WO2013067039A1 - Profil de dent d'engrenage ayant un relief de mélange de zones de transition - Google Patents

Profil de dent d'engrenage ayant un relief de mélange de zones de transition Download PDF

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Publication number
WO2013067039A1
WO2013067039A1 PCT/US2012/062840 US2012062840W WO2013067039A1 WO 2013067039 A1 WO2013067039 A1 WO 2013067039A1 US 2012062840 W US2012062840 W US 2012062840W WO 2013067039 A1 WO2013067039 A1 WO 2013067039A1
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WIPO (PCT)
Prior art keywords
curve
dedendum
gear
addendum
blending
Prior art date
Application number
PCT/US2012/062840
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English (en)
Inventor
John Robert Colbourne
Bernard E. BERLINGER
Original Assignee
Genesis Partners, L.P.
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Genesis Partners, L.P. filed Critical Genesis Partners, L.P.
Priority to EP12844774.5A priority Critical patent/EP2805084A1/fr
Publication of WO2013067039A1 publication Critical patent/WO2013067039A1/fr

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Classifications

    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16H—GEARING
    • F16H55/00—Elements with teeth or friction surfaces for conveying motion; Worms, pulleys or sheaves for gearing mechanisms
    • F16H55/02—Toothed members; Worms
    • F16H55/08—Profiling

