Helical gears and reducers

Abstract

A disclosed helical gear (12) comprises: a helical portion (2) formed by forming a helical tooth trace on an outer cylindrical surface of a cylindrical rim (1); and a thinned portion (3) formed by recessing an area on one end surface, in an axial direction, of the rim (1), in which a distance to an axis (D) is equal to or less than a prescribed value, toward the other end surface side. If a ratio of a value obtained by subtracting a thinned thickness (H) of the thinned portion (3) from a thickness (G) of the rim (1), to a tooth thickness (J) of the helical portion (2) is defined as a first ratio (P), and a ratio of a recessed dimension (F) to an overall length dimension (E), in the axial direction, of the rim (1) is defined as a second ratio (Q), relationships between the first ratio (P) and two end points (m, n) of a range of the second ratio (Q) are P=12.628m-25.78, and P=9.8605n-88.24 (P: first ratio [%]; m: one end point [%]; n: other end point [%]).

Description

[Technical Field]

[0001] The present invention relates to a helical gear and a reducer including the helical gear. [Background technology]

[0002] Conventionally, helical gears (helical gears) have been known, in which the tooth traces are inclined in a helical manner relative to the rotation axis among cylindrical gears (see Patent Document 1). The breakage resistance of such gears varies depending on the size of the teeth and rotation characteristics. For example, increasing the size of the entire gear increases the face width and tooth thickness, reducing the tooth root stress of the gear, thereby suppressing the occurrence of breakage or damage. In addition, increasing the pressure angle of the gear or reducing the rotational speed can also reduce the possibility of breakage or damage. [Prior art documents] [Patent documents]

[0003] [Patent Document 1] Special Publication No. 2007-537415 Summary of the Invention [Problem to be solved by the invention]

[0004] On the other hand, increasing the size of the gears increases the overall size of the device to which the gears are applied, making miniaturization difficult. Furthermore, design constraints and requirements may make it impossible to change the rotational characteristics of the gears. For example, increasing the pressure angle of the gears reduces the meshing ratio. To address these issues, it may be possible to improve breakage resistance without changing the shape by manufacturing gears using high-strength materials. However, high