Differential gear mechanism and design method therefor

Abstract

To compactify a differential gear mechanism while ensuring the strength of a side gear and a pinion gear excellently.SOLUTION: In a differential gear mechanism, a reference pressure angle of each side gear tooth of a side gear and a reference pressure angle of each pinion gear tooth of a pinion gear increase from an intermediate part of a tooth trace toward an inner end side, and increase from the intermediate part toward an outer end side; a tooth thickness on a pitch cone of the side gear decreases from the intermediate part of the tooth trace toward the inner end side, and increases from the intermediate part toward the outer end side compared to a reference side gear; and a tooth thickness on a pitch cone of the pinion gear increases from the intermediate part of the tooth trace toward the inner end side, and decreases from the intermediate part toward the outer end side compared to a reference pinion gear.SELECTED DRAWING: Figure 2

Description

[Technical field]

[0001] The present disclosure relates to a differential gear mechanism including a pair of side gears and a plurality of pinion gears meshing with the pair of side gears, and a method for designing the same. [Background technology]

[0002] Conventionally, a differential gear is known in which a pinion gear, which is a straight bevel gear supported rotatably by a pinion shaft fixed to a case, is meshed with a pair of side gears (see, for example, Patent Document 1). In this differential gear, in order to ensure the thickness of the inner end of the pinion gear (the end on the center side of the differential gear), the inner end of the tooth bottom of the pinion gear is inclined so as to be located closer to the tooth tip cone than the tooth bottom cone of the pinion gear. Also, the inner end of the tooth tip of the gear teeth of the side gear is inclined so as to be located closer to the tooth bottom cone than the tooth tip cone of the side gear, and the inner end of the tooth bottom of the pinion gear extends along the inner end of the tooth bottom of the pinion gear.

[0003] Also, a differential mechanism including a pinion shaft fixed to a case, a pinion gear that is a bevel gear rotatably supported by the pinion shaft, and a pair of side gears that are bevel gears that mesh with the pinion gears has been conventionally known (see, for example, Patent Document 2). In this differential mechanism, in order to reduce the axial length of the differential mechanism while suppressing a decrease in strength of the side gears, the outer end (end on the outer periphery) of the tooth bottom of each side gear is inclined so as to be located closer to the tooth tip cone side than the tooth bottom cone of the side gear. Also, the outer end of the tooth tip of the pinion gear tooth of the pinion gear is inclined so as to be located closer to the tooth bottom cone side than the tooth tip cone of the pinion gear, and extends along the outer end of the tooth bottom of the side gear. [Prior art documents] [Patent documents]

[0004] [Patent Document 1] JP 2005-048903 A [Patent Document 2] JP 2014-185666 A Summary of the Invention [Problem to be solved by the invention]

[0005] However, as described in Patent Document 1, when the inner end of the tooth bottom of the pinion gear is inclined so as to be located closer to the tooth tip cone than the tooth bottom cone of the pinion gear, the tooth thickness of the root of the pinion gear teeth at the inner end of the pinion gear (the end on the center side of the differential gear) becomes smaller, and the strength of the pinion gear decreases. For this reason, unless some measure is taken, it becomes difficult to make the pinion gear small in diameter and to make the differential gear compact while ensuring the strength of the pinion gear. Also, as described in Patent Document 2, when the outer end of the tooth bottom of the side gear is inclined so as to be located closer to the tooth tip cone than the tooth bottom cone of the side gear, the tooth thickness of the root of the gear teeth at the outer end of the side gear (differential mechanism) becomes smaller, and the strength of the side gear decreases. For this reason, unless some measure is taken, it becomes difficult to shorten the axial length of the differential mechanism in the axial direction of the side gear while ensuring the strength of the side gear.

[0006] Therefore, the main objective of the present disclosure is to compact a differential gear mechanism including a pair of side gears and a plurality of pinion gears meshing with the pair of side gears while ensuring good strength of the side gears and pinion gears. [Means for solving the problem]

[0007] The differential gear mechanism of the present disclosure includes a pair of side gears, which are bevel gears each having a plurality of side gear teeth, and a plurality of pinion gears, each being bevel gears having a plurality of pinion gear teeth, which mesh with the pair of side gears, wherein an outer end of a tooth bottom of the side gear is inclined so as to be located closer to a tooth tip cone of the side gear than a tooth bottom cone of the side gear, and an inner end of a tooth tip of the side gear tooth is inclined so as to be located closer to the tooth bottom of the side gear than the tooth tip cone of the side gear. a reference pressure angle which is an angle between a radius line passing through a pitch point of the side gear tooth and a tangent to a tooth profile of the pinion gear tooth, an inner end of a tooth bottom of the pinion gear being inclined so as to be located closer to the tooth tip cone side of the pinion gear than the tooth bottom cone of the pinion gear, an outer end of a tooth tip of the pinion gear tooth being inclined so as to be located closer to the tooth bottom cone side of the pinion gear than the tooth tip cone of the pinion gear, and an angle between a radius line passing through a pitch point of the pinion gear tooth and a tangent to the tooth profile of the pinion gear tooth, a reference pressure angle, which is determined by the differential gear mechanism according to the present invention, increases from a middle portion of a tooth trace between the inner end of the tip of the side gear tooth and the outer end of the tip of the pinion gear tooth in the tooth trace direction, toward the inner end side, and increases from the middle portion toward the outer end side; a tooth thickness on a pitch cone of the side gear decreases from the middle portion to the inner end side and increases from the middle portion to the outer end side, compared to a reference side gear in which an intersection line between a tooth flank of a side gear tooth and a pitch cone is a straight line passing through the center of the differential gear mechanism and the reference pressure angle is constant in the tooth trace direction; and a tooth thickness on a pitch cone of the pinion gear increases from the middle portion to the inner end side and decreases from the middle portion to the outer end side, compared to a reference pinion gear in which an intersection line between a tooth flank of a pinion gear tooth and a pitch cone is a straight line passing through the center and the reference pressure angle is constant in the tooth trace direction.

[0008] The present disclosure also provides a method for designing a differential gear mechanism, comprising: a pair of side gears, each of which is a bevel gear having a plurality of side gear teeth; and a plurality of pinion gears, each of which is a bevel gear having a plurality of pinion gear teeth, meshing with the pair of side gears, wherein an outer end of the tooth bottom of the side gear is inclined so as to be located closer to the tooth tip cone side of the side gear than the tooth bottom cone of the side gear; and an inner end of the tooth tip of the side gear tooth is located closer to the tooth bottom cone side of the side gear than the tooth tip cone of the side gear. a pinion gear having a tooth tip cone side of the pinion gear, an inner end of a tooth bottom of the pinion gear being inclined so as to be located closer to the tooth tip cone side of the pinion gear than the tooth bottom cone of the pinion gear, and an outer end of a tooth tip of the pinion gear tooth being inclined so as to be located closer to the tooth bottom cone side of the pinion gear than the tooth tip cone of the pinion gear, A reference pressure angle, which is an angle between the tooth flank of the side gear tooth and the pitch cone, is increased from a middle portion of the tooth flank between the inner end of the tooth tip of the side gear tooth and the outer end of the tooth tip of the pinion gear tooth in the tooth flank direction toward the inner end side and is also increased from the middle portion toward the outer end side, and the tooth thickness on the pitch cone of the side gear is determined based on a reference size where an intersection line between the tooth flank of the side gear tooth and the pitch cone is a straight line passing through the center of the differential gear mechanism and the reference pressure angle is constant in the tooth flank direction. Compared to a reference pinion gear, the tooth thickness on the pitch cone of the pinion gear is made smaller from the middle portion to the inner end side and larger from the middle portion to the outer end side, and the tooth thickness on the pitch cone of the pinion gear is made larger from the middle portion to the inner end side and smaller from the middle portion to the outer end side, compared to a reference pinion gear in which the intersection line between the tooth flank of the pinion gear tooth and the pitch cone is a straight line passing through the center and the reference pressure angle is constant in the tooth trace direction. [Brief description of the drawings]

