WO2024135129A1 - Flexible meshing type gear device - Google Patents

Abstract

The purpose of the technology of the present disclosure is to provide a flexible meshing type gear device that can reduce decreases in tooth strength and lifespan of an external gear.　A flexible meshing type gear device comprises: a vibrator; an external gear that is flexed and deformed by the vibrator; a first internal gear that meshes with the external gear; and a second internal gear that is disposed beside the first internal gear in an axial direction, and meshes with the external gear. The external gear has a first external tooth part that meshes with the first internal gear, and a second external tooth part that meshes with the second internal gear. The second external tooth part includes a second external tooth thickest part with a maximum tooth thickness, and a second external tooth inside tooth-thickness-decreasing part in which the tooth thickness decreases from the second external tooth thickest part toward the inside in the axial direction. An internal tooth part of the second internal gear includes a second internal tooth thickest part with a maximum tooth thickness, and a second internal tooth inside tooth-thickness-decreasing part in which the tooth thickness decreases from the second internal tooth thickest part toward the inside in the axial direction.

Description

Flexible mesh gear device

The present invention relates to a flexible mesh gear device.

A flexural meshing gear device is known that includes a vibration exciter, an external gear that is flexibly deformed by the vibration exciter, a first internal gear that meshes with the external gear, and a second internal gear that is axially aligned with the first internal gear and meshes with the external gear (see, for example, Patent Document 1).

Patent Document 1 shows a technology for suppressing excessive wear on the teeth of the external gear, first internal gear, and second internal gear by devising the tooth trace shape of the external gear in a flat-type flexible mesh gear device.

JP 2019-120325 A

The flexible mesh gear device of Patent Document 1 has the effect of suppressing excessive wear on the teeth of the external gear, the first internal gear, and the second internal gear, but there is room for improvement in terms of the strength and lifespan of the teeth of the external gear.

The present invention aims to provide a flexible mesh gear device that can suppress deterioration in the strength and lifespan of the teeth of an external gear.

A flexible mesh gear device according to one aspect of the present invention comprises:
A flexible meshing gear device including: a vibration exciter; an external gear that is flexibly deformed by the vibration exciter; a first internal gear that meshes with the external gear; and a second internal gear that is arranged in line with the first internal gear in the axial direction and meshes with the external gear,
the external gear has a first external tooth portion that meshes with the first internal gear and a second external tooth portion that meshes with the second internal gear,
the second external tooth portion has a second external tooth thickest portion where the tooth thickness is maximum, and a second external tooth inner tooth thickness reducing portion where the tooth thickness decreases from the second external tooth thickest portion toward the inside in the axial direction,
The internal tooth portion of the second internal gear has a second internal tooth thickest portion where the tooth thickness is maximum, and a second internal tooth inner tooth thickness reducing portion where the tooth thickness decreases from the second internal tooth thickest portion toward the axially inward.

The present invention provides a flexible mesh gear device that can suppress deterioration in the strength and lifespan of the external gear teeth.

1 is a cross-sectional view showing a flexible mesh gear device according to a first embodiment. FIG. 2 is a diagram for explaining tooth trace shapes of the external gear, the first internal gear, and the second internal gear of FIG. 1 . FIG. 2 is a diagram for explaining tooth tip shapes of the external gear, the first internal gear, and the second internal gear in FIG. 1 . FIG. 10 is a diagram for explaining tooth trace shapes of the external gear, the first internal gear, and the second internal gear of a flexible mesh gear device according to a second embodiment. FIG. 10 is a diagram for explaining the tooth tip shapes of the external gear, the first internal gear, and the second internal gear of a flexible mesh gear device according to a second embodiment. FIG. 13 is a diagram for explaining tooth trace shapes of the external gear, the first internal gear, and the second internal gear of a flexible mesh gear device according to a third embodiment. FIG.

Hereinafter, one or more embodiments will be described with reference to the drawings, and the features and technical effects of the embodiments will be understood from the following detailed description and drawings. However, the scope of the present invention is not limited to the embodiments disclosed below. The drawings are provided for illustrative purposes only, and the scope of the present invention is not limited to the examples in the drawings. The same or equivalent components, parts, and steps shown in each drawing are given the same reference numerals, and duplicated descriptions are omitted as appropriate. The dimensions of the components in each drawing are appropriately enlarged or reduced for ease of understanding. Some of the components that are not important for explaining the embodiments in each drawing are omitted. Terms including ordinal numbers such as "first" and "second" are used to describe various components, but the ordinal numbers of these terms are used only for the purpose of distinguishing one component from another component, and the components are not limited by the ordinal numbers of these terms.

(Embodiment 1)
1 is a cross-sectional view showing a flexible mesh gear device 100 according to a first embodiment. The flexible mesh gear device 100 reduces the speed of input rotation and outputs it. The flexible mesh gear device 100 is a so-called flat type (flat type is also called cylindrical type) flexible mesh gear device. Note that the present invention is applicable not only to the flat type flexible mesh gear device 100 but also to so-called cup type or top hat type flexible mesh gear devices, for example.

The flexible mesh gear device 100 includes a wave generator 2, an external gear 4 that is flexibly deformed by the wave generator 2, a first internal gear 6 that meshes with the external gear 4, a second internal gear 8 that is arranged axially alongside (adjacent to) the first internal gear 6 and meshes with the external gear 4, a casing 10, a first regulating member 12, a second regulating member 14, a main bearing 16, a first bearing housing 18, and a second bearing housing 20. A lubricant (e.g., grease) is sealed in the flexible mesh gear device 100. The lubricant lubricates the meshing portions between the external gear 4 and the first internal gear 6 and second internal gear 8, as well as the various bearings, etc.

The wave generator 2 has an exciter shaft 22, a first exciter bearing 21a arranged between the exciter shaft 22 and the external gear 4 (specifically, the first external tooth portion 4a of the external gear 4), and a second exciter bearing 21b arranged between the exciter shaft 22 and the external gear 4 (specifically, the second external tooth portion 4b of the external gear 4). The first exciter bearing 21a includes a plurality of first rolling elements 24a, a first retainer 26a that holds the plurality of first rolling elements 24a, and a first outer ring member 28a that is fitted into the external gear 4. The second exciter bearing 21b includes a plurality of second rolling elements 24b, a second retainer 26b that holds the plurality of second rolling elements 24b, and a second outer ring member 28b that is fitted into the external gear 4. The vibrator shaft 22 is an input shaft, and is connected to a rotary drive source such as a motor, and rotates around the rotation axis R. The vibrator shaft 22 is integrally formed with a vibrator 22a, the cross section of which perpendicular to the rotation axis R is substantially elliptical.

Each of the first rolling bodies 24a has a generally cylindrical shape and is spaced apart in the circumferential direction with its axial direction generally parallel to the direction of the rotation axis R. The first rolling bodies 24a are held by the first retainer 26a so as to be freely rollable, and roll on the outer peripheral surface 22b of the exciter 22a. In other words, the inner ring of the first exciter bearing 21a is integrally formed with the outer peripheral surface 22b of the exciter 22a, but this is not limited thereto, and a dedicated inner ring separate from the exciter 22a may be provided. The second rolling body 24b is configured in the same manner as the first rolling body 24a. The second rolling bodies 24b are held by the second retainer 26b arranged so as to be aligned with the first retainer 26a in the axial direction so as to be freely rollable, and roll on the outer peripheral surface 22b of the exciter 22a. That is, the inner ring of the second vibrator bearing 21b is integrally formed with the outer circumferential surface 22b of the vibrator 22a, but this is not limited thereto, and a dedicated inner ring separate from the vibrator 22a may be provided. Hereinafter, the first rolling body 24a and the second rolling body 24b are collectively referred to as "rolling body 24". Also, the first retainer 26a and the second retainer 26b are collectively referred to as "retainer 26".

The first outer race member 28a surrounds the multiple first rolling bodies 24a. The first outer race member 28a is flexible and is bent into an elliptical shape by the vibrator 22a via the multiple first rolling bodies 24a. When the vibrator 22a (i.e., the vibrator shaft 22) rotates, the first outer race member 28a is continuously bent and deformed to match the shape of the vibrator 22a. The second outer race member 28b is configured in the same manner as the first outer race member 28a. The second outer race member 28b is formed separately from the first outer race member 28a. The second outer race member 28b may be formed integrally with the first outer race member 28a. Hereinafter, the first outer race member 28a and the second outer race member 28b are collectively referred to as "outer race members 28".

The external gear 4 is a flexible annular member, into which the vibration exciter 22a, rolling elements 24, and outer ring member 28 fit. The external gear 4 is bent into an elliptical shape by the vibration exciter 22a, rolling elements 24, and outer ring member 28 fitting. When the vibration exciter 22a rotates, the external gear 4 is continuously bent and deformed to match the shape of the vibration exciter 22a. The external gear 4 includes a first external tooth portion 4a located on the outside of the first outer ring member 28a, a second external tooth portion 4b located on the outside of the second outer ring member 28b, and a base material 4c. The first external tooth portion 4a and the second external tooth portion 4b are formed on a single base material, the base material 4c, and have the same number of teeth.

The first internal gear 6 is a rigid annular member with a first internal toothing portion 6a formed on its inner circumference. The first internal toothing portion 6a surrounds the first external toothing portion 4a of the external gear 4, which is bent into an elliptically shape, and meshes with the first external toothing portion 4a in two specified regions near the major axis of the vibration exciter 22a. The first internal toothing portion 6a has more teeth than the first external toothing portion 4a.

The second internal gear 8 and the first internal gear 6 are arranged side by side in the axial direction, with the second internal gear 8 adjacent to the first internal gear 6. The second internal gear 8 is a rigid cylindrical member, with a second internal gear portion 8a formed on its inner circumference. The second internal gear portion 8a surrounds the second external gear portion 4b of the external gear 4 that is bent into an elliptically shape, and meshes with the second external gear portion 4b in two predetermined regions in the major axis direction of the vibration exciter 22a. The second internal gear portion 8a has the same number of teeth as the second external gear portion 4b. Therefore, the second internal gear 8 rotates in synchronization with the rotation of the second external gear portion 4b and, ultimately, the external gear 4.

