US2961888A - Hypoid gearing - Google Patents

Hypoid gearing Download PDF

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US2961888A
US2961888A US741280A US74128058A US2961888A US 2961888 A US2961888 A US 2961888A US 741280 A US741280 A US 741280A US 74128058 A US74128058 A US 74128058A US 2961888 A US2961888 A US 2961888A
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tooth
gear
teeth
point
line
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Wildhaber Ernest
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    • FMECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16HGEARING
    • F16H1/00Toothed gearings for conveying rotary motion
    • F16H1/02Toothed gearings for conveying rotary motion without gears having orbital motion
    • F16H1/04Toothed gearings for conveying rotary motion without gears having orbital motion involving only two intermeshing members
    • F16H1/12Toothed gearings for conveying rotary motion without gears having orbital motion involving only two intermeshing members with non-parallel axes
    • F16H1/14Toothed gearings for conveying rotary motion without gears having orbital motion involving only two intermeshing members with non-parallel axes comprising conical gears only
    • F16H1/145Toothed gearings for conveying rotary motion without gears having orbital motion involving only two intermeshing members with non-parallel axes comprising conical gears only with offset axes, e.g. hypoïd gearings
    • FMECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16HGEARING
    • F16H55/00Elements with teeth or friction surfaces for conveying motion; Worms, pulleys or sheaves for gearing mechanisms
    • F16H55/02Toothed members; Worms
    • F16H55/08Profiling
    • F16H55/0853Skewed-shaft arrangement of the toothed members
    • YGENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y10TECHNICAL SUBJECTS COVERED BY FORMER USPC
    • Y10TTECHNICAL SUBJECTS COVERED BY FORMER US CLASSIFICATION
    • Y10T29/00Metal working
    • Y10T29/49Method of mechanical manufacture
    • Y10T29/49462Gear making
    • Y10T29/49467Gear shaping
    • Y10T29/49476Gear tooth cutting
    • YGENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y10TECHNICAL SUBJECTS COVERED BY FORMER USPC
    • Y10TTECHNICAL SUBJECTS COVERED BY FORMER US CLASSIFICATION
    • Y10T74/00Machine element or mechanism
    • Y10T74/19Gearing
    • Y10T74/19949Teeth
    • Y10T74/19958Bevel

Definitions

  • FIG/l Nov. 29, 1960 United States Patent HYPOID GEARING Ernest Wildhaber, Brighton, N.Y. (124 Summit'Drive, Rochester 20, N.Y.)
  • the present invention relates to hypoid gearing, having angularly disposed and offset axes, wher'eat least one member of the gear pair has spirally arranged teeth adapted for successive engagement along the tooth length. Particularly it relates to a twisted or warped tooth shape such that the lines of instantaneous tooth contact include relatively large angles with the lengthwise'direction of the teeth, and such that an intimate tooth contact is att ained.
  • Tooth shapes of this general character are disclosed in my Patent No. 1,816,272, granted July 28, 1931, and furtherin my pending patent applications entitled Gearing, filed November 1, 1955, and Hypoid Gearing, filed May 8, 1958, Serial Nos. 544,270 and 733,990, respectively.
  • the intimacy of tooth contact of conjugate tooth surfaces varies'along the length of the teeth and is most intimate at one end, opposite tooth sides having their most intimate contact at opposite ends of the teeth.
  • One object of the invention is to so shape the teeth that they can be used up to the very point where the curvatures of mating tooth surfaces are fully matched, so that in all sections through that point the convex and concave intersection curves of mating tooth surfaces have equal curvature radii, and almost surface contact is achieved at that end point.
  • a related object is to increase the load capacity of such teeth and their usable face width.
  • a further object is to so shape the teeth of a hypoid gear pair consisting of a gear and a pinion, to provide such a tooth shape thereon, that the most intimate tooth contact exists not only at an end point but along the whole end profile of a gear tooth.
  • a still other aim is to provide teeth of the last-named character that have constant profiles from end to end of the teeth on at least the gear member, and teeth that have constant profiles on both the gear and the pinion and that can be produced by form cutting in the manner outlined hereafter.
  • a related aim is to provide mating tooth surfaces that mesh along a helical surface of action.
  • a further object is to devise teeth of the character referred to, whose side tooth surfaces are composed of straight profiles on both the gear and the pinion, and to so form the ends of the gear teeth that the maximum intimacy of contact is had all along the end profiles of the gear teeth.
  • An alternative aim is to provide standard ends on the gear teeth and to provide constant and'moderately curved profiles on the gear and pinion tooth sides, so that maximum intimacy of contact is attained all along the end profiles of the gear teeth.
  • a further object is to provide pinionteeth overlapping in length the ends of the gear teeth and to relieve the ends of the pinion teeth on the side where the tooth contact is most intimate, relief starting at the line that en gages the end profile of the gear teeth, to render tooth contact with matched curvatures possible without interference.
  • Fig. 1 is a diagramamtic view of a hypoid gear pair shown chiefly by its pitch surfaces and constructed according to the present invention, the view being taken along the gear axis.
  • Fig. l is further an explanatory diagram, and also shows the helical surface of action of this gear pair.
  • Fig. 2 is a view and diagram corresponding to Fig. 1, the view being taken in the direction of the center line of the gear pair.
  • Fig. 3 is a view of a hypoid gear pair corresponding to Figures 1 and 2, and taken in direction of the center line of the gear pair, the gear member being shown in axial section.
  • Fig. 4 is a mean normal section taken through a few teeth of this gear pair, through mean point 41.
  • Fig. 5 is a fragmentary View showing a tooth space of the gear 36 of Fig. 3, taken at right angles to its pitch surface.
  • Fig. 6 is a diagrammatic view corresponding to Figures 1 and 2, taken at right angles to a plane containing the axis of the helical surface of action and the center line of the gear pair.
  • Figures 7 and 8 are diagrams corresponding to Fig. 6, looking along the axis of the helical surface of action, and referring to opposite sides of the teeth respectively.
  • Fig. 9 is a diagrammatic view of a hypoid gear pair constructed according to a modification, taken along the center line of the gear pair, the gear being shown in axial section.
  • Fig. 1O is a fragmentary mean normal section through meshing teeth of the gear pair shown in Fig. 9, at a larger scale.
  • Fig. 11 is a diagrammatic view and section similar to Fig. 9 but referring to a further modification.
  • Figures 12 to 18 are enlarged sectional views corresponding to the embodiment of Figures 1 to 8.
  • Figures 12 and 13 are fragmentary peripheral sections of the hypoid gear, taken along lines 12-42 and 1313 respectively.
  • Fig. 14 is an axial section of the hypoid gear, showing opposite sides of the teeth.
  • Fig. 15 is a fragmentary section taken along the pitch surface of the gear and viewed at right angles to the pitch surface.
  • Fig. 17 is an axial section of the mating pinion, showing opposite tooth sides, interfering teeth being omitted for convenience.
  • Fig. 18 is a sectional view of a pinion tooth, taken along the pitch surface, its central pitch line being developed into a plane.
  • Figures 19 and 20 are diagrams illustrating a way of rough cutting opposite sides of the gear teeth.
  • Fig. 21 is a normal section taken through a tooth surface of the gear, showing also a finish-cutting tool in engagement with one side thereof.
  • Fig. 22 is a side view of the tool shown in Fig. 21.
  • Fig. 23 is an end view of this tool, looking at the cutting portion.
  • Figures 24 to 27 are diagrams illustrative of a way of rough-cutting the pinion, a fragmentary normal section through a tooth space being shown. Cross-hatching is omitted to better show the dotted lines.
  • FIG. 28 is a diagrammatic and fragmentary view of a gear pitch surface, taken at right angles thereto, and Fig. 29 is a corresponding front elevational view, both figures illustrating a modified form of production resulting in 'a somewhat modified "form of'teeth.
  • Figures 1 to 5" show a tape'redgear 30 in engagement with a' pinion" 31T'Th'e gear and'piiiion are rotatably mounted on angularly disposed and offset axes 32, 33 respectively, here shown at right angles to each other.
  • Numeral 34 denotes the center line of the gear pair, intersected at right angles by the axes 32, 33.
  • the pitch surface 30 of the gear 30 has a convex contour 35, that is a convex profile in axial section.
  • the mating pitch surface 31 of the pinion 31 contains a concave contour 36 such that the two pitch surfaces 30, 31 contact along a line 37 (Fig. l).
  • gear teeth are shown in section at 29 in Fig. l, the section being taken along the pitch surface 30.
  • Some tooth tops 47 are also shown, and a conical section 47' through opposite ends of the convex tooth tops. The section is seen to bulge out between the tooth ends.
  • mating tooth surfaces have constant matching profiles and are such as can be traced on the rotating gear and pinion by a line describing a helical surface 38 that extends at a constant lead and at a constant distance from an axis 40.
  • the helical path 37 of mean point 41 of the describing line is the contact line of the pitch surfaces 30', 31' and the mean path of contact.
  • the mating teeth contact along the describing line (57, 58 respectively) in all turning positions.
  • axis 40, the lead along it and the turning ratio about it have to conform to the axis, lead and turning ratio of a basic helical member of the hypoid gear pair.
  • Basic helical members are known. They have the same kind of relative motion with respect to the hypoid pair as the members of the hypoid pair themselves. This motion can at any instant be considered a helical motion about an instantaneous axis. This motion should not only be about the same axis, but also should have the same lead. Reference is made to the companion application Serial No. 733,990 for more detailed information. An outline shall be given here however.
  • Axis 40 should lie in a plane parallel to the axes 32, 33. Its direction is assumed to provide a suitable inclination of the path of contact 37.
  • the direction of the said instantaneous axis is determined as if the gears 30, 31 were bevel gears with intersecting axes parallel to the axes 32, 33 and having the given tooth ratio.
  • the turning ratio about axis 40 can be determined as if for a bevel gear whose axis is parallel to axis 40 and passes through the intersection point of the axes of said bevel gears, having the same instantaneous axis as these. This provides the turning motion for any assumed direction of axis 40.