[0009] [Figure 1] FIG. 1 is a schematic configuration diagram showing a differential gear mechanism according to the present disclosure. [Diagram 2] FIG. 2 is a partial cross-sectional view showing a differential gear mechanism of the present disclosure. [Diagram 3] 4 is a chart showing the relationship between cone distance and reference pressure angle in the side gears and pinion gears of the differential gear mechanism of the present disclosure. [Figure 4] 4 is a diagram showing the relationship between the cone distance and the tooth thickness on the pitch cone in the side gears of the differential gear mechanism of the present disclosure. [Diagram 5] 4 is a diagram showing the relationship between the cone distance and the tooth thickness on the pitch cone in the pinion gear of the differential gear mechanism of the present disclosure. [Figure 6] 1 is a diagram showing the relationship between cone distance and tooth thickness at the base in a side gear of a differential gear mechanism of the present disclosure. [Figure 7] 4 is a chart showing the relationship between the cone distance and the tooth thickness at the base of the pinion gear of the differential gear mechanism of the present disclosure. [Figure 8] FIG. 2 is an enlarged view showing a main portion of the differential gear mechanism of the present disclosure. [Figure 9] FIG. 2 is an enlarged view showing a main portion of the differential gear mechanism of the present disclosure. [Figure 10] 1 is an explanatory diagram illustrating an example of tooth pointing that may occur in a pinion gear of a differential gear mechanism of the present disclosure; FIG. [Figure 11] 1 is an explanatory diagram illustrating an example of undercutting of a tooth root that may occur in a pinion gear of a differential gear mechanism of the present disclosure; FIG. [Figure 12] FIG. 2 is a schematic configuration diagram showing an engagement state of side gears and pinion gears in a differential gear mechanism according to the present disclosure. [Figure 13] 4 is a table for explaining a procedure for adjusting a pressure angle in a pinion gear of a differential gear mechanism of the present disclosure. [Figure 14] 4 is a table illustrating an example of pressure angle adjustment amounts in side gears and pinion gears of the differential gear mechanism of the present disclosure. [Figure 15] 4 is a table illustrating an example of pressure angle adjustment amounts in side gears and pinion gears of the differential gear mechanism of the present disclosure. [Figure 16] 4 is a table for explaining a procedure for adjusting a pressure angle in a pinion gear of a differential gear mechanism of the present disclosure. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0010] Next, an embodiment of the present disclosure will be described with reference to the drawings.

[0011] FIG. 1 is a perspective view showing a differential gear mechanism 1 of the present disclosure, and FIG. 2 is a partial cross-sectional view showing a main part of the differential gear mechanism 1. The differential gear mechanism 1 shown in these drawings is included in a differential gear mounted on a vehicle together with a differential ring gear and a differential case (not shown). The differential gear mechanism 1 includes a pair of side gears 2 and a plurality of pinion gears 3 (for example, 2 to 4 in this embodiment) meshing with the pair of side gears 2. The pair of side gears 2 are fixed to corresponding drive shafts (not shown). In addition, each pinion gear 3 is inserted with one of a plurality of pinion shafts that are supported by the differential case and extend radially so as to be perpendicular to the axial direction of the pair of side gears 2. As a result, each pinion gear 3 is rotatably supported by the differential case via the pinion shafts.

[0012] Each side gear 2 is a bevel gear, and includes a plurality of side gear teeth 20 formed so as to extend radially from a center O of the differential gear mechanism 1 through which the axes of each side gear 2 and each pinion gear 3 pass, and a plurality of tooth roots 25 located between adjacent side gear teeth 20, as shown in Figs. 1 and 2. Each side gear tooth 20 includes a pair of tooth surfaces 21 formed based on a spherical involute curve, and a tooth tip 23 formed between the pair of tooth surfaces 21, as shown in Fig. 2. In this embodiment, the outer end 25o of the tooth root 25 of each side gear 2 (a region on the outer periphery side of the side gear 2 from the boundary B2 in Fig. 2) is inclined so as to be located on the tooth tip cone TC2 side of the side gear 2 from the tooth root cone RC2 of the side gear 2. This makes it possible to suppress a decrease in the thickness of the outer periphery of the side gear 2 and suppress a decrease in the strength of the side gear 2.

[0013] Each pinion gear 3 is a bevel gear, and includes a plurality of pinion gear teeth 30 formed to extend radially from the center O of the differential gear mechanism 1, and a plurality of tooth roots 35 located between adjacent pinion gear teeth 30, as shown in Figs. 1 and 2. Each pinion gear tooth 30 includes a pair of tooth surfaces 31 formed based on a spherical involute curve, and a tooth tip 33 formed between the pair of tooth surfaces 31, as shown in Fig. 2. In this embodiment, an inner end 35i of the tooth root 35 of each pinion gear 3 (a region on the center O side of the boundary B3 in Fig. 2) is inclined so as to be located on the tooth tip cone TC3 side of the pinion gear 3 rather than the tooth root cone RC3 of the pinion gear 3. This makes it possible to suppress a reduction in the thickness of the inner end (the end on the center O side) of the pinion gear 3 and ensure the strength of the pinion gear 3. The side gear 2 and the pinion gear 3 are formed by generating the tooth profile of one gear using the tooth profile of the other gear while their axis centers are aligned in the meshed state, and they are in a conjugate relationship with each other when meshed.

[0014] 2, the inner end 23i of the tooth tip 23 of each side gear tooth 20 is formed to extend along the inner end 35i of the tooth bottom 35 of the pinion gear 3. That is, the inner end 23i of the tooth tip 23 of each side gear tooth 20 is inclined so as to be located closer to the tooth bottom cone RC2 side than the tooth tip cone TC2 of the side gear 2. Furthermore, the outer end 33o of the tooth tip 33 of each pinion gear tooth 30 is formed to extend along the outer end 25o of the tooth bottom 25 of the side gear 2. That is, the outer end 33o of the tooth tip 33 of each pinion gear tooth 30 is inclined so as to be located closer to the tooth bottom cone RC3 side than the tooth tip cone TC3 of the pinion gear 3.

[0015] 2, if the outer end 25o of the tooth bottom 25 of the side gear 2 is inclined so as to be located closer to the tooth tip cone TC2 than the tooth bottom cone RC2 of the side gear 2, the tooth thickness of the base of each side gear tooth 20 on the outer periphery of the side gear 2 will be reduced, reducing the strength of each side gear tooth 20 and therefore the side gear 2. Therefore, in order to shorten the axial length of the differential gear mechanism 1 in the axial direction of the side gear 2 (drive shaft), it is necessary to suppress the reduction in the strength of each side gear tooth 20, i.e., the side gear 2, while keeping the outer end 25o of the tooth bottom 25 inclined toward the tooth tip 23.

[0016] Furthermore, if the inner end 35i of the tooth bottom 35 of the pinion gear 3 is inclined so as to be located closer to the tooth tip cone TC3 side than the tooth bottom cone RC3 of the pinion gear 3, the tooth thickness of the base of each pinion gear tooth 30 at the inner end (end on the center O side) of the pinion gear 3 will be smaller, reducing the strength of each pinion gear tooth 30 and therefore the pinion gear 3. Therefore, in order to reduce the diameter of the pinion gear 3 and make the differential gear mechanism 1 compact, it is necessary to suppress a reduction in the strength of each pinion gear tooth 30, i.e., the pinion gear 3, while keeping the inner end 35i of the tooth bottom 35 inclined toward the tooth tip 33 side.