The first regulating member 12 is a flat ring-shaped member and is arranged between the external gear 4, the first outer ring member 28a, and the first retainer 26a and the first bearing housing 18. The second regulating member 14 is a flat ring-shaped member and is arranged between the external gear 4, the second outer ring member 28b, and the second retainer 26b and the second bearing housing 20. The first regulating member 12 and the second regulating member 14 regulate the axial movement of the external gear 4, the outer ring member 28, and the retainer 26. The first regulating member 12 and the second regulating member 14 are also called thrust plates.

The casing 10 is a substantially cylindrical member that surrounds the second internal gear 8. The first internal gear 6 is spigot-fitted to the casing 10, and the first internal gear 6 is integrally assembled to the casing 10 with bolts (not shown). A main bearing 16 is disposed between the casing 10 and the second internal gear 8. In this embodiment, the main bearing 16 is a cross roller bearing, and includes a plurality of rollers (rolling elements) 46 that are spaced apart in the circumferential direction. The rollers 46 roll on the rolling surface 8b of the second internal gear 8 and the rolling surface 10a of the casing 10. In other words, the outer circumferential side of the second internal gear 8 functions as the inner ring of the main bearing 16, and the inner circumferential side of the casing 10 functions as the outer ring of the main bearing 16. The casing 10 supports the second internal gear 8 via the main bearing 16 so that it can rotate freely relative to the main bearing 16. The type of the main bearing 16 is not particularly limited, and may be, for example, a four-point contact ball bearing.

The first bearing housing 18 is an annular member and surrounds the vibration exciter shaft 22. Similarly, the second bearing housing 20 is an annular member and surrounds the vibration exciter shaft 22. The first bearing housing 18 and the second bearing housing 20 are arranged to sandwich the external gear 4, the rolling elements 24, the retainer 26, the outer ring member 28, the first regulating member 12 and the second regulating member 14 in the axial direction. The first bearing housing 18 is spigot-fitted to the first internal gear 6 and bolted. The second bearing housing 20 is spigot-fitted to the second internal gear 8 and bolted. A bearing 30 is incorporated in the inner circumference of the first bearing housing 18, and a bearing 32 is incorporated in the inner circumference of the second bearing housing 20. The vibration exciter shaft 22 is supported rotatably relative to the first bearing housing 18 and the second bearing housing 20 via the bearings 30 and 32.

An oil seal 40 is arranged between the vibration exciter shaft 22 and the first bearing housing 18, an O-ring 34 is arranged between the first bearing housing 18 and the first internal gear 6, an O-ring 36 is arranged between the first internal gear 6 and the casing 10, an oil seal 42 is arranged between the casing 10 and the second internal gear 8, an O-ring 38 is arranged between the second internal gear 8 and the second bearing housing 20, and an oil seal 44 is arranged between the second bearing housing 20 and the vibration exciter shaft 22. This prevents the lubricant in the flexible mesh gear device 100 from leaking.

A first regulating member 12 is sandwiched between the outer ring of the bearing 30 and the external gear 4. The thickness T12 of the first regulating member 12 is set to match the distance from the outer ring of the bearing 30 to the external gear 4 along the axial direction, taking into consideration the distance from the internal gear 6 to the internal gear 8 along the axial direction. For example, from among a plurality of thrust plates with different thicknesses, a thrust plate having a thickness equal to the distance from the outer ring of the bearing 30 to the external gear 4 along the axial direction is selected, and the selected thrust plate is assembled between the external gear 4, the first outer ring member 28a, and the first retainer 26a and the first bearing housing 18 and the outer ring of the bearing 30. The selected thrust plate is the first regulating member 12. The distance from the outer ring of the bearing 30 to the external gear 4 along the axial direction may be actually measured when the flexible mesh gear device 100 is assembled, or may be calculated from the actual size of each part and each assembly when the flexible mesh gear device 100 is assembled. The thickness T12 of the first restricting member 12 may be set to match the distance from the first bearing housing 18 to the external gear 4 along the axial direction.

A second regulating member 14 is sandwiched between the outer ring of the bearing 32 and the external gear 4. The thickness T14 of the second regulating member 14 is set to match the distance from the outer ring of the bearing 32 to the external gear 4 along the axial direction, taking into consideration the distance from the internal gear 6 to the internal gear 8 along the axial direction. For example, from among a plurality of thrust plates having different thicknesses, a thrust plate having a thickness equal to the distance from the outer ring of the bearing 32 to the external gear 4 along the axial direction is selected, and the selected thrust plate is assembled between the external gear 4, the second outer ring member 28b, and the second retainer 26b and the second bearing housing 20 and the outer ring of the bearing 32. The selected thrust plate is the second regulating member 14. The distance from the outer ring of the bearing 32 to the external gear 4 along the axial direction may be actually measured when the flexible mesh gear device 100 is assembled, or may be calculated from the actual measured sizes of each part and each assembly when the flexible mesh gear device 100 is assembled. The thickness T14 of the second restricting member 14 may be set to match the distance from the second bearing housing 20 to the external gear 4 along the axial direction.
The thickness T14 of the second regulating member 14 may be different from the thickness T12 of the first regulating member 12. The thickness T14 of the second regulating member 14 may be equal to the thickness T12 of the first regulating member 12.

The operation of the flexible mesh gear device 100 configured as above will now be described. Here, an example will be described in which the first external toothed portion 4a has 100 teeth, the second external toothed portion 4b has 100 teeth, the first internal toothed portion 6a has 102 teeth, and the second internal toothed portion 8a has 100 teeth. In addition, an example will be described in which the second internal toothed gear 8 and the second bearing housing 20 are connected to a driven member.

When the vibrator shaft 22 rotates while the first external toothed portion 4a is engaged with the first internal toothed portion 6a at two points in the long axis direction of the ellipse, the meshing position between the first external toothed portion 4a and the first internal toothed portion 6a also moves in the circumferential direction. Since the first external toothed portion 4a and the first internal toothed portion 6a have different numbers of teeth, the first external toothed portion 4a rotates relative to the first internal toothed portion 6a. Since the first internal tooth gear 6 and the first bearing housing 18 are fixed, the first external toothed portion 4a rotates by an amount corresponding to the difference in the number of teeth. In other words, the rotation of the vibrator shaft 22 is significantly decelerated and output to the first external toothed portion 4a. The reduction ratio is as follows:
Reduction ratio=(number of teeth of first external toothed portion 4a−number of teeth of first internal toothed portion 6a)/number of teeth of first external toothed portion 4a=(100−102)/100
= -1/50

The second external toothed portion 4b is formed integrally with the first external toothed portion 4a, and therefore rotates integrally with the first external toothed portion 4a. Because the second external toothed portion 4b and the second internal toothed portion 8a have the same number of teeth, no relative rotation occurs, and the second external toothed portion 4b and the second internal toothed portion 8a rotate integrally. For this reason, the same rotation as the rotation of the first external toothed portion 4a is output to the second internal toothed portion 8a. As a result, an output can be taken from the second internal tooth gear 8 that is slowed down to -1/50 the rotation of the vibration exciter shaft 22.

Next, the configurations of the external gear 4, the first internal gear 6, and the second internal gear 8 will be described in more detail. The external gear 4, the first external gear portion 4a, the second external gear portion 4b, the first internal gear 6, the first internal gear portion 6a, the second internal gear 8, and the second internal gear portion 8a in this embodiment correspond to the external gear, the first external gear portion, the second external gear portion, the first internal gear portion, the second internal gear portion, and the second internal gear portion in the claims, respectively. On the other hand, the external gear 4, the first external gear portion 4a, the second external gear portion 4b, the first internal gear 6, the first internal gear portion 6a, the second internal gear 8, and the second internal gear portion 8a in this embodiment can also be considered to correspond to the external gear, the second external gear portion, the first external gear portion, the second internal gear portion, the second internal gear portion, the first internal gear portion, and the first internal gear portion in the claims, respectively.

<Tooth trace shape>
FIG. 2 is a diagram for explaining the tooth trace shapes of the external gear 4, the first internal gear 6, and the second internal gear 8 in FIG. 1. FIG. 2 shows a cross-sectional view of the external gear 4, the first internal gear 6, and the second internal gear 8 cut by a virtual cylinder passing through the pitch circle of the external gear 4. In FIG. 2, one of the external teeth of the external gear 4 and two internal teeth adjacent to it in the circumferential direction are shown. To facilitate understanding, in FIG. 2, the first internal tooth portion 6a and the second internal tooth portion 8a are shown in a state in which they are slid away from the external gear 4 in the circumferential direction, and the tooth trace shapes of the first external tooth portion 4a, the second external tooth portion 4b, the first internal tooth portion 6a, and the second internal tooth portion 8a are exaggerated. The horizontal axis in FIG. 2 is parallel to the axial direction, and the horizontal axis indicates the axial position from a certain reference position. The axial direction and the tooth trace direction are parallel to each other, and the axial direction can also be said to be the tooth trace direction. The vertical axis indicates the dimension in the circumferential direction. In other words, it can be said that the vertical axis represents the tooth thickness of the external teeth of the external gear 4.

In this embodiment, the first external toothing 4a and the first internal toothing 6a have a range in the axial direction, the range of the first external toothing 4a is wider than the range of the first internal toothing 6a, and the first internal toothing 6a meshes with the first external toothing 4a over its entire range. The second external toothing 4b and the second internal toothing 8a have a range in the axial direction, the range of the second external toothing 4b is wider than the range of the second internal toothing 8a, and the second internal toothing 8a meshes with the second external toothing 4b over its entire range.