  • E denotes the offset of the axes 32, 33
  • E and the lead L about axis 40 can be computed with the formulas inclinations, which increase from the outer end 50m the inner end 51 on the longitudinally convex side 48 of the teeth, and decrease on the opposite side 49.
  • the change of profile inclination of the normal sectional profiles is at least twenty degrees from end to end of the teeth.
  • the difference of the average inclination of these profiles on the opposite sides 48, 49 should depend on the limit pressure angle: A normal plane laid through mean point 41 at right angles to the pitch line and to the tooth direction intersects the center line 34 at a point 52 (Fig. l).
  • the connecting line 41-52 is what I have called the limit normal.
  • the two side surfaces 48, 49 should be about equally inclined to the limit normal when they pass through mean point 41.
  • Fig. 4 is a normal section through teeth contacting at 41. It shows the path 55 along which the pitch line of the pinion approaches the pitch ,point 41 of the gear and recedes from it. In the immediate vicinity of the pitch point (41) the relative path is in a direction 56 that is inclined at the limit pressure angle to the pitch vertical 45.
  • the limit pressure angle is understood to be the inclination of the limit normal 41-52 to the pitch surfaces at mean point 41, or to their tangent plane.
  • hypoid gears differ from bevel gears with intersecting axes, where the last approach is at right angles to the pitch surface. This will be further referred to.
  • numeral 57 denotes the describing line or generating line that describes the longitudinally convex side 48 of the gear teeth and the mating tooth sides of the pinion. It is a straight line in this embodiment.
  • the straight line 58 is the describing line for the longitudinally concave side of the gear teeth and the mating longitudinally convex side of the pinion teeth.
  • Line 57 is determined when it passes through the outer end point 53 of the path of contact 37. It should then have a pressure angle equal to the limit pressure angle at that point. That is, it should lie in a plane perpendicular to the limit normal.
  • the limit normal is the connecting line of point 53 with a point 60 (Figs. 1, 6, 7) of the center line 34.
  • the limit normal fulfills the condition that its leverages with respect to the two axes are in the proportion of the respective tooth numbers. In other words, a force directed along this normal should exert turning moments on the two members of the gear pair in the proportion of their tooth numbers.
  • the limit normal 53-60 includes an angle k with the direction of the pinion axis 33.
  • the said force can be. resolved into two components. center line 34, and the other lies in a plane perpendicular to center line 34 and includes the above said angle k with the direction of the pinion axis.
  • the component along center line 34 intersects both axes 32, 33 and therefore exerts no turning moment on either member.
  • the other component exerts a turning moment on the gearproportional to the horizontal component F cos k of the force F and. to the distance (E+B), that is F cos k(E+B). It exerts a turning moment F(sin k)B on the pinion.
  • (E+B) cos k MB sin k through transformation:
  • the describing line 57 or at least its tangent at point 53 should lie in a plane perpendicular to the limit normal 53-60.
  • Line 57 or its tangent also lies in the tangent plane of the assumed helical surface of action. This helical surface may coincide with the helical surface containing the pitch vertical 45.
  • the describing line or its tangent can be determined as the intersection line of said tangent plane and the plane perpendicular to the limit normal.
  • Trace 61 (Fig. 7) has the same distance from axis 40 as trace 61" and a different angular position. With respect to trace61 it is tu-rned through the same angle 41-40-53 (Fig. 8) as end point 53 is turned from mean point 41.
  • Point 53 has a distance 66 from the drawing plane of Fig. 7 which is perpendicular to axis 40 and contains center line 34. In Fig. 6 this distance appears as the distance of point 53 from center line 34.
  • distance 66 in Fig. 7 on a line 60-60 perpendicular to the projected limit normal 53-66, draw line 60"-53 and a line 53-67 perpendicular thereto.
  • Line 68 is drawn parallel to projected line 60-53 at the aforesaid distance 64 therefrom. Itintersects line 53-67 at point 67.
  • the sought trace 65 passes through point 67 and is perpendicular to the projected limit normal 53-60.
  • the two traces 61 and 65 inter- One of these extends along sect at a point 70.
  • the describing'lin'e 57 or its tangent is a portion of the connecting line 53-70.
  • Tooth surfaces 48of the gear'and the mating tooth surfaces of the pinion are described by moving line 57 helically about and along axis 40 at the lead L while the gears turn on their axes 32, 33 as if they would run together.
  • the turning motion about axis 40 thereby should conform to the turning motions of the gear pair in the above described manner.
  • Line 57 also traces the helical surface of action in space.
  • the describing line 58 for the opposite side of the teeth is determined at the inner end position, at point 54 of the path of contact 37.
  • the procedure is analogous to the one described.
  • First the limit normal at point 54 is determined in Fig. 2 as the connecting line 34-54, to obtain another angle k.
  • a new distance B is computed with the given formula.
  • Distance B may then be plotted in Fig. 6 and in Fig. 8 from the pinion axis on center line 34 to obtain the intersection point 601' of the limit normal 54-60i.
  • Line 54-601 is drawn and through point 54 a line 54-67i perpendicular thereto.
  • Line 681' is drawn parallel to the projected limit normal 54-60i at the distance 64 (Fig. 6) therefrom. Its intersection with line 54-67i is the sought point 67i.
  • Trace 65i is drawn through point 67i at right angles tothe projected limit normal 54-6tli.
  • the two traces 651' and 61i intersect at 7 01'.
  • the tangent to the describing line 58 or the line itself is part of the connecting line 54-70i.
  • the gearing is also applicable to gear pairs whose shaft angle differs home right angle. In such cases the limit normal no longer intersects the center line of the gear pair. It may be determined in accordance with my aforesaid articles.
  • the tangent plane of the contacting pitch surfaces is first determined. It is referred to as the pitch plane.
  • the inclinations of the gear and pinion axes from this plane are referred to as the pitch angles, and the distances of their intersections with this pitch plane from the said point are referred to as the cone distances.
  • the limit normal is perpendicular to the pitch lines contacting at said point, and its inclination to the pitch plane is referred to as the limit pressure angle. Itcan be determined with Formula 15 given in Article II.
  • Tooth ends of gear the describing lines 57, 58 are straight lines, and the tooth ends 50, 51 of the gear are so Shaped or dimensioned that the curvatures of contacting teeth are completely matched, or closely and equally matched, along a whole gear end-profile, when its points are in contact position.
  • the longitudinally convex sides 48 of the gear teeth they are matched on the end profile that passes through point 53 at the outer end.
  • the longitudinally concave sides 49 of the gear they are matched on the inner end profile that passes through point 54.
  • the tangents may be substituted for the profiles of the end surfaces so determined.
  • the surfaces 50,- 51 are then conical surfaces coaxial with the gear. Their straight profiles in axial sections are seen to converge in a direction from tooth bottom to tooth top, at an angle larger than thirty degrees, so that the face width at the tooth tops 47 is smaller than at the tooth bottom 46.
  • Planes are considered that are perpendicular to the describing line, and their traces are determined in the drawing plane of Figs. 7 and 8, which plane contains the center line 34 and is perpendicular to axis 40.
  • the considered planes have traces at right angles to the describing line.
  • Such a plane at point 53 (Fig. 7) has a trace 71 that intersects the center line 34 at 60, because this plane contains the limit normal passing through point 60.
  • the plane normal to the describing line 57 through point 53' thereof has a trace 71' parallel to trace 71.
  • the limit normal at point 53' can be directly drawn in the view Fig. 2, and determines the angle k used for computing the distance B. Knowing the new B we can plot the point 60 (Fig. 7) where the new limit normal intersects the center line 34. As trace 71' is seen to be offset from point 69 the surface normal of the teeth contacting at point 53 does not coincide with the limit normal 53'60' at that point. To make it coincide a helical displacement of point 53' in counter-clockwise direction is needed. A helical displacement about axis .40 may be assumed; and the above procedure is then repeated until the position 53 of point 53' is found, where the surface normal coincides with the limit normal.
  • the so determined point 53" is a point of the gear outside surface 50. Other points may be similarly determined. Surface 50 also contains point 53.
  • the plane perpendicular to the describing line 58 at point 54 intersects the drawing plane in a trace 72 (Fig. 8) that passes through point 60i.
  • the trace 72' of the plane perpendicular to the describing line at point 54 thereof is parallel to trace 72.
  • the limit normal at point 54' is determined with the above described procedure. It intersects the center line 34 at a point 60i' offset from trace 72'. A small clockwise helical motion of point 54 about axis 40 is here required.
  • the inside surface 51 is the surface that contains point 54" in addition to point 54.
  • the tooth ends 50, 51 may also be determined experimentally by trial.
  • FIG. 9 differs from the described embodiment merely in the shape of its end surfaces 50', 51' and in the curvature of the describing lines. Everything else is the same as described, including the tangents of the describing lines at their mean point (41) and the helical mean path of contact 37.
  • Conventional end surfaces 50', 51 are used, that have parallel straight profiles. However any suitable shape may be assumed if desired.
  • the describing lines and tooth profiles are here determined from the assumed shape of the surfaces 50', 51'.
  • the tooth profiles of a mean normal section of the teeth are shown in Fig. 10, at an enlarged scale as compared with Fig. 9. This section is understood to be at right angles to the tooth direction.
  • the gear has convex profiles 74, and the pinion has concave profiles 75. They are shown in relation to the pitch vertical 45.
  • axis 240 of the basic helical member is not at a distance from the tooth zone, but lies on the root surface of the gear 230. It can be considered the line of contact of mating pitch surfaces and a path of contact.
  • the describing lines 257, 258 are shown at mean point 241.
  • the describing line 257 is further shown in a position where it passes through the outer end point 253 of the path of contact, where its direction is determined in the manner described.
  • Line 257 corresponds to the longitudinally convex side of the gear teeth and to the mating side of the pinion teeth.
  • the opposite describing line 258 is further shown passing through the inner end point 254 of the path of contact.