Definitions

  • the present technology relates to gear tooth profiles and corresponding cutter profiles.
  • U.S. Patent 6,101,892 (“the 892 patent") describes gear tooth pairs in which the dedendum of the first gear is conjugate with the addendum of the second gear, and the addendum of the first gear is conjugate with the dedendum of the second gear.
  • the dedendum of each gear is predominately concave and the addendum of each gear is predominately convex.
  • Portions of gear pairs are conjugate with one another when the respective profiles of these portions are in continuous contact as the gears turn. Because the profiles are in continuous contact, the angular velocity ratio is constant.
  • the profiles of both gears may be designed so that the relative curvature of the profiles at contacting points is constant or nearly constant. Because the relative curvature of the profiles at contacting points is constant or nearly constant, the contact stress is nearly constant. If the value of the relative curvature is sufficiently small, the maximum contact stress is lower than the maximum contact stress in other types of gears.
  • tooth profiles designed in accordance with the 892 patent have a transition zone between the addendum and dedendum where no-contact takes place.
  • the remaining parts of the profiles can be designed so that the relative curvature is significantly lower than the Euler-Savary value.
  • U.S. Patent No. 6,964,210 (“the 210 patent”) describes a method by which the transition zones of the gears can be hobbed or ground without causing any undercut in the remaining parts of the profiles.
  • the method consists of designing a pair of basic cutters which are complementary in their dedendum and addendum segments, and which overlap in the transition zone. Since the gear tooth profiles are conjugate to the basic cutter profiles, the gear tooth profiles are conjugate to each other in their dedendum and addendum segments, and there is no-contact between the gear tooth profiles in the transition zones, where the basic cutter profiles overlap.
  • the profile points at each end of the transit ion zone are known as transition points, or sometimes as the dedendum and addendum transition points.
  • the basic cutter profiles designed according to the 210 patent are continuous and have continuous slope at the transition points.
  • the distance between the two tooth profiles in the transition zone as the two gears mesh is known as pitch relief.
  • Pitch relief may correspondingly be described as the distance by which the two respective gear basic cutters overlap in the transition zone along the pitch line.
  • the distance between the transition points along the center line in each basic cutter is known as the pitch relief width.
  • the basic cutter transition zones are generally designed so that the transition points are equidistant from the pitch line. However, transition zones may be designed so that the transition points are not equidistant from the pitch line. When the transition points are equidistant from the pitch line, the distance from the pitch line to each transition point is referred to as the pitch relief half-width.
  • micropitting may occur at the addendum and dedendum transition points. Micropitting may be especially problematic on the pinion at the dedendum transition point. Finite element analysis conducted on gear pairs designed according to the 892 patent and the 210 patent indicates that the transition point on a gear may experience a greater force than the value given by the Hertz contact theory.
  • lubricant film thickness may be reduced in the area of the transition point since the transition zone creates a relatively larger cavity into which lubricant can flow.
  • a reduction in lubricant film thickness at the transition points may reduce the lubrication pressure at those points and correspondingly increase pressure on the gear itself.
  • the gear tooth profile may be modified to incorporate transition zone blending relief.
  • Transition zone blending relief involves reducing the tooth thickness in at least one gear of a gear pair proximate to the transition zones at either the dedendum, addendum, or both the dedendum and addendum.
  • Transition zone blending relief extends the no-contact zone of the transition zone of the gear tooth profiles into the dedendum or addendum (or both).
  • the transition zone blending relief may be configured so that the curves of the dedendum or addendum and the blending region have continuity of profile, profile slope, and profile curvature at the transition zone blending point.
  • a gear pair may be designed that comprises a first gear having a first plurality of teeth, each tooth having a first profile that includes a first transition zone disposed between a first addendum and a first dedendum, the first transition zone defined between a first addendum transition point and a first dedendum transition point, the first addendum including a first convex portion defined by a first curve, and the first dedendum including a first concave portion defined by a second curve, the first dedendum further including a blending relief disposed between the first dedendum transition point and a blending point and defined by a third curve, wherein the second curve and the third curve are different and the slope and curvature of the second curve and the third curve are identical at the blending point.
  • the gear pair further comprises a second gear having a second plurality of teeth, each tooth having a second profile that includes a second transition zone disposed between a second addendum and a second dedendum, the second transition zone defined between a second addendum transition point and a second dedendum transition point, the second addendum including a second convex portion defined by a fourth curve that is conjugate to the second curve, and the second dedendum including a second concave portion defined by a fifth curve that is conjugate to the first curve.
