US2368559A - Method and apparatus for smoothfinish gear grinding - Google Patents
Method and apparatus for smoothfinish gear grinding Download PDFInfo
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- US2368559A US2368559A US442884A US44288442A US2368559A US 2368559 A US2368559 A US 2368559A US 442884 A US442884 A US 442884A US 44288442 A US44288442 A US 44288442A US 2368559 A US2368559 A US 2368559A
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- gear
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B23—MACHINE TOOLS; METAL-WORKING NOT OTHERWISE PROVIDED FOR
- B23F—MAKING GEARS OR TOOTHED RACKS
- B23F5/00—Making straight gear teeth involving moving a tool relatively to a workpiece with a rolling-off or an enveloping motion with respect to the gear teeth to be made
- B23F5/02—Making straight gear teeth involving moving a tool relatively to a workpiece with a rolling-off or an enveloping motion with respect to the gear teeth to be made by grinding
- B23F5/06—Making straight gear teeth involving moving a tool relatively to a workpiece with a rolling-off or an enveloping motion with respect to the gear teeth to be made by grinding the tool being a grinding disc with a plane front surface
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- Thisinventi'on relates to the art of-gear grinding; -i. e, that of grinding the teeth of hardened ge'ars'to generate involute face-curves with the highest obtainable accuracy of dimensions and form. Its object'is to g'ive to the work asmoother, and generally-more desirable quality of surface finish than is obtainable by the grinding instruments and procedures-"-heretoforeused, and at the-same time to make thefinished teeth at leastas accurate as the best results of prior practices. v
- Generative gear tooth grinding is accomplished by producing a relative rolling movement between the gear being ground and agrinding wheel, similar to thatbetween a gear and arack running in. mesh, .while' the wheel is rapidly rotated-at eificient cutting'speed. In many cases a relative displacement is effected between'the gear and grinding wheel in the direction of the Y axis of the gear to distribute the grinding effect uniformly throughout the-length of the teeth.
- grinding wheels have been generally employed for performing this class'of work.
- One type of wheel is provided with a hatgrinding face occupying a-plane perpendicular to its axis of rotation andis-set with its active faceat an oblique a'ngle to the direction of the translative component of the relative rolling motion, j such that theportion of itssurface nearest tothe gear coincides with the'face of a rack'toothconjugate-to the gear.
- The” other type of wheel is provided with convex conical faces at opposite-sides-of its circ'umference, the elements of which include between-them an angle" equal to that between the opposite side faces of such a" conjugate rack,
- the invention consists in :thecombina'tion of a grinding wheel having a cjonic'al activeiace', of which the elements are inclined to the plane of rotation at adistinctangle whichis less than the pressure angle of the gear 'to lee ground; with other machine elements, organized to-supneither perpendicular to the tran slative component of motion between wheel and work gear,-
- Fig. 2 is a fragmentary side elevation of the machine showing the work-gear and grinding wheel, with-part 'of'the means for supporting thein in the samecooperativerelation as in- Fig- 1;
- Fig. 3 is a diametra-lsectioiial view oh a larger scale, "of' the upper 1 half "of the-grinding wheel shown in Figs. 1 and- 2 inits cooperative relation withone of the teeth of a were" gear;
- Fig. 4 is a side-view of one of the-gear teethfinis'hed by themean's of-the present invention
- a work gear G so that in effect a pitch circle pc of the gear rolls without slip on a straight pitch line pl.
- Many types and forms of means for effecting such rolling movement are available in the art, and I have chosen as typically illustra tive the machine disclosed in my Patent No. 2,364,542, granted December 5, 1944, on an application Serial No. 438,136, filed April 8, 1942.
- the work gear is mounted on a spindle I, rotatable for indexing purposes in a carrier 2, to
- the grinding wheel W is secured to a spindle, not shown, rotatably mounted in a holder 6 and driven at suitable speed by a motor 1.
- the projection on the plane of the drawing of the axis of rotation is designated by the line aa and it is arranged transversely to the axis of the work gear and at a suitable distance therefrom to enable one edge of the grinding wheel to cross the pitch line pl and enter between two teeth of the gear.
- the wheel holder 6 is coupled by a pivot 8 with a base 9 so thatthe inclination of the axis 11-11 to the pitch line pl can be varied and adjusted.