[0017] In light of this, the inventors conducted intensive research to compact the differential gear mechanism 1 while ensuring the strength of each side gear 2 and each pinion gear 3, and in the process focused on the reference pressure angle, which is the pressure angle at the pitch point of the side gear tooth 20 (the angle made by a radial line passing through the pitch point and a tangent to the tooth flank (tooth profile)), and the reference pressure angle, which is the pressure angle at the pitch point of the pinion gear tooth 30 (the angle made by a radial line passing through the pitch point and a tangent to the tooth flank (tooth profile)). The inventors then decided to change the reference pressure angle of the side gear teeth 20 and the reference pressure angle of the pinion gear teeth 30 (hereinafter referred to as the "reference pressure angle α"), which coincide with each other, in the differential gear mechanism 1 in the extension direction (hereinafter referred to as the "tooth trace direction") of the tooth trace (the intersection line between the pitch cone PC2 of the side gear 2 and the tooth flank 21 of the side gear teeth 20 and the intersection line between the pitch cone PC3 of the pinion gear 3 and the tooth flank 31 of the pinion gear teeth 30).

[0018] That is, in the differential gear mechanism 1, the reference pressure angle α of each side gear tooth 20 and each pinion gear tooth 30 gradually increases from a middle part M of the tooth trace toward the inner end side (toward the center O) and also gradually increases from the middle part M toward the outer end side (the outer circumferential side of the side gear 2) as shown in Fig. 3. In this embodiment, the middle part M of the tooth trace is a point determined near the midpoint of the tooth trace between the inclined inner end 23i of the tip 23 of the side gear tooth 20 and the inclined outer end 33o of the tip 33 of the pinion gear tooth 30 in the tooth trace direction, i.e., such that the meshing between the side gear tooth 20 and the pinion gear tooth 30 is included in the range S (the range between the two dashed double-dot lines in Fig. 2) defined only by the tip cone TC2 of the side gear 2 and the tip cone TC3 of the pinion gear 3. In this embodiment, the range S is about 40-60% of the meshing range between the side gear teeth 20 and the pinion gear teeth 30 in the tooth trace direction with the middle portion M as the center.

[0019] The intermediate portion M may be the midpoint of the tooth trace. In the example of FIG. 2, the inner end 23i of the tooth tip 23 of the side gear 2 is located closer to the center O than the outer end 33o of the tooth tip 33 of the pinion gear tooth 30 in the tooth trace direction, but this is not limited to this. For example, the inner end 23i of the tooth tip 23 of the side gear 2 may extend to the outer circumferential side (opposite the center O) in the tooth trace direction than the outer end 33o of the tooth tip 33 of the pinion gear tooth 30. In this case, the intermediate portion M can be determined to be included in the above-mentioned range S. Furthermore, the position of the outer peripheral side end of the inner end 23i in the tooth trace direction may coincide with the position of the end of the outer end 33o on the center O side in the tooth trace direction. In this case, the intermediate portion M coincides with the position of the outer peripheral side end of the inner end 23i in the tooth trace direction and the position of the end of the outer end 33o on the center O side in the tooth trace direction.

[0020] Furthermore, in the differential gear mechanism 1, in addition to changing the reference pressure angle α in the tooth trace direction as shown in Fig. 3, the tooth thickness (circular tooth thickness) on the pitch cone PC2 of the side gear 2 is determined so as to become smaller from the middle portion M toward the inner end side (toward the center O) and to become larger from the middle portion M toward the outer end side (the outer periphery side of the side gear 2) as shown by the solid line in Fig. 4, compared to the reference side gear (see the dashed line in Fig. 4). Also, in the differential gear mechanism 1, the tooth thickness (circular tooth thickness) on the pitch cone PC3 of the pinion gear 3 is determined so as to become larger from the middle portion M toward the inner end side and to become smaller from the middle portion M toward the outer end side as shown by the solid line in Fig. 5, compared to the reference pinion gear (see the dashed line in Fig. 5).

[0021] The reference side gear is a straight bevel gear in which the intersection line between the tooth flanks of the side gear teeth and the pitch cone is a straight line passing through the center of the differential gear mechanism, and the reference pressure angle α is constant in the tooth trace direction. In the reference side gear, a cross section of the side gear teeth cut by a spherical surface centered on the center of the differential gear mechanism is enlarged or reduced along the axis of the reference side gear at a similarity ratio according to the distance from the center (radius of the spherical surface). In addition, the reference pinion gear is a straight bevel gear in which the intersection line between the tooth flanks of the pinion gear teeth and the pitch cone is a straight line passing through the center of the differential gear mechanism, and the reference pressure angle α is constant in the tooth trace direction. In the reference pinion gear, a cross section of the pinion gear teeth cut by a spherical surface centered on the center of the differential gear mechanism is enlarged or reduced along the axis of the reference pinion gear at a similarity ratio according to the distance from the center (radius of the spherical surface). The intermediate portion of the tooth trace of the reference side gear and the reference pinion gear is a point determined near the midpoint of the tooth trace so as to be included in the range S between the inclined inner end of the tip of the side gear tooth and the inclined outer end of the tip of the pinion gear tooth in the tooth trace direction. The intermediate portion M of the side gear 2 and the pinion gear 3 coincides with the intermediate portion of the reference side gear and the reference pinion gear.

[0022] As a result, as shown by the solid line in Fig. 6, the tooth thickness (circular tooth thickness) of the root at the outer end 25o (outer end side of the boundary B2) of the tooth bottom 25 of the side gear 2 is larger than that in the case where the reference pressure angle α and the tooth thickness on the pitch cone PC2 are not adjusted (see the dashed line in Fig. 6). Also, as shown by the solid line in Fig. 7, the tooth thickness (circular tooth thickness) of the root at the inner end 35i (inner end side of the boundary B3) of the tooth bottom 35 of the pinion gear 3 is larger than that in the case where the reference pressure angle α and the tooth thickness on the pitch cone PC3 are not adjusted (see the dashed line in Fig. 7).

[0023] Therefore, as shown in Fig. 8, it is possible to sufficiently secure the tooth thickness di2 at the base of the side gear teeth 20 at the inner end (end on the center O side) of the side gear 2, while increasing the tooth thickness do2 at the base of the side gear teeth 20 at the outer periphery of the side gear 2, as shown by the dotted line in Fig. 9. Also, as shown in Fig. 9, it is possible to sufficiently secure the tooth thickness do3 at the base of the pinion gear teeth 30 at the outer end of the pinion gear 3, while increasing the tooth thickness di3 at the base of the pinion gear teeth 30 at the inner end of the pinion gear 3, as shown by the dotted line in Fig. 8. As a result, it is possible to reduce the axial length of the differential gear mechanism 1 in the axial direction of the side gear 2 and reduce the diameter of the pinion gear 3, while satisfactorily securing the strength of the side gear 2 and the pinion gear 3, thereby making the differential gear mechanism 1 compact.

[0024] Incidentally, in the side gear tooth 20 and the pinion gear tooth 30 in which the reference pressure angle α and the tooth thickness on the pitch cones PC2, PC3 are changed in the tooth trace direction, there is a risk of tooth tip pointing occurring in a region where the reference pressure angle α is relatively large, as shown by the dashed line in Fig. 10 (Fig. 10 shows the pinion gear tooth 30 as an example). Also, in the side gear tooth 20 and the pinion gear tooth 30 in which the reference pressure angle α and the tooth thickness on the pitch cones PC2, PC3 are changed in the tooth trace direction, there is a risk of undercutting occurring at the tooth root in a region where the reference pressure angle α is relatively small, as shown by the dashed line in Fig. 11 (Fig. 11 shows the pinion gear tooth 30 as an example).

[0025] Furthermore, the tooth tip pointing and undercutting of the side gear teeth 20 and the pinion gear teeth 30 may occur in any of the first, second, third and fourth regions A1, A2, A3 and A4 in Fig. 12. As shown in Fig. 12, the first region A1 is a region on the inner side of the intermediate portion M (a plane including the intermediate portion M and perpendicular to the tooth tip direction) in the tooth trace direction, and on the tooth tip cone TC2 of the side gear 2 and the tooth root cone RC3 of the pinion gear 3 side from the pitch cones PC2 and PC3 of the side gear 2 and the pinion gear 3 side. The second region A2 is a region on the inner side of the intermediate portion M in the tooth trace direction, and on the tooth root cone RC2 of the side gear 2 and the tooth tip cone TC3 of the pinion gear 3 side from the pitch cones PC2 and PC3.