  • a gear pair may comprise a first gear having a first plurality of teeth, each tooth having a first profile that includes a first transition zone disposed between a first addendum and a first dedendum, the first transition zone defined between a first addendum transition point and a first dedendum transition point, the first addendum including a first convex portion defined by a first curve, the first addendum further including a blending relief disposed between the first addendum transition point and a blending point and defined by a second curve, wherein the first curve and the second curve are different and the slope and curvature of the first curve and the second curve are identical at the blending point; and the first dedendum including a first concave portion defined by a third curve.
  • the gear pair may further comprise a second gear having a second plurality of teeth, each tooth having a second profile that includes a second transition zone disposed between a second addendum and a second dedendum, the second transition zone defined between a second addendum transition point and a second dedendum transition point, the second addendum including a second convex portion defined by a fourth curve that is conjugate to the first curve, and the second dedendum including a second concave portion defined by a fifth curve that is conjugate to the first curve.
  • Figs. 1A-1D show a variety of types of gearing systems in which transition zone blending relief may be incorporated;
  • Fig. 2 shows conjugate profiles of a gearing system in which transition zone blending
  • Fig. 3 shows a gear basic cutter profile
  • Fig. 4 is a basic cutter relief diagram with the vertical scale exaggerated.
  • Figs. 1 A-1D show various types of gear pairs 10 in which transition zone blending relief may be incorporated.
  • Fig. 1 A shows a spur gearing system wherein the axis of rotation of a first gear 20a is parallel to the axis of rotation of a mating gear 40a.
  • Fig. IB shows a crossed helical gearing system wherein the axis of rotation of a first gear 20b is perpendicular to the axis of rotation of a mating gear 40b.
  • Fig. 1C shows a hypoid gearing system wherein the axis of rotation of the first gear 20c does not intersect the axis of rotation of the second gear 40c.
  • Fig. 1 A shows a spur gearing system wherein the axis of rotation of a first gear 20a is parallel to the axis of rotation of a mating gear 40a.
  • Fig. IB shows a crossed helical gearing system wherein the axis of rotation of a first gear 20b is per
  • a gear tooth profile 20y such as that of first gear 20 shown in Fig. 2 includes a first transition zone 24 disposed between a first concave portion 22a lying within the dedendum 22 of the first gear and a first convex portion 26a lying within the addendum 26 of the first gear.
  • a gear basic cutter 100 and corresponding gear basic cutter profile 102 as shown in Fig.
  • the gear basic cutter profile is conjugate to its tooth profile such that the addendum 122 of the gear basic cutter profile includes a convex portion 122a that is conjugate to the concave portion 22a of dedendum 22 of the corresponding gear tooth profile.
  • the dedendum 126 of the gear basic cutter profile includes a concave portion 126a that is conjugate to the convex portion 26a of the addendum 26 of the corresponding gear tooth profile.
  • Cutter 100 may also be configured to be conjugate with the profile 40y of gear 40 such that addendum 122 of the cutter profile 102 includes the convex portion 122a that may be conjugate to the concave portion 42a of dedendum 22 of the corresponding gear tooth profile.
  • the dedendum 126 of the gear basic cutter profile includes the concave portion 126a that may be conjugate to the convex portion 46a of the addendum 26 of the corresponding gear tooth profile.
  • the transition zone 24, 44 is configured to be a recessed no-contact zone as gear 20 meshes with gear 40.
  • Transition zone 124 of the cutter profile 102 is conjugate to this no-contact zone such that transition zone 124 has a protruding area.
  • gears 20 and 40 together create a no-contact zone in the transition zone
  • the gear basic cutters 100 for these gears correspondingly overlap in the transition zone.
  • features of both the gear tooth profile 20y, 40y and the corresponding gear basic cutter profile 102 will be understood to be conjugate to each other. In this way, features of the gear tooth profile 20y, 40y describe features of the cutter profile 102, and vice versa.
  • gear tooth profile 20y, 40y and the corresponding gear basic cutter profile 102 may also be described in relation to centerlines CL of those profiles.
  • the centerlines CL of each of the tooth and cutter profiles extend through the center along the length of these profiles in the longitudinal direction, such that one set of the concave and convex portions 22a, 26a, 42a, 46a, 126a, 122a of a tooth is on one side of the centerline and the other set of concave and convex portions of that tooth is on the opposing side of the centerline.
  • Gear tooth profile 20y, 40y may further be described in relation to a pitch circle.
  • a pitch circle PC may be described as the curve of the intersection of a pitch surface of revolution and a plane of rotation.
  • the cutter profile may be described in terms of a pitch line PL.
  • the pitch line PL is a line that extends perpendicular to the centerline CL of the cutter profile 102 through a point on the cutter 100 that corresponds to a point on the gear tooth profile 20y, 40y where the pitch circle PC intersects the gear tooth profile 20y, 40y.
  • Transition zone blending relief is accomplished through a thickening of the addendum, dedendum, or both the addendum and dedendum of the gear basic cutter profile 102 proximate to the transition zone 124.
  • Thickening of the gear basic cutter profile 102 corresponds to a thinning of the conjugate gear tooth profile 20y, 40y.
  • the thickening of the gear basic cutter profile and corresponding thinning of the tooth profile the design of the structures of the addendum, dedendum, and transition zone as taught by the 892 and 210 patents will first be described.
  • a gear pair 10 includes a first gear 20 having a first plurality of teeth 20x. As described above, each tooth has a first tooth profile 20y.
  • a mating gear 40 has a second plurality 40x of teeth each having a second tooth profile 40y.
  • the first profile 20y of the first plurality of teeth 20x of the first gear 20 includes the first transition zone 24 disposed between the first concave portion 22a lying within the dedendum 22 of the first gear and the first convex portion 26a lying within the addendum 26 of the first gear.