- Base 9 is in turn adjustably mounted on a sub base ..H and the latter is secured to a bed 12 which is reciprocable lengthwise of the work spindle axis and is so reciprocated by means fully shown in said Patent No. 2,364,542 and made a part hereof, to transport the grinding wheel from. end to end of the tooth being ground in order that the grinding effect may be equally distributed over the face of the gear.
- the grinding wheel of this invention differs from the grinding wheels of the prior art in that it active part is a convex conical zone 0 contiguous to the circumference, the radial elements of which make an angle m with the plane of rotation of the wheel (here typified by the surface p perpendicular to the axis a-a.) which is smaller than the pressure angle of the work gear.
- the pressure angle is the angle pa between the pitch line on which the gear meshes with its conjugate base rack, indicated by pl in Figs. 1 and 3, and the line of action, indicated by the line la in Fig. 3.
- the tooth faces of the base rack are perpendicular to the line of action.
- the other type of prior art wheel previously mentioned is formed with convex conical active faces, adjacent to the circumference, at opposite sides of its median plane, the radial elements of such conical faces make angles with the mean active face 0 contiguous to the circumference lying in a plane perpendicular to the axis of rotation, and the wheel is'mounted for operdian plane equal to the pressure angle; wherefore the profile of the wheel at the-rim is similar in outline to a tooth of the base rack.
- the conical faces are intended and adapted to generate the respectively opposite faces of two gear teeth; and the wheel is set up for operation with it axis parallel, nd its median plane perpendicular, to the pitch line of the relative rolling movement.
- the wheel W of this invention is set for operation with its axis aa making an angle 7L, equal to the difference between the pressure angle pa and angle m, with the line lc-l parallel to the' pitch line of rolling movement. Its value is such that the element of the active zone c momentarily in central tangent contact with the work is perpendicular to the line of action and coincides with a tooth face of the imaginary base rack.
- wheels W and W have been hown in these drawings in their proper relationship with the same work gear and base rack, having a pressure angle of 14.
- Wheels made and used in accordance with this invention may be designed for grinding gears of any pressure angle; but, whatever the specific proportions and dimensions of any given wheel may be, the same characteristic differences exist between it and the wheels of plane faced and rack profile type.
- Fig. 8 is a fragmentary section on a plane coinciding with the line of action.
- the finish accomplished by the present invention is composed of straight lines, which are finer, shallower, more closely spaced, and more uniform than those out by the rack type wheel, and they a work gear of any pressure angle.
- the active face of the wheel in the plane of action is a curve, but its radius at the contact point with the work is substantially longer than that of the rack type wheel, and may be several or many times as long. Thus a wider contact is obtained between the wheel and the work.
- the contact between a curve of any radius, however large, and a straight line is always a point, yet where similar relations occur between material articles, the properties of the materials and other conditions cause modifications, wherefore, actually there is an extended contact between the large radius curve of the cutting zone 0 and the work gear tooth.
- Cutting action occurs simultaneously at both sides of the mid tangent point r to a greater extent than in the case of the rack type wheel, and this contributes to the greater uniformity and smoothness of finish.
- the length of contact is limited, as compared with the long area of contact of the plane faced wheel, gradually fading out at each side of the center of contact r.
- the new wheel has a freer cutting action than the plane faced wheel, giving better opportunity for escape of chips and avoiding the clogging, impairment of cutting action and over-heating which occurs with such extended contact.
- any desired value may be given to the cone angle m of my improved grinding wheel, provided it is smaller than the pressure angle but has a positive value. Excellent results have been obtained with an angle of 1, and also with larger angles.
- the principles of the invention are not limited to the particulars of means for effecting relative rolling traverse between the gear and the grinding wheel. Any means available for that purpose may be used, whether operating to impart both components to the work, or the angular component to the work and the lineardisplacement to the wheel, provided only that the correct ratio between these components is maintained to effect non-slip rolling action between a prescribed pitch curve of the work piece and a straight tangent pitch line, It is essential that the whe'el be sup. parte with its rotational plane parallel to the length dimension of the 'work gear teeth', whether 'the gear'is a spur or a'helical gear.