[0026] The third region A3 is a region on the outer side of the intermediate portion M in the tooth trace direction, and on the side of the tip cone TC2 of the side gear 2 and the side of the root cone RC3 of the pinion gear 3 from the pitch cones PC2, PC3. The fourth region A4 is a region on the inner side of the intermediate portion M in the tooth trace direction, and on the side of the root cone RC2 of the side gear 2 and the side of the tip cone TC3 of the pinion gear 3 from the pitch cones PC2, PC3. If the side gear teeth 20 or the pinion gear teeth 30 are sharpened or undercut in at least any of the first to fourth regions A1-A4, it becomes impossible to ensure a good tooth height and a good mesh ratio of the side gear teeth 20 and the pinion gear teeth 30.

[0027] Taking these factors into consideration, in the differential gear mechanism 1, if, as a result of adjusting the reference pressure angle α and the tooth thickness on the pitch cone PC3 as described above, for example, a pointed tooth tip occurs on the pinion gear tooth 30 in the above-mentioned second region A2 on the inner end side that does not include the inclined outer end portion 33o of the tooth tip 33 of the pinion gear tooth 30, the pressure angle (the angle between a radial line passing through a point on the tooth surface 21 or 31 and the tangent to the tooth surface (tooth profile)) on the tooth flank 21 of each side gear tooth 20 and the tooth flank 31 of each pinion gear tooth 30 is adjusted within the range of the second region A2. In this case, the pressure angle on the tooth flank 31 included in the second region A2 of each pinion gear tooth 30 is adjusted so as to become smaller on the inner end side of the middle portion M in the tooth trace direction, as shown in Figure 13, toward the tooth tip cone TC3 side of the pinion gear 3, compared to the second reference pinion gear (see dashed line in Figure 13).

[0028] The second reference pinion gear is adjusted such that the reference pressure angle α is increased from the middle portion M toward the inner end side and increased from the middle portion M toward the outer end side as shown in FIG. 3. As shown in FIG. 13, the pressure angle on the tooth surface of each pinion gear tooth on the inner end side of the second reference pinion gear is larger than the pressure angle on the tooth surface of the middle portion M. In addition, the adjustment amount δ of the pressure angle of the pinion gear 3 in the second region A2 (hereinafter referred to as the "pressure angle adjustment amount") is set to a negative value that is zero on the pitch cone PC3 and becomes smaller (the absolute value becomes larger) from the pitch cone PC3 toward the tooth tip cone TC3 side of the pinion gear 3 on the inner end side of the middle portion M in the tooth trace direction as shown in FIG. 14. The horizontal axis in FIG. 14 indicates the rotation angle of the pinion gear 3 (similar to FIG. 15).

[0029] Furthermore, for the side gear 2 conjugate with the pinion gear 3, the pressure angle on the tooth flank 21 included in the second region A2 of each side gear tooth 20 is adjusted to be smaller from the pitch cone PC2 of the side gear 2 to the bottom cone RC2 of the side gear 2 on the inner end side of the middle portion M in the tooth trace direction, as compared to the second reference side gear. The second reference side gear is adjusted such that the reference pressure angle α of the above-mentioned reference side gear is larger from the middle portion M to the inner end side and larger from the middle portion M to the outer end side, as shown in Fig. 3. The pressure angle on the tooth flank of each side gear tooth on the inner end side of the second reference side gear is also larger than the pressure angle on the tooth flank of the middle portion M. 14, the pressure angle adjustment amount δ of the side gear 2 in the second region A2 is set to a negative value that is zero on the pitch cone PC2 and becomes smaller (the absolute value becomes larger) on the inner end side of the intermediate portion M in the tooth trace direction from the pitch cone PC2 toward the tooth root cone RC2 of the side gear 2. As a result, it is possible to eliminate the sharpness of the tooth tips of the pinion gear teeth 30 in the second region A2 and to satisfactorily secure the tooth height and the contact ratio of the side gear teeth 20 and the pinion gear teeth 30. The intermediate portions of the tooth traces of the second reference side gear and the second reference pinion gear coincide with the intermediate portions of the reference side gear and the reference pinion gear and the intermediate portion M of the side gear 2 and the pinion gear 3.

[0030] In addition, as a result of adjustment of the reference pressure angle α and the tooth thickness on the pitch cone PC2, for example, if a tooth tip sharpness occurs in the side gear tooth 20 in the third region A3 on the outer end side not including the inclined inner end 23i of the tooth tip 23 of the side gear tooth 20, the pressure angle adjustment amount δ of the side gear 2 and the pinion gear 3 in the third region A3 is set to a negative value that becomes smaller (the absolute value becomes larger) from the pitch cones PC2, PC3 toward the tip cone TC2 of the side gear 2 and the bottom cone RC3 of the pinion gear 3 on the outer end side of the intermediate portion M in the tooth trace direction, as shown in Fig. 14. As a result, the pressure angle on the tooth surface 21 included in the third region A3 of each side gear tooth 20 is adjusted to become smaller from the pitch cone PC2 of the side gear 2 toward the bottom cone RC2 of the side gear 2 on the outer end side of the intermediate portion M in the tooth trace direction, compared to the second reference side gear. Similarly, the pressure angle on the tooth flank 31 included in the third region A3 of each pinion gear tooth 30 is adjusted to become smaller on the outer end side of the intermediate portion M in the tooth trace direction from the pitch cone PC3 of the pinion gear 3 toward the tooth tip cone TC3 of the pinion gear 3, compared to the second reference pinion gear. As a result, it is possible to eliminate the sharpness of the tooth tips of the side gear teeth 20 in the third region A3 and to ensure a good tooth height and mesh ratio of the side gear teeth 20 and the pinion gear teeth 30.

[0031] Furthermore, if, as a result of adjusting the reference pressure angle α and the tooth thickness on the pitch cone PC3, for example, undercutting occurs at the root of the pinion gear tooth 30 in the above-mentioned third region A3 on the outer end side not including the inner end portion 35i of the bottom 35 of the pinion gear 3, the pressure angle adjustment amount δ within the range of the third region A3 becomes zero on the pitch cone PC3 as shown in FIG. 15, and is set to a positive value that becomes larger toward the tip cone TC2 of the side gear 2 and the bottom cone RC3 of the pinion gear 3 on the outer end side of the intermediate portion M in the tooth trace direction from the pitch cones PC2, PC3. As a result, the pressure angle on the tooth surface 31 included in the third region A3 of each pinion gear tooth 30 is adjusted to be larger from the pitch cone PC3 of the pinion gear 3 toward the tooth bottom cone RC3 of the pinion gear 3, as compared to the second reference pinion gear (see the broken line in FIG. 16), on the outer end side of the intermediate portion M in the tooth trace direction. Similarly, the pressure angle on the tooth surface 21 included in the third region A3 of each side gear tooth 20 is adjusted to be larger from the pitch cone PC2 of the side gear 2 toward the tooth tip cone TC2 of the side gear 2, as compared to the second reference side gear, on the outer end side of the intermediate portion M in the tooth trace direction. As a result, it is possible to eliminate undercutting of the root of the pinion gear tooth 30 in the third region A3 and to ensure good tooth height and mesh ratio of the side gear tooth 20 and the pinion gear tooth 30.