  • Axis 240 intersects the center line of the gear pair. Its inclination (i) and its offset (E,.) from the pinion axis 33, as well as the lead (L,) are determined in exactly the same way as in the previously described embodiments. The inclination (i) of course is here smaller.
  • the root surface of the gear contains the straightline element 240 offset from its axis 32, it is a hyperboloid of revolution.
  • the profile 246 of an axial section of this root surface is concave.
  • the axial profile 239 of the outside surface of the pinion 231 should also be concave, but only slightly so.
  • a straight profile il: .111 1. 1 J. may bessubstituted therefor.
  • the. outside surface of the gear 230 may be made straight, unlessxthergear. hasa small tooth number. In that case it is preferably made convex.
  • .F igures 12 and 13 further illustrate the warped or twisted tooth surfaces, and their rapid change of profile inclination;
  • Fig.- 14 shows on the left the longitudinally convexside 48 of the gear teeth, and at the. right the longitudinally concave side 49 thereof.
  • the surface normals coincide with The axial profile 247 r,
  • eta-tar thegears riuna direction so that mesh starts at the outer, ends of theteeth, the, pitch line approach of the pinion to point53. of the. gear is in a relative path 55 to point 53, and the recess is in a path 55'.
  • thelimit normals,-and mating tooth surfaces have equal andmatching convex and concave curvature.
  • the surface normals-coincide with the limit normal so that the same kindof very intimate contact results.
  • the axial section of the pinion 31, Fig. 17, shows below therlongitudinally concave tooth side 81, that meshes with side 48 of the gear. Its longitudinally convex tooth side-82 is shown above. It meshes with side 49 of the gear:
  • the pinion should have an outside surface whose axialprofile is moderately concave, as indicated in Fig. 3. :LA; conical surface 83 is shown substituted therefor, asrma'y be done sometimes in practice. This may result instooth tops whose width is smallest in a region intermediate the ends of the teeth.
  • the pinion teeth 84 overlap the ends of the gear teeth. They do not terminate at the points 53, 54 (Fig. 1) but reachcbeyond.
  • Pinion tooth surface 81 contains a line 85: that corresponds to the end profile 76 of the gear tooth-surfaces 48 and gets into gear contact with said profile. It is its mating line of the pinion.
  • On the pinion tooth surface 82 is a line 86 mating with end profile 77 of the gear.
  • the pinion tooth surfaces 81 are relieved adjacent end 50, starting at line 85. Andzthe pinion tooth surfaces 82 are relieved adjac'en't end 51',starting at line 86. This applies to all described embodiments.
  • the relief is best seen in Fig. 18, and is also shown in Fig. 3.
  • The'-relieved portion 87 is at an angle to surface 81. Likewise the relieved portion 88 is at an angle to surface 82. The said angles differ from 180 degrees by l'ess' tha'n twelve degrees. It should be enough to prevent contact. at portions 87, 88 at any actual running condition. This is not a mere ease-off, but a deliberate destru'ction'of the surface.
  • the surfaces 81, 87 and 82, 88 meet in a ridge, which may however be rounded. It may. be said that they meet in a near-ridge.
  • Fig. 16 This is a normal section through the teeth contacting at end point 53, as if the teeth would continue.
  • thepaths 55, 55' are in the direction of tangent 56, inclined at the limit pressure angle to the vertical, ,as was described for a mean section with Fig. 4.
  • this is also the inclination of the tooth surface, which is perpendicular to the limit normal. In other words, this direction follows the tooth surface and is tangent thereto.
  • the dotted portion 55 of the path seemingly interferes with the gear tooth.
  • the invention prevents interference by using warped tooth surfaces and providing working surfaces 81, 82 on the pinion that terminate at lines 85, 86 respectively.
  • the relieved remainder of the tooth length is for strength, not for tooth action.
  • Fig. 16 further illustrates the; leaning teeth usually found at the outer end.
  • One side profile of the teeth is negatively inclined, see also Fig. 5.
  • FIG. 19 and 20 show a pair .of tools, 90,.90' for rough-cutting opposite sides of the toothspaces 91 shown in dotted lines-
  • the workpiece is,continuously and uniformly rotated on its axis, while the tools 90,90 perform periodic helical reciprocations, each about its own axis (40).
  • a pluralityoftool pairs 90 are used. Their axes are angularly spaced about the workpiece. The duration of the reciprocation is such that each tool enters a different tooth space on successive strokes.
  • the workpiece in effect is indexed from stroke to stroke through a numberof teeth. This number should be prime to the tooth number of the workpiece, so that each tool successively cuts inall toothspaces.
  • Tool 90 cuts with side 92 and, end 93. Tool 90' cuts with, the oppositeside 92, and end 93. Together they rough out the tooth spaces.
  • the depthwise feed and also the clapping motion are preferably made up of an axial motion of the gear blank or, workpiece and of a turning motion about the gear axis, so that the feed path about bisects the angle between opposite tooth sides at the mid-section.
  • Fig. 14 shows at the left various positions of the describing line .(57) to be represented by a finish-cutting edge. It is seen that the inclination of the describing line to the tooth bottom 46 varies. This variation presents a problem in cutting clearance, both in end clearance and in side clearance.
  • On roughing tools 98, 90" I may solve this problem by tilting each tool as it goes through the cut, so as to obtain more nearly constant cutting clearances;
  • the direction of the tilt axis ismade up of a direction adapted to keep the end clearance right and of a direction to keep the side clearance right. It is obtainable by vectorial addition.
  • the tilt axis is inclined to the axis (48) of the helical 'tool stroke and preferably passes through the center 94 of the edge round of the tool.
  • I may change the phase of the tilting motion with increasing depth of cut accordingly.
  • Tool 95 has a finish-cutting 11 edge 96 formed at the intersection of a cutting face 97 with a side surface 9 8.
  • the tool is preferably designed for contour grinding, to provide maximum cutting clearance. It is sharpened by regrinding a narrow strip 98 of side surface 98, that follows the cutting edge 96. After sharpening the tool is adjusted to advance the newly formed cutting edge to the original position. This adjustment is in a direction parallel to the cutting face 97.
  • the blade is aligned angularly with the cutting face, so that sidewise displacement provides the required direction of adjustment.
  • the tool is secured in diflerent sidewise positions by using parallels 99 of different thickness.
  • Fig. shows that the direction of a warped tooth surface in sections parallel to the drawing plane depends much on the depth level of the section.
  • To attain improved side clearance on the contourground finishing edge I vary the lateral inclination of strip 98' at different depths in accordance with the difference in cutting direction.
  • Cutting at mean point 41 is in a direction 100.
  • the sectionalprofile there is in a direction 102, while near the top of the cutting tooth it is in a direction 101 and near the bottom it is in a direction 103.
  • the strip 98' is not a plane but a twisted surface of varying inclination. It is approximately a helical surface following edge 96.
  • Such strips of varying inclination may also be used with curved cutting edges.
  • the finishing blades may be used in the same cutter assembly with the multiple pairs of roughing blades. In this case they are kept clear of the workpiece during the depth feed, and are advanced into cutting position when full cutting depth is reached. They may be advanced by a slight displacement in the direction of the axis of their helical cutting motion.
  • a finishing blade may be tilted about the cutting edge as it goes through the cut.
  • the pinions may be finished like the gear, except that the clapping motion is usually not along and about the work axis, but in a direction more nearly perpendicular to the pinion pitch surface.
  • Figures 24 to 27 illustrate a roughing operation chiefly for pinions.
  • tool 105 is fed in its helically reciprocating slide part to follow the tooth profile 110, starting from a position 105'.
  • Tool 108, Fig. 27 starts from a position 108' and is fed to follow tooth profile 111.
  • These tools are also tilted as they go through the cutting stroke, preferably about axes that pass through the centers 94 of the edge rounds. These axes partake in the helical motion of the respective tools and in the feed motion.
  • the intermediate tools 106, 107 are similarly tilted about axes intersecting their end cutting edge.
  • Tool 106 is fed from a starting position 106, while tool 107 starts from a position 107' in its helically reciprocating slide part.
  • the four tools completely cover the entire width of the tooth space even where it is widest. They work together, in support of each other, because each tool enters a ditferent tooth space in successive strokes.
  • each tool is preferably in the direction of its feeding motion.
  • the tools 106, 107 are wider than the minimum slot width of the tooth space, and their feed is terminated in the position shown in full lines. From here on the tools 105, 108 only of the four tools proceed with the depth feed.
  • the axis 122 of the sought helical surface intersects normal at right angles at a point 123 such that the required change of profile inclination is obtained lengthwise of the tooth as Well as the curvature required on helix 119.
  • Axis 122 is inclined to plane 124 at an angle smaller than sixty degrees.
  • Plane 124 is the tangent plane of the pitch surface at mean point 41.
  • the workpiece is intermittently indexed to present other tooth spaces to the cutting edge.
  • the tooth sides of the pinion are here produced in a generating operation, in which helically reciprocating cutting edgesde scribe tooth sides of the gear while thepinion meshes with and rolls on said gear. 7 v
  • the tooth sides of the gear are described by helically moving cutting edges while the gear turns on its axis at a slow enough rate that each cutting edge enters adjacent tooth spaces on successive strokes.
  • the pinion is here also produced by generation wherein cutting edges describe tooth sides of the rotating gear- Still further modifications may be made.
  • Hypoid gearing comprising a pair of gears having angularly disposed and offset axes, the teeth of each member of said pair following a surface of revolution coaxial with said member and their side surfaces being warped surfaces whose profile inclination to the normals of said surface of revolution changes along the length of the teeth and decreases on one side of the teeth while increasing on the opposite side from one tooth end to the other, the tooth surface normals at points adjacent one end of the teeth coinciding approximately with the limit normals at said points, so that near-surface contact is achieved at said points.
  • gear teeth are curved lengthwise and extend between outer and inner ends, and wherein the tooth surface normals at the points of the outer end profile coincide with the limit normals at said points on the longitudinally convex side of the gear teeth, and wherein the tooth surface normals at the points of the inner end profile coincide with the limit normals at said points on the longitudinally concave side of the gear teeth.