- Apparatus for generatively grinding gears comprising a rotatably'mounted grinding wheel having a convex conical grinding face contiguous to its circumference, of which the angle between its radial elements and the plane of rotation is substantially smaller than the pressure angle of the gear being ground, means for effecting a relative rolling movement between the work gear and said grinding wheel on a pitch line inclined to the axis of the wheel at an angle equal to the difference between the pressure angle and the before named angle, and means for effecting a relative 2.
- a machine for generatively grinding gear teeth comprising a supporting structure, a work support'including a spindle adapted to carry a work gear and a grinding wheel support both mounted on the supporting structure, means for effecting relative movements between said work support and grinding wheel support compounded of rotation of the spindle and relative displacement in a straight path transverse to said spindle, a grinding Wheel mounted rotatably on said supporting structure in position to act upon the tooth face of a gear mounted on the spindle, said wheel having a convex conical active face contiguous to the circumference, of which the cone angle with respect to the plane of rotation i substantially smaller than the pressure angle of the gear, and the wheel being located with the portion of'its active face nearest to the gear extending across the path of relative translation at an angle to such path which is the complement of the said pressure angle, and means for effecting relative displacement between the work holder and grinding wheel in the general direction of the axis of the gear to distribute the grinding action lengthwise ing movement between such gear and a grinding 5L0 wheel
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- Grinding Of Cylindrical And Plane Surfaces (AREA)
Description
.E. w. MILLER 2,368,559 METHOD AND APPARATUS FOR SMOOTH-FINISH GEAR GRINDING Jm so, 1945.
2 Sheets-Sheet 1 Filed May '14, 1942 v Patented Jan. 30, 1945 UNITED STATES PATENT OFFICE.
. I I 7 2,368,559 f I Memorials!) APPARATUS ron 'sMoo-rn- FINISH GEAR. GRINDING Edward W. Miller, springfield vt, iassigiior lto The enews [Ge't'ifShaper Company, Spring-.- ileld, Vt., a corporation of Vermont Application May 14, 1942,.Serial No. 442,884
4 Claims.
Thisinventi'on relates to the art of-gear grinding; -i. e, that of grinding the teeth of hardened ge'ars'to generate involute face-curves with the highest obtainable accuracy of dimensions and form. Its object'is to g'ive to the work asmoother, and generally-more desirable quality of surface finish than is obtainable by the grinding instruments and procedures-"-heretoforeused, and at the-same time to make thefinished teeth at leastas accurate as the best results of prior practices. v
Generative gear tooth grinding is accomplished by producing a relative rolling movement between the gear being ground and agrinding wheel, similar to thatbetween a gear and arack running in. mesh, .while' the wheel is rapidly rotated-at eificient cutting'speed. In many cases a relative displacement is effected between'the gear and grinding wheel in the direction of the Y axis of the gear to distribute the grinding effect uniformly throughout the-length of the teeth. Usually both components of rolling motion (translative displacement and rotation)---a're' i'mparted to-the'gear, but in some instances the gear is rotated only while the grinding wheel is displaced tangentially of, and at the same linear speed as, a pitch circle of the gear "with respect to which the rolling movement is'established.
Heretofore two different types or; grinding wheels have been generally employed for performing this class'of work. One type of wheel is provided with a hatgrinding face occupying a-plane perpendicular to its axis of rotation andis-set with its active faceat an oblique a'ngle to the direction of the translative component of the relative rolling motion, j such that theportion of itssurface nearest tothe gear coincides with the'face of a rack'toothconjugate-to the gear. The" other type of wheel is provided with convex conical faces at opposite-sides-of its circ'umference, the elements of which include between-them an angle" equal to that between the opposite side faces of such a" conjugate rack,
port and rotate the: wheelinaplane which is is desirable "for other purposes. It is "for the purpose of rapidly generating gear teeth faces with a satisfactorily smooth :finish, and without over-heating, that the present invention-has been devised.
