WO2025033241A1 - Differential gear mechanism and method for designing same - Google Patents

Abstract

In a differential gear mechanism according to the present disclosure, 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 portion of the tooth trace toward the inner end side and also increase from the intermediate portion toward the outer end side. The tooth thickness on a pitch cone of the side gear decreases from the intermediate portion of the tooth trace toward the inner end side and increases from the intermediate portion toward the outer end side as compared to a reference side gear. The tooth thickness on a pitch cone of the pinion gear increases from the intermediate portion of the tooth trace toward the inner end side and decreases from the intermediate portion toward the outer end side as compared to a reference pinion gear.

Description

Differential gear mechanism and design method thereof

This disclosure relates to a differential gear mechanism including a pair of side gears and multiple pinion gears that mesh with the pair of side gears, and a method for designing the same.

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 toward the center 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 extends along the inner end of the tooth bottom of the pinion gear.

　Also, a differential mechanism is known that includes a pinion shaft fixed to a case, a pinion gear that is a bevel gear supported rotatably by the pinion shaft, and a pair of side gears that are bevel gears that mesh with the pinion gear (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 positioned closer to the tooth tip cone than the tooth bottom cone of the side gear. Also, the outer end of the tooth tip of the pinion gear teeth of the pinion gear is inclined so as to be positioned closer to the tooth bottom cone than the tooth tip cone of the pinion gear, and extends along the outer end of the tooth bottom of the side gear.

JP 2005-048903 A JP 2014-185666 A

However, as described in Patent Document 1, if 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 pinion gear tooth root at the inner end of the pinion gear (the end toward the center 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 compact in size while ensuring the strength of the pinion gear. Also, as described in Patent Document 2, if 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 gear tooth root 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.

The primary objective of this disclosure is to provide a differential gear mechanism that includes a pair of side gears and multiple pinion gears that mesh with the pair of side gears, and to provide a compact differential gear mechanism while ensuring sufficient strength of the side gears and pinion gears.

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 a bevel gear having a plurality of pinion gear teeth, which mesh with the pair of side gears, in which the outer ends of the tooth bottoms of the side gears are inclined so as to be positioned closer to the tooth tip cone of the side gear than the tooth bottom cone of the side gear, and the inner ends of the tooth tips of the side gear teeth are inclined so as to be positioned closer to the tooth tip cone of the side gear than the tooth tip cone of the side gear. a reference pressure angle that is an angle between a radius line passing through a pitch point of the side gear tooth and a tangent to the 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 on the side of the tooth tip cone of the pinion gear relative to 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 on the side of the tooth bottom cone of the pinion gear relative to the tooth tip cone of the pinion gear, A certain reference pressure angle increases from the middle part of the 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 the tooth trace direction toward the inner end side and also increases from the middle part toward the outer end side, the tooth thickness on the pitch cone of the side gear decreases from the middle part toward the inner end side and increases from the middle part toward the outer end side compared to a reference side gear in which the intersection line between the tooth surface 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 trace direction, and the tooth thickness on the pitch cone of the pinion gear increases from the middle part toward the inner end side and also decreases from the middle part toward the outer end side compared to a reference pinion gear in which the intersection line between the tooth surface 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.

Furthermore, the design method of the differential gear mechanism disclosed herein includes 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, in which the outer ends of the tooth bottoms of the side gears are 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 the inner ends of the tooth tips of the side gear teeth are inclined so as to be 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 bottom inclined 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 inclined 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 with a tangent, is increased from a middle portion of a tooth trace 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 the inner end side and 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 surface 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 trace direction. Compared to a standard pinion gear, the tooth thickness on the pitch cone of the pinion gear is smaller from the middle portion to the inner end side and larger from the middle portion to the outer end side, and the intersection line between the tooth surface 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, compared to a standard pinion gear, the tooth thickness on the pitch cone of the pinion gear is larger from the middle portion to the inner end side and smaller from the middle portion to the outer end side.

FIG. 1 is a schematic configuration diagram showing a differential gear mechanism according to the present disclosure. FIG. 2 is a partial cross-sectional view showing a differential gear mechanism of the present disclosure. 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. 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. 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. 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. 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. FIG. 2 is an enlarged view showing a main portion of the differential gear mechanism of the present disclosure. FIG. 2 is an enlarged view showing a main portion of the differential gear mechanism of the present disclosure. 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. 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. 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. 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. 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. 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. 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.