The first external tooth portion 4a may have a symmetric shape with respect to a tooth thickness center plane S4 of the first external tooth portion 4a, or may include a partially asymmetric portion. The tooth thickness center plane S4 refers to a plane passing through the center in the tooth thickness direction of the thickest part where the tooth thickness of the first external tooth portion 4a is maximum and the rotation axis R. The tooth thickness of the first external tooth portion 4a refers to the distance from the tooth thickness center plane S4 to the tooth surface.
Similarly, the second external teeth 4b may have a symmetric shape with respect to the tooth thickness center plane of the second external teeth 4b, or may include a partially asymmetric portion. The tooth thickness center plane of the second external teeth 4b coincides with the tooth thickness center plane S4 of the first external teeth 4a.
Similarly, the first internal tooth portion 6a may have a shape that is symmetrical with respect to the tooth thickness center plane S6 of the first internal tooth portion 6a, or may include a partially asymmetrical portion.
Similarly, the second internal tooth portion 8a may have a symmetric shape with respect to a tooth thickness center plane S8 of the second internal tooth portion 8a, or may include a partially asymmetric portion. Since the first internal tooth portion 6a and the second internal tooth portion 8a have different numbers of teeth, the tooth thickness center plane S8 of the second internal tooth portion 8a does not coincide with the tooth thickness center plane S6 of the first internal tooth portion 6a.

<<Tooth trace shapes of first external tooth portion 4a and first internal tooth portion 6a>>
The tooth trace shapes of the first external tooth portion 4a and the first internal tooth portion 6a will be described with reference to FIG. 2. In the following description, the tooth trace shapes of the first external tooth portion 4a and the first internal tooth portion 6a in a cylindrical cross section along the pitch circle will be representatively described, and the tooth trace shapes of the first external tooth portion 4a and the first internal tooth portion 6a in a cylindrical cross section displaced in the radial direction from the cylindrical cross section along the pitch circle are also similar to the tooth trace shapes described below. The tooth trace shape of the first external tooth portion 4a described below may be entirely reflected in the range from the tooth bottom to the vicinity of the tooth tip of the first external tooth portion 4a, or may be partially reflected in a part of the range from the tooth bottom to the vicinity of the tooth tip of the first external tooth portion 4a. The tooth trace shape of the first internal tooth portion 6a described below may be entirely reflected in the range from the tooth bottom to the vicinity of the tooth tip of the first internal tooth portion 6a, or may be partially reflected in a part of the range from the tooth bottom to the vicinity of the tooth tip of the first internal tooth portion 6a.

When the first external tooth portion 4a is divided in the axial direction, the first external tooth portion 4a has a first external tooth thickest portion 4a1, a first external tooth inner tooth thickness reduced portion 4a2, and a first external tooth outer tooth thickness reduced portion 4a3. The first external tooth inner tooth thickness reduced portion 4a2 is located axially inward from the first external tooth thickest portion 4a1, and the first external tooth outer tooth thickness reduced portion 4a3 is located axially outward from the first external tooth thickest portion 4a1. Here, the axially inner side refers to the direction approaching the center between the first external tooth portion 4a and the second external tooth portion 4b along the axial direction. The axially outer side refers to the direction moving away from the center between the first external tooth portion 4a and the second external tooth portion 4b along the axial direction. In addition, the center between the first external tooth portion 4a and the second external tooth portion 4b refers to the boundary between the range of the first external tooth portion 4a in the axial direction and the range of the second external tooth portion 4b in the axial direction. The imaginary plane P0 that passes through the center between the first external tooth portion 4a and the second external tooth portion 4b and is perpendicular to the axial direction is called the central plane P0. The position of the central plane P0 in the axial direction is between the first internal tooth portion 6a and the second internal tooth portion 8a.

The tooth thickness of the first external tooth portion 4a varies in the axial direction. Specifically, the tooth thickness of the first external tooth thickest portion 4a1 corresponds to the maximum tooth thickness of the first external tooth portion 4a, the tooth thickness of the first external tooth inner tooth thickness reduced portion 4a2 gradually decreases from the first external tooth thickest portion 4a1 toward the axial inside, and the tooth thickness of the first external tooth outer tooth thickness reduced portion 4a3 gradually decreases from the first external tooth thickest portion 4a1 toward the axial outside.

When the first internal tooth portion 6a is divided in the axial direction, the first internal tooth portion 6a has a first internal tooth thickest portion 6a1 and a first internal tooth inner tooth thickness reduced portion 6a2. The first internal tooth inner tooth thickness reduced portion 6a2 is located axially inward of the first internal tooth thickest portion 6a1.

The tooth thickness of the first internal tooth portion 6a varies in the axial direction. Specifically, the tooth thickness of the first internal tooth thickest portion 6a1 corresponds to the maximum tooth thickness of the first internal tooth portion 6a, and the tooth thickness of the first internal tooth inner tooth thickness reduction portion 6a2 gradually decreases from the first internal tooth thickest portion 6a1 toward the inside in the axial direction.

The first outer tooth thickest portion 4a1 may have a range of a predetermined width in the axial direction, or may be a single point without having a range in the axial direction. In the example shown in Fig. 2, the first outer tooth thickest portion 4a1 is a single point without having a range in the axial direction.
The first internal tooth thickest part 6a1 may have a range of a predetermined width in the axial direction, or may be one point without having a range in the axial direction. In the example shown in Fig. 2, the first internal tooth thickest part 6a1 has a range in the axial direction. When the first internal tooth thickest part 6a1 has a range in the axial direction, the axially outer end of the first internal tooth thickest part 6a1 corresponds to the axially outer end of the first internal tooth part 6a, and when the first internal tooth thickest part 6a1 does not have a range in the axial direction and is one point, the first internal tooth thickest part 6a1 corresponds to the axially outer end of the first internal tooth part 6a.
As shown in Fig. 2, when the first external tooth thickest part 4a1 is a single point without a range in the axial direction and the first internal tooth thickest part 6a1 has a range in the axial direction, the position of the first external tooth thickest part 4a1 in the axial direction is inside the range of the first internal tooth thickest part 6a1. Note that when the first external tooth thickest part 4a1 has a range in the axial direction and the first internal tooth thickest part 6a1 is a single point without a range in the axial direction, the position of the first internal tooth thickest part 6a1 in the axial direction may be inside the range of the first external tooth thickest part 4a1. Also, when the first external tooth thickest part 4a1 has a range in the axial direction and the first internal tooth thickest part 6a1 has a range in the axial direction, the range of the first external tooth thickest part 4a1 and the range of the first internal tooth thickest part 6a1 may overlap partially or entirely. When the first outer tooth thickest portion 4a1 is a single point without any range in the axial direction, and the first inner tooth thickest portion 6a1 is a single point without any range in the axial direction, the positions of the first outer tooth thickest portion 4a1 and the first inner tooth thickest portion 6a1 in the axial direction may be aligned with each other.

The first external tooth inner tooth thickness reduced portion 4a2 has a range in the axial direction. When the first internal tooth thickest portion 6a1 has a range in the axial direction as in the example shown in FIG. 2, the range of the first external tooth inner tooth thickness reduced portion 4a2 partially overlaps with the range of the first internal tooth thickest portion 6a1. The axial inner end of the first external tooth inner tooth thickness reduced portion 4a2 corresponds to the center between the first external tooth portion 4a and the second external tooth portion 4b.

The first internal tooth inner tooth thickness reduced portion 6a2 has a range in the axial direction. The range of the first internal tooth inner tooth thickness reduced portion 6a2 is narrower than the range of the first external tooth inner tooth thickness reduced portion 4a2, and the entire range of the first internal tooth inner tooth thickness reduced portion 6a2 is included in the range of the first external tooth inner tooth thickness reduced portion 4a2. The range of the first external tooth inner tooth thickness reduced portion 4a2 extends axially inward from the axially inner end of the range of the first internal tooth inner tooth thickness reduced portion 6a2, but in contrast, the axially inner end of the range of the first external tooth inner tooth thickness reduced portion 4a2 may be aligned with the axially inner end of the range of the first internal tooth inner tooth thickness reduced portion 6a2. The range of the first external tooth inner tooth thickness reduced portion 4a2 extends axially outward from the axially outer end of the range of the first internal tooth inner tooth thickness reduced portion 6a2. The axially inner end of the first internal tooth inner tooth thickness reduced portion 6a2 corresponds to the axially inner end of the first internal tooth portion 6a.

The tooth thickness reduction rate of the first internal tooth inner tooth thickness reduction portion 6a2 is greater than the tooth thickness reduction rate of the first external tooth inner tooth thickness reduction portion 4a2. Therefore, in a cross section such as that in FIG. 2, the tooth trace curve drawn by the first internal tooth inner tooth thickness reduction portion 6a2 is steeper than the tooth trace curve drawn by the first external tooth inner tooth thickness reduction portion 4a2. Here, the tooth thickness reduction rate of the first internal tooth inner tooth thickness reduction portion 6a2 refers to the reduction in the tooth thickness of the first internal tooth inner tooth thickness reduction portion 6a2 when displaced by a unit distance in the tooth trace direction, specifically in the axial inward direction, divided by that unit distance. In other words, the tooth thickness reduction rate of the first internal tooth inner tooth thickness reduction portion 6a2 can also be said to be the reduction in the tooth thickness of the first internal tooth inner tooth thickness reduction portion 6a2 per unit distance in the tooth trace direction. The tooth thickness reduction ratio of the first external tooth inner tooth thickness reduced portion 4a2 refers to the reduction in the tooth thickness of the first external tooth inner tooth thickness reduced portion 4a2 when displaced a unit distance in the tooth trace direction, specifically in the axial direction, divided by that unit distance. The tooth thickness reduction ratio of the first external tooth inner tooth thickness reduced portion 4a2 can also be said to be the reduction in the tooth thickness of the first external tooth inner tooth thickness reduced portion 4a2 per unit distance in the tooth trace direction.

