EP2805084A1

EP2805084A1 - Gear tooth profile with transition zone blending relief

Info

Publication number: EP2805084A1
Application number: EP12844774.5A
Authority: EP
Inventors: John Robert Colbourne; Bernard E. BERLINGER
Original assignee: Genesis Partners LP
Current assignee: Genesis Partners LP
Priority date: 2011-10-31
Filing date: 2012-10-31
Publication date: 2014-11-26
Also published as: WO2013067039A1

Abstract

A gear pair comprises a first gear having 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.

Description

GEAR TOOTH PROFILE WITH TRANSITION ZONE BLENDING RELIEF

CROSS REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority to U.S. Provisional Application No. 61/553,406, filed October 31, 201 1, the contents of which is incorporated by reference. This application is related by subject matter to the inventions disclosed in the following commonly assigned patents: U.S. Patent No. 6, 101,892, issued August 15, 2000 and entitled "Gear Form Constructions"; and U.S. Patent No. 6964,210, issued on November 15, 2005 and entitled "Gear Tooth Profile." The disclosure of each patent is incorporated by reference herein in its entirety.

FIELD OF THE TECHNOLOGY

[0002] The present technology relates to gear tooth profiles and corresponding cutter profiles.

BACKGROUND

[0003] 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.

[0004] As described in the 892 patent, the relative curvature of conjugate tooth profiles at their pitch diameters cannot be reduced below a certain value, given by the Euler- Savary equation. For this reason, 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.

[0005] 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.

[0006] 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.

SUMMARY

[0007] When gears are designed according to the methods described in the 892 patent and the 210 patent, 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.

[0008] It is not clear why the Hertz contact theory does not necessarily predict the forces at the transition points. While not being bound by any theory, one possible reason that the force at the transition point is greater than that predicted by the Hertz contact theory is that this added force may result from the adjacent profile segment having no-contact with the

corresponding addendum or dedendum of the other gear of the pair. Another potential reason for the greater force is that 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.

[0009] To address the issue of micropitting at the transition points (and its possible underlying cause of added force at those points) in the gear configurations taught by the 892 patent and the 210 patent, 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.

[0010] Accordingly, 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.

[0011] Alternately, 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.

BRIEF DESCRIPTION OF THE DRAWINGS

[0012] Figs. 1A-1D show a variety of types of gearing systems in which transition zone blending relief may be incorporated;

[0013] Fig. 2 shows conjugate profiles of a gearing system in which transition zone blending

[0014] Fig. 3 shows a gear basic cutter profile; and

[0015] Fig. 4 is a basic cutter relief diagram with the vertical scale exaggerated.

DETAILED DESCRIPTION OF ILLUSTRATIVE EMBODIMENTS

[0016] Figs. 1 A-1D show various types of gear pairs 10 in which transition zone blending relief may be incorporated. For example, 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. ID shows a spiral bevel gearing system wherein the axis of rotation of the first gear 20d is at an angle to the axis of rotation of mating gear 20d. [0017] Transition zone blending relief may be described in relation to features of gear tooth profiles and gear basic cutter profiles outlined in the 892 patent and the 210 patent. 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. 3 may be configured to correspond to the tooth profile of a gear, such as first gear 20. 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.

[0018] Unlike the dedendum 22,42 and the addendum 26, 46, 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. Where 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. Throughout the specification, 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.

[0019] Features of both the 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. In other words, it is the imaginary circle that rolls without slipping with the pitch circle of the mating gear. 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.

[0020] 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. To put into context 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.

DESIGN OF ADDENDUM AND DEDENDUM

[0021] Referring to FIG. 2, 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.

[0022] 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.

[0023] As described in the 892 patent, 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. When 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. For example, in Gerotor internal gear pumps, the lobes of the outer rotor are circular. Less commonly still, the shape of the contact path is chosen. For example, cycloidal gears can be defined as having profiles for which the contact path consists of two circular arcs.