Next, the form for implementing the disclosed invention will be explained with reference to the drawings.

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) that mesh 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 into one of a corresponding number 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.

Each side gear 2 is a bevel gear, and includes a plurality of side gear teeth 20 formed to extend radially from the center O of the differential gear mechanism 1 through which the axes of each side gear 2 and each pinion gear 3 pass, as shown in Figs. 1 and 2, and a plurality of tooth roots 25 located between adjacent side gear teeth 20. As shown in Fig. 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. In this embodiment, the outer end 25o of the tooth root 25 of each side gear 2 (the area 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.

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, the inner end 35i of the tooth root 35 of each pinion gear 3 (the area 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 in a conjugate relationship when meshed, with the tooth profile of one gear being generated using the tooth profile of the other gear, with their axes aligned in the meshed position.

Furthermore, 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, as shown in FIG. 2. 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, as shown in FIG. 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.

Here, as shown in FIG. 2, if the outer end 25o of the tooth bottom 25 of the side gear 2 is inclined so that it is positioned 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 smaller, and the strength of each side gear tooth 20 and therefore the side gear 2 will decrease. 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 decrease in 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.

Furthermore, if the inner end 35i of the tooth root 35 of the pinion gear 3 is inclined so as to be located closer to the tooth tip cone TC3 than the tooth root 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, and the strength of each pinion gear tooth 30 and therefore the pinion gear 3 will decrease. 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 the decrease in strength of each pinion gear tooth 30, i.e., the pinion gear 3, while keeping the inner end 35i of the tooth root 35 inclined toward the tooth tip 33.

In light of this, the inventors conducted extensive research to compact the differential gear mechanism 1 while ensuring good 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 that 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 that pitch point and a tangent to the tooth flank (tooth profile)). The inventors 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 surface 21 of the side gear teeth 20, and the intersection line between the pitch cone PC3 of the pinion gear 3 and the tooth surface 31 of the pinion gear teeth 30).

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 the middle part M of the tooth trace toward the inner end side (toward the center O) as shown in FIG. 3, and also gradually increases from the middle part M toward the outer end side (the outer periphery side of the side gear 2). 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 tooth tip 23 of the side gear tooth 20 and the inclined outer end 33o of the tooth tip 33 of the pinion gear tooth 30 in the tooth trace direction, i.e., a point determined near the midpoint of the tooth trace so that the meshing between the side gear tooth 20 and the pinion gear tooth 30 is included within the range S (the range between the two dashed double-dot lines in FIG. 2) defined only by the tooth tip cone TC2 of the side gear 2 and the tooth tip cone TC3 of the pinion gear 3. In this embodiment, range S is approximately 40-60% of the meshing range between the side gear teeth 20 and the pinion gear teeth 30 in the tooth trace direction, centered on the middle part M.

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 periphery 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 range S. Furthermore, the position of the outer peripheral 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 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.

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 (arc tooth thickness) on the pitch cone PC2 of the side gear 2 is set to be smaller from the middle part M toward the inner end side (toward the center O) and larger from the middle part M toward the outer end side (the outer periphery 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 (arc tooth thickness) on the pitch cone PC3 of the pinion gear 3 is set to be larger from the middle part M toward the inner end side and smaller from the middle part 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).

The reference side gear is a straight bevel gear in which the intersection between the tooth surface 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 α is constant in the tooth trace direction. In the reference side gear, a cross section of the side gear tooth cut with 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 between the tooth surface of the pinion gear tooth 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 tooth cut with 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 middle part 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 middle part M of the side gear 2 and the pinion gear 3 coincides with the middle part of the reference side gear and the reference pinion gear.

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

Therefore, as shown in FIG. 8, it is possible to sufficiently secure the tooth thickness di2 of the tooth root 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 of the tooth root 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 of the tooth root of the pinion gear teeth 30 at the outer end of the pinion gear 3, while increasing the tooth thickness di3 of the tooth root 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 ensuring the strength of the side gear 2 and the pinion gear 3, thereby making the differential gear mechanism 1 compact.