The maximum reduction in tooth thickness of the first internal tooth inner tooth thickness reduced portion 6a2 is greater than the maximum reduction in tooth thickness of the first external tooth inner tooth thickness reduced portion 4a2. The ratio between the maximum reduction in tooth thickness of the first internal tooth inner tooth thickness reduced portion 6a2 and the maximum reduction in tooth thickness of the first external tooth inner tooth thickness reduced portion 4a2 is expressed as "maximum reduction in tooth thickness of the first external tooth inner tooth thickness reduced portion 4a2: maximum reduction in tooth thickness of the first internal tooth inner tooth thickness reduced portion 6a2 = 1:2 to 4". Here, the maximum reduction in tooth thickness of the first internal tooth inner tooth thickness reduced portion 6a2 refers to the maximum tooth thickness of the first internal tooth inner tooth thickness reduced portion 6a2 at the axially outer end of the first internal tooth inner tooth thickness reduced portion 6a2 minus the minimum tooth thickness of the first internal tooth inner tooth thickness reduced portion 6a2 at the axially inner end of the first internal tooth inner tooth thickness reduced portion 6a2. The maximum reduction in tooth thickness of the first external tooth inner tooth thickness reduced portion 4a2 refers to the maximum tooth thickness of the first external tooth inner tooth thickness reduced portion 4a2 at the axially outer end of the first external tooth inner tooth thickness reduced portion 4a2 minus the minimum tooth thickness of the first external tooth inner tooth thickness reduced portion 4a2 at the axially inner end of the first external tooth inner tooth thickness reduced portion 4a2.

The first external tooth outer tooth thickness reduced portion 4a3 has a range in the axial direction. When the first internal tooth thickest portion 6a1 has a range in the axial direction as in the example shown in FIG. 2, the range of the first external tooth outer tooth thickness reduced portion 4a3 partially overlaps the range of the first internal tooth thickest portion 6a1. The range of the first external tooth outer tooth thickness reduced portion 4a3 extends axially outward beyond the first internal tooth thickest portion 6a1. The axially outer end of the first external tooth outer tooth thickness reduced portion 4a3 corresponds to the axially outer end of the first external tooth portion 4a.

The tooth thickness reduction rate of the first external tooth outer tooth thickness reduced portion 4a3 is greater than the tooth thickness reduction rate of the first external tooth inner tooth thickness reduced portion 4a2. Therefore, in a cross section such as that shown in FIG. 2, the tooth trace curve of the first external tooth outer tooth thickness reduced portion 4a3 is steeper than the tooth trace curve of the first external tooth inner tooth thickness reduced portion 4a2. Here, the tooth thickness reduction rate of the first external tooth outer tooth thickness reduced portion 4a3 refers to the amount of reduction in the tooth thickness of the first external tooth outer tooth thickness reduced portion 4a3 when displaced a unit distance in the tooth trace direction, specifically, axially outward, divided by that unit distance. The tooth thickness reduction rate of the first external tooth outer tooth thickness reduced portion 4a3 can also be said to be the amount of reduction in the tooth thickness of the first external tooth outer tooth thickness reduced portion 4a3 per unit distance in the tooth trace direction.

<<Tooth trace shapes of second external tooth portion 4b and second internal tooth portion 8a>>
The tooth trace shapes of the second external tooth portion 4b and the second internal tooth portion 8a will be described. In the following description, the tooth trace shapes of the second external tooth portion 4b and the second internal tooth portion 8a in a cylindrical cross section along the pitch circle will be representatively described, and the tooth trace shapes of the second external tooth portion 4b and the second internal tooth portion 8a in a cylindrical cross section displaced in the radial direction from the cylindrical cross section along the pitch circle are also similar to the tooth trace shapes described below. The tooth trace shape of the second external tooth portion 4b described below may be entirely reflected in the range from the tooth bottom to the vicinity of the tooth tip of the second external tooth portion 4b, or may be partially reflected in a part of the range from the tooth bottom to the vicinity of the tooth tip of the second external tooth portion 4b. The tooth trace shape of the second internal tooth portion 8a described below may be entirely reflected in the range from the tooth bottom to the vicinity of the tooth tip of the second internal tooth portion 8a, or may be partially reflected in a part of the range from the tooth bottom to the vicinity of the tooth tip of the second internal tooth portion 8a.

When the second external tooth portion 4b is divided in the axial direction, the second external tooth portion 4b has a second external tooth thickest portion 4b1, a second external tooth inner tooth thickness reduced portion 4b2, and a second external tooth outer tooth thickness reduced portion 4b3. The second external tooth inner tooth thickness reduced portion 4b2 is located axially inward of the second external tooth thickest portion 4b1, and the second external tooth outer tooth thickness reduced portion 4b3 is located axially outward of the second external tooth thickest portion 4b1.

The tooth thickness of the second external tooth portion 4b varies in the axial direction. Specifically, the tooth thickness of the second external tooth thickest portion 4b1 corresponds to the maximum tooth thickness of the second external tooth portion 4b, the tooth thickness of the second external tooth inner tooth thickness reduced portion 4b2 gradually decreases from the second external tooth thickest portion 4b1 toward the axial inside, and the tooth thickness of the second external tooth outer tooth thickness reduced portion 4b3 gradually decreases from the second external tooth thickest portion 4b1 toward the axial outside.

When the second internal tooth portion 8a is divided in the axial direction, the second internal tooth portion 8a has a second internal tooth thickest portion 8a1 and a second internal tooth inner tooth thickness reduced portion 8a2. The second internal tooth inner tooth thickness reduced portion 8a2 is located axially inward of the second internal tooth thickest portion 8a1.

The tooth thickness of the second internal tooth portion 8a varies in the axial direction. Specifically, the tooth thickness of the second internal tooth thickest portion 8a1 corresponds to the maximum tooth thickness of the second internal tooth portion 8a, and the tooth thickness of the second internal tooth inner tooth thickness reduction portion 8a2 gradually decreases from the second internal tooth thickest portion 8a1 toward the inside in the axial direction.

The second outer tooth thickest portion 4b1 may have a range in the axial direction, or may be a single point without having a range in the axial direction. In the example shown in Fig. 2, the second outer tooth thickest portion 4b1 is a single point without having a range in the axial direction.
The second internal tooth thickest part 8a1 may have a range in the axial direction, or may be one point without having a range in the axial direction. In the example shown in FIG. 2, the second internal tooth thickest part 8a1 has a range in the axial direction. When the second internal tooth thickest part 8a1 has a range in the axial direction, the axially outer end of the second internal tooth thickest part 8a1 corresponds to the axially outer end of the second internal tooth part 8a, and when the second internal tooth thickest part 8a1 does not have a range in the axial direction and is one point, the second internal tooth thickest part 8a1 corresponds to the axially outer end of the second internal tooth part 8a.
As shown in Fig. 2, when the second external tooth thickest part 4b1 is one point without a range in the axial direction and the second internal tooth thickest part 8a1 has a range in the axial direction, the position of the second external tooth thickest part 4b1 in the axial direction is inside the range of the second internal tooth thickest part 8a1. Note that when the second external tooth thickest part 4b1 has a range in the axial direction and the second internal tooth thickest part 8a1 is one point without a range in the axial direction, the position of the second internal tooth thickest part 8a1 in the axial direction may be inside the range of the second external tooth thickest part 4b1. Also, when the second external tooth thickest part 4b1 has a range in the axial direction and the second internal tooth thickest part 8a1 has a range in the axial direction, the range of the second external tooth thickest part 4b1 and the range of the second internal tooth thickest part 8a1 may overlap partially or entirely. When the second outer tooth thickest portion 4b1 is a single point without any range in the axial direction, and the second inner tooth thickest portion 8a1 is a single point without any range in the axial direction, the positions of the second outer tooth thickest portion 4b1 and the second inner tooth thickest portion 8a1 in the axial direction may be aligned with each other.

The second external tooth inner tooth thickness reduced portion 4b2 has a range in the axial direction. When the second internal tooth thickest portion 8a1 has a range in the axial direction as in the example shown in FIG. 2, the range of the second external tooth inner tooth thickness reduced portion 4b2 partially overlaps with the range of the second internal tooth thickest portion 8a1. The axial inner end of the second external tooth inner tooth thickness reduced portion 4b2 corresponds to the center between the first external tooth portion 4a and the second external tooth portion 4b.

The second internal tooth inner tooth thickness reduced portion 8a2 has a range in the axial direction. The range of the second internal tooth inner tooth thickness reduced portion 8a2 is narrower than the range of the second external tooth inner tooth thickness reduced portion 4b2, and the entire range of the second internal tooth inner tooth thickness reduced portion 8a2 is included in the range of the second external tooth inner tooth thickness reduced portion 4b2. The axially inner end of the range of the second external tooth inner tooth thickness reduced portion 4b2 is aligned with the axially inner end of the range of the second internal tooth inner tooth thickness reduced portion 8a2, but the range of the second external tooth inner tooth thickness reduced portion 4b2 may extend axially inward beyond the axially inner end of the range of the second internal tooth inner tooth thickness reduced portion 8a2. The range of the second external tooth inner tooth thickness reduced portion 4b2 extends axially outward beyond the axially outer end of the range of the second internal tooth inner tooth thickness reduced portion 8a2. The axially inner end of the second internal tooth inner tooth thickness reduced portion 8a2 corresponds to the axially inner end of the second internal tooth portion 8a.

The tooth thickness reduction rate of the second internal tooth inner tooth thickness reduction portion 8a2 is greater than the tooth thickness reduction rate of the second external tooth inner tooth thickness reduction portion 4b2. Therefore, in a cross section such as that shown in FIG. 2, the tooth trace curve drawn by the second internal tooth inner tooth thickness reduction portion 8a2 is steeper than the tooth trace curve drawn by the second external tooth inner tooth thickness reduction portion 4b2. Here, the tooth thickness reduction rate of the second internal tooth inner tooth thickness reduction portion 8a2 refers to the amount of reduction in the tooth thickness of the second internal tooth inner tooth thickness reduction portion 8a2 when displaced a unit distance in the tooth trace direction, specifically in the axial inward direction, divided by that unit distance. The tooth thickness reduction rate of the second internal tooth inner tooth thickness reduction portion 8a2 can also be said to be the amount of reduction in the tooth thickness of the second internal tooth inner tooth thickness reduction portion 8a2 per unit distance in the tooth trace direction. The tooth thickness reduction ratio of the second external tooth inner tooth thickness reduced portion 4b2 refers to the reduction in the tooth thickness of the second external tooth inner tooth thickness reduced portion 4b2 when displaced a unit distance in the tooth trace direction, specifically in the axial direction inward, divided by that unit distance. The tooth thickness reduction ratio of the second external tooth inner tooth thickness reduced portion 4b2 can also be said to be the reduction in the tooth thickness of the second external tooth inner tooth thickness reduced portion 4b2 per unit distance in the tooth trace direction.