.The invention consists in :thecombina'tion of a grinding wheel having a cjonic'al activeiace', of which the elements are inclined to the plane of rotation at adistinctangle whichis less than the pressure angle of the gear 'to lee ground; with other machine elements, organized to-supneither perpendicular to the tran slative component of motion between wheel and work gear,-
nor perpendicular to the 'lineof rolling-action,
butris atan intermediate angIe suchthatthe active face e'lementsof the wheel, when im tangent contactwitha tooth face of the work, 00-
incide with the tooth face ofan imaginary rack conjugate to the gear. It :further consists in a method for *I procedure by which: such a wheel is caused tooperate on-a -work piece in the manner set. forth. The characteristics and particu lars' of ting-invention will now be further ex visions for effecting operative coaction between the-grinding wheeland a gear being ground;
Fig. 2is a fragmentary side elevation of the machine showing the work-gear and grinding wheel, with-part 'of'the means for supporting thein in the samecooperativerelation as in- Fig- 1;
Fig. 3 is a diametra-lsectioiial view oh a larger scale, "of' the upper 1 half "of the-grinding wheel shown in Figs. 1 and- 2 inits cooperative relation withone of the teeth of a were" gear;
Fig; 4 is a side-view of one of the-gear teethfinis'hed by themean's of-the present invention,
gnawing in a diagrammatiewaya eoinpansen r the surface produced by this grinding wheel and the finish produced grinding wheelsofthe' priorart; e H U Fig. Eris a fragmentarysectionalviewgtar n on line 5 4-01 fig. s,qaricei awn ofia mauen 56 scale, to illustrate the' characterof'contact between the grinding w he'el 'of -thisinventionand the worli';" i r Fig 6 I is a view surfin -w Fig. 3" showing a lane faced grinding' wheelwof the -"prior artand :the work in performits -c'ooperat1verelation in'g' its grinding-action;
displacing laterally, and rotating about its axis, I
a work gear G so that in effect a pitch circle pc of the gear rolls without slip on a straight pitch line pl. Many types and forms of means for effecting such rolling movement are available in the art, and I have chosen as typically illustra tive the machine disclosed in my Patent No. 2,364,542, granted December 5, 1944, on an application Serial No. 438,136, filed April 8, 1942. The work gear is mounted on a spindle I, rotatable for indexing purposes in a carrier 2, to
. which are fixed camsor formers 3 entering between and supported by inclined abutments 4 and 5. The contact faces of the former 3 and the abutments 4 and 5 are suitably correlated to cause translative movement of the carrier and spindle to right or left according as the carrier is turned in clockwise or counterclockwise rotation, respectively, at a rate which effects the desired non-slip rolling of the pitch circle pc on the pitch line pl. ,The movement of the gear then is the same as though it were rolled, on a stationary'conjugate rack, such as the rack R shown in broken lines in Fig. 3.
The grinding wheel W is secured to a spindle, not shown, rotatably mounted in a holder 6 and driven at suitable speed by a motor 1. The projection on the plane of the drawing of the axis of rotation is designated by the line aa and it is arranged transversely to the axis of the work gear and at a suitable distance therefrom to enable one edge of the grinding wheel to cross the pitch line pl and enter between two teeth of the gear. The wheel holder 6 is coupled by a pivot 8 with a base 9 so thatthe inclination of the axis 11-11 to the pitch line pl can be varied and adjusted. Base 9 is in turn adjustably mounted on a sub base ..H and the latter is secured to a bed 12 which is reciprocable lengthwise of the work spindle axis and is so reciprocated by means fully shown in said Patent No. 2,364,542 and made a part hereof, to transport the grinding wheel from. end to end of the tooth being ground in order that the grinding effect may be equally distributed over the face of the gear.
The grinding wheel of this invention differs from the grinding wheels of the prior art in that it active part is a convex conical zone 0 contiguous to the circumference, the radial elements of which make an angle m with the plane of rotation of the wheel (here typified by the surface p perpendicular to the axis a-a.) which is smaller than the pressure angle of the work gear. The pressure angle is the angle pa between the pitch line on which the gear meshes with its conjugate base rack, indicated by pl in Figs. 1 and 3, and the line of action, indicated by the line la in Fig. 3. The tooth faces of the base rack are perpendicular to the line of action.
The plane faced prior art grinding wheels, of which an example is shown at W in Fig. 6, have ation with this plane perpendicular to the line of action la and the part of the zone c contiguous to the tooth being ground coinciding with the face of a tooth of the imaginary base rack. The axis a'-a' of this wheel then is parallel to the line of action. In Fig. 6 the lines 1fg and ,fh are respectively parallel and perpendicular to the pitch line on which the relative rolling motion takes place between the work and the wheel W, and the angle between the axis a'-a.' and the line j--g, as well as that between the plane of the active zone 0 and the line fh is equal to the pressure angle pa.