In the side gear teeth 20 and pinion gear teeth 30 in which the reference pressure angle α and the tooth thickness on the pitch cones PC2 and PC3 are changed in the tooth trace direction, there is a risk of tooth tip sharpening occurring in the 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). In addition, in the side gear teeth 20 and pinion gear teeth 30 in which the reference pressure angle α and the tooth thickness on the pitch cones PC2 and PC3 are changed in the tooth trace direction, there is a risk of undercutting occurring at the tooth root in the 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).

Furthermore, the tooth tips of the side gear teeth 20 and the pinion gear teeth 30 may be sharpened or undercut 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 located 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 side of the tooth tip cone TC2 of the side gear 2 and the tooth root cone RC3 of the pinion gear 3, and on the side of the pitch cones PC2 and PC3 of the side gear 2 and the pinion gear 3, respectively. The second region A2 is a region located on the inner side of the intermediate portion M in the tooth trace direction, and on the side of the tooth root cone RC2 of the side gear 2 and the tooth tip cone TC3 of the pinion gear 3, and on the side of the pitch cones PC2 and PC3 of the pinion gear 3, respectively.

The third region A3 is the region on the outer side of the intermediate portion M in the tooth trace direction, and on the tooth tip cone TC2 side of the side gear 2 and the tooth root cone TC3 side of the pinion gear 3 from the pitch cones PC2, PC3. The fourth region A4 is the 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 from the pitch cones PC2, PC3. If the tooth tips of the side gear teeth 20 or the pinion gear teeth 30 become pointed or undercut in at least any of the first to fourth regions A1-A4, it will be impossible to ensure a good tooth height or mesh ratio for the side gear teeth 20 and the pinion gear teeth 30.

In light of this, 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 sharp 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 surface 21 of each side gear tooth 20 and the tooth surface 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 surface 31 included in the second region A2 of each pinion gear tooth 30 is adjusted so as to become smaller from the pitch cone PC3 of the pinion gear 3 toward the tooth tip cone TC3 of the pinion gear 3, as shown in FIG. 13, on the inner end side of the middle part M in the tooth trace direction, compared to the second reference pinion gear (see the dashed line in FIG. 13).

The second reference pinion gear is adjusted such that the reference pressure angle α is larger from the middle part M toward the inner end side as shown in FIG. 3, and is larger from the middle part M toward the outer end side. 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 part 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 as shown in FIG. 14, 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 part M in the tooth trace direction. The horizontal axis in FIG. 14 indicates the rotation angle of the pinion gear 3 (similar to FIG. 15).

Furthermore, for the side gear 2 which is in a conjugate relationship 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 on the inner end side of the intermediate portion M in the tooth trace direction as it moves from the pitch cone PC2 of the side gear 2 to the bottom cone RC2 side of the side gear 2, compared to the second reference side gear. The second reference side gear is adjusted with respect to the above-mentioned reference side gear such that the reference pressure angle α is larger as it moves from the intermediate portion M to the inner end side and also larger as it moves from the intermediate portion M to the outer end side, as shown in Figure 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 intermediate portion M. In addition, as shown in FIG. 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) from the pitch cone PC2 toward the bottom cone RC2 of the side gear 2 on the inner end side of the middle part M in the tooth trace direction. 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 ensure a good tooth height and mesh ratio of the side gear teeth 20 and the pinion gear teeth 30. Note that the middle part of the tooth trace of the second reference side gear and the second reference pinion gear coincides with the middle part of the reference side gear and the reference pinion gear and the middle part M of the side gear 2 and the pinion gear 3.

Furthermore, if, as a result of adjusting the reference pressure angle α and the tooth thickness on the pitch cone PC2, for example, a tooth tip sharpness occurs on the side gear tooth 20 in the above-mentioned third region A3 on the outer end side that does not include 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 pinion gear 3 in the third region A3 is set to a negative value that becomes smaller (the absolute value becomes larger) on the outer end side of the middle portion M in the tooth trace direction, as shown in Figure 14, from the pitch cones PC2, PC3 toward the tooth tip cone TC2 of the side gear 2 and the tooth root cone RC3 of the pinion gear 3. As a result, the pressure angle of the tooth surface 21 included in the third region A3 of each side gear tooth 20 is adjusted to be smaller from the pitch cone PC2 of the side gear 2 toward the tooth 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 of the tooth surface 31 included in the third region A3 of each pinion gear tooth 30 is adjusted to be smaller 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, the tooth tip sharpness of the side gear tooth 20 in the third region A3 is eliminated, and the tooth height and mesh ratio of the side gear tooth 20 and the pinion gear tooth 30 can be secured favorably.