The maximum reduction in tooth thickness of the second internal tooth inner tooth thickness reduced portion 8a2 is greater than the maximum reduction in tooth thickness of the second external tooth inner tooth thickness reduced portion 4b2. The ratio between the maximum reduction in tooth thickness of the second internal tooth inner tooth thickness reduced portion 8a2 and the maximum reduction in tooth thickness of the second external tooth inner tooth thickness reduced portion 4b2 is such that "the maximum reduction in tooth thickness of the second external tooth inner tooth thickness reduced portion 4b2: the maximum reduction in tooth thickness of the second internal tooth inner tooth thickness reduced portion 8a2 = 1: 2 to 4". Here, the maximum reduction in tooth thickness of the second internal tooth inner tooth thickness reduced portion 8a2 refers to the maximum tooth thickness of the second internal tooth inner tooth thickness reduced portion 8a2 at the axially outer end of the second internal tooth inner tooth thickness reduced portion 8a2 minus the minimum tooth thickness of the second internal tooth inner tooth thickness reduced portion 8a2 at the axially inner end of the second internal tooth inner tooth thickness reduced portion 8a2. The maximum reduction in tooth thickness of the second external tooth inner tooth thickness reduced portion 4b2 refers to the maximum tooth thickness of the second external tooth inner tooth thickness reduced portion 4b2 at the axially outer end of the second external tooth inner tooth thickness reduced portion 4b2 minus the minimum tooth thickness of the second external tooth inner tooth thickness reduced portion 4b2 at the axially inner end of the second external tooth inner tooth thickness reduced portion 4b2.

The maximum reduction in tooth thickness of the second internal tooth inner tooth thickness reduction portion 8a2 is greater than the maximum reduction in tooth thickness of the first internal tooth inner tooth thickness reduction portion 6a2.

The second external tooth outer tooth thickness reduced portion 4b3 has a range in the axial direction. When the second internal tooth thickest portion 8a1 has a range in the axial direction as in the example shown in FIG. 2, the range of the second external tooth outer tooth thickness reduced portion 4b3 partially overlaps the range of the second internal tooth thickest portion 8a1. The range of the second external tooth outer tooth thickness reduced portion 4b3 extends axially outward beyond the second internal tooth thickest portion 8a1. The axially outer end of the second external tooth outer tooth thickness reduced portion 4b3 corresponds to the axially outer end of the second external tooth portion 4b.

The tooth thickness reduction rate of the second external tooth outer tooth thickness reduced portion 4b3 is greater than the tooth thickness reduction rate of the second external tooth inner tooth thickness reduced portion 4b2. Therefore, in a cross section such as that shown in FIG. 2, the tooth trace curve of the second external tooth outer tooth thickness reduced portion 4b3 is steeper than the tooth trace curve of the second external tooth inner tooth thickness reduced portion 4b2. Here, the tooth thickness reduction rate of the second external tooth outer tooth thickness reduced portion 4b3 refers to the amount of reduction in the tooth thickness of the second external tooth outer tooth thickness reduced portion 4b3 when displaced a unit distance in the tooth trace direction, specifically, axially outward, divided by that unit distance. The tooth thickness reduction rate of the second external tooth outer tooth thickness reduced portion 4b3 can also be said to be the amount of reduction in the tooth thickness of the second external tooth outer tooth thickness reduced portion 4b3 per unit distance in the tooth trace direction.

<Tooth tip shape>
FIG. 3 is a diagram for explaining the tooth tip shapes of the external gear 4, the first internal gear 6, and the second internal gear 8 in FIG. 1. FIG. 3 shows the tooth tips of the first external tooth portion 4a and the second external tooth portion 4b as viewed from the circumferential direction, and the tooth tips of the first internal tooth portion 6a and the second internal tooth portion 8a. In FIG. 3, in order to facilitate understanding, the tooth tips of the first internal tooth portion 6a and the tooth tips of the second internal tooth portion 8a are shown in a state in which they are slid away from the external gear 4 radially outward, and the tooth tip shapes of the first external tooth portion 4a, the second external tooth portion 4b, the first internal tooth portion 6a, and the second internal tooth portion 8a are exaggerated. In FIG. 3, the horizontal axis indicates the axial position from a certain reference position. The vertical axis indicates the radial dimension.

<<Tooth tip shapes of first external tooth portion 4a and first internal tooth portion 6a>>
The tooth tip shapes of the first external tooth portion 4a and the first internal tooth portion 6a will be described with reference to Fig. 3. The first external tooth portion 4a and the first internal tooth portion 6a have the tooth trace shape described above, but may not have the tooth tip shape described below. When the first external tooth portion 4a and the first internal tooth portion 6a do not have the tooth tip shape described below, the tooth tip shapes of the first external tooth portion 4a and the first internal tooth portion 6a may be flat, for example.

When the tooth tip of the first external tooth portion 4a is divided in the axial direction, the first external tooth portion 4a has a first external tooth maximum outer diameter portion 4a6, a first external tooth inner outer diameter reduced portion 4a7, and a first external tooth outer outer diameter reduced portion 4a8. The first external tooth inner outer diameter reduced portion 4a7 is located axially inward of the first external tooth maximum outer diameter portion 4a6, and the first external tooth outer outer diameter reduced portion 4a8 is located axially outward of the first external tooth maximum outer diameter portion 4a6.

The outer diameter of the first external tooth portion 4a varies in the axial direction. Specifically, the outer diameter of the first external tooth maximum outer diameter portion 4a6 corresponds to the maximum outer diameter of the first external tooth portion 4a, the outer diameter of the first external tooth inner outer diameter reduced portion 4a7 gradually decreases from the first external tooth maximum outer diameter portion 4a6 toward the axially inward direction, and the outer diameter of the first external tooth outer diameter reduced portion 4a8 gradually decreases from the first external tooth maximum outer diameter portion 4a6 toward the axially outward direction. The outer diameter of the first external tooth portion 4a refers to the distance from the rotation axis R to the tooth tip of the first external tooth portion 4a.

When the tooth tip of the first internal tooth portion 6a is divided in the axial direction, the first internal tooth portion 6a has a first internal tooth minimum inner diameter portion 6a6 and a first internal tooth inner diameter increasing portion 6a7. The first internal tooth inner diameter increasing portion 6a7 is located axially inward of the first internal tooth minimum inner diameter portion 6a6.

The inner diameter of the first internal tooth portion 6a changes in the axial direction. Specifically, the inner diameter of the first internal tooth minimum inner diameter portion 6a6 corresponds to the minimum inner diameter of the first internal tooth portion 6a, and the inner diameter of the first internal tooth inner diameter increasing portion 6a7 gradually increases from the first internal tooth minimum inner diameter portion 6a6 toward the inside in the axial direction. The inner diameter of the first internal tooth portion 6a refers to the distance from the rotation axis R to the tooth tip of the first internal tooth portion 6a.

The first outer tooth maximum outer diameter portion 4a6 may have a range in the axial direction, or may be a single point without having a range in the axial direction. In the example shown in Fig. 3, the first outer tooth maximum outer diameter portion 4a6 has no range in the axial direction and is a single point.
The first internal tooth minimum inner diameter portion 6a6 may have a range in the axial direction, or may be one point without having a range in the axial direction. In the example shown in Fig. 3, the first internal tooth minimum inner diameter portion 6a6 has a range in the axial direction. When the first internal tooth minimum inner diameter portion 6a6 has a range in the axial direction, the axially outer end of the first internal tooth minimum inner diameter portion 6a6 corresponds to the axially outer end of the first internal tooth portion 6a, and when the first internal tooth minimum inner diameter portion 6a6 does not have a range in the axial direction and is one point, the first internal tooth minimum inner diameter portion 6a6 corresponds to the axially outer end of the first internal tooth portion 6a.
As shown in Fig. 3, when the first external tooth maximum outer diameter portion 4a6 does not have a range in the axial direction but is a single point, and the first internal tooth minimum inner diameter portion 6a6 has a range in the axial direction, the position of the first external tooth maximum outer diameter portion 4a6 in the axial direction is inside the range of the first internal tooth minimum inner diameter portion 6a6. Note that when the first external tooth maximum outer diameter portion 4a6 has a range in the axial direction and the first internal tooth minimum inner diameter portion 6a6 has a single point without having a range in the axial direction, the position of the first internal tooth minimum inner diameter portion 6a6 in the axial direction may be inside the range of the first external tooth maximum outer diameter portion 4a6. Also, when the first external tooth maximum outer diameter portion 4a6 has a range in the axial direction and the first internal tooth minimum inner diameter portion 6a6 has a range in the axial direction, the range of the first external tooth maximum outer diameter portion 4a6 and the range of the first internal tooth minimum inner diameter portion 6a6 may overlap partially or entirely. When the first outer tooth maximum outer diameter portion 4a6 is a single point without any range in the axial direction, and the first internal tooth minimum inner diameter portion 6a6 is a single point without any range in the axial direction, the positions of the first outer tooth maximum outer diameter portion 4a6 and the first internal tooth minimum inner diameter portion 6a6 in the axial direction may be aligned with each other.

The first external tooth inner outer diameter reduced portion 4a7 has a range in the axial direction. When the first internal tooth minimum inner diameter portion 6a6 has a range in the axial direction as in the example shown in FIG. 3, the range of the first external tooth inner outer diameter reduced portion 4a7 partially overlaps with the range of the first internal tooth minimum inner diameter portion 6a6. The axially inner end of the first external tooth inner outer diameter reduced portion 4a7 corresponds to the center between the first external tooth portion 4a and the second external tooth portion 4b.