10024] Consider the following method for designing conjugate gear tooth profiles. There are two important properties of conjugate profiles, which are described by Buckingham. First, they must satisfy the Law of Gearing, which states that the common normal at the contact point (also known as the line of action) always passes through the pitch point. Secondly, the radii of curvature pi and p₂ of the profiles must satisfy the Euler-Savary equation ("Equation 1"),

where R_p) and R_p2 are the pitch circle radii, φ 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 p₂ 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.

[0025] It is important to note that whenever contact between meshing teeth is referred to herein it is understood that in fact for practical reasons meshing teeth of gears often only make contact through a thin lubricating film. Therefore, distinctions between "contact" and "no- contact" are made based on a standard of thickness of and transmission of forces through such thin lubricating films.

[0026] If the relative curvature is to remain constant, the radii of curvature should satisfy the following relation ("Equation 2"),

1 1

— +— = constant

Pi PI

[0027] In other words, the gearing system shown in, for example, FIG. 2, or the like, may be designed such that the relative curvature of the first tooth profile and the second tooth profile is a constant. [0028] If, instead, the contact stress is to remain constant, the radii of curvature should satisfy the following relation (" = constant

[0029] in other words, 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.

[0030] 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 p₂, whenever the values of S and φ are known.

[0031] The profiles of the two gears can now be found in the following manner. Choose an initial point S=So, φ=<ρο on the contact path near the pitch point, where S and φ are the polar coordinates of the point. The radii Ri and R₂ of the two profile points, and the corresponding profile angles φι and φ₂, can now be found by conventional methods.

[0032] Once S and φ are known, the values of pi and p₂ can be calculated. It is now possible to construct a small increment of the tooth profile of the first gear as a circular arc of radius pi. Then the radius Ri, and the profile angle φι at the end of the increment are calculated, and using the conventional theory of conjugate profiles the corresponding values of R₂, <p_¾ S and φ may also be calculated. The process is repeated as often as desired to construct the addendum of the first gear 20 and the conjugate dedendum of the mating gear 40 so as to form the curves 22b, 46b of the concave and convex portions 22a, 46a, respectively. Curve 22b defines at least a portion of concave portion 22a and curve 46b defines at least a portion of convex portion 46a.

[0033] Since the coordinates of a number of points on the contact path have been found, the shape of the basic cutter can be deduced by conventional methods. 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.

[0034] To find the shape of the dedendum of the first gear and the addendum of the mating gear, the entire procedure explained above is repeated, starting from an initial point on the contact path on the opposite side of the pitch point. A suitable initial point is given by S=-So, φ=φο, but it is not essential to use these values. The recommended value of So lies between 0.1 modules and 0.5 modules, where the module is a length defined in terms of the center distance C and the tooth numbers Ni and N₂, as 2C/(Nj +N₂), while q>o can be any value such that the profile angles q>i and φ₂ are positive at both initial points. 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.

DESIGN OF TRANSITION ZONE

10035] As described above, 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. For example, 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.

[0036] 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.

[0037] Transition zones 24, 44, 124 may further be defined in terms of pitch relief and pitch relief width. As described above, 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. The diagram shows the pitch relief 121 as dimension on the exaggerated vertical scale, the pinion dedendum transition zone blending relief 123, the pinion tip relief 125, and the basic cutter pitch lines PL. In one embodiment, 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.

[0038] When the transition zone 124 is centered about the pitch line PL, 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. In one embodiment, 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.

[0039] When the transition zone width is not centered about the pitch line PL, 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.

DESIGN OF TRANSITION ZONE BLENDING RELIEF

[0040] Once the transition zone width 120 has been chosen, the position of the first basic cutter addendum transition point 124a is known. To provide the gear 20, 40 dedendum transition zone blending relief, 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. In a first embodiment, 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. In this first embodiment, 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. In a second embodiment, 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. In this second embodiment, 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.

