper in depth in such fashion that the points or tips of the crown gear teeth are in line with their apexes or centers. The mean radius ref the cutter, the average cone distance and the spiral angle h, of the crown gears are then in a certain mter-relation, which may be have the same inclination to this axis, the following formula can be derived:

tan p cos H tan P cos 7:.

cos H ca han 1 1 on determined by sealing the drawing or with the following formula:

(1 sin h tan a cos h D, (5)

perpendicular to the teeth. The actual de dendu m at the center of the face equals cos h -D, where N C is the average tooth number of the crown gear.

While I prefer to generate longitudinally curved tooth gears with this invention, by using rotary annular face mills, it will be understood that, if desired, planing tools may be used instead which are reciprocated across the face of the blank in separate paths curved about the center of curvature of the crown gear teeth as a center. The principles of the present invention are applicable, also, to the production of longitudinally curved tooth gears in a hobbing or continuous indexing process whether a face mill ora worm hob be employed or a pair of planing tools reciprocating in straight paths across the face ofa continuously rotating gear blank.

The present invention is not limited to the production of gears by planing or milling tools, but may be employed also in grinding or lapping.

In general, it may be said, that while this invention hasbeen described with reference to particular embodiments, it will be under stood that the invention is not limited to the embodiments discussed, but is capable of further modification, and that this application is intended to cover any variations, uses, or adaptations of the invention, following, in general, the principles of the invention and including such departures from the present disclosure as come within known or custom-, ary practise 1n the gear art and may be ap--- plied to the essential features hereinbefore set forth and as fall within the scope of themvention and the, limits of the appended claims.

Having thus described my invention, what I claim is 1. The method of producing a pair of hypoid gears which consists in cutting the side tooth surfaces of each member of the palr by moving atool across the face of a tapered gear blank in a path inclined to a straight generatrix of the pitch surface of the tapered gear blank in a path inclined to a straight generatrix of the pitch surface of the blank while smiultaneously producing a rela tive motion between thevtool andblank corresponding to that of a gear meshing with a crown gear whoseaxis is offset from the axis of'the blanln 3Qlhe method of producing a pair of hypoid gears which consists in cutting the side tooth faces of each member of the pair by moving a tool in a circular arcuate path across the face of a tapered gear blank while rotating the blank on its axis and simultaneously moving the tool and blank relatively to each other about an axis offset from the blank axis.

hypoid gears which consists in cutting the side tooth faces of each member of the'pair by moving a tool in a circular arcuate path across the face'of a tapered gear blank while imparting an additional relative movement be tween the tool and blank corresponding to that of a gear meshing with a crown, gear whose axis is offset from the axis of the blank.

5. he method of producing a' pair of hypoid gears which consists in cutting the side tooth surfaces of each member of the pair by producing a relative moyemcnt'between the tool employed and a tapered gear blank corresponding to that of a gear meshing with a crown gear whose axis is offset from the axis of ,theblank, while moving the tool across the face of the blank in a path in clincd. to a straight. generatrix of the pitch surface of the crown gear to describe thereby a tooth surface of the crown gear.

G. The method of producing a pair of h poid ears which consists in cutting" the side tooth surfaces of each membenof the pair by producing a relative movement between the tool employed and a tapered gear blank corresponding to that of a gear mesh ing with a crown gear whose axis is offset from the axis of the blank while moving the tool in a curved pat-h across the face of the blank to describe thereby astooth surface of the crowngear.

7. The method wherebyv the tooth surfaces of each member-of a pair of hypoi; gears may be cuttwo sides simultaneously, which consists in moving a pair of cutting edges across the face of a tapered gear blank in paths in,-

clined to straight generatrices of the pitch surface of the blank, while'rotating the blank 4-. The method of producing a pair .of

on its axis and simultaneously producing an additional relative movement between the l edges and blank about an axis offset un'the blank LX]S.'

each member of a pair of hypoid gears may be cut two sides simultaneously, which consists in moving a pair of cuttingedgesacross the face-of a tapered gear blank in paths inclined tostraight generatricescf the pitch surface of the blank, while simultaneously producing an additional relative movement producing an additional relative movement between the cutt ng edges and blank about i an axis offset from the blank axis.