The first internal tooth inner diameter increasing portion 6a7 has a range in the axial direction. The range of the first internal tooth inner diameter increasing portion 6a7 is narrower than the range of the first external tooth inner outer diameter decreasing portion 4a7, and the entire range of the first internal tooth inner inner diameter increasing portion 6a7 is included in the range of the first external tooth inner outer diameter decreasing portion 4a7. The range of the first external tooth inner outer diameter decreasing portion 4a7 extends axially inward from the axially inner end of the range of the first internal tooth inner inner diameter increasing portion 6a7, but the axially inner end of the range of the first external tooth inner outer diameter decreasing portion 4a7 may be aligned with the axially inner end of the range of the first internal tooth inner inner diameter increasing portion 6a7. The range of the first external tooth inner outer diameter decreasing portion 4a7 extends axially outward from the axially outer end of the range of the first internal tooth inner inner diameter increasing portion 6a7. The axially inner end of the first internal tooth inner inner diameter increasing portion 6a7 corresponds to the axially inner end of the first internal tooth portion 6a.

The inner diameter increase rate of the first internal tooth inner diameter increasing portion 6a7 is greater than the outer diameter decrease rate of the first external tooth inner diameter decreasing portion 4a7. Therefore, in FIG. 3, the tooth tip curve drawn by the first internal tooth inner diameter increasing portion 6a7 is steeper than the tooth tip curve drawn by the first external tooth inner diameter decreasing portion 4a7. Here, the inner diameter increase rate of the first internal tooth inner diameter increasing portion 6a7 refers to the increase in the inner diameter of the first internal tooth inner diameter increasing portion 6a7 when displaced inward in the axial direction by a unit distance, divided by that unit distance. The inner diameter increase rate of the first internal tooth inner diameter increasing portion 6a7 can also be said to be the increase in the inner diameter of the first internal tooth inner diameter increasing portion 6a7 per unit distance in the axial direction. The outer diameter decrease rate of the first external tooth inner outer diameter decreasing portion 4a7 refers to the decrease in the outer diameter of the first external tooth inner outer diameter decreasing portion 4a7 when displaced inward in the axial direction by a unit distance, divided by that unit distance. The outer diameter reduction rate of the first outer tooth inner outer diameter reduction portion 4a7 can also be said to be the amount of reduction in the inner diameter of the first outer tooth inner outer diameter reduction portion 4a7 per unit distance in the axial direction.

The maximum increase in the inner diameter of the first internal tooth inner diameter increasing portion 6a7 is greater than the maximum decrease in the outer diameter of the first external tooth inner diameter decreasing portion 4a7. The ratio of the maximum increase in the inner diameter of the first internal tooth inner diameter increasing portion 6a7 to the maximum decrease in the outer diameter of the first external tooth inner diameter decreasing portion 4a7 is such that "maximum decrease in the outer diameter of the first external tooth inner diameter decreasing portion 4a7: maximum increase in the inner diameter of the first internal tooth inner diameter increasing portion 6a7 = 1:2 to 4". Here, the maximum increase in the inner diameter of the first internal tooth inner diameter increasing portion 6a7 refers to the maximum inner diameter of the first internal tooth inner diameter increasing portion 6a7 at the axially inner end of the first internal tooth inner diameter increasing portion 6a7 minus the minimum inner diameter of the first internal tooth inner diameter increasing portion 6a7 at the axially outer end of the first internal tooth inner diameter increasing portion 6a7. The maximum reduction in the outer diameter of the first outer tooth inner outer diameter reduced portion 4a7 refers to the maximum outer diameter of the first outer tooth inner outer diameter reduced portion 4a7 at the axially outer outer end of the first outer tooth inner outer diameter reduced portion 4a7 minus the minimum outer diameter of the first outer tooth inner outer diameter reduced portion 4a7 at the axially inner end of the first outer tooth inner outer diameter reduced portion 4a7.

The first external tooth outer diameter reduced portion 4a8 has a range in the axial direction. When the first internal tooth minimum inner diameter portion 6a6 has a range in the axial direction as in the example shown in FIG. 3, the range of the first external tooth outer diameter reduced portion 4a8 partially overlaps with the range of the first internal tooth minimum inner diameter portion 6a6. The range of the first external tooth outer diameter reduced portion 4a8 extends axially outward beyond the first internal tooth minimum inner diameter portion 6a6. The axially outer end of the first external tooth outer diameter reduced portion 4a8 corresponds to the axially outer end of the first external tooth portion 4a.

The rate of reduction in the outer diameter of the first outer tooth outer diameter reduced portion 4a8 is greater than the rate of reduction in the outer diameter of the first outer tooth inner diameter reduced portion 4a7. Therefore, in a cross section such as that shown in FIG. 3, the tooth tip curve drawn by the first outer tooth outer diameter reduced portion 4a8 is steeper than the tooth tip curve drawn by the first outer tooth inner outer diameter reduced portion 4a7. Here, the rate of reduction in the outer diameter of the first outer tooth outer diameter reduced portion 4a8 refers to the amount of reduction in the outer diameter of the first outer tooth outer diameter reduced portion 4a8 when displaced axially outward by a unit distance divided by that unit distance.

<<Tooth Tip Shapes of Second External Tooth Portion 4b and Second Internal Tooth Portion 8a>>
The tooth tip shapes of the second external tooth portion 4b and the second internal tooth portion 8a will be described. The second external tooth portion 4b and the second internal tooth portion 8a have the tooth trace shape described above, but may not have the tooth tip shape described below. If the second external tooth portion 4b and the second internal tooth portion 8a do not have the tooth tip shape described below, the tooth tip shapes of the second external tooth portion 4b and the second internal tooth portion 8a may be flat, for example.

When the tooth tip of the second external tooth portion 4b is divided in the axial direction, the second external tooth portion 4b has a second external tooth maximum outer diameter portion 4b6, a second external tooth inner outer diameter reduced portion 4b7, and a second external tooth outer outer diameter reduced portion 4b8. The second external tooth inner outer diameter reduced portion 4b7 is located axially inward of the second external tooth maximum outer diameter portion 4b6, and the second external tooth outer outer diameter reduced portion 4b8 is located axially outward of the second external tooth maximum outer diameter portion 4b6.

The outer diameter of the second external tooth portion 4b varies in the axial direction. Specifically, the outer diameter of the second external tooth maximum outer diameter portion 4b6 corresponds to the maximum outer diameter of the second external tooth portion 4b, the outer diameter of the second external tooth inner outer diameter reduced portion 4b7 gradually decreases from the second external tooth maximum outer diameter portion 4b6 toward the axially inner side, and the outer diameter of the second external tooth outer diameter reduced portion 4b8 gradually decreases from the second external tooth maximum outer diameter portion 4b6 toward the axially outer side. The outer diameter of the second external tooth portion 4b refers to the distance from the rotation axis R to the tooth tip of the second external tooth portion 4b.

When the second internal tooth portion 8a is divided in the axial direction, the second internal tooth portion 8a has a second internal tooth minimum inner diameter portion 8a6 and a second internal tooth inner diameter increasing portion 8a7. The second internal tooth inner diameter increasing portion 8a7 is located axially inward of the second internal tooth minimum inner diameter portion 8a6.

The inner diameter of the second internal tooth portion 8a changes in the axial direction. Specifically, the inner diameter of the second internal tooth minimum inner diameter portion 8a6 corresponds to the minimum inner diameter of the second internal tooth portion 8a, and the inner diameter of the second internal tooth inner diameter increasing portion 8a7 gradually increases from the second internal tooth minimum inner diameter portion 8a6 toward the inside in the axial direction. The inner diameter of the second internal tooth portion 8a refers to the distance from the rotation axis R to the tooth tip of the second internal tooth portion 8a.

The second outer tooth maximum outer diameter portion 4b6 may have a range in the axial direction, or may be a single point without having a range in the axial direction. In the example shown in Fig. 3, the second outer tooth maximum outer diameter portion 4b6 has no range in the axial direction and is a single point.
The second internal tooth minimum inner diameter portion 8a6 may have a range in the axial direction, or may be one point without having a range in the axial direction. In the example shown in Fig. 3, the second internal tooth minimum inner diameter portion 8a6 has a range in the axial direction. When the second internal tooth minimum inner diameter portion 8a6 has a range in the axial direction, the axially outer end of the second internal tooth minimum inner diameter portion 8a6 corresponds to the axially outer end of the second internal tooth portion 8a, and when the second internal tooth minimum inner diameter portion 8a6 does not have a range in the axial direction and is one point, the second internal tooth minimum inner diameter portion 8a6 corresponds to the axially outer end of the second internal tooth portion 8a.
As shown in Fig. 3, when the second external tooth maximum outer diameter portion 4b6 does not have a range in the axial direction but is a single point, and the second internal tooth minimum inner diameter portion 8a6 has a range in the axial direction, the position of the second external tooth maximum outer diameter portion 4b6 in the axial direction is inside the range of the second internal tooth minimum inner diameter portion 8a6. Note that when the second external tooth maximum outer diameter portion 4b6 has a range in the axial direction and the second internal tooth minimum inner diameter portion 8a6 has a single point without having a range in the axial direction, the position of the second internal tooth minimum inner diameter portion 8a6 in the axial direction may be inside the range of the second external tooth maximum outer diameter portion 4b6. Also, when the second external tooth maximum outer diameter portion 4b6 has a range in the axial direction and the second internal tooth minimum inner diameter portion 8a6 has a range in the axial direction, the range of the second external tooth maximum outer diameter portion 4b6 and the range of the second internal tooth minimum inner diameter portion 8a6 may overlap partially or entirely. When the second outer tooth maximum outer diameter portion 4b6 is a single point without any range in the axial direction, and the second internal tooth minimum inner diameter portion 8a6 is a single point without any range in the axial direction, the positions of the second outer tooth maximum outer diameter portion 4b6 and the second internal tooth minimum inner diameter portion 8a6 in the axial direction may be aligned with each other.