Furthermore, as a result of adjusting the reference pressure angle α and the tooth thickness on the pitch cone PC3, for example, if 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 35i of the tooth 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 Figure 15, and is set to a positive value that becomes larger toward the outer end side of the middle portion M in the tooth trace direction from the pitch cones PC2, PC3 toward the tooth tip cone TC2 of the side gear 2 and the tooth bottom cone RC3 of the pinion gear 3. 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 shown in FIG. 16, on the outer end side of the intermediate portion M in the tooth trace direction, compared to the second reference pinion gear (see the broken line in FIG. 16). 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 shown in FIG. 16, on the outer end side of the intermediate portion M in the tooth trace direction, compared to the second reference side gear. As a result, it is possible to eliminate the undercutting of the root of the pinion gear tooth 30 in the third region A3 and ensure a good tooth height and mesh ratio of the side gear tooth 20 and the pinion gear tooth 30.

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 tooth 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 tooth bottom cone RC2 of the side gear 2 and the tooth 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 Figure 15. As a result, the pressure angle at 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 tooth 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 surface 31 included in the second region A2 of each pinion gear tooth 30 is adjusted to be larger on the inner end side of the middle part 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 teeth 20 in the second region A2 and ensure good tooth height and mesh ratio of the side gear teeth 20 and the pinion gear teeth 30.

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 intermediate 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 of the tooth surface 21 included in the fourth region A4 of each side gear tooth 20 can be made smaller on the outer end side of the intermediate portion M in the tooth trace direction, from the pitch cone PC2 of the side gear 2 toward the bottom cone RC2 of the side gear 2, compared to the second reference side gear. As a result, the tooth tips of the pinion gear teeth 30 in the fourth region A4 are eliminated, and the tooth height and mesh ratio of the side gear teeth 20 and the pinion gear teeth 30 can be secured satisfactorily.

Furthermore, if, as a result of adjusting the reference pressure angle α and the tooth thickness on the pitch cone PC2, for example, 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 surface 21 included in the first region A1 of each side gear tooth 20 can be made smaller on the inner end side of the middle portion M in the tooth trace direction, toward the tooth tip cone TC2 of the side gear 2, compared to the second reference side gear. In addition, the pressure angle of the tooth surface 31 included in the first region A1 of each pinion gear tooth 30 can be made smaller from the pitch cone PC3 of the pinion gear 3 toward the bottom 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 eliminated, and it is possible to ensure a good tooth height and mesh ratio of the side gear teeth 20 and the pinion gear teeth 30.

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 tooth 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 middle portion M in the tooth trace direction toward the tooth 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 surface 31 included in the fourth region A4 of each pinion gear tooth 30 can 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 tooth base of the side gear teeth 20 in the fourth region A4, and to ensure good tooth height and mesh ratio of the side gear teeth 20 and the pinion gear teeth 30.

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 at 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 of the tooth surface 21 included in the first region A1 of each side gear tooth 20 can be increased from the pitch cone PC2 of the side gear 2 toward the tip cone TC2 of the side gear 2, on the inner side of the intermediate portion M in the tooth trace direction, compared to the second reference side gear. As a result, it is possible to eliminate undercutting of the root of the pinion gear teeth 30 in the first region A1, and to ensure good tooth height and mesh ratio of the side gear teeth 20 and the pinion gear teeth 30.

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 single point on the tooth trace, and may be secured to a predetermined length in the tooth trace direction. Furthermore, in the differential gear mechanism 1, the tooth profiles of the side gear teeth 20 and the pinion gear teeth 30 before adjustment by the pressure angle adjustment amount δ are formed by spherical involute curves, but are not limited to this. That is, the tooth profiles of the side gear teeth 20 and the pinion gear teeth 30 before 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, tooth thickness adjustment may be performed after adjustment of the reference pressure angle α and adjustment of the pressure angle by the pressure angle adjustment amount δ.