The other type of prior art wheel previously mentioned, is formed with convex conical active faces, adjacent to the circumference, at opposite sides of its median plane, the radial elements of such conical faces make angles with the mean active face 0 contiguous to the circumference lying in a plane perpendicular to the axis of rotation, and the wheel is'mounted for operdian plane equal to the pressure angle; wherefore the profile of the wheel at the-rim is similar in outline to a tooth of the base rack. The conical faces are intended and adapted to generate the respectively opposite faces of two gear teeth; and the wheel is set up for operation with it axis parallel, nd its median plane perpendicular, to the pitch line of the relative rolling movement.
By contrast to the operative organization of the prior art tools, the wheel W of this invention is set for operation with its axis aa making an angle 7L, equal to the difference between the pressure angle pa and angle m, with the line lc-l parallel to the' pitch line of rolling movement. Its value is such that the element of the active zone c momentarily in central tangent contact with the work is perpendicular to the line of action and coincides with a tooth face of the imaginary base rack.
For purposes of comparison, the wheels W and W have been hown in these drawings in their proper relationship with the same work gear and base rack, having a pressure angle of 14. Wheels made and used in accordance with this invention may be designed for grinding gears of any pressure angle; but, whatever the specific proportions and dimensions of any given wheel may be, the same characteristic differences exist between it and the wheels of plane faced and rack profile type.
Experience has demonstrated that grinding wheels embodying the characteristics of this invention produce smoother surfaces and a better quality of finish than wheels of the rack profile type made of the same grade and quality of abrasive grains and operated under like conditions. Wheels of the plane faced type produce a mottled finish made up of curved lines due to the fact that the wheel makes continuous contact with the workthroughout so much of the length of the tooth as is overlapped by the wheel face. When the wheel is moved lengthwise of the gear, or vice versa, in grinding wide faced gears, the curved lines cross each other. The nature of these crossing curved lines is shown diagrammatically in Fig. 7, which represents one side of the work gear tooth t, shown in Fig. 6, after having been ground with the wheel W. They are finer, more numerous, and more closely spaced than as indicated in the diagram, and are always present in gears so ground. The contact between the gear tooth lengthwise thereof and wheel is shown in Fig. 8, which is a fragmentary section on a plane coinciding with the line of action.
In the case of the rack type wheel, contact is type of finish is desirable.
greater refinement of finish is more desirable in made with the "work at the midpoint 'Of a curve which approximates closely the arc of a circle or which the r adiu's is equal to the length or the line of actionfrom the point "of contact to its,
and i shorter at points inward fromthe circumference. Essentially [point contact occurs withth'e work. owing to this narrow contact, andthe fact that the wheel must b'e'tra'versed back and forth along the gear toothface, the surface finish is composed of parallel lines. This l However, a still some instances.
The finish accomplished by the present invention is composed of straight lines, which are finer, shallower, more closely spaced, and more uniform than those out by the rack type wheel, and they a work gear of any pressure angle.
at the same time it is a definite angle of positive value. Thus the active face of the wheel in the plane of action is a curve, but its radius at the contact point with the work is substantially longer than that of the rack type wheel, and may be several or many times as long. Thus a wider contact is obtained between the wheel and the work. Although, in geometrical concept, the contact between a curve of any radius, however large, and a straight line is always a point, yet where similar relations occur between material articles, the properties of the materials and other conditions cause modifications, wherefore, actually there is an extended contact between the large radius curve of the cutting zone 0 and the work gear tooth.
Cutting action occurs simultaneously at both sides of the mid tangent point r to a greater extent than in the case of the rack type wheel, and this contributes to the greater uniformity and smoothness of finish.
At the same time, the length of contact is limited, as compared with the long area of contact of the plane faced wheel, gradually fading out at each side of the center of contact r. Hence the new wheel has a freer cutting action than the plane faced wheel, giving better opportunity for escape of chips and avoiding the clogging, impairment of cutting action and over-heating which occurs with such extended contact.
Any desired value may be given to the cone angle m of my improved grinding wheel, provided it is smaller than the pressure angle but has a positive value. Excellent results have been obtained with an angle of 1, and also with larger angles.