[0032] Furthermore, as a result of adjusting the reference pressure angle α and the tooth thickness on the pitch cone PC2, for example, when undercutting occurs at the base of the side gear tooth 20 in the second region A2 on the inner end side not including the inclined outer end 25o of the bottom 25 of the side gear 2, the pressure angle adjustment amount δ in the second region A2 is set to a positive value that increases from the pitch cones PC2, PC3 toward the bottom cone RC2 of the side gear 2 and the tip cone TC3 of the pinion gear 3 on the inner end side of the intermediate portion M in the tooth trace direction, as shown in Fig. 15. As a result, the pressure angle on the tooth surface 21 included in the second region A2 of each side gear tooth 20 is adjusted to increase from the pitch cone PC2 of the side gear 2 toward the bottom cone RC2 of the side gear 2 on the inner end side of the intermediate portion M in the tooth trace direction, compared to the second reference side gear. Similarly, the pressure angle on the tooth flank 31 included in the second region A2 of each pinion gear tooth 30 is adjusted to become larger on the inner end side of the intermediate portion M in the tooth trace direction, compared to the second reference pinion gear, from the pitch cone PC3 of the pinion gear 3 toward the tooth tip cone TC3 of the pinion gear 3. As a result, it is possible to eliminate undercutting of the tooth base of the side gear tooth 20 in the second region A2 and to ensure good tooth heights and contact ratios of the side gear tooth 20 and the pinion gear tooth 30.

[0033] Furthermore, if, as a result of adjusting the reference pressure angle α and the tooth thickness on the pitch cone PC3, for example, a tooth tip sharpness occurs on the pinion gear tooth 30 in the above-mentioned fourth region A4 on the outer end side including the inclined outer end portion 33o of the tooth tip 33 of the pinion gear tooth 30, the pressure angle on the tooth surface 31 included in the fourth region A4 of each pinion gear tooth 30 can be made smaller on the outer end side of the middle portion M in the tooth trace direction, toward the tooth tip cone TC3 of the pinion gear 3, compared to the above-mentioned second reference pinion gear. In addition, the pressure angle on the tooth flank 21 included in the fourth region A4 of each side gear tooth 20 may be made smaller on the outer end side of the intermediate portion M in the tooth trace direction, compared to the second reference side gear, from the pitch cone PC2 of the side gear 2 toward the tooth root cone RC2 of the side gear 2. As a result, it is possible to eliminate the sharpness of the tooth tips of the pinion gear teeth 30 in the fourth region A4 and ensure good tooth heights and contact ratios of the side gear teeth 20 and the pinion gear teeth 30.

[0034] In addition, as a result of adjusting the reference pressure angle α and the tooth thickness on the pitch cone PC2, for example, if a tooth tip sharpness occurs on the side gear tooth 20 in the first region A1 on the inner end side including the inclined inner end 23i of the tooth tip 23 of the side gear tooth 20, the pressure angle on the tooth flank 21 included in the first region A1 of each side gear tooth 20 may be made smaller from the pitch cone PC2 of the side gear 2 toward the tooth tip cone TC2 of the side gear 2, on the inner end side of the intermediate portion M in the tooth trace direction, compared to the second reference side gear. In addition, the pressure angle on the tooth flank 31 included in the first region A1 of each pinion gear tooth 30 may be made smaller from the pitch cone PC3 of the pinion gear 3 toward the tooth root cone RC3 of the pinion gear 3, on the inner end side of the intermediate portion M in the tooth trace direction, compared to the second reference pinion gear. As a result, the tooth tips of the side gear teeth 20 in the first region A1 are not sharpened, and the tooth height and the meshing ratio of the side gear teeth 20 and the pinion gear teeth 30 can be secured satisfactorily.

[0035] Furthermore, if, as a result of adjusting the reference pressure angle α and the tooth thickness on the pitch cone PC2, for example, undercutting occurs at the root of the side gear tooth 20 in the above-mentioned fourth region A4 on the outer end side including the inclined outer end 25o of the bottom 25 of the side gear 2, the pressure angle at the tooth surface 21 included in the fourth region A4 of each side gear tooth 20 can be made larger on the outer end side of the intermediate portion M in the tooth trace direction, toward the bottom cone RC2 of the side gear 2, compared to the above-mentioned second reference side gear. In addition, the pressure angle on the tooth flank 31 included in the fourth region A4 of each pinion gear tooth 30 may be increased from the pitch cone PC3 of the pinion gear 3 toward the tooth tip cone TC3 of the pinion gear 3 on the outer end side of the intermediate portion M in the tooth trace direction, compared to the second reference pinion gear. As a result, it is possible to eliminate undercutting of the root of the side gear tooth 20 in the fourth region A4, and to ensure good tooth heights and contact ratios of the side gear teeth 20 and the pinion gear teeth 30.

[0036] Furthermore, if, as a result of adjusting the reference pressure angle α and the tooth thickness on the pitch cone PC3, for example, undercutting occurs at the root of the pinion gear tooth 30 in the first region A1 on the inner end side including the inner end 35i of the tooth bottom 35 of the pinion gear 3, the pressure angle on the tooth surface 31 included in the first region A1 of each pinion gear tooth 30 can be made larger on the inner end side of the middle portion M in the tooth trace direction, toward the tooth bottom cone RC3 of the pinion gear 3, compared to the second reference pinion gear. In addition, the pressure angle on the tooth flank 21 included in the first region A1 of each side gear tooth 20 may be made larger on the inner end side of the intermediate portion M in the tooth trace direction, compared to the second reference side gear, from the pitch cone PC2 of the side gear 2 toward the tooth tip cone TC2 of the side gear 2. As a result, it is possible to eliminate undercutting of the root of the pinion gear teeth 30 in the first region A1 and ensure good tooth heights and contact ratios of the side gear teeth 20 and the pinion gear teeth 30.

[0037] The intermediate portion M can be arbitrarily determined within the range S (the range between the two dashed double-dot lines in FIG. 2). The intermediate portion M is not limited to a point on the tooth trace, and may be provided with a predetermined length in the tooth trace direction. In the differential gear mechanism 1, the tooth profiles of the side gear teeth 20 and the pinion gear teeth 30 before the adjustment by the pressure angle adjustment amount δ are formed by spherical involute curves, but are not limited thereto. That is, the tooth profiles of the side gear teeth 20 and the pinion gear teeth 30 before the adjustment by the pressure angle adjustment amount δ may be formed by, for example, an octoid curve, a trochoid curve, or the like. In addition, when designing the side gears 2 and the pinion gears 3, the tooth thickness may be adjusted after the adjustment of the reference pressure angle α and the adjustment of the pressure angle by the pressure angle adjustment amount δ.

[0038] As described above, the differential gear mechanism of the present disclosure includes a pair of side gears (2) that are bevel gears each having a plurality of side gear teeth (20), and a plurality of pinion gears (3) that are bevel gears each having a plurality of pinion gear teeth (30) and mesh with the pair of side gears (2). In this differential gear mechanism (1), the outer end (25o) of the tooth bottom (25) of the side gear (2) is inclined so as to be located closer to the tooth tip cone (TC2) of the side gear (2) than the tooth bottom cone (RC2) of the side gear (2), and the tooth tips (2 An inner end (23i) of a tooth root (35) of the pinion gear (3) is inclined so as to be located closer to the tooth root cone (RC2) of the side gear (2) than the tooth tip cone (TC2) of the side gear (2), an inner end (35i) of a tooth root (35) of the pinion gear (3) is inclined so as to be located closer to the tooth tip cone (TC3) of the pinion gear (3) than the tooth root cone (RC3) of the pinion gear (3), and an outer end (33o) of a tooth tip (33) of the pinion gear tooth (30) is located closer to the tooth root cone (RC3) of the pinion gear (3) than the tooth tip cone (TC3) of the pinion gear (3). a reference pressure angle (α) which is an angle between a radial line passing through a pitch point of the side gear tooth (20) and a tangent to a tooth profile, and a reference pressure angle (α) which is an angle between a radial line passing through a pitch point of the pinion gear tooth (30) and a tangent to a tooth profile, increase from a middle portion (M) of a tooth trace included between the inner end portion (23i) of the tooth tip (23) of the side gear tooth (20) and the outer end portion (33o) of the tooth tip (33) of the pinion gear tooth (30) in the tooth trace direction toward the inner end side, and decrease from the middle portion (M) toward the outer end side. a tooth thickness on a pitch cone (PC2) of the side gear (2) becomes smaller from the middle portion (M) toward the inner end side and becomes larger from the middle portion (M) toward the outer end side, compared to a reference side gear in which the reference pressure angle is constant in the tooth trace direction, and a tooth thickness on a pitch cone (PC3) of the pinion gear (3) becomes smaller from the middle portion (M) toward the inner end side and becomes larger from the middle portion (M) toward the outer end side, compared to a reference side gear in which the reference pressure angle is constant in the tooth trace direction,Moreover, compared to a reference pinion gear in which the reference pressure angle is constant in the tooth trace direction, the reference pressure angle becomes larger from the middle portion (M) toward the inner end side and becomes smaller from the middle portion (M) toward the outer end side.