10 T he method whereby the tooth surfaces of each member of a pair of hypoid gears may be out two sides sinniltaneously, which con-1 sists in n'ioving a pair of cutting edges in separate concentrically curved paths across the face of a tapered gear blank while simultaneously producing a relative movement be-- tween the cutting edges and blank corresponding to that of agear meshing with a crown gear whoseaxis is offset from the axis of the blank.- I

11. The method whereby the tooth surfaces of each member of a pair of hypoid gears may be out two sides simultaneously which consists in employing, in each case, a rotary annular face mill, having a plurality of cutting s adapted to finish cut adjacent side tooth races of a gear blank, and rotating said tool in engagement with a tapered blank while rotating the blank on its axis and siniul-v 'taneously producing an'additional relative sidetooth faces of a gear blanlna'nd rotating 8. The method whereby thetooth surfaces the face of a tapered gear blank while rotatmg the ilank on its axis and simultaneously said tool i-n'engagement with a tapered gear I blank while simultaneously'producinga relative movement between the tool and blank corresponding to that of a gear meshing with a crown gear whose axis is offset from the axis of the blank.

' 13. The method of producing a pair of hypoid gearswhich consists in cutting the side tooth faces of one member of the pair surface of the latter basic gear across conjugate to an offset basic gear having teeth inclined to the straight generatrices of its pitch surface, by n'ioving a tool, representing a tooth surface of-the basic gear, across the face of a tapered gear blank while imparting a relative movement between the tool and blank in the manner of a gear meshing with said basic gear, while maintaining the axis of the blank onset from the axis of said basic gear, and in cutting the side faces of the other member of the pair conjugate to another offset basic gear whose teeth have the same inclination angle as the teeth of the first basic gear by moving a tool, representing a tooth the face of a tapered gear blank hile imparting a relative movement between the latter tool. and blank in the manner of a gear meshing with said basic gear with its axis offset from the axis of the basic gear.

14. The method of producing a pair of hypoid gears which consists in cutting tooth surfaces of each member of the pair conjugate to an offset basic gear, having teeth inclined to the straight generatrices of its pitch surface, by moving a tool, representing tooth surfaces of the basic gear, cross the face of a tapered gear blank while imparting a relative movement between. the tool and blank in the manner of a gear mesaing with said basic gear with its axis offset from the axis of said basic gear, the basic gears to which the two men'ibers of the pair are generated. conjugate, having the same tooth in clination angles, but having axes offset different amounts from the axes of the respective blanks during the generation of the two gears 15. The method of producing a pair of hypoid gears wl 'ch consists in cutting the tooth surfaces of each member of the pair, conjugate to an offset basic gear having longitudinally curved teeth, by moving tool, representing a tooth surface of said basic gear, in a curved path across the face of a tapered gear blank while imparting arelative movement between, the tool and blank in the manner of a gear meshine with s gear with its axis offset from the aims of sa d basic g gear, the basic gears to which the two men'ibers of the pair are generated conrugatc, having the same tooth inclination angles, but having axes offset different amounts from the axes of the respective blanks-during the generation of the two gears. V

16. The method of roducing a pair of hypoid gears which consists in cutting the tooth surfaces of each member of the pair conjugate to an of set basic gear having longitudinally curved teeth by rotating an annular face mill in engagement witl'i a tapered blank while imparting a relative movement between said tool and blank in the man nor of a gear meshing with said basic gear with its axis offset from the axis of said-basic I poid gears which consists l. I,

gear, the basic gears to which the two members are generated conjugate having the same tooth inclination angles but having axes offset different amounts from the axes of the re spective blanks during the generation of the two gears.