  • Hypoid gearing comprising a gear and a pinion adapted to mesh with each other and having angularly disposed and offset axes, the teeth of said gear being curved lengthwise and extending between outer and inner ends along a surface of revolution coaxial with its axis, the side surfaces of said teeth being warped surfaces whose profile inclination to the normals of said surface of revolution changes along the length of the teeth, decreasing from the outer end to the inner end on the longitudinally concave side of the gear teeth while increasing on the longitudinally convex side, the teeth of the pinion overlapping the ends of the gear teeth, the longitudinally concave tooth sides of the pinion that mate with the longitudinally convex tooth sides of the gear being relieved adjacent their outer end, the opposite tooth sides of the pinion being relieved adjacent their inner end, relief starting with a near-ridge at a line of the pinion tooth surfaces that corresponds to and meshes with the outer and inner end profiles of the gear respectively, so that interference is avoided in the region of near-surface contact.
  • Hypoid gearing comprising a gear and a pinion adapted to mesh with each other and having angularly disposed and offset axes, the teeth of said gear following a surface of revolution coaxial with its axis and extending between an outer and an inner end surface, the side surfaces of said gear teeth being warped surfaces whose profile inclination to the normals of said surface of revolution changes from end to end of said teeth by at least twenty degrees, decreasing on one side of the teeth and increasing on the opposite side, said end surfaces converging from bottom to top of the gear teeth, and the pinion tooth surfaces being relieved at the end of lower profile inclination of the tooth sides, relief starting with a near-ridge along a line that mates with the end profile of the gear teeth.
  • gearing consists of a gear and a pinion, and wherein the gear contains convex tooth profiles and the pinion contains concave tooth profiles.
  • a tapered gear having longitudinally curved teeth that extend between an outer end surface and an inner end surface and follow a surface of revolution coaxial with the gear, the side surfaces of said teeth being warped surfaces whose profile inclination to the normals of said surface of revolution changes by at least twenty degrees from the outer end of said teeth to their inner end, decreasing on the longitudinally concave side of the gear teeth and increasing on the longitudinally convex side, said end surfaces being surfaces of revolution converging from bottom to top of the teeth, so that the face width is smaller at the tooth tops than at the tooth bottoms.
  • a tapered pinion having spirally arranged and longitudinally curved teeth extending along a surface of revolution coaxial with said pinion between an outer end and an inner end, the side surfaces of said teeth being warped surfaces whose profile inclination to the normals of said surface of revolution changes by at least twenty degrees from the outer end of said teeth to their inner end, decreasing on the longitudinally convex side of the teeth and increasing on the longitudinally concave sides, the working portions of said side surfaces terminating at one end of the teeth with a near-ridge followed by a relieved portion angularly inclined to said working portion at an angle differing from degrees by less than twelve degrees, said near-ridge and relieved portion being adjacent the inner and outer tooth ends on the longitudinally convex and concave tooth sides respectively.

Description

Nov. 29, 1960 E. WILDHABER 2,961,888 I HYPOID GEARING Filed June 11. 1958 4 Sheets-Sheet l J 47 i INVENTOR;
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Nov; 29, 1960 E. WILDHABER HYPOID GEARING 4 Sheets-Sheet 2 Filed June 11; 1958 INVENTOR.
FIG/l Nov. 29, 1960 United States Patent HYPOID GEARING Ernest Wildhaber, Brighton, N.Y. (124 Summit'Drive, Rochester 20, N.Y.)
Filed June 11, 1958, Ser. No. 741,280 17 Claims. 01. 74-4595 The present invention relates to hypoid gearing, having angularly disposed and offset axes, wher'eat least one member of the gear pair has spirally arranged teeth adapted for successive engagement along the tooth length. Particularly it relates to a twisted or warped tooth shape such that the lines of instantaneous tooth contact include relatively large angles with the lengthwise'direction of the teeth, and such that an intimate tooth contact is att ained.
Tooth shapes of this general character are disclosed in my Patent No. 1,816,272, granted July 28, 1931, and furtherin my pending patent applications entitled Gearing, filed November 1, 1955, and Hypoid Gearing, filed May 8, 1958, Serial Nos. 544,270 and 733,990, respectively.
In the tooth shapes referred to, the intimacy of tooth contact of conjugate tooth surfaces varies'along the length of the teeth and is most intimate at one end, opposite tooth sides having their most intimate contact at opposite ends of the teeth.
One object of the invention is to so shape the teeth that they can be used up to the very point where the curvatures of mating tooth surfaces are fully matched, so that in all sections through that point the convex and concave intersection curves of mating tooth surfaces have equal curvature radii, and almost surface contact is achieved at that end point. A related object is to increase the load capacity of such teeth and their usable face width.
A further object is to so shape the teeth of a hypoid gear pair consisting of a gear and a pinion, to provide such a tooth shape thereon, that the most intimate tooth contact exists not only at an end point but along the whole end profile of a gear tooth.
A still other aim is to provide teeth of the last-named character that have constant profiles from end to end of the teeth on at least the gear member, and teeth that have constant profiles on both the gear and the pinion and that can be produced by form cutting in the manner outlined hereafter. A related aim is to provide mating tooth surfaces that mesh along a helical surface of action.
A further object is to devise teeth of the character referred to, whose side tooth surfaces are composed of straight profiles on both the gear and the pinion, and to so form the ends of the gear teeth that the maximum intimacy of contact is had all along the end profiles of the gear teeth.
An alternative aim is to provide standard ends on the gear teeth and to provide constant and'moderately curved profiles on the gear and pinion tooth sides, so that maximum intimacy of contact is attained all along the end profiles of the gear teeth.
A further object is to provide pinionteeth overlapping in length the ends of the gear teeth and to relieve the ends of the pinion teeth on the side where the tooth contact is most intimate, relief starting at the line that en gages the end profile of the gear teeth, to render tooth contact with matched curvatures possible without interference.
I 2,961,888 Patented Nov. 29, 1960 Also the production of 'such gearing shall be improved.
Other objects will appear in the courseof the specification and in the recital of the appended claims. These objects may be attained singly or in any combination.
In the drawings:
Fig. 1 is a diagramamtic view of a hypoid gear pair shown chiefly by its pitch surfaces and constructed according to the present invention, the view being taken along the gear axis. Fig. l is further an explanatory diagram, and also shows the helical surface of action of this gear pair.
Fig. 2 is a view and diagram corresponding to Fig. 1, the view being taken in the direction of the center line of the gear pair. I
Fig. 3 is a view of a hypoid gear pair corresponding to Figures 1 and 2, and taken in direction of the center line of the gear pair, the gear member being shown in axial section.
Fig. 4 is a mean normal section taken through a few teeth of this gear pair, through mean point 41.
Fig. 5 is a fragmentary View showing a tooth space of the gear 36 of Fig. 3, taken at right angles to its pitch surface.
Fig. 6 is a diagrammatic view corresponding to Figures 1 and 2, taken at right angles to a plane containing the axis of the helical surface of action and the center line of the gear pair.
Figures 7 and 8 are diagrams corresponding to Fig. 6, looking along the axis of the helical surface of action, and referring to opposite sides of the teeth respectively.
Fig. 9 is a diagrammatic view of a hypoid gear pair constructed according to a modification, taken along the center line of the gear pair, the gear being shown in axial section.
Fig. 1O is a fragmentary mean normal section through meshing teeth of the gear pair shown in Fig. 9, at a larger scale.
Fig. 11 is a diagrammatic view and section similar to Fig. 9 but referring to a further modification.
Figures 12 to 18 are enlarged sectional views corresponding to the embodiment of Figures 1 to 8. Figures 12 and 13 are fragmentary peripheral sections of the hypoid gear, taken along lines 12-42 and 1313 respectively. Fig. 14 is an axial section of the hypoid gear, showing opposite sides of the teeth. Fig. 15 is a fragmentary section taken along the pitch surface of the gear and viewed at right angles to the pitch surface. Fig. 17 is an axial section of the mating pinion, showing opposite tooth sides, interfering teeth being omitted for convenience. Fig. 18 is a sectional view of a pinion tooth, taken along the pitch surface, its central pitch line being developed into a plane.
Figures 19 and 20 are diagrams illustrating a way of rough cutting opposite sides of the gear teeth.
Fig. 21 is a normal section taken through a tooth surface of the gear, showing also a finish-cutting tool in engagement with one side thereof.
Fig. 22 is a side view of the tool shown in Fig. 21.
Fig. 23 is an end view of this tool, looking at the cutting portion.
Figures 24 to 27 are diagrams illustrative of a way of rough-cutting the pinion, a fragmentary normal section through a tooth space being shown. Cross-hatching is omitted to better show the dotted lines.
.Fig. 28 is a diagrammatic and fragmentary view of a gear pitch surface, taken at right angles thereto, and Fig. 29 is a corresponding front elevational view, both figures illustrating a modified form of production resulting in 'a somewhat modified "form of'teeth.
Figures 1 to 5"show a tape'redgear 30 in engagement with a' pinion" 31T'Th'e gear and'piiiion are rotatably mounted on angularly disposed and offset axes 32, 33 respectively, here shown at right angles to each other. Numeral 34 denotes the center line of the gear pair, intersected at right angles by the axes 32, 33.
The pitch surface 30 of the gear 30 has a convex contour 35, that is a convex profile in axial section. The mating pitch surface 31 of the pinion 31 contains a concave contour 36 such that the two pitch surfaces 30, 31 contact along a line 37 (Fig. l).
' Pitch surfaces of this kind and teeth built around them have been disclosed in my companion application Serial No. 733,990. They have an increased duration of pitch line contact and more teeth in simultaneous contact than conventional designs.
Some gear teeth are shown in section at 29 in Fig. l, the section being taken along the pitch surface 30. Some tooth tops 47 are also shown, and a conical section 47' through opposite ends of the convex tooth tops. The section is seen to bulge out between the tooth ends.