[0039] In the differential gear mechanism of the present disclosure, the outer ends of the tooth bottoms of the side gears, the inner ends of the tooth tips of the side gear teeth, the inner ends of the tooth bottoms of the pinion gears, and the outer ends of the tooth tips of the pinion gear teeth are inclined, so that the thickness of the inner ends of the pinion gears can be ensured and the axial length of the differential gear mechanism in the axial direction of the side gears can be shortened. Also, the reference pressure angles of the side gear teeth and the pinion gear teeth increase from the middle part of the tooth trace toward the inner end and from the middle part toward the outer end. As a result, by making the tooth thickness on the pitch cone of the side gear smaller from the intermediate portion toward the inner end side and larger from the intermediate portion toward the outer end side compared to the reference side gear, it is possible to ensure a sufficient tooth thickness at the root of the side gear teeth at the inner end (end toward the center) of the side gear, while making the tooth thickness at the root of the side gear teeth larger at the outer end (end toward the center) of the side gear, compared to the reference side gear having a constant reference pressure angle in the tooth trace direction. Furthermore, by making the tooth thickness on the pitch cone of the pinion gear larger from the intermediate portion toward the inner end side and smaller from the intermediate portion toward the outer end side compared to the reference pinion gear, it is possible to ensure a sufficient tooth thickness at the root of the pinion gear teeth at the outer end (end toward the outer circumference of the side gear), while making the tooth thickness at the root of the pinion gear teeth larger at the inner end (end toward the center of the differential gear mechanism) of the pinion gear, compared to the reference pinion gear having a constant reference pressure angle in the tooth trace direction. As a result, it is possible to reduce the axial length of the differential gear mechanism in the axial direction of the side gear and the diameter of the pinion gear to make the differential gear mechanism compact while ensuring the strength of the side gear and the pinion gear. The intermediate portion of the tooth trace can be arbitrarily determined between the inclined inner end of the tip of the side gear tooth and the inclined outer end of the tip of the pinion gear tooth in the tooth trace direction, i.e., within a range in which the meshing between the side gear tooth and the pinion gear tooth is determined only by the tooth tip cone of the side gear and the tooth tip cone of the pinion gear, and may be a point on the tooth trace or may be secured by a predetermined length in the tooth trace direction.

[0040] Further, a first region (A1) located on the inner end side of the intermediate portion (M) in the tooth trace direction and on the side of the tip cone (TC2) of the side gear (2) and the root cone (RC3) of the pinion gear (3) on the inner end side of the intermediate portion (M) in the tooth trace direction and on the side of the tip cone (TC2) of the side gear (2) and the root cone (RC3) of the pinion gear (3) on the pitch cones (PC2, PC3) of the side gear (2) and the pinion gear (3); and a second region (A2) on the tip cone (TC3) side of the pinion gear (3), a third region (A3) on the outer end side of the intermediate portion (M) in the tooth trace direction and on the tip cone (TC2) of the side gear (2) and the root cone (RC3) side of the pinion gear (3) on the pitch cone (PC2, PC3), and a fourth region (A4) on the inner end side of the intermediate portion (M) in the tooth trace direction and on the root cone (RC3) side of the side gear (2) on the pitch cone (PC2, PC3). In at least one of the pitch cone (RC2) and a fourth region (A4) on the tip cone (TC3) side of the pinion gear (3), the pressure angle on the tooth flank (21) of the side gear tooth (20) is larger from the pitch cone (PC2, PC3) to the root cone (RC2) side of the side gear (2) or the tooth tip, compared to a second reference side gear in which the reference pressure angle increases from the middle portion to the inner end side and also increases from the middle portion to the outer end side. The pressure angle on the tooth surface (31) of the pinion gear tooth (30) may be smaller from the pitch cone (PC2, PC3) toward the tip cone (TC3) side or the root cone (RC3) side of the pinion gear (3), compared to a second reference pinion gear in which the reference pressure angle becomes larger from the middle portion toward the inner end side and becomes larger from the middle portion toward the outer end side.

[0041] This makes it possible to eliminate sharpness at the tips of the side gear teeth or the pinion gear teeth and ensure a good tooth height and meshing ratio for the side gear teeth and the pinion gear teeth.

[0042] Further, a first region (A1) located on the inner end side of the intermediate portion (M) in the tooth trace direction and on the side of the tip cone (TC2) of the side gear (2) and the root cone (RC3) of the pinion gear (3) on the inner end side of the intermediate portion (M) in the tooth trace direction and on the side of the tip cone (TC2) of the side gear (2) and the root cone (RC3) of the pinion gear (3) on the pitch cones (PC2, PC3) of the side gear (2) and the pinion gear (3); and a second region (A2) on the tip cone (TC3) side of the pinion gear (3), a third region (A3) on the outer end side of the intermediate portion (M) in the tooth trace direction and on the tip cone (TC2) of the side gear (2) and the root cone (RC3) side of the pinion gear (3) on the pitch cone (PC2, PC3), and a fourth region (A4) on the inner end side of the intermediate portion (M) in the tooth trace direction and on the root cone (RC3) side of the side gear (2) on the pitch cone (PC2, PC3). In at least one of the pitch cone (RC2) and a fourth region (A4) on the tip cone (TC3) side of the pinion gear (3), the pressure angle on the tooth flank (21) of the side gear tooth (20) is larger from the pitch cone (PC2, PC3) to the root cone (RC2) side of the side gear (2) or the tooth tip, compared to a second reference side gear in which the reference pressure angle increases from the middle portion to the inner end side and also increases from the middle portion to the outer end side. The pressure angle on the tooth surface (21) of the pinion gear tooth (30) may be larger from the pitch cone (PC2, PC3) toward the tip cone (TC3) side or the root cone (RC3) side of the pinion gear (3), compared to a second reference pinion gear in which the reference pressure angle is larger from the middle portion toward the inner end side and is larger from the middle portion toward the outer end side.

[0043] This makes it possible to eliminate undercutting of the bases of the side gear teeth or pinion gear teeth, thereby ensuring a good tooth height and meshing ratio for the side gear teeth and pinion gear teeth.