if. The metho-a of prod uciug a pair of byin cutting the side tooth faces of each inem )er of the pa r two sides simultaneously, conjugate to an offset basic gear, having teeth inclined to the straight generatrices of its pitch surface, by moving a pair of cutt 1g edges, representing tooth surfacesof said basic gear, across the face of a tapered gear blank while imparting a relative movement between the cutting edges and blank in the manner of a meshing with said basic gear with its axis offset from the axis of said basic gear, the basic gears to which the two members of the pair are generated conjugate having the same tooth inclination angles but having axes offset different amounts from the axes of the respective blanks during the generation of the two gears.

l8. She method of producing a pair of hypoid gears which consists in cutting each member of the pair two side faces simultaneously conjugate to offset basic gears havlongitudinally curved teeth by moving a pair of cutting edges in separate curved paths across the face of a tapered blank while imparting a relative movementbetween the cutting edges and blank in the manner of a gear meshing with said basic gear with its axis offset from the axis of said basic gear, the basic gears to which the two members are generate conjugate having the same tooth inclination angles but having axes offset clifferent amounts from the axes of the respectivc blanks during the generation'of the two 7 gears.

- 15). The method o producing a pair of hypoid geam which con sts cutting the side tooth surfaces of each member of the pair conjugate to offset basic gears having longi tudinally curved teeth by rotating an annular face mill, provided with a plurality of cutting edges adapted to finish cut adjacent side tooth. faces of a. gear blank, in engagement with a. tapered gear blank while imparting a relative movement between the tool and blank in the manner of a gear meshing with saidbasic with its axis offset from the axis of said basic gear,"the basic gears to which the two members are 'cnerated conjugate having the same tooth inclination angles but having axes offset differentamounts from the axes ofthe respective blanks during the generation of. the two gears.

20. The method of producing a pair of hypoid gears which consists in cutting the tooth surfaces of each member of the pair conjugate to an offset basic gear, having teeth inclined to the straight generatrices of lll) its pitch surface,fbymoving a tool, representing a tooth surface of the basic gear,

across the face of a tapered gear blank while imparting a relative movement between the tool and blank in the manner of a gear meshing with said basic gear with its axis offset from the axis of said basic gear, the basic gears to which the two members of the pair, are respectively generated conpigate, having tapered gear blank while imparting a rela-' tive movement between the tooland blank in t 1e manner a gea meshing with said basic gear with its axis offset from the axis of said basic gear, the basic gears to which thetwo members of the pair are generated conjugate, having the same tooth inclination anglesbut different cone distances.

22. The method of producing a pair of hypoid gears which consists in cutting the side tooth faces of each member of the pair two sides simultaneously, conjugate to an oifset basic gear, having teeth inclined to the straight generatrices of its pitch surface, by movin'g'apair of cutting edges, representing tooth surfaces of said basic gear, across the faceof a tapered gear blank while impart ing a relative movement between the cutting edges and blank in the manner of a gear meshing with said basic gear with its axis offset from the axis of said basic gear, the basic gears to which the two members of the pair are generated conjugate having the same tooth inclination angles but different cone distances.

23. The method of producing a pair of hypoid gears which consists in cutting each member of the pair two side faces simultaneously conjugate to offset basic gears having 7 longitudinally curved teeth by moving a pair of cutting edges in separate curved paths across the face of a tapered gear blank while imparting a relative movement between the 7 cutting edges and blank in the mannerof a gearmeshing with a basicgear with its axis offset from the axis of said basic gear, the basic gears to which the two members of the pair are respectively generated conjugate having the same tooth inclination angles but different cone distances.

2%. The method of producing a pairof hypoid gears which consists in cutting the side tooth surfaces of each member of the pair conjugate to an offset basic gear having longitudinally curved teeth, by rotating an annular face mill, provided with a plurality of cutting edges adapted to finish cut adjacent side tooth faces of a gear blank, in

engagement with a tapered gear blank while imparting a relative movement between the tool and blank 1n the manner of a gear meshing with a basic gear with its'axisoifset from the axis of said basic gear, the basic gears to which the two members are generated con- 1 jugate havingthe same toot-h inclination angles but different cone distances.

ERNEST wILDHABER.

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