In a mathematically exact embodiment without easeoff mating tooth surfaces have constant matching profiles and are such as can be traced on the rotating gear and pinion by a line describing a helical surface 38 that extends at a constant lead and at a constant distance from an axis 40. The helical path 37 of mean point 41 of the describing line is the contact line of the pitch surfaces 30', 31' and the mean path of contact. The mating teeth contact along the describing line (57, 58 respectively) in all turning positions.
To provide these conditions, the position of axis 40, the lead along it and the turning ratio about it have to conform to the axis, lead and turning ratio of a basic helical member of the hypoid gear pair. Basic helical members are known. They have the same kind of relative motion with respect to the hypoid pair as the members of the hypoid pair themselves. This motion can at any instant be considered a helical motion about an instantaneous axis. This motion should not only be about the same axis, but also should have the same lead. Reference is made to the companion application Serial No. 733,990 for more detailed information. An outline shall be given here however.
Axis 40 should lie in a plane parallel to the axes 32, 33. Its direction is assumed to provide a suitable inclination of the path of contact 37.
Next the direction of the said instantaneous axis is determined as if the gears 30, 31 were bevel gears with intersecting axes parallel to the axes 32, 33 and having the given tooth ratio. The turning ratio about axis 40 can be determined as if for a bevel gear whose axis is parallel to axis 40 and passes through the intersection point of the axes of said bevel gears, having the same instantaneous axis as these. This provides the turning motion for any assumed direction of axis 40.
Axis 40 furthermore should intersect the center line 34, and should have a definite distance E =4344 (Fig. 1) from the pinion axis 33, depending on the inclination i (Fig. 2) of axis 40 to the direction of the pinion axis 33. When E denotes the offset of the axes 32, 33, E and the lead L about axis 40 can be computed with the formulas inclinations, which increase from the outer end 50m the inner end 51 on the longitudinally convex side 48 of the teeth, and decrease on the opposite side 49. The change of profile inclination of the normal sectional profiles is at least twenty degrees from end to end of the teeth.
The difference of the average inclination of these profiles on the opposite sides 48, 49 should depend on the limit pressure angle: A normal plane laid through mean point 41 at right angles to the pitch line and to the tooth direction intersects the center line 34 at a point 52 (Fig. l). The connecting line 41-52 is what I have called the limit normal. The two side surfaces 48, 49 should be about equally inclined to the limit normal when they pass through mean point 41.
A further meaning of the limit normal is illustrated with Fig. 4, which is a normal section through teeth contacting at 41. It shows the path 55 along which the pitch line of the pinion approaches the pitch ,point 41 of the gear and recedes from it. In the immediate vicinity of the pitch point (41) the relative path is in a direction 56 that is inclined at the limit pressure angle to the pitch vertical 45. The limit pressure angle is understood to be the inclination of the limit normal 41-52 to the pitch surfaces at mean point 41, or to their tangent plane.
The inclined direction (56) of approach is further described in Article V of my eight articles on the Basic Relationship of Hypoid Gears that were published in American Machinist in 1946, see Fig. 32, thereof. In this respect hypoid gears differ from bevel gears with intersecting axes, where the last approach is at right angles to the pitch surface. This will be further referred to.
Surface of action In principle there is a surface of action for each of the two sides of the teeth, both surfaces containing path 37. In conventional gearing the surfaces of action of opposite tooth sides intersect and include a substantial angle with each other. If this is followed here, the outside ends of the two helical surfaces of action contain coaxial spaced helices. This generally results in root surfaces that are differently tapered on opposite sides of the teeth. That is, the ends of the generating lines of opposite tooth sides describe root lines of different taper. It is desirable to have a common root surface for both tooth sides, that is a surface of revolution. This is attainable in accordance with the invention by providing a pair of surfaces of action which nearly coincide, and which are tangent to each other along the mean path of contact 37.
In Fig. l numeral 57 denotes the describing line or generating line that describes the longitudinally convex side 48 of the gear teeth and the mating tooth sides of the pinion. It is a straight line in this embodiment. The straight line 58 is the describing line for the longitudinally concave side of the gear teeth and the mating longitudinally convex side of the pinion teeth.
Line 57 is determined when it passes through the outer end point 53 of the path of contact 37. It should then have a pressure angle equal to the limit pressure angle at that point. That is, it should lie in a plane perpendicular to the limit normal.
The limit normal The limit normal is the connecting line of point 53 with a point 60 (Figs. 1, 6, 7) of the center line 34. The distance B=4460 of point 60 from the pinion axis 33 will now be computed. Like any other contact normal, the limit normal fulfills the condition that its leverages with respect to the two axes are in the proportion of the respective tooth numbers. In other words, a force directed along this normal should exert turning moments on the two members of the gear pair in the proportion of their tooth numbers.
In the view along center line 34, Fig. 2, the limit normal 53-60 includes an angle k with the direction of the pinion axis 33. At point 60 the said force can be. resolved into two components. center line 34, and the other lies in a plane perpendicular to center line 34 and includes the above said angle k with the direction of the pinion axis. The component along center line 34 intersects both axes 32, 33 and therefore exerts no turning moment on either member. The other component exerts a turning moment on the gearproportional to the horizontal component F cos k of the force F and. to the distance (E+B), that is F cos k(E+B). It exerts a turning moment F(sin k)B on the pinion. The two moments should be in the proportion M=Nln of their tooth numbers, N being the gear tooth number. Hence (E+B) cos k=MB sin k through transformation:
B- M tan lc-l The limit normal 53-60 can now be plotted in Figures 6 and 7.
Hitherto it has been considered impossible to have conjugate tooth action up to points whose tooth surface normal coincides with the limit normal. I have found that with the measures disclosed hereafter it is possible to have tooth action up to these very points. Not only does this extend the duration of contact of such warped teeth, but it secures the most intimate contact. 7 At these points the curvatures of contacting tooth surfaces are matched completely, so that the contact achieved is almost surface contact.
The describing line To this end, the describing line 57 or at least its tangent at point 53 should lie in a plane perpendicular to the limit normal 53-60. Line 57 or its tangent also lies in the tangent plane of the assumed helical surface of action. This helical surface may coincide with the helical surface containing the pitch vertical 45. Thus the describing line or its tangent can be determined as the intersection line of said tangent plane and the plane perpendicular to the limit normal.
We may first consider the said tangent plane in the position where it passes through mean point 41.: It contains the pitch vertical 45 and the helix tangent at point 41, that is the tangent to path 37. Its trace 61' (Fig. 7) on a plane 62 (Fig. 6) through point 41 can readily be determined with known procedure. Plane 62 and plane 63 are both parallel to the drawing plane of Fig. 7 and perpendicular to axis 40. The trace 61" with plane 63 is parallel to trace 61" and its distance therefrom corresponds to the distance 64 (Fig. 6) of the planes 62, 63. The tangent plane of the helical surface of action at end point 53 has a trace 61 on plane 62. This plane has the said distance 64 from point 53. Trace 61 (Fig. 7) has the same distance from axis 40 as trace 61" and a different angular position. With respect to trace61 it is tu-rned through the same angle 41-40-53 (Fig. 8) as end point 53 is turned from mean point 41.
Next we consider the plane through 53 perpendicular to the limit normal 53-60 and determine its trace 65 with the same plane (62). Point 53 has a distance 66 from the drawing plane of Fig. 7 which is perpendicular to axis 40 and contains center line 34. In Fig. 6 this distance appears as the distance of point 53 from center line 34. We may plot distance 66 in Fig. 7 on a line 60-60 perpendicular to the projected limit normal 53-66, draw line 60"-53 and a line 53-67 perpendicular thereto. Line 68 is drawn parallel to projected line 60-53 at the aforesaid distance 64 therefrom. Itintersects line 53-67 at point 67. The sought trace 65 passes through point 67 and is perpendicular to the projected limit normal 53-60. The two traces 61 and 65 inter- One of these extends along sect at a point 70. The describing'lin'e 57 or its tangent is a portion of the connecting line 53-70.
Tooth surfaces 48of the gear'and the mating tooth surfaces of the pinion are described by moving line 57 helically about and along axis 40 at the lead L while the gears turn on their axes 32, 33 as if they would run together. The turning motion about axis 40 thereby should conform to the turning motions of the gear pair in the above described manner. Line 57 also traces the helical surface of action in space. V
The describing line 58 for the opposite side of the teeth is determined at the inner end position, at point 54 of the path of contact 37. The procedure is analogous to the one described. First the limit normal at point 54 is determined in Fig. 2 as the connecting line 34-54, to obtain another angle k. Then a new distance B is computed with the given formula. Distance B may then be plotted in Fig. 6 and in Fig. 8 from the pinion axis on center line 34 to obtain the intersection point 601' of the limit normal 54-60i.
Again we determine the traces in a plane parallel to the drawing plane of Figures 7 and 8 and having the distance 64 from point 54. The trace 611i of the same tangent plane has the same distance from axis 46 as trace 61" of Fig. 7, and is merely turned with respect to it. The trace 651' of the plane perpendicular to the limitnormal 54-6tii passes through a point 67i. To determine this point, a distance 66i is plotted in Fig. 8 on a line 6tli-6tli drawn at right angles to the projected limit normal, to obtain a point 601'". Distance 661' equals the projected distance of point 54 from center line 34' in Fig. 6. Line 54-601 is drawn and through point 54 a line 54-67i perpendicular thereto. Line 681' is drawn parallel to the projected limit normal 54-60i at the distance 64 (Fig. 6) therefrom. Its intersection with line 54-67i is the sought point 67i. Trace 65i is drawn through point 67i at right angles tothe projected limit normal 54-6tli. The two traces 651' and 61i intersect at 7 01'. The tangent to the describing line 58 or the line itself is part of the connecting line 54-70i.
As line 58 is moved helically about axis 40, at the prescribed ratio and lead,,it describes side 4? of the gear teeth and the mating tooth surfaces of the pinion on the rotating gear and pinion, and in space describes the surface of action.