[0041] Since there is no change of the basic cutter tooth thickness at the addendum transition zone blending relief start point 1 13, the profile is continuous at that point. To provide continuity of slope and curvature, the simplest function for the increase in tooth thickness using a curve 1 13a is a cubic curve 1 13a, of the form Ay=c(Ax)3, where Ay is the tooth thickness increase, Δχ is the distance from the start point, and c is a constant chosen so that the tooth thickness increase at the addendum transition point has the required value. There are however, other types of curves that can be successfully used and include but are not limited to logarithmic and quadratic curves 1 13a.

[0042] 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.

[0043] A similar process may be employed to create transition zone blending on the addendum of the gear 20, 40. Once the transition zone width 120 has been chosen, the position of the first basic cutter dedendum transition point 124b is known. To provide the gear 20, 40 addendum transition zone blending relief, 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. In a first embodiment, 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. In this first embodiment, 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. In a second embodiment, 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. In this second embodiment 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. [0044] Since there is no change of the basic cutter tooth thickness at the dedendum transition zone blending relief start point 1 14, the profile is continuous at that point. To provide continuity of slope and curvature, the simplest function for the increase in tooth thickness using a curve 1 14a is a cubic curve 1 14a, of the form Ay=c(Ax)3, where Ay is the tooth thickness increase, Δχ is the distance from the start point, and c is a constant chosen so that the tooth thickness increase at the dedendum transition point has the required value. There are however, other types of curves that can be successfully used and include but are not limited to logarithmic and quadratic curves 114a.

[0045] 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.

[0046] By way of example, studies carried out using FEA methods showed that a particular curve used in blending a pair of subject gears at 3.0 module in size (defined as twice the center distance divided by the sum of the numbers of teeth in pinion and gear) resulted in significant reductions in Hertz stresses at and near the dedendum transition point. The point at which the blending curve connected to the active dedendum profile matched the active profile in profile, profile slope, and profile curvature.

[0047] Non-involute gear pairs are only conjugate when they operate at the design center distance. For non-involute gear pairs the transverse module can be defined as twice the design center distance, divided by the sum of the tooth numbers. In the case of involute gear pairs, 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.

[0048] The present invention has been described by illustrating preferred embodiments. The present invention is not limited to the configuration or dimensions provided in the specification, but rather should be entitled to the full scope as defined in the claims. For example, while 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.

Claims

What is Claimed:

1. A gear pair comprising;

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; and

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.

2. The gear pair of claim 1 , wherein the third curve is defined by one of a cubic, logarithmic, or quadratic equation.

3. The gear pair of claim 2, wherein the third curve is a cubic equation.

4. The gear pair of claim 1 , wherein the first tooth profile defines a pitch circle and the distance between the pitch circle and the blending point along a longitudinal centerline of the tooth is between approximately 0.6 and 0.9 transverse modules.

5. The gear pair of claim 4, wherein the distance between the pitch circle and the blending point along the longitudinal centerline of the tooth is approximately 0.75 transverse modules.

6. The gear pair of claim 1, wherein the first addendum further includes a second blending relief.

7. The gear pair of claim 1 , wherein the second addendum further includes a second blending relief.

8. The gear pair of claim 1, wherein the second dedendum further includes a second blending relief.

9. A gear pair comprising:

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; and 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

10. The gear pair of claim 9, wherein the third curve is defined by one of a cubic, logarithmic, or quadratic equation.

1 1. The gear pair of claim 10, wherein the third curve is a cubic equation.

12. The gear pair of claim 9, wherein the first tooth profile defines a pitch circle and the distance between the pitch circle and the dedendum transition point along a longitudinal centerline of the tooth is between approximately 0.6 and 0.9 transverse modules.

13. The gear pair of claim 12, wherein the distance between the pitch circle and the dedendum transition point along the longitudinal centerline of the tooth is approximately 0.75 transverse modules.

14. The gear pair of claim 9, wherein the first dedendum further includes a second blending relief

15. The gear pair of claim 9, wherein the second addendum further includes a second blending relief.

16. The gear pair of claim 9, wherein the second dedendum further includes a second blending relief.