[0044] The present disclosure relates to a method for designing a differential gear mechanism, the method comprising: designing a differential gear mechanism including a pair of side gears (2), each of which is a bevel gear having a plurality of side gear teeth (20); and a plurality of pinion gears (3), each of which is a bevel gear having a plurality of pinion gear teeth (30) and meshing with the pair of side gears (2), wherein an outer end (25o) of a tooth root (25) of the side gear (2) is inclined so as to be located closer to a tooth tip cone (TC2) of the side gear (2) than a tooth root cone (RC2) of the side gear (2), and an inner end (23i) of a tooth tip (23) of the side gear teeth (20) is inclined so as to be located closer to a tooth tip cone (TC2) of the side gear (2), a differential gear mechanism (2) inclined so as to be located closer to the root cone (RC2) of the side gear (2) than the tip cone (TC2) of the side gear (2), an inner end (35i) of a tooth bottom (35) of the pinion gear (3) inclined so as to be located closer to the tip cone (TC3) of the pinion gear (3) than the root cone (RC3) of the pinion gear (3), and an outer end (33o) of a tooth tip (33) of the pinion gear tooth (30) inclined so as to be located closer to the root cone (RC3) of the pinion gear (3) than the tip cone (TC3) of the pinion gear (3). 1), wherein a reference pressure angle (α) which is an angle between a radial line passing through a pitch point of the side gear tooth (20) and a tangent to a tooth profile and a reference pressure angle (α) which is an angle between a radial line passing through a pitch point of the pinion gear tooth (30) and a tangent to a tooth profile are increased from a middle portion (M) of a tooth trace included between the inner end portion (23i) of the tooth tip (23) of the side gear tooth (20) and the outer end portion (33o) of the tooth tip (33) of the pinion gear tooth (30) in the tooth trace direction toward the inner end side, and the reference pressure angle (α) which is an angle between a radial line passing through a pitch point of the side gear tooth (20) and a tangent to a tooth profile is increased from the middle portion (M) toward the outer end side a tooth thickness on a pitch cone (PC2) of the side gear (2) is increased as the line of intersection between the tooth flanks of the side gear teeth and the pitch cone is a straight line passing through the center of the differential gear mechanism, and the reference pressure angle is decreased from the middle portion (M) to the inner end side and increased from the middle portion (M) to the outer end side, compared to a reference side gear in which the reference pressure angle is constant in the tooth trace direction; and a tooth thickness on a pitch cone (PC3) of the pinion gear (3) is increased as the line of intersection between the tooth flanks of the pinion gear teeth and the pitch cone is a straight line passing through the center,Moreover, compared to a reference pinion gear in which the reference pressure angle is constant in the tooth trace direction, the reference pressure angle is made larger from the middle portion (M) toward the inner end side and is made smaller from the middle portion (M) toward the outer end side.

[0045] According to this method, it is possible to reduce the axial length of the differential gear mechanism in the axial direction of the side gears and the diameter of the pinion gears while ensuring the strength of the side gears and pinion gears, thereby making the differential gear mechanism more compact.

[0046] Further, a first region (A1) is disposed on the inner end side of the intermediate portion (M) in the tooth trace direction and on the side of the tip cone (TC2) of the side gear (2) and the root cone (RC3) of the pinion gear (3) on the inner end side of the intermediate portion (M) in the tooth trace direction and on the side of the tip cone (TC2) of the side gear (2) and the root cone (RC3) of the pinion gear (3) on the pitch cones (PC2, PC3) of the side gear (2) and the pinion gear (3). ), a second region (A2) on the tip cone (TC3) side of the pinion gear (3), a third region (A3) on the outer end side of the intermediate portion (M) in the tooth trace direction and on the tip cone (TC2) of the side gear (2) and the root cone (RC3) side of the pinion gear (3) on the pitch cones (PC2, PC3), and a fourth region (A4) on the inner end side of the intermediate portion (M) in the tooth trace direction and on the pitch cones (PC2, PC3) of the side gear (2). In at least one of the root cone (RC2) and a fourth region (A4) on the tip cone (TC3) side of the pinion gear (3), the pressure angle on the tooth surface (21) of the side gear tooth (20) is set to be larger from the pitch cone (PC2, PC3) to the root cone (RC2) side of the side gear (2) or a fourth region (A4) on the tip cone (TC3) side of the pinion gear (3) than that of a second reference side gear in which the reference pressure angle increases from the middle portion to the inner end side and increases from the middle portion to the outer end side. may be smaller toward the tip cone (TC2) side, and the pressure angle on the tooth flank (31) of the pinion gear tooth (30) may be smaller from the pitch cone (PC2, PC3) toward the tip cone (TC3) side or the root cone (RC3) side of the pinion gear (3), compared to a second reference pinion gear in which the reference pressure angle becomes larger toward the inner end side from the middle portion and becomes larger toward the outer end side from the middle portion.

[0047] Further, a first region (A1) is provided which is located on the inner end side of the intermediate portion (M) in the tooth trace direction and on the side of the tip cone (TC2) of the side gear (2) and the root cone (RC3) of the pinion gear (3) relative to the pitch cones (PC2, PC3) of the side gear (2) and the pinion gear (3); and a second region (A2) is provided which is located on the inner end side of the intermediate portion (M) in the tooth trace direction and on the side of the root cone (RC2) of the side gear (2) relative to the pitch cones (PC2, PC3). ), a second region (A2) on the tip cone (TC3) side of the pinion gear (3), a third region (A3) on the outer end side of the intermediate portion (M) in the tooth trace direction and on the tip cone (TC2) of the side gear (2) and the root cone (RC3) side of the pinion gear (3) on the pitch cones (PC2, PC3), and a fourth region (A4) on the inner end side of the intermediate portion (M) in the tooth trace direction and on the pitch cones (PC2, PC3) of the side gear (2). In at least one of the root cone (RC2) and a fourth region (A4) on the tip cone (TC3) side of the pinion gear (3), the pressure angle on the tooth surface (21) of the side gear tooth (20) is set to be larger from the pitch cone (PC2, PC3) to the root cone (RC2) side of the side gear (2) or a fourth region (A4) on the tip cone (TC3) side of the pinion gear (3) than that of a second reference side gear in which the reference pressure angle increases from the middle portion to the inner end side and increases from the middle portion to the outer end side. may be increased toward the tip cone (TC2) side, and the pressure angle on the tooth flank (21) of the pinion gear tooth (30) may be increased from the pitch cone (PC2, PC3) toward the tip cone (TC3) side or the root cone (RC3) side of the pinion gear (3), compared to a second reference pinion gear in which the reference pressure angle increases from the middle portion to the inner end side and also increases from the middle portion to the outer end side.

[0048] The present disclosure is not limited to the above embodiment, and various modifications can be made within the scope of the present disclosure. Furthermore, the above embodiment is merely a specific form of the invention described in the Summary of the Invention, and does not limit the elements of the invention described in the Summary of the Invention. [Industrial Applicability]

[0049] The invention of the present disclosure can be used in the manufacturing industry of differential gear mechanisms including a pair of side gears and a plurality of pinion gears meshing with the pair of side gears. [Explanation of symbols]

[0050] 1 differential gear mechanism, 2 side gear, 20 side gear teeth, 21 tooth flank, 23 tooth tip, 23i inner end, 25 tooth root, 25o outer end, 3 pinion gear, 30 pinion gear teeth, 31 tooth flank, 33 tooth tip, 33o outer end, 35 tooth root, 35i inner end, di2,di3,do2,do3 tooth thickness, M intermediate portion, PC2,PC3 pitch cone, RC2,RC3 root cone, TC2,TC3 tip cone.

Claims

1. A differential gear mechanism including a pair of side gears, each of which is a bevel gear having a plurality of side gear teeth, and a plurality of pinion gears, each of which is a bevel gear having a plurality of pinion gear teeth, meshing with the pair of side gears, an outer end of a tooth bottom of the side gear is inclined so as to be located closer to a tooth tip cone of the side gear than a tooth bottom cone of the side gear; an inner end of a tooth tip of the side gear tooth is inclined so as to be located closer to the tooth root cone of the side gear than the tooth tip cone of the side gear; an inner end portion of a tooth bottom of the pinion gear is inclined so as to be located closer to a tooth tip cone side of the pinion gear than a tooth bottom cone of the pinion gear; an outer end of a tip of the pinion gear tooth is inclined so as to be located closer to the root cone of the pinion gear than the tip cone of the pinion gear; a reference pressure angle, which is the angle between a radial line passing through a pitch point of the side gear tooth and a tangent to a tooth profile, and a reference pressure angle, which is the angle between a radial line passing through a pitch point of the pinion gear tooth and a tangent to a tooth profile, become larger from a middle portion of a tooth trace included between the inner end portion of the tip of the side gear tooth and the outer end portion of the tip of the pinion gear tooth in a tooth trace direction toward the inner end side, and also become larger from the middle portion toward the outer end side, a tooth thickness on the pitch cone of the side gear becomes smaller from the intermediate portion to the inner end side and becomes larger from the intermediate portion to the outer end side, compared to a reference side gear in which an intersection line between the tooth flanks of the side gear teeth and the pitch cone is a straight line passing through the center of the differential gear mechanism and the reference pressure angle is constant in the tooth trace direction, and a tooth thickness on the pitch cone of the pinion gear becomes larger from the intermediate portion to the inner end side and becomes smaller from the intermediate portion to the outer end side, compared to a reference pinion gear in which an intersection line between the tooth flanks of the pinion gear teeth and the pitch cone is a straight line passing through the center and the reference pressure angle is constant in the tooth trace direction.