-So far fully conjugate tooth surfaces have been described, where the too-th bearing sweeps the entire length of the gear teeth in the given running position. It is desirable and customary to slightly ease off the tooth ends on one or both members of the gear pair, to render the gears less sensitive to deflection under load and to slight errors in alignment and manufacture.
This may be attained by slight departures from the mathematically exact procedures to be described, such departures being customary in the art. It should be understood that the description of the exact form is intended to include the slight departures of intended ease-off. The describing profiles themselves may be slightly mismatched. Thus for instance a straight cutting edge may be used on one member and a slightly concave one on the mate, but we still call them matching profiles.
The gearing is also applicable to gear pairs whose shaft angle differs home right angle. In such cases the limit normal no longer intersects the center line of the gear pair. It may be determined in accordance with my aforesaid articles. At any point (53 or 54) the tangent plane of the contacting pitch surfaces is first determined. It is referred to as the pitch plane. The inclinations of the gear and pinion axes from this plane are referred to as the pitch angles, and the distances of their intersections with this pitch plane from the said point are referred to as the cone distances. The limit normal is perpendicular to the pitch lines contacting at said point, and its inclination to the pitch plane is referred to as the limit pressure angle. Itcan be determined with Formula 15 given in Article II.
Tooth ends of gear In accordance with one aspect of the invention the describing lines 57, 58 are straight lines, and the tooth ends 50, 51 of the gear are so Shaped or dimensioned that the curvatures of contacting teeth are completely matched, or closely and equally matched, along a whole gear end-profile, when its points are in contact position. On the longitudinally convex sides 48 of the gear teeth they are matched on the end profile that passes through point 53 at the outer end. On the longitudinally concave sides 49 of the gear they are matched on the inner end profile that passes through point 54.
The tangents may be substituted for the profiles of the end surfaces so determined. The surfaces 50,- 51 are then conical surfaces coaxial with the gear. Their straight profiles in axial sections are seen to converge in a direction from tooth bottom to tooth top, at an angle larger than thirty degrees, so that the face width at the tooth tops 47 is smaller than at the tooth bottom 46.
It will now be shown how the inclination of the tooth ends 50, 51 may be determined.
Planes are considered that are perpendicular to the describing line, and their traces are determined in the drawing plane of Figs. 7 and 8, which plane contains the center line 34 and is perpendicular to axis 40. The considered planes have traces at right angles to the describing line. Such a plane at point 53 (Fig. 7) has a trace 71 that intersects the center line 34 at 60, because this plane contains the limit normal passing through point 60. The plane normal to the describing line 57 through point 53' thereof has a trace 71' parallel to trace 71.
The limit normal at point 53' can be directly drawn in the view Fig. 2, and determines the angle k used for computing the distance B. Knowing the new B we can plot the point 60 (Fig. 7) where the new limit normal intersects the center line 34. As trace 71' is seen to be offset from point 69 the surface normal of the teeth contacting at point 53 does not coincide with the limit normal 53'60' at that point. To make it coincide a helical displacement of point 53' in counter-clockwise direction is needed. A helical displacement about axis .40 may be assumed; and the above procedure is then repeated until the position 53 of point 53' is found, where the surface normal coincides with the limit normal. The so determined point 53" is a point of the gear outside surface 50. Other points may be similarly determined. Surface 50 also contains point 53.
While I have described chiefly geometrical procedures, the determination can of course also be made by computation, which expresses the described procedure. In this case point 53' is preferably assumed at an infinitesimal distance from point 53. The required inclination of the conical end surfaces is computed with the known procedures of mathematics dealing with infinitesimal changes.
On the opposite side of the teeth, the plane perpendicular to the describing line 58 at point 54 intersects the drawing plane in a trace 72 (Fig. 8) that passes through point 60i. The trace 72' of the plane perpendicular to the describing line at point 54 thereof is parallel to trace 72. The limit normal at point 54' is determined with the above described procedure. It intersects the center line 34 at a point 60i' offset from trace 72'. A small clockwise helical motion of point 54 about axis 40 is here required. At a position 54" the limit normal there coincides with the normal of the contacting tooth surfaces. The inside surface 51 is the surface that contains point 54" in addition to point 54.
The tooth ends 50, 51 may also be determined experimentally by trial.
Modifications The embodiment illustrated in Fig. 9 differs from the described embodiment merely in the shape of its end surfaces 50', 51' and in the curvature of the describing lines. Everything else is the same as described, including the tangents of the describing lines at their mean point (41) and the helical mean path of contact 37. Conventional end surfaces 50', 51 are used, that have parallel straight profiles. However any suitable shape may be assumed if desired.
Instead of determining the inclination of the end surfaces from assumed describing lines and tooth profiles, the describing lines and tooth profiles are here determined from the assumed shape of the surfaces 50', 51'.
We consider point 53' of Fig. 7 and its limit normal 53'60'. The normal to the tooth surfaces contacting at 53 depends on the direction of the describing line at that point. By curving the describing line 157 we could bring this normal into coincidence with its limit normal 53'60'. Then it should be so curved that its tangent at 53' lies in a plane perpendicular to the limit normal 53-60'. The profile curvature is best determined by computation, assuming an infinitesimal distance 53-53.
When line 157 is curved in a plane parallel to axis 40, so that in Fig. 7 the tangent at 53 in projection coincides with the tangent 57 at point 53, then the trace of the plane normal to profile 157 at 53' remains parallel to trace 71' and is shifted laterally. The curvature should be such that the shifted trace passes through point 60. This requires a convex profile 157 on the gear, and a matching concave one on the pinion.
Instead of determining the curvature required to make point 53' an end point of tooth action, the helix passing through 53' is determined, and its intersection with the outside surface 50' of the gear. This means displacing point 53 in clockwise direction in Fig. 7. The described construction is then repeated for this point. It results in a profile 157 more convex on the gear than if 53', as shown, were the end point.
The opposite side of the teeth is similarly treated. A slightly convex profile on the gear causes the surface normal at point 54' to pass through point 60i and to coincide with the limit normal 5460i. The intersection point of the helix through 54 with end surface 51' is displaced in counter-clockwise direction from point 54. When the construction is repeated for this intersection point a convex profile 158 of more curvature results.
The tooth profiles of a mean normal section of the teeth are shown in Fig. 10, at an enlarged scale as compared with Fig. 9. This section is understood to be at right angles to the tooth direction. The gear has convex profiles 74, and the pinion has concave profiles 75. They are shown in relation to the pitch vertical 45.
A further embodiment is illustrated in Fig. 11. Here the axis 240 of the basic helical member is not at a distance from the tooth zone, but lies on the root surface of the gear 230. It can be considered the line of contact of mating pitch surfaces and a path of contact.
The describing lines 257, 258 are shown at mean point 241. The describing line 257 is further shown in a position where it passes through the outer end point 253 of the path of contact, where its direction is determined in the manner described. Line 257 corresponds to the longitudinally convex side of the gear teeth and to the mating side of the pinion teeth. The opposite describing line 258 is further shown passing through the inner end point 254 of the path of contact.
Axis 240 intersects the center line of the gear pair. Its inclination (i) and its offset (E,.) from the pinion axis 33, as well as the lead (L,) are determined in exactly the same way as in the previously described embodiments. The inclination (i) of course is here smaller.
As the root surface of the gear contains the straightline element 240 offset from its axis 32, it is a hyperboloid of revolution. The profile 246 of an axial section of this root surface is concave. Theoretically the axial profile 239 of the outside surface of the pinion 231 should also be concave, but only slightly so. A straight profile il: .111 1. 1 J. may bessubstituted therefor. the. outside surface of the gear 230 may be made straight, unlessxthergear. hasa small tooth number. In that case it is preferably made convex.
Characteristics ,Themain characteristics will now be further described withFigures 12 to 18. While these correspond directly to the first described embodiment of Figures 1 to 8, they apply; also in a general way to the other described emime t The teeth follow pitch surfaces, which are surfaces of revolution coaxial with the respective gear. The side snrfaces of the teeth are warped surfaces whose profile inclination to the normals of their pitch surfaces changes, generally by at least twenty degrees from end to end of the,teet h. U
. F igures 12 and 13 further illustrate the warped or twisted tooth surfaces, and their rapid change of profile inclination; Fig.- 14 shows on the left the longitudinally convexside 48 of the gear teeth, and at the. right the longitudinally concave side 49 thereof. Along the end profile 76 of side 48 the surface normals coincide with The axial profile 247 r,
eta-tar thegears riuna direction so that mesh starts at the outer, ends of theteeth, the, pitch line approach of the pinion to point53. of the. gear is in a relative path 55 to point 53, and the recess is in a path 55'. Immediately thelimit normals,-and mating tooth surfaces have equal andmatching convex and concave curvature. Along the end profile 77 of the opposite side also the surface normals-coincide with the limit normal, so that the same kindof very intimate contact results.
The intimacy of tooth contact remains high all along the, length of the teeth, although it decreases gradually. Even at the opposite end it compares favorably with the tooth contact attained with conventional teeth.
The, position of the end profiles 76, 77 of matched contact is further shown in Fig. 15. In the upper part of this figure,'these profiles are at the actual ends of the teeth. The lower part has the same end profiles 76, 77, withgsupporting portions 78, 80 added at opposite ends to increase the tooth strength.
..,.The axial section of the pinion 31, Fig. 17, shows below therlongitudinally concave tooth side 81, that meshes with side 48 of the gear. Its longitudinally convex tooth side-82 is shown above. It meshes with side 49 of the gear: The pinion should have an outside surface whose axialprofile is moderately concave, as indicated in Fig. 3. :LA; conical surface 83 is shown substituted therefor, asrma'y be done sometimes in practice. This may result instooth tops whose width is smallest in a region intermediate the ends of the teeth.