While the exact value of the angle is not critical,
the fact that a contact curve of definite radius, substantially larger than the radius of the rack type wheel, may be obtained, is critical.
The principles of the invention are not limited to the particulars of means for effecting relative rolling traverse between the gear and the grinding wheel. Any means available for that purpose may be used, whether operating to impart both components to the work, or the angular component to the work and the lineardisplacement to the wheel, provided only that the correct ratio between these components is maintained to effect non-slip rolling action between a prescribed pitch curve of the work piece and a straight tangent pitch line, It is essential that the whe'el be sup. parte with its rotational plane parallel to the length dimension of the 'work gear teeth', whether 'the gear'is a spur or a'helical gear. For operating on spur gears-such rotational plane is parallel to I the axis of the gear, while in -connection with helical gears it is disposed at an inclination to the: gear axis equal to the helix angle of the gear. It isfurther'practically important thatthe whee1 be mounted with provision for. angular adjustme'nt of its axis so that the contact element a tooth face of the imaginary conjugate-rack in meshing relation with the work gear. By means of such adjustment a grinding wheel having its active face disposed at any angle to the rotational plane may be brought to the correct relation with What I claim and desire to secure by Letters Patent is:
1. Apparatus for generatively grinding gears comprising a rotatably'mounted grinding wheel having a convex conical grinding face contiguous to its circumference, of which the angle between its radial elements and the plane of rotation is substantially smaller than the pressure angle of the gear being ground, means for effecting a relative rolling movement between the work gear and said grinding wheel on a pitch line inclined to the axis of the wheel at an angle equal to the difference between the pressure angle and the before named angle, and means for effecting a relative 2. A generative gear grinding machine .com-
prising a grinding wheel, means supporting said wheel rotatably, means for rotating the wheel, a work holder, means for effecting relative movementsof rotation and translation between said which the cone angle with the plane of rotation is substantially less than the pressure angle of the gear to be ground, means for effecting relative translative displacement between the wheel and gear lengthwise of the gear teeth, and means for angularlyadjusting the wheel supporting means to bring the axis of the wheel at an angle to said pitch line equal to the difference between the said pressure angle and said cone angle.
3. A machine for generatively grinding gear teeth comprising a supporting structure, a work support'including a spindle adapted to carry a work gear and a grinding wheel support both mounted on the supporting structure, means for effecting relative movements between said work support and grinding wheel support compounded of rotation of the spindle and relative displacement in a straight path transverse to said spindle, a grinding Wheel mounted rotatably on said supporting structure in position to act upon the tooth face of a gear mounted on the spindle, said wheel having a convex conical active face contiguous to the circumference, of which the cone angle with respect to the plane of rotation i substantially smaller than the pressure angle of the gear, and the wheel being located with the portion of'its active face nearest to the gear extending across the path of relative translation at an angle to such path which is the complement of the said pressure angle, and means for effecting relative displacement between the work holder and grinding wheel in the general direction of the axis of the gear to distribute the grinding action lengthwise ing movement between such gear and a grinding 5L0 wheel such that a pitch circle of the gear, other than its base circle, in effect rolls without slip on a straight pitch line, such a grinding wheel having a conical active face adjacent to its periphery, of which the cone angle with respect to its plane of rotation is greater than 0 and substantially less than said pressure angle, and being .located so that the rim of the whee1 crosses said pitch line and the plane of rotation of the wheel is inclined to such line at an angle less than the pressure angle, rotating the wheel in said plane while the relative rolling movement takes place,'
and relatively displacing the gear and wheel lengthwise of the axis of the wheel.
EDWARD W. WELLER.
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US442884A US2368559A (en) | 1942-05-14 | 1942-05-14 | Method and apparatus for smoothfinish gear grinding |
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US442884A US2368559A (en) | 1942-05-14 | 1942-05-14 | Method and apparatus for smoothfinish gear grinding |
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Cited By (1)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US3584424A (en) * | 1967-01-06 | 1971-06-15 | Peter Herbert Cleff | Means for generating involute and noninvolute gears |
-
1942
- 1942-05-14 US US442884A patent/US2368559A/en not_active Expired - Lifetime
Cited By (1)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US3584424A (en) * | 1967-01-06 | 1971-06-15 | Peter Herbert Cleff | Means for generating involute and noninvolute gears |
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