  • the second profile 40y of the second plurality 40x of teeth of mating gear 40 includes the second transition zone 44 disposed between the second concave portion 42a lying within the dedendum 42 of the mating gear 40 and a second convex portion 46a lying within the addendum 46 of the mating gear 40.
  • the second concave portion 46a of the second profile of the second plurality of teeth of mating gear 40 is conjugate to the first convex portion 26a of the first tooth profile of the first plurality of teeth of first gear 20 and the second convex portion 46a of the second profile of the second plurality of teeth of mating gear 40 is conjugate to the first concave portion 42a of the first tooth profile of the first plurality of teeth of the first gear.
  • the transition zones 24, 44 are not conjugate with each other and instead form a no-contact zone. As described above, as the gears 20, 40 rotate in mesh with one another, the concave portions 22a, 42a and convex portions 26a, 46a are in continuous contact such that angular velocity ratio is constant.
  • gears 20, 40 with conjugate profiles can be defined by either the pinion tooth profile, the gear tooth profile, the basic rack profile, or the shape of the contact path.
  • any one of these four shapes is known, it is possible to calculate the other three shapes.
  • the methods by which these shapes are found have been described by Buckingham, Analytical Mechanics of Gears, McGraw-Hill, New York, 1949, republished by Dover, N.Y., 1963, incorporated in its entirety herein.
  • the most common method for defining a pair of profiles is to choose the shape of the basic rack. For example, if the basic rack profile is straight, involute gears are obtained. Less commonly, the shape of one tooth profile is chosen.
  • lobes of the outer rotor are circular.
  • shape of the contact path is chosen.
  • cycloidal gears can be defined as having profiles for which the contact path consists of two circular arcs.
  • R p) and R p2 are the pitch circle radii
  • ⁇ is the gear pair pressure angle, namely the angle between the line of action and the line through the pitch point perpendicular to the line of centers
  • S is the distance from the pitch point to the contact point, positive when the contact point lies on one side of the line of centers, and negative on the other
  • pi and p 2 are the radii of curvature, positive for convex profiles and negative for concave profiles.
  • the reciprocals of the radii of curvature, 1/pl and l/p2, are known as the curvatures.
  • the gearing system shown, for example, in FIG. 2, or the like may be designed such that the contact stress between meshing teeth of the first gear 20 with the mating gear 40 is a constant.
  • Equations (2) and (2a) may be replaced by any predetermined mathematical function set to a constant and parameterized (as are equation (2) and (2a)) by the radius of curvature associated with the first tooth profile and the radius of curvature associated with the second tooth profile.
  • Equations (1) and (2), (1 ) and (2a), or (1) and any predetermined mathematical function (parameterized by the radii of curvature) set to a constant may be solved to find the values of pi and p 2 , whenever the values of S and ⁇ are known.
  • a family of gears is composed of gears that are conjugate to a basic cutter.
  • the basic rack is the complement of the basic cutter, and the tooth profile of the basic rack is therefore the same as that of a gear belonging to the family with an infinite number of teeth.
  • the dedendum of the first gear 20 and the addendum of the mating gear 40 include the curves 26b, 46b of the convex and concave portions 26a, 42a, respectively.
  • Curve 26b defines at least a portion of concave portion 26a and curve 42b defines at least a portion of concave portion 42a.
  • transition zones 24, 44 are designed so that these zones do not contact each other. Accordingly, contact between meshing teeth is made only along the convex addendum and concave dedendum portions, but not between the transition zones.
  • a gear and pinion system may be designed so that contact is made between at least a portion of the convex addendum portion of the gear and at least a portion of the concave dedendum portion of the pinion and between at least a portion of the convex addendum portion of the pinion and at least a portion of the concave dedendum portion of the gear.
  • Transition zones 24, 44 of the gears may be described in terms of gear tooth profiles 20y, 40y, as well as the gear basic cutter 100 and its profile 102 that is conjugate.
  • Transition zones 24, 44, 124 are defined along profiles 20y, 40y, 102 between addendum transition points 24b, 44b, 124a and dedendum transition points 24a, 44a, 124b.
  • Transition zones 24, 44, 124 may further be defined in terms of pitch relief and pitch relief width.
  • pitch relief may be described in terms of the distance by which the respective cutter profiles of a gear pair overlap.
  • the basic cutters for a conjugate gear pair are complementary, so that if they are placed together, they will be in contact along their entire active profiles. In practice the basic cutter profiles may overlap slightly, and these overlapping segments will correspond to segments of the gear teeth where there is relief.
  • Fig. 4 shows the basic cutter relief diagram for a Convoloid gear pair. Line R represents the amount by which the cutters overlap, with the vertical scale exaggerated.
  • the pinion basic cutter root is at the left end of the figure, and its tooth tip at the right end, while the orientation of the gear basic cutter is reversed.
  • gear basic cutter tooth profile 102 has a pitch relief 121 that may be between 0.010 transverse modules and 0.030 transverse modules, with a preferred value of 0.015 transverse modules.
  • gear basic cutter tooth profile 102 has a half pitch relief width 120 defined by the distance between the addendum and dedendum transition points (corresponding to the dedendum and addendum transition points of the gear tooth profile, respectively) at the center line CL.
  • the half pitch relief width 120 represents half of the total pitch relief width.
  • the half pitch relief may be between 0.050 transverse modules and 0.150 transverse modules, with a preferred value of 0.075 transverse modules.