Summary of the embodiment
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 root (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 root cone (RC2) of the side gear (2), and the inner end (23i) of the tooth tip (23) of the side gear tooth (20) is inclined so as to be located closer to the tooth tip cone (TC2) of the side gear (2). a reference pressure 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 of the side gear tooth (20); an inner end (35i) of a tooth bottom (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 bottom cone (RC3) of the pinion gear (3); and an outer end (33o) of a tooth tip (33) of the pinion gear tooth (30) is inclined so as to be located closer to the tooth bottom 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 pinion gear tooth (30) and a tangent to a tooth profile, increases from a middle portion (M) of a tooth trace included between the inner end (23i) of the tooth tip (23) of the side gear tooth (20) and the outer end (33o) of the tooth tip (33) of the pinion gear tooth (30) in the tooth trace direction toward the inner end side and also increases from the middle portion (M) toward the outer end side, and a tooth thickness on a pitch cone (PC2) of the side gear (2) is such that an intersection line between the tooth surface of the side gear tooth and the pitch cone is a straight line passing through the center of the differential gear mechanism, Furthermore, compared to a reference side gear in which the reference pressure angle is constant in the tooth trace direction, the reference pressure angle becomes smaller from the middle portion (M) to the inner end side and becomes larger from the middle portion (M) to the outer end side, and the tooth thickness on a pitch cone (PC3) of the pinion gear (3) is such that 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 compared to a reference pinion gear in which the reference pressure angle is constant in the tooth trace direction, the tooth thickness becomes larger from the middle portion (M) to the inner end side and becomes smaller from the middle portion (M) to the outer end side.

In the differential gear mechanism disclosed herein, 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, ensuring the thickness of the inner ends of the pinion gears and shortening the axial length of the differential gear mechanism in the axial direction of the side gears. In addition, 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 also increase from the middle part toward the outer end. By making the tooth thickness on the pitch cone of the side gear smaller from the intermediate portion toward the inner end and larger from the intermediate portion toward the outer end 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 and smaller from the intermediate portion toward the outer end 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 compact the differential gear mechanism by shortening the axial length of the differential gear mechanism in the axial direction of the side gear and by reducing the diameter of the pinion gear 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 in the tooth trace direction and the inclined outer end of the tip of the pinion gear tooth, i.e., within the 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.

Furthermore, 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 bottom cone (RC3) of the pinion gear (3) from the pitch cones (PC2, PC3) of the side gear (2) and the pinion gear (3); and a second region (A2) located on the inner end side of the intermediate portion (M) in the tooth trace direction and on the side of the bottom cone (RC2) of the side gear (2) from the pitch cones (PC2, PC3). 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 tooth root cone (RC3) side of the pinion gear (3) on the pitch cone (PC2, PC3). In at least one of the bottom cone (RC2) and 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 larger from the pitch cone (PC2, PC3) to the bottom cone (RC2) side of the side gear (2) or the tip cone (TC3) side of the pinion gear (3), compared to 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. The pressure angle on the tooth surface (31) of the pinion gear tooth (30) may be smaller as it moves from the pitch cone (PC2, PC3) to 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 increases from the middle portion to the outer end side.

This makes it possible to eliminate sharp edges on the side gear teeth or pinion gear teeth and ensure good tooth height and mesh ratio for the side gear teeth and pinion gear teeth.

Furthermore, 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 bottom cone (RC3) of the pinion gear (3) from the pitch cones (PC2, PC3) of the side gear (2) and the pinion gear (3); and a second region (A2) located on the inner end side of the intermediate portion (M) in the tooth trace direction and on the side of the bottom cone (RC2) of the side gear (2) from the pitch cones (PC2, PC3). 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 tooth root cone (RC3) side of the pinion gear (3) on the pitch cone (PC2, PC3). In at least one of the bottom cone (RC2) and 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 larger from the pitch cone (PC2, PC3) to the bottom cone (RC2) side of the side gear (2) or the tip cone (TC3) side of the pinion gear (3), compared to 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. 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.

This eliminates undercutting of the tooth base of the side gear teeth or pinion gear teeth, making it possible to ensure good tooth height and mesh ratio for the side gear teeth and pinion gear teeth.