The second external tooth inner outer diameter reduced portion 4b7 has a range in the axial direction. When the second internal tooth minimum inner diameter portion 8a6 has a range in the axial direction as in the example shown in FIG. 3, the range of the second external tooth inner outer diameter reduced portion 4b7 partially overlaps with the range of the second internal tooth minimum inner diameter portion 8a6. The axially inner end of the second external tooth inner outer diameter reduced portion 4b7 corresponds to the center between the first external tooth portion 4a and the second external tooth portion 4b.

The second internal tooth inner diameter increasing portion 8a7 has a range in the axial direction. The range of the second internal tooth inner diameter increasing portion 8a7 is narrower than the range of the second external tooth inner diameter decreasing portion 4b7, and the entire range of the second internal tooth inner diameter increasing portion 8a7 is included in the range of the second external tooth inner diameter decreasing portion 4b7. The axially inner end of the range of the second external tooth inner diameter decreasing portion 4b7 is aligned with the axially inner end of the range of the second internal tooth inner diameter increasing portion 8a7, but the range of the second external tooth inner diameter decreasing portion 4b7 may extend axially inward beyond the axially inner end of the range of the second internal tooth inner diameter increasing portion 8a7. The range of the second external tooth inner diameter decreasing portion 4b7 extends axially outward beyond the axially outer end of the range of the second internal tooth inner diameter increasing portion 8a7. The axially inner end of the second internal tooth inner diameter increasing portion 8a7 corresponds to the axially inner end of the second internal tooth portion 8a.

The inner diameter increase rate of the second internal tooth inner diameter increasing portion 8a7 is greater than the outer diameter decrease rate of the second external tooth inner diameter decreasing portion 4b7. Therefore, in FIG. 3, the tooth tip curve drawn by the second internal tooth inner diameter increasing portion 8a7 is steeper than the tooth tip curve drawn by the second external tooth inner diameter decreasing portion 4b7. Here, the inner diameter increase rate of the second internal tooth inner diameter increasing portion 8a7 refers to the increase in the inner diameter of the second internal tooth inner diameter increasing portion 8a7 when displaced inward in the axial direction by a unit distance, divided by that unit distance. The inner diameter increase rate of the second internal tooth inner diameter increasing portion 8a7 can also be said to be the increase in the inner diameter of the second internal tooth inner diameter increasing portion 8a7 per unit distance in the axial direction. The outer diameter decrease rate of the second external tooth inner outer diameter decreasing portion 4b7 refers to the decrease in the outer diameter of the second external tooth inner outer diameter decreasing portion 4b7 when displaced inward in the axial direction by a unit distance, divided by that unit distance. The outer diameter reduction rate of the second outer tooth inner outer diameter reduction portion 4b7 can also be said to be the amount of reduction in the outer diameter of the second outer tooth inner outer diameter reduction portion 4b7 per unit distance in the axial direction.

The maximum increase in the inner diameter of the second internal tooth inner diameter increasing portion 8a7 is greater than the maximum decrease in the outer diameter of the second external tooth inner diameter decreasing portion 4b7. The ratio of the maximum increase in the inner diameter of the second internal tooth inner diameter increasing portion 8a7 to the maximum decrease in the outer diameter of the second external tooth inner diameter decreasing portion 4b7 is such that "the maximum decrease in the outer diameter of the second external tooth inner diameter decreasing portion 4b7: the maximum increase in the inner diameter of the second internal tooth inner diameter increasing portion 8a7 = 1: 2 to 4". Here, the maximum increase in the inner diameter of the second internal tooth inner diameter increasing portion 8a7 refers to the maximum inner diameter of the second internal tooth inner diameter increasing portion 8a7 at the axially inner end of the second internal tooth inner diameter increasing portion 8a7 minus the minimum inner diameter of the second internal tooth inner diameter increasing portion 8a7 at the axially outer end of the second internal tooth inner diameter increasing portion 8a7. The maximum reduction in the outer diameter of the second outer tooth inner outer diameter reduced portion 4b7 refers to the maximum outer diameter of the second outer tooth inner outer diameter reduced portion 4b7 at the axially outer outer end of the second outer tooth inner outer diameter reduced portion 4b7 minus the minimum outer diameter of the second outer tooth inner outer diameter reduced portion 4b7 at the axially inner end of the second outer tooth inner outer diameter reduced portion 4b7.

The maximum increase in the inner diameter of the second inner tooth inner diameter increasing portion 8a7 is greater than the maximum decrease in the tooth thickness of the first inner tooth inner diameter increasing portion 6a7.

The second external tooth outer diameter reduced portion 4b8 has a range in the axial direction. When the second internal tooth minimum inner diameter portion 8a6 has a range in the axial direction as in the example shown in FIG. 3, the range of the second external tooth outer diameter reduced portion 4b8 partially overlaps with the range of the second internal tooth minimum inner diameter portion 8a6. The range of the second external tooth outer diameter reduced portion 4b8 extends axially outward beyond the second internal tooth minimum inner diameter portion 8a6. The axially outer end of the second external tooth outer diameter reduced portion 4b8 corresponds to the axially outer end of the second external tooth portion 4b.

The outer diameter reduction rate of the second outer tooth outer diameter reduced portion 4b8 is greater than the outer diameter reduction rate of the second outer tooth inner outer diameter reduced portion 4b7. Therefore, in FIG. 3, the tooth trace curve of the second outer tooth outer diameter reduced portion 4b8 is steeper than the tooth trace curve of the second outer tooth inner outer diameter reduced portion 4b7. Here, the outer diameter reduction rate of the second outer tooth outer diameter reduced portion 4b8 refers to the amount of reduction in the outer diameter of the second outer tooth outer diameter reduced portion 4b8 when displaced a unit distance outward in the axial direction divided by that unit distance. The outer diameter reduction rate of the second outer tooth outer diameter reduced portion 4b8 can also be said to be the amount of reduction in the outer diameter of the second outer tooth outer diameter reduced portion 4b8 per unit distance in the axial direction.

Advantageous Technical Effects
The tooth thickness of the first external tooth inner tooth thickness reduced portion 4a2 of the first external tooth portion 4a gradually decreases toward the inside in the axial direction. Therefore, the tooth surface of the first external tooth portion 4a smoothly contacts the tooth surface of the first internal tooth portion 6a, the one-sided contact load generated at the end of the first external tooth portion 4a in the axial direction inward is reduced, and excessive wear of the first external tooth portion 4a and the first internal tooth portion 6a can be reduced. The fact that the tooth thickness of the first internal tooth inner tooth thickness reduced portion 6a2 of the first internal tooth portion 6a gradually decreases toward the inside in the axial direction also brings about a similar effect.

Since the first external tooth portion 4a and the first internal tooth portion 6a have the first external tooth inner tooth thickness reduced portion 4a2 and the first internal tooth inner tooth thickness reduced portion 6a2, respectively, the tooth thickness of the first external tooth portion 4a and the first internal tooth portion 6a is not excessively small. In other words, the maximum reduction in the tooth thickness of the first external tooth inner tooth thickness reduced portion 4a2 and the maximum reduction in the tooth thickness of the first internal tooth inner tooth thickness reduced portion 6a2 do not need to be excessively large. Therefore, while both the first external tooth portion 4a and the first internal tooth portion 6a have a moderate strength in a well-balanced manner, excessive wear of both the first external tooth portion 4a and the first internal tooth portion 6a can be reduced, and the life of the external gear 4 and the first internal gear 6 is improved. This effect is most noticeable when the following relationship is established: "Maximum reduction in tooth thickness of first outer tooth inner tooth thickness reduced portion 4a2: Maximum reduction in tooth thickness of first inner tooth inner tooth thickness reduced portion 6a2 = 1:2 to 4."

Since one or both of the first external tooth thickest portion 4a1 and the first internal tooth thickest portion 6a1 have a range that spans a specified width in the axial direction, the first external tooth thickest portion 4a1 and the first internal tooth thickest portion 6a1 come into contact with each other even if there is a positional error in the axial direction of the first internal tooth gear 6. Therefore, there is no wobble in the meshing of the first external tooth portion 4a and the first internal tooth portion 6a.

The second external tooth portion 4b and the second internal tooth portion 8a also produce the same effect as the first external tooth portion 4a and the first internal tooth portion 6a.

Even if each component of the flexible mesh gear device 100 has dimensional errors, the above-mentioned advantageous technical effects are reliably achieved by the regulating members 12 and 14. This is because the thickness T12 of the first regulating member 12 is optimally set to match the distance from the outer ring of the bearing 30 to the external gear 4 along the axial direction, and the thickness T14 of the second regulating member 14 is optimally set to match the distance from the outer ring of the bearing 32 to the external gear 4 along the axial direction. In other words, the thicknesses T12 and T14 of the regulating members 12 and 14 appropriately determine the relative position of the tooth trace of the external gear 4 (see FIG. 2) to the tooth trace of the internal gears 6 and 8 (see FIG. 2) in the axial direction, so that the one-sided load generated at the axial inner end of the first external tooth portion 4a is reliably reduced, and excessive wear of the first external tooth portion 4a and the first internal tooth portion 6a is also reliably reduced.

(Embodiment 2)
A second embodiment will be described with reference to Figures 4 and 5. The second embodiment is different from the first embodiment in the following respects, and is similar to the first embodiment except for the following points.

As shown in FIG. 4, the tooth trace of the second internal tooth portion 8a is such that the second internal tooth inner tooth thickness reduced portion 8a2 has an outer region 8a2o and an inner region 8a2i. The inner region 8a2i is located axially inward of the outer region 8a2o. The inner region 8a2i in the axial direction occupies the inner side of the entire range of the second internal tooth inner tooth thickness reduced portion 8a2 in the axial direction, and the outer region 8a2o in the axial direction occupies the outer side of the entire range of the second internal tooth inner tooth thickness reduced portion 8a2 in the axial direction. The tooth thickness of the outer region 8a2o gradually decreases from the second internal tooth thickest portion 8a1 toward the inner side in the axial direction, and the tooth thickness of the inner region 8a2i gradually decreases from the outer region 8a2o toward the inner side in the axial direction. The tooth thickness reduction rate of the inner region 8a2i is greater than the tooth thickness reduction rate of the outer region 8a2o.