The pinion teeth 84 overlap the ends of the gear teeth. They do not terminate at the points 53, 54 (Fig. 1) but reachcbeyond. Pinion tooth surface 81 contains a line 85: that corresponds to the end profile 76 of the gear tooth-surfaces 48 and gets into gear contact with said profile. It is its mating line of the pinion. On the pinion tooth surface 82 is a line 86 mating with end profile 77 of the gear.
In accordance with the invention the pinion tooth surfaces 81 are relieved adjacent end 50, starting at line 85. Andzthe pinion tooth surfaces 82 are relieved adjac'en't end 51',starting at line 86. This applies to all described embodiments. The relief is best seen in Fig. 18, and is also shown in Fig. 3.
--The'-relieved portion 87 is at an angle to surface 81. Likewise the relieved portion 88 is at an angle to surface 82. The said angles differ from 180 degrees by l'ess' tha'n twelve degrees. It should be enough to prevent contact. at portions 87, 88 at any actual running condition. This is not a mere ease-off, but a deliberate destru'ction'of the surface. The surfaces 81, 87 and 82, 88 meet in a ridge, which may however be rounded. It may. be said that they meet in a near-ridge.
The reason for this important feature will now be described with Fig. 16. This is a normal section through the teeth contacting at end point 53, as if the teeth would continue. Let us consider the pitch line contact. When adjacent point 53 thepaths 55, 55' are in the direction of tangent 56, inclined at the limit pressure angle to the vertical, ,as was described for a mean section with Fig. 4. At point 53 this is also the inclination of the tooth surface, which is perpendicular to the limit normal. In other words, this direction follows the tooth surface and is tangent thereto. The dotted portion 55 of the path seemingly interferes with the gear tooth. Although the gear tooth terminates at 53, there would be actual interference if the tooth surface of the pinion would continue beyond this point without relief, because at this end the contactingsurfaces are so closely matched as to have equal convex and concave curvatures in all sections through point 53.
The invention prevents interference by using warped tooth surfaces and providing working surfaces 81, 82 on the pinion that terminate at lines 85, 86 respectively. The relieved remainder of the tooth length is for strength, not for tooth action. e I
Fig. 16 further illustrates the; leaning teeth usually found at the outer end. One side profile of the teeth is negatively inclined, see also Fig. 5.
Production A preferred form of production is by form-cutting both members of the hyp'oid gear pair. Figures 19 and 20 show a pair .of tools, 90,.90' for rough-cutting opposite sides of the toothspaces 91 shown in dotted lines- Preferably the workpiece is,continuously and uniformly rotated on its axis, while the tools 90,90 perform periodic helical reciprocations, each about its own axis (40). Preferably a pluralityoftool pairs 90, are used. Their axes are angularly spaced about the workpiece. The duration of the reciprocation is such that each tool enters a different tooth space on successive strokes. Thus the workpiece in effect is indexed from stroke to stroke through a numberof teeth. This number should be prime to the tooth number of the workpiece, so that each tool successively cuts inall toothspaces.
Tool 90 cuts with side 92 and, end 93. Tool 90' cuts with, the oppositeside 92, and end 93. Together they rough out the tooth spaces. There is also a clapping motion to keepthe tools clear of theworkpiece during the return strokes. The depthwise feed and also the clapping motion are preferably made up of an axial motion of the gear blank or, workpiece and of a turning motion about the gear axis, so that the feed path about bisects the angle between opposite tooth sides at the mid-section.
Fig. 14 shows at the left various positions of the describing line .(57) to be represented by a finish-cutting edge. It is seen that the inclination of the describing line to the tooth bottom 46 varies. This variation presents a problem in cutting clearance, both in end clearance and in side clearance. On roughing tools 98, 90" I may solve this problem by tilting each tool as it goes through the cut, so as to obtain more nearly constant cutting clearances; The direction of the tilt axis ismade up of a direction adapted to keep the end clearance right and of a direction to keep the side clearance right. It is obtainable by vectorial addition. This axis-partakes in the helical. motion of the tool and lies on the slide member of said motion. Generally the tilt axis is inclined to the axis (48) of the helical 'tool stroke and preferably passes through the center 94 of the edge round of the tool. As the tool clearances change with changing depth of cut, I may change the phase of the tilting motion with increasing depth of cut accordingly.
A pair of tools are provided for finishing opposite sides of the teeth. Each of these tools cuts with one side only and isskept clear of the tooth bottom. One such tool is shown in Figures 21 to 23. Tool 95 has a finish-cutting 11 edge 96 formed at the intersection of a cutting face 97 with a side surface 9 8. The tool is preferably designed for contour grinding, to provide maximum cutting clearance. It is sharpened by regrinding a narrow strip 98 of side surface 98, that follows the cutting edge 96. After sharpening the tool is adjusted to advance the newly formed cutting edge to the original position. This adjustment is in a direction parallel to the cutting face 97. The blade is aligned angularly with the cutting face, so that sidewise displacement provides the required direction of adjustment. The tool is secured in diflerent sidewise positions by using parallels 99 of different thickness.
Fig. shows that the direction of a warped tooth surface in sections parallel to the drawing plane depends much on the depth level of the section. Thus the different points of a finishing edge (96) cut in different directions. To attain improved side clearance on the contourground finishing edge I vary the lateral inclination of strip 98' at different depths in accordance with the difference in cutting direction. This is illustrated in Fig. 23 by sections taken at different levels parallel to the drawing plane. For clarity the sectional lines are shown extended beyond the narrow strip 98. Cutting at mean point 41 is in a direction 100. The sectionalprofile there is in a direction 102, while near the top of the cutting tooth it is in a direction 101 and near the bottom it is in a direction 103. Although the shown cutting edge is straight, the strip 98' is not a plane but a twisted surface of varying inclination. It is approximately a helical surface following edge 96. Such strips of varying inclination may also be used with curved cutting edges.
The finishing blades may be used in the same cutter assembly with the multiple pairs of roughing blades. In this case they are kept clear of the workpiece during the depth feed, and are advanced into cutting position when full cutting depth is reached. They may be advanced by a slight displacement in the direction of the axis of their helical cutting motion.
To decrease the change of cutting clearance during the cutting strokes, a finishing blade may be tilted about the cutting edge as it goes through the cut.
The pinions may be finished like the gear, except that the clapping motion is usually not along and about the work axis, but in a direction more nearly perpendicular to the pinion pitch surface.
Figures 24 to 27 illustrate a roughing operation chiefly for pinions. Here four different roughing tools 105, 106, 107, 108 are provided, each shown in one of the four figures. Tool 105 is fed in its helically reciprocating slide part to follow the tooth profile 110, starting from a position 105'. Tool 108, Fig. 27, starts from a position 108' and is fed to follow tooth profile 111. These tools are also tilted as they go through the cutting stroke, preferably about axes that pass through the centers 94 of the edge rounds. These axes partake in the helical motion of the respective tools and in the feed motion. The intermediate tools 106, 107 are similarly tilted about axes intersecting their end cutting edge. Tool 106 is fed from a starting position 106, while tool 107 starts from a position 107' in its helically reciprocating slide part. The four tools completely cover the entire width of the tooth space even where it is widest. They work together, in support of each other, because each tool enters a ditferent tooth space in successive strokes.
The clapping of each tool is preferably in the direction of its feeding motion. The tools 106, 107 are wider than the minimum slot width of the tooth space, and their feed is terminated in the position shown in full lines. From here on the tools 105, 108 only of the four tools proceed with the depth feed.
Tool clearance problems are minimized in the embodiment now to be described with Figures 28 and 29. Here the warped tooth surface of thegear is approximated by a helical surface of constant lead, such as may be described by a cutting edge that moves helically along and about an axis while the workpiece stands still. Helix 119 is described by mean point 41 of the cutting edge so that it approximates the required pitch line. Its curvature and curvature plane coincides with the curvature and curvature plane of the pitch line. pitch-line normal that lies in the curvature plane. Curvature center 121 lies on this normal. The axis 122 of the sought helical surface intersects normal at right angles at a point 123 such that the required change of profile inclination is obtained lengthwise of the tooth as Well as the curvature required on helix 119. Axis 122 is inclined to plane 124 at an angle smaller than sixty degrees. Plane 124 is the tangent plane of the pitch surface at mean point 41.
The workpiece is intermittently indexed to present other tooth spaces to the cutting edge. The tooth sides of the pinion are here produced in a generating operation, in which helically reciprocating cutting edgesde scribe tooth sides of the gear while thepinion meshes with and rolls on said gear. 7 v
In a further embodiment the tooth sides of the gear are described by helically moving cutting edges while the gear turns on its axis at a slow enough rate that each cutting edge enters adjacent tooth spaces on successive strokes. The pinion is here also produced by generation wherein cutting edges describe tooth sides of the rotating gear- Still further modifications may be made. This application is intended to cover any variations, uses, oradaptations of the invention following, in general, the principles of the invention and including such departures from the present disclosure as come within the known or customary practice in the art to which the invention pertains and as may be applied to the essential features herein set forth and as fall within the scope of the invention or the limits of the appended claims.
I claim:
1. Hypoid gearing comprising a pair of gears having angularly disposed and offset axes, the teeth of each member of said pair following a surface of revolution coaxial with said member and their side surfaces being warped surfaces whose profile inclination to the normals of said surface of revolution changes along the length of the teeth and decreases on one side of the teeth while increasing on the opposite side from one tooth end to the other, the tooth surface normals at points adjacent one end of the teeth coinciding approximately with the limit normals at said points, so that near-surface contact is achieved at said points.
2. Hypoid gearing comprising a gear and a pinion adapted to mesh with each other and having angularly disposed and offset axes, the teeth of said gear following a surface of revolution coaxial with its axis and their side surfaces being warped surfaces whose profile inclination to the normals of said surface of revolution changes along the length of the teeth and decreases on one side of the teeth while increasing on the opposite side from one tooth end to the other, the tooth surface normals at points of one end profile of said gear teeth coinciding approximately with the limit normals at said points, so that near-surface contact is achieved at said points. i
3. Hypoid gearing according to claim 2, wherein the gear teeth are curved lengthwise and extend between outer and inner ends, and wherein the tooth surface normals at the points of the outer end profile coincide with the limit normals at said points on the longitudinally convex side of the gear teeth, and wherein the tooth surface normals at the points of the inner end profile coincide with the limit normals at said points on the longitudinally concave side of the gear teeth.