The design method of the differential gear mechanism disclosed herein includes a pair of side gears (2), which are bevel gears each having a plurality of side gear teeth (20), and a plurality of pinion gears (3), which are bevel gears each having a plurality of pinion gear teeth (30) and mesh with the pair of side gears (2), in which the outer end (25o) of the tooth root (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 root cone (RC2) of the side gear (2), and the inner end (23i) of the tooth tip (23) of the side gear teeth (20) is inclined so as to be located closer to the side gear (2) than the tooth tip cone (TC2) of the side gear (2). a pinion gear (3) having an inner end (35i) of a tooth bottom (35) of the pinion gear (3) inclined so as to be located on the side of the tooth bottom cone (RC2) of the pinion gear (2), an inner end (35i) of a tooth bottom (35) of the pinion gear (3) inclined so as to be located on the side of the tooth tip cone (TC3) of the pinion gear (3) relative to the tooth bottom 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 on the side of the tooth bottom cone (RC3) of the pinion gear (3), The quasi-pressure angle (α) and the reference pressure angle (α), which is the angle between a radial line passing through a pitch point of the pinion gear tooth (30) and a tangent to the tooth profile, are increased from a middle portion (M) of the tooth trace included between the inner end (23i) of the tooth tip (23) of the side gear tooth (20) and the outer end (33o) of the tooth tip (33) of the pinion gear tooth (30) in the tooth trace direction toward the inner end side and are also increased from the middle portion (M) toward the outer end side, and the tooth thickness on the pitch cone (PC2) of the side gear (2) is set so that the intersection line between the tooth surface of the side gear tooth and the pitch cone is a straight line passing through the center of the differential gear mechanism. The reference pressure angle is smaller from the middle portion (M) toward the inner end side and 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 the tooth thickness on the pitch cone (PC3) of the pinion gear (3) is larger from the middle portion (M) toward the inner end side and smaller from the middle portion (M) toward the outer end side compared to a reference pinion gear in which the intersection line between the tooth surface 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.

This method makes it 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, while ensuring good strength of the side gear and pinion gear, thereby making the differential gear mechanism more compact.

Furthermore, a first region (A1) 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 bottom cone (RC3) of the pinion gear (3) from the pitch cones (PC2, PC3) of the side gear (2) and the pinion gear (3); 2), 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 pitch cone (PC2, PC3) side of the side gear (2). and a fourth region (A4) on the side of the tip cone (TC3) of the pinion gear (3), the pressure angle on the tooth surface (21) of the side gear tooth (20) is set to be smaller than that of a second reference side gear in which the reference pressure angle increases from the intermediate portion toward the inner end side and increases from the intermediate portion toward the outer end side, the pressure angle on the tooth surface (21) of the side gear tooth (20) is set to be smaller than that of a second reference side gear in which the reference pressure angle increases from the pitch cone (PC2, PC3) toward the root cone (RC2) of the side gear (2). or toward the tip cone (TC2) side, and 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 increases from the middle portion toward the inner end side and increases from the middle portion toward the outer end side.

Furthermore, 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 bottom cone (RC3) of the pinion gear (3) from the pitch cones (PC2, PC3) of the side gear (2) and the pinion gear (3); 2), 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 pitch cone (PC2, PC3) side of the side gear (2). and a fourth region (A4) on the side of the tip cone (TC3) of the pinion gear (3), the pressure angle on the tooth surface (21) of the side gear tooth (20) is set to be smaller than that of a second reference side gear in which the reference pressure angle increases from the intermediate portion toward the inner end side and increases from the intermediate portion toward the outer end side, the pressure angle on the tooth surface (21) of the side gear tooth (20) is set to be smaller than that of a second reference side gear in which the reference pressure angle increases from the pitch cone (PC2, PC3) toward the root cone (RC2) of the side gear (2). or toward the tip cone (TC2) side, and the pressure angle on the tooth surface (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 toward the inner end side and increases from the middle portion toward the outer end side.

The invention disclosed herein is in no way limited to the above embodiment, and it goes without saying that various modifications can be made within the scope of the present disclosure. Furthermore, the above embodiment is merely one specific form of the invention described in the Summary of the Invention section, and does not limit the elements of the invention described in the Summary of the Invention section.

The disclosed invention can be used in the manufacturing industry of differential gear mechanisms that include a pair of side gears and multiple pinion gears that mesh with the pair of side gears.

Claims (6)

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. 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. 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. 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 and 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 bottom 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 bottom 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 bottom 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 bottom 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. 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. 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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