2. 2. The differential gear mechanism according to claim 1, a first region located on the inner end side of the intermediate portion in the tooth trace direction and on the side of the tip cone of the side gear and the side of the root cone of the pinion gear relative to the pitch cone of the side gear and the pinion gear; a second region located on the inner end side of the intermediate portion in the tooth trace direction and on the side of the root cone of the side gear and the side of the root cone of the pinion gear relative to the pitch cone; a third region located on the outer end side of the intermediate portion in the tooth trace direction and on the side of the tip cone of the side gear and the side of the root cone of the pinion gear relative to the pitch cone; and a fourth region on the side of the first reference side gear, the pressure angle on the tooth flank of the side gear tooth becomes smaller from the pitch cone to the root cone side or the tip cone side of the side gear, compared to a second reference side gear in which the reference pressure angle becomes larger from the middle portion to the inner end side and also becomes larger from the middle portion to the outer end side, and the pressure angle on the tooth flank of the pinion gear tooth becomes smaller from the pitch cone to the tip cone side or the root cone side of the pinion gear, compared to a second reference pinion gear in which the reference pressure angle becomes larger from the middle portion to the inner end side and also becomes larger from the middle portion to the outer end side.

3. 2. The differential gear mechanism according to claim 1, a first region located on the inner end side of the intermediate portion in the tooth trace direction and on the side of the tip cone of the side gear and the side of the root cone of the pinion gear relative to the pitch cone of the side gear and the pinion gear; a second region located on the inner end side of the intermediate portion in the tooth trace direction and on the side of the root cone of the side gear and the side of the root cone of the pinion gear relative to the pitch cone; a third region located on the outer end side of the intermediate portion in the tooth trace direction and on the side of the tip cone of the side gear and the side of the root cone of the pinion gear relative to the pitch cone; and a fourth region on the side of the first reference side gear, the pressure angle on the tooth flank of the side gear tooth becomes larger as it moves from the pitch cone to the root cone side or the tip cone side of the side gear, compared to a second reference side gear in which the reference pressure angle becomes larger as it moves from the middle portion to the inner end side and also becomes larger as it moves from the middle portion to the outer end side, and the pressure angle on the tooth flank of the pinion gear tooth becomes larger as it moves from the pitch cone to the tip cone side or the root cone side of the pinion gear, compared to a second reference pinion gear in which the reference pressure angle becomes larger as it moves from the middle portion to the inner end side and also becomes larger as it moves from the middle portion to the outer end side.

4. A method for designing a differential gear mechanism including a pair of side gears, each of which is a bevel gear having a plurality of side gear teeth, and a plurality of pinion gears, each of which is a bevel gear having a plurality of pinion gear teeth, meshing with the pair of side gears, wherein an outer end of a bottom of the side gears is inclined so as to be located closer to the tip cone of the side gear than the root cone of the side gear, an inner end of a tip of the side gear teeth is inclined so as to be located closer to the root cone of the side gear than the tip cone of the side gear, an inner end of a bottom of the pinion gear is inclined so as to be located closer to the tip cone of the pinion gear than the root cone of the pinion gear, and an outer end of a tip of the pinion gear teeth is inclined so as to be located closer to the root cone of the pinion gear than the tip cone of the pinion gear, a reference pressure angle, which is an angle between a radius line passing through a pitch point of the side gear tooth and a tangent to a tooth profile, and a reference pressure angle, which is an angle between a radius line passing through a pitch point of the pinion gear tooth and a tangent to a tooth profile, are increased from a middle portion of a tooth trace included between the inner end of the tooth tip of the side gear tooth and the outer end of the tooth tip of the pinion gear tooth in a tooth trace direction toward an inner end side, and also increased from the middle portion toward an outer end side, a reference side gear in which an intersection line between a tooth flank of a side gear tooth and the pitch cone is a straight line passing through the center of the differential gear mechanism and the reference pressure angle is constant in the tooth trace direction, the tooth thickness of the side gear being smaller from the intermediate portion to the inner end side and larger from the intermediate portion to the outer end side, and the tooth thickness of the pinion gear being larger from the intermediate portion to the inner end side and smaller from the intermediate portion to the outer end side, the tooth thickness of the pinion gear being larger from the intermediate portion to the inner end side and smaller from the intermediate portion to the outer end side, the tooth thickness of the pinion gear being larger from the intermediate portion to the inner end side and smaller from the intermediate portion to the outer end side, the tooth thickness of the pinion gear being larger from the intermediate portion to the inner end side and smaller from the intermediate portion to the outer end side, the tooth thickness of the pinion gear being larger from the intermediate portion to the inner end side

5. 5. The method for designing a differential gear mechanism according to claim 4, a first region on the inner end side of the intermediate portion in the tooth trace direction and on the side of the tip cone of the side gear and the tooth root cone of the pinion gear from the pitch cone of the side gear and the pinion gear; a second region on the inner end side of the intermediate portion in the tooth trace direction and on the side of the root cone of the side gear and the tooth tip cone of the pinion gear from the pitch cone; a third region on the outer end side of the intermediate portion in the tooth trace direction and on the side of the tip cone of the side gear and the tooth root cone of the pinion gear from the pitch cone; a pressure angle on the tooth flank of the side gear teeth being smaller from the pitch cone toward the root cone side or the tip cone side of the side gear, in at least one of a first region and a fourth region, compared to a second reference side gear in which the reference pressure angle is larger from the middle portion toward the inner end side and also larger from the middle portion toward the outer end side, and a pressure angle on the tooth flank of the pinion gear teeth being smaller from the pitch cone toward the tip cone side or the root cone side of the pinion gear, compared to a second reference pinion gear in which the reference pressure angle is larger from the middle portion toward the inner end side and also larger from the middle portion toward the outer end side.

6. 5. The method for designing a differential gear mechanism according to claim 4, a first region on the inner end side of the intermediate portion in the tooth trace direction and on the side of the tip cone of the side gear and the tooth root cone of the pinion gear from the pitch cone of the side gear and the pinion gear; a second region on the inner end side of the intermediate portion in the tooth trace direction and on the side of the root cone of the side gear and the tooth tip cone of the pinion gear from the pitch cone; a third region on the outer end side of the intermediate portion in the tooth trace direction and on the side of the tip cone of the side gear and the tooth root cone of the pinion gear from the pitch cone; a pressure angle on the tooth flank of the side gear teeth is made larger from the pitch cone toward the root cone side or the tip cone side of the side gear, in at least one of a first region and a fourth region, compared to a second reference side gear in which the reference pressure angle is larger from the middle portion toward the inner end side and also is larger from the middle portion toward the outer end side, and a pressure angle on the tooth flank of the pinion gear teeth is made larger from the pitch cone toward the tip cone side or the root cone side of the pinion gear, compared to a second reference pinion gear in which the reference pressure angle is larger from the middle portion toward the inner end side and also is larger from the middle portion toward the outer end side.

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