The second internal tooth inner tooth thickness reduction portion 8a2 has an outer region 8a2o and an inner region 8a2i, so that the tooth thickness of the second internal tooth portion 8a is reduced toward the axially inner end while the reduction in tooth thickness at the center of the second internal tooth portion 8a in the axial direction is suppressed. This improves the rigidity of the second internal tooth gear 8 and the torsional rigidity of the flexible mesh gear device 100.

In the example shown in FIG. 4, the second internal tooth inner tooth thickness reduced portion 8a2 has an outer region 8a2o and an inner region 8a2i. Similarly, the first internal tooth inner tooth thickness reduced portion 6a2 has an outer region and an inner region located axially inward, and the tooth thickness reduction rate of the inner region may be greater than the tooth thickness reduction rate of the outer region.

As shown in FIG. 5, the second internal tooth portion 8a has an outer region 8a7o and an inner region 8a7i with respect to the tooth tip of the second internal tooth portion 8a. The inner region 8a7i is located axially inward of the outer region 8a7o. The inner region 8a7i in the axial direction occupies the inner side of the entire range of the second internal tooth portion 8a7 in the axial direction, and the outer region 8a7o in the axial direction occupies the outer side of the entire range of the second internal tooth portion 8a7 in the axial direction. The inner diameter of the outer region 8a7o gradually increases from the second internal tooth minimum inner diameter portion 8a6 toward the inner side in the axial direction, and the inner diameter of the inner region 8a7i gradually increases from the outer region 8a7o toward the inner side in the axial direction. The inner diameter increase rate of the inner region 8a7i is greater than the inner diameter increase rate of the outer region 8a7o.

In the example shown in FIG. 5, the second inner tooth inner diameter increasing portion 8a7 has an outer region 8a7o and an inner region 8a7i. Similarly, the first inner tooth inner diameter increasing portion 6a7 has an outer region and an inner region located axially inward therefrom, and the inner diameter increase rate of the inner region may be greater than the inner diameter increase rate of the outer region.

(Embodiment 3)
A third embodiment will be described with reference to Fig. 6. The third embodiment is different from the first embodiment in the following respects, and is similar to the first embodiment except for the following description.

Just as the first external tooth portion 4a has a first external tooth outer tooth thickness reduced portion 4a3, the first internal tooth portion 6a further has a first internal tooth outer tooth thickness reduced portion 6a3. The first internal tooth outer tooth thickness reduced portion 6a3 is located axially outward of the first internal tooth thickest portion 6a1. The tooth thickness of the first internal tooth outer tooth thickness reduced portion 6a3 gradually decreases from the first internal tooth thickest portion 6a1 toward the axially outward. The first internal tooth outer tooth thickness reduced portion 6a3 has a range in the axial direction, and the range of the first internal tooth outer tooth thickness reduced portion 6a3 partially or entirely overlaps with the range of the first external tooth outer tooth thickness reduced portion 4a3.

Just as the second external tooth portion 4b has a second external tooth outer tooth thickness reduced portion 4b3, the second internal tooth portion 8a further has a second internal tooth outer tooth thickness reduced portion 8a3. The second internal tooth outer tooth thickness reduced portion 8a3 is located axially outward of the second internal tooth thickest portion 8a1. The tooth thickness of the second internal tooth outer tooth thickness reduced portion 8a3 gradually decreases from the second internal tooth thickest portion 8a1 toward the axially outward. The second internal tooth outer tooth thickness reduced portion 8a3 has a range in the axial direction, and the range of the second internal tooth outer tooth thickness reduced portion 8a3 partially or entirely overlaps with the range of the second external tooth outer tooth thickness reduced portion 4b3.

The first internal tooth outer tooth thickness reduced portion 6a3 contributes to the tooth surface of the first internal tooth portion 6a smoothly contacting the tooth surface of the first external tooth portion 4a and reducing the one-sided contact load generated at the axially outer end of the first internal tooth portion 6a. The second internal tooth outer tooth thickness reduced portion 8a3 contributes to the tooth surface of the second internal tooth portion 8a smoothly contacting the tooth surface of the second external tooth portion 4b and reducing the one-sided contact load generated at the axially outer end of the second internal tooth portion 8a.

The fact that the first internal tooth portion 6a has a first internal tooth outer tooth thickness reduction portion 6a3 may be applied to embodiment 2. Similarly, the fact that the second internal tooth portion 8a has a second internal tooth outer tooth thickness reduction portion 8a3 may be applied to embodiment 2.

Furthermore, the first internal tooth portion 6a may have a first internal tooth outer inner diameter increasing portion in addition to the first internal tooth minimum inner diameter portion 6a6 and the first internal tooth inner diameter increasing portion 6a7. The first internal tooth outer inner diameter increasing portion is located axially outward from the first internal tooth minimum inner diameter portion 6a6, and the inner diameter of the first internal tooth outer inner diameter increasing portion gradually increases from the first internal tooth minimum inner diameter portion 6a6 toward the axially outward. The fact that the first internal tooth portion 6a has a first internal tooth outer inner diameter increasing portion may be applied to embodiment 2.

Furthermore, the second internal tooth portion 8a may have a second internal tooth outer inner diameter increasing portion in addition to the second internal tooth minimum inner diameter portion 8a6 and the second internal tooth inner diameter increasing portion 8a7. The second internal tooth outer inner diameter increasing portion is located axially outward from the second internal tooth minimum inner diameter portion 8a6, and the inner diameter of the second internal tooth outer inner diameter increasing portion gradually increases from the second internal tooth minimum inner diameter portion 8a6 toward the axially outward. The fact that the second internal tooth portion 8a has a second internal tooth outer inner diameter increasing portion may be applied to embodiment 2.

4 External gear 4a First external tooth part 4a1 First external tooth thickest part 4a2 First external tooth inner tooth thickness reduced part 4a3 First external tooth reduced thickness part 4a6 First external tooth maximum outer diameter part 4a7 First External tooth inner outer diameter reduced part 4a8 First external tooth outer reduced outer diameter part 4b Second external tooth part 4b1 Second outer tooth thickest part 4b2 2nd external tooth inner tooth thickness reduced part 4b3 2nd external tooth outer tooth thickness reduced part 4b6 2nd external tooth maximum outer diameter part 4b7 2nd external tooth inner reduced outer diameter part 4b8 2nd external tooth outer outer diameter reduced part 6 1 Internal gear 6a First internal tooth part 6a1 First internal tooth thickest part 6a2 First internal tooth reduced thickness part on the inside 6a3 First internal tooth reduced thickness on the outside 6a6 1st internal tooth minimum inner diameter part 6a7 First internal tooth inner diameter increasing portion 8 Second internal tooth gear 8a Second internal tooth portion 8a1 Second internal tooth thickest portion 8a2 Second internal tooth inner tooth thickness decreasing portion 8a2i Inner region 8a2o Outer region 8a3 Second internal tooth outer Tooth thickness decreasing portion 8a6 Second internal tooth minimum inner diameter portion 8a7 Second internal tooth inner inner diameter increasing portion 8a7i Inner region 8a7o Outer region 8b Rolling surface 22 Vibrator shaft 22a Vibrator 100 Flexible mesh type gear device

Claims (8)

1. A flexible meshing gear device including: a vibration exciter; an external gear that is flexibly deformed by the vibration exciter; a first internal gear that meshes with the external gear; and a second internal gear that is arranged in line with the first internal gear in the axial direction and meshes with the external gear,
   the external gear has a first external tooth portion that meshes with the first internal gear and a second external tooth portion that meshes with the second internal gear,
   the second external tooth portion has a second external tooth thickest portion where the tooth thickness is maximum, and a second external tooth inner tooth thickness reducing portion where the tooth thickness decreases from the second external tooth thickest portion toward the inside in the axial direction,
   A flexible meshing gear device in which the internal tooth portion of the second internal gear has a second internal tooth thickest portion where the tooth thickness is maximum, and a second internal tooth inner tooth thickness reducing portion where the tooth thickness decreases from the second internal tooth thickest portion toward the axially inward.
2. the first external tooth portion has a first external tooth thickest portion where the tooth thickness is maximum, and a first external tooth inner tooth thickness reducing portion where the tooth thickness decreases from the first external tooth thickest portion toward the inside in the axial direction,
   2. The flexible meshing gear device according to claim 1, wherein the internal tooth portion of the first internal gear has a first internal tooth thickest portion where the tooth thickness is maximum, and a first internal tooth inner tooth thickness reducing portion where the tooth thickness decreases from the first internal tooth thickest portion toward the inside in the axial direction.
3. 3. The flexible meshing gear device according to claim 2, wherein the first external tooth portion and the first internal gear have different numbers of teeth, the second external tooth portion and the second internal gear have the same number of teeth, and a maximum reduction in tooth thickness is greater in the second internal tooth inner tooth thickness reduced portion than in the first internal tooth inner tooth thickness reduced portion.
4. 4. The flexible mesh gear device according to claim 1, wherein the second external tooth portion has a second external tooth outer tooth thickness reducing portion in which the tooth thickness decreases from the second external tooth thickest portion toward the outside in the axial direction.
5. 4. A flexible meshing gear device according to claim 1, wherein the internal tooth portion of the second internal gear has a second internal tooth outer tooth thickness reducing portion in which the tooth thickness decreases from the second internal tooth thickest portion toward the axially outer side.
6. 4. The flexible mesh gear device according to claim 1, wherein at least one of the second external tooth thickest portion and the second internal tooth thickest portion is provided over a predetermined width in the axial direction.
7. 4. The flexible mesh gear device according to claim 1 , wherein a reduction in tooth thickness per unit distance in a tooth trace direction is greater in the second internal tooth inner tooth thickness reduced portion than in the second external tooth inner tooth thickness reduced portion.
8. the second internal tooth inner tooth thickness reduced portion has an outer region continuing from the second internal tooth thickest portion and an inner region located axially inside the outer region,
   4. The flexible mesh gear device according to claim 1, wherein a reduction in tooth thickness per unit distance in a tooth trace direction is greater in the inner region than in the outer region.

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