  • the pitch relief width may be defined by the distance along the center line CL from the addendum and dedendum transition points of the gear basic cutter tooth profile 102.
  • the tooth thickness of the basic cutter 100 must be increased in the segment starting at point 1 13 a certain distance from the pitch line PL and ending at the addendum transition point 124a.
  • the distance from the pitch line to the transition zone blending relief start point 1 13 along the centerline CL may be between 0.6 transverse modules and 0.9 transverse modules, with a preferred value of 0.75 transverse modules.
  • the distance from the pitch line to the transition zone blending relief start point 1 13 along the centerline CL may be between 0.6 transverse modules and 0.9 transverse modules, with a preferred value of 0.75 transverse modules.
  • the increase of the basic cutter tooth thickness at the start point 113 may be zero, and the increase of the tooth thickness at the dedendum transition point 124a may be between 0.05 times the pitch relief and 0.2 times the pitch relief, with a preferred value of 0.1 times the pitch relief.
  • the distance from the pitch line to the transition zone blending relief start point 1 13 along the centerline CL may be between 0.2 transverse modules and 0.4 transverse modules, with a preferred value of 0.3 transverse modules.
  • the increase of the basic cutter tooth thickness at the start point 113 may be zero, and the increase of the tooth thickness at the dedendum transition point 124a may be between 0.1 times the pitch relief and 0.4 times the pitch relief, with a preferred value of 0.2 times the pitch relief.
  • This tooth thickness increase in the cutter profile 102 translates to a tooth thickness decrease in the gear tooth profile 20y, 40y. By decreasing the gear tooth thickness, the no-contact zone of the transition zone 24, 44 is extended into the dedendum 22, 42.
  • the tooth thickness of the basic cutter at the addendum transition point and the slope of the basic cutter profile at that point are now known.
  • the tooth thickness of the basic cutter at the pitch line and the profile slope at the pitch line are also known, as described in the 210 patent.
  • These points can now be joined by a curve, such as a cubic curve, giving continuity of profile and profile slope at these points.
  • These points do not necessarily require continuity of curvature since the transition zone blending relief and the pitch relief are designed so that there is no contact between the gear teeth at the points conjugate to the basic cutter addendum transition point and pitch point. If it is found that micropitting still occurs on the gear teeth at or near their dedendum transition points, the amount of the transition zone blending relief can be modified until the micropitting ceases.
  • a similar process may be employed to create transition zone blending on the addendum of the gear 20, 40.
  • the position of the first basic cutter dedendum transition point 124b is known.
  • the tooth thickness of the basic cutter 100 must be increased in the segment starting at point 1 14 a certain distance from the pitch line PL and ending at the dedendum transition point 124b.
  • the distance from the pitch line to the transition zone blending relief start point 114 along the centerline CL may be between 0.6 transverse modules and 0.9 transverse modules, with a preferred value of 0.75 transverse modules.
  • the increase of the basic cutter tooth thickness at the start point 1 14 may be zero, and the increase of the tooth thickness at the dedendum transition point 124b may be between 0.05 times the pitch relief and 0.2 times the pitch relief, with a preferred value of 0.1 times the pitch relief.
  • the distance from the pitch line to the transition zone blending relief start point 1 14 along the centerline CL may be between 0.2 transverse modules and 0.4 transverse modules, with a preferred value of 0.3 transverse modules.
  • the increase of the basic cutter tooth thickness at the start point 1 14 may be zero, and the increase of the tooth thickness at the dedendum transition point 124b may be between 0.1 times the pitch relief and 0.4 times the pitch relief, with a preferred value of 0.2 times the pitch relief.
  • Ay the tooth thickness increase
  • ⁇ the distance from the start point
  • c a constant chosen so that the tooth thickness increase at the dedendum transition point has the required value.
  • the tooth thickness of the basic cutter at the dedendum transition point and the slope of the basic cutter profile at that point are now known.
  • the tooth thickness of the basic cutter at the pitch line and the profile slope at the pitch line are also known, as described in the 210 patent.
  • These points can now be joined by a curve, such as a cubic curve, giving continuity of profile and profile slope at these points.
  • These points do not necessarily require continuity of curvature since the transition zone blending relief and the pitch relief are designed so that there is no contact between the gear teeth at the points conjugate to the basic cutter dedendum transition point and pitch point. If it is found that micropitting still occurs on the gear teeth at or near their addendum transition points, the amount of the transition zone blending relief can be modified until the micropitting ceases.
  • This tooth thickness increase in the cutter profile 102 translates to a tooth thickness decrease in the gear tooth profile 20y, 40y. By decreasing the gear tooth thickness, the no-contact zone of the transition zone 24, 44 is extended into the addendum 26, 46.
  • Non-involute gear pairs are only conjugate when they operate at the design center distance.
  • the transverse module can be defined as twice the design center distance, divided by the sum of the tooth numbers.
  • the transverse module is defined differently, but the value is the same as that given by the present definition when the operating center distance is equal to the standard center distance.
  • transition zone blending has been described in relation to transition zone blending within the addendum or dedendum of a gear
  • transition zone blending may be applied to both the addendum and dedendum of a gear, or the dedendums of both gears of a gear pair, of the addendums of both gears of a gear pair, or the addendum of one gear of a gear pair and the dedendum of the other gear of the gear pair.