4. Hypoid gearing according to claim 2, wherein the teeth of the pinion overlap the ends of the gear teeth lenghtwise, the tooth sides of said pinion being relieved at the end that meshes with near-surface contact, relief Numeral 120 denotes the' starting at a line that corresponds to and meshes with the end profile of the gear teeth.
5. Hypoid gearing comprising a gear and a pinion adapted to mesh with each other and having angularly disposed and offset axes, the teeth of said gear being curved lengthwise and extending between outer and inner ends along a surface of revolution coaxial with its axis, the side surfaces of said teeth being warped surfaces whose profile inclination to the normals of said surface of revolution changes along the length of the teeth, decreasing from the outer end to the inner end on the longitudinally concave side of the gear teeth while increasing on the longitudinally convex side, the teeth of the pinion overlapping the ends of the gear teeth, the longitudinally concave tooth sides of the pinion that mate with the longitudinally convex tooth sides of the gear being relieved adjacent their outer end, the opposite tooth sides of the pinion being relieved adjacent their inner end, relief starting with a near-ridge at a line of the pinion tooth surfaces that corresponds to and meshes with the outer and inner end profiles of the gear respectively, so that interference is avoided in the region of near-surface contact.
6. Hypoid gearing according to claim 5, wherein the gear teeth are leaning at their outer end to such an extent that the longitudinally convex side is negatively inclined to the normals of the surface of revolution along which the teeth extend.
7. Hypoid gearing according to claim 2, wherein the gear and pinion have approximately straight profiles in a mid-section normal to the teeth, and wherein the teeth of the gear extend between end surfaces that converge from bottom to top of the gear, so that the face width is smaller at the tooth tops than at the bottoms.
8. Hypoid gearing comprising a gear and a pinion adapted to mesh with each other and having angularly disposed and offset axes, the teeth of said gear following a surface of revolution coaxial with its axis and extending between an outer and an inner end surface, the side surfaces of said gear teeth being warped surfaces whose profile inclination to the normals of said surface of revolution changes from end to end of said teeth by at least twenty degrees, decreasing on one side of the teeth and increasing on the opposite side, said end surfaces converging from bottom to top of the gear teeth, and the pinion tooth surfaces being relieved at the end of lower profile inclination of the tooth sides, relief starting with a near-ridge along a line that mates with the end profile of the gear teeth.
9. Hypoid gearing having approximately complementary tooth profiles in a mean section normal to the tooth direction, the teeth of one member overlapping the tooth ends of the other member of the gear pair, the tooth sides of said one member being relieved adjacent one end, relief starting with a near-ridge along a line that mates with the end profile of the other member.
10. Hypoid gearing according to claim 9, wherein the gearing consists of a gear and a pinion, and wherein the gear contains convex tooth profiles and the pinion contains concave tooth profiles.
11. Hypoid gearing according to claim 1, wherein the 14 tooth sides of at least one member of the gear pair are surfaces containing a constant line all along their working length, and are such as may be described on the uniformly rotating one member by said line moving at a uniform rate in a helical path, the axis of said path being inclined to and offset from the axis of said one member.
12. Hypoid gearing according to claim 11, wherein the mean direction of the describing line is offset from the axis of its helical path.
13. Hypoid gearing according to claim 11, wherein the describing line is a straight line whose extension is offset from the axis of its helical path.
14. Hypoid gearing according to claim 2, wherein the tooth sides of each member of the gear pair contain a constant line all along their working length, and are such as may be described on the respective uniformly rotating member by said line performing a uniform helical motion of constant lead, approximately as if said line were rigid with a basic helical member of the hypoid gear pair.
15. A tapered gear having longitudinally curved teeth that extend between an outer end surface and an inner end surface and follow a surface of revolution coaxial with the gear, the side surfaces of said teeth being warped surfaces whose profile inclination to the normals of said surface of revolution changes by at least twenty degrees from the outer end of said teeth to their inner end, decreasing on the longitudinally concave side of the gear teeth and increasing on the longitudinally convex side, said end surfaces being surfaces of revolution converging from bottom to top of the teeth, so that the face width is smaller at the tooth tops than at the tooth bottoms.
16. A tapered gear according to claim 15, wherein the end surfaces converge at an angle of at least thirty degrees and wherein the tooth tops lie in a surface of revolution of convex profile in axial section.
17. A tapered pinion having spirally arranged and longitudinally curved teeth extending along a surface of revolution coaxial with said pinion between an outer end and an inner end, the side surfaces of said teeth being warped surfaces whose profile inclination to the normals of said surface of revolution changes by at least twenty degrees from the outer end of said teeth to their inner end, decreasing on the longitudinally convex side of the teeth and increasing on the longitudinally concave sides, the working portions of said side surfaces terminating at one end of the teeth with a near-ridge followed by a relieved portion angularly inclined to said working portion at an angle differing from degrees by less than twelve degrees, said near-ridge and relieved portion being adjacent the inner and outer tooth ends on the longitudinally convex and concave tooth sides respectively.
References Cited in the file of this patent UNITED STATES PATENTS 2,105,104 Wildhaber et al Ian. 11, 1938 2,174,814 Ackerman Oct. 3, 1939 2,183,285 Wildhaber Dec. 12, 1939 2,302,942 Golber Nov. 24, 1942 2,358,489 Carlsen Sept. 19, 1944 2,374,890 Pelphrey May 1, 1945
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Cited By (12)

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US3524361A (en) * 1968-08-29 1970-08-18 Hitosi Iyoi Gear transmission and cam mechanism of a point contact system with axes at angles to each other
US4307797A (en) * 1979-09-26 1981-12-29 Illinois Tool Works Inc. Curved tooth gear coupling
US6324931B1 (en) * 2000-04-19 2001-12-04 Dana Corporation Straight bevel gears with improved tooth root area geometry and method for manufacturing forging die for making thereof
WO2005044482A1 (en) * 2003-11-07 2005-05-19 Bishop Innovation Limited Method and apparatus for forging gear teeth
US20050115071A1 (en) * 2003-12-02 2005-06-02 Yakov Fleytman Manufacturing for face gears
DE102012214437A1 (en) 2011-08-17 2013-02-21 GM Global Technology Operations LLC (n. d. Gesetzen des Staates Delaware) DOPPELEVOLVENTEN-GEAR-crown gear-DRIVE SYSTEM
US20150082930A1 (en) * 2012-03-19 2015-03-26 Toyota Jidosha Kabushiki Kaisha Gear mechanism and manufacturing method of gear mechanism
US20180021960A1 (en) * 2016-07-22 2018-01-25 Cambridge Medical Robotics Limited Gear packaging for robotic joints
US11225107B1 (en) 2020-09-09 2022-01-18 Mahindra N.A. Tech Center Axle carrier housing with reinforcement structure
US11535057B2 (en) 2020-09-09 2022-12-27 Mahindra N.A. Tech Center Axle assembly with sealed wheel end bearings and sealed pinion input bearings
US11648745B2 (en) 2020-09-09 2023-05-16 Mahindra N.A. Tech Center Modular tooling for axle housing and manufacturing process
US11655891B2 (en) 2020-09-09 2023-05-23 Mahindra N.A. Tech Center Method of machining an axle carrier housing

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US2183285A (en) * 1937-04-17 1939-12-12 Gleason Works Gear
US2302942A (en) * 1939-06-07 1942-11-24 Miehle Printing Press & Mfg Method of making gears
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Cited By (15)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US3524361A (en) * 1968-08-29 1970-08-18 Hitosi Iyoi Gear transmission and cam mechanism of a point contact system with axes at angles to each other
US4307797A (en) * 1979-09-26 1981-12-29 Illinois Tool Works Inc. Curved tooth gear coupling
US6324931B1 (en) * 2000-04-19 2001-12-04 Dana Corporation Straight bevel gears with improved tooth root area geometry and method for manufacturing forging die for making thereof
AU2004287509B2 (en) * 2003-11-07 2007-11-22 Bishop Innovation Limited Method and apparatus for forging gear teeth
US20070125148A1 (en) * 2003-11-07 2007-06-07 Juergen Dohmann Method and apparatus for forging gear teeth
WO2005044482A1 (en) * 2003-11-07 2005-05-19 Bishop Innovation Limited Method and apparatus for forging gear teeth
US20050115071A1 (en) * 2003-12-02 2005-06-02 Yakov Fleytman Manufacturing for face gears
DE102012214437A1 (en) 2011-08-17 2013-02-21 GM Global Technology Operations LLC (n. d. Gesetzen des Staates Delaware) DOPPELEVOLVENTEN-GEAR-crown gear-DRIVE SYSTEM
US20150082930A1 (en) * 2012-03-19 2015-03-26 Toyota Jidosha Kabushiki Kaisha Gear mechanism and manufacturing method of gear mechanism
US20180021960A1 (en) * 2016-07-22 2018-01-25 Cambridge Medical Robotics Limited Gear packaging for robotic joints
US11597102B2 (en) * 2016-07-22 2023-03-07 Cmr Surgical Limited Gear packaging for robotic joints
US11225107B1 (en) 2020-09-09 2022-01-18 Mahindra N.A. Tech Center Axle carrier housing with reinforcement structure
US11535057B2 (en) 2020-09-09 2022-12-27 Mahindra N.A. Tech Center Axle assembly with sealed wheel end bearings and sealed pinion input bearings
US11648745B2 (en) 2020-09-09 2023-05-16 Mahindra N.A. Tech Center Modular tooling for axle housing and manufacturing process
US11655891B2 (en) 2020-09-09 2023-05-23 Mahindra N.A. Tech Center Method of machining an axle carrier housing

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