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  • Engineering & Computer Science (AREA)
  • General Engineering & Computer Science (AREA)
  • Mechanical Engineering (AREA)
  • Gears, Cams (AREA)

Abstract

L'invention concerne une paire d'engrenages qui comprend un premier engrenage ayant une première zone de transition disposée entre une première saillie et un premier pied dent, la première zone de transition étant définie entre un premier point de transition de saillie et un premier point de transition de pied de dent, la première saillie comprenant une première partie convexe définie par une première courbe et le premier pied de dent comprenant une première partie concave définie par une deuxième courbe, le premier pied de dent comprenant en outre un relief de mélange disposé entre le premier point de transition de pied de dent et un point de mélange et défini par une troisième courbe, la deuxième courbe et la troisième courbe étant différentes et l'inclinaison et la courbure de la deuxième courbe et de la troisième courbe étant identiques au niveau du point de mélange.
PCT/US2012/062840 2011-10-31 2012-10-31 Profil de dent d'engrenage ayant un relief de mélange de zones de transition WO2013067039A1 (fr)

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EP12844774.5A EP2805084A1 (fr) 2011-10-31 2012-10-31 Profil de dent d'engrenage ayant un relief de mélange de zones de transition

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US201161553406P 2011-10-31 2011-10-31
US61/553,406 2011-10-31

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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN108019463A (zh) * 2017-12-15 2018-05-11 华南理工大学 一种可变角度传动的线齿轮机构
CN113513573A (zh) * 2021-05-17 2021-10-19 西安长剑飞控机电有限责任公司 正弦曲线齿形应用于谐波齿轮的修型方法

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US5022280A (en) * 1988-03-29 1991-06-11 Boiko Leonid S Novikov gearing
US6964210B2 (en) * 2002-04-22 2005-11-15 Genesis Partners, L.P. Gear tooth profile
US20090165585A1 (en) * 2005-07-05 2009-07-02 German Alexandrovich Zhuravlev Zhuravlev Gear Drive

Patent Citations (3)

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Publication number Priority date Publication date Assignee Title
US5022280A (en) * 1988-03-29 1991-06-11 Boiko Leonid S Novikov gearing
US6964210B2 (en) * 2002-04-22 2005-11-15 Genesis Partners, L.P. Gear tooth profile
US20090165585A1 (en) * 2005-07-05 2009-07-02 German Alexandrovich Zhuravlev Zhuravlev Gear Drive

Non-Patent Citations (1)

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Title
LITVIN, FL ET AL.: "New Version of Novikov-Wildhaber Helical Gears: Computerized Design, Simulation of Meshing and Stress Analysis.", COMPUT. METHODS APPL. MECH. ENGRG., vol. 191, 2002, pages 5707 - 5740, XP001197265 *

Cited By (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN108019463A (zh) * 2017-12-15 2018-05-11 华南理工大学 一种可变角度传动的线齿轮机构
WO2019114452A1 (fr) * 2017-12-15 2019-06-20 华南理工大学 Mécanisme d'engrenage linéaire transmettant à un angle variable
US11149821B2 (en) 2017-12-15 2021-10-19 South China University Of Technology Line gear mechanism with variable-angle transmission
CN108019463B (zh) * 2017-12-15 2023-07-18 华南理工大学 一种可变角度传动的线齿轮机构
CN113513573A (zh) * 2021-05-17 2021-10-19 西安长剑飞控机电有限责任公司 正弦曲线齿形应用于谐波齿轮的修型方法
CN113513573B (zh) * 2021-05-17 2022-07-01 西安长剑飞控机电有限责任公司 正弦曲线齿形应用于谐波齿轮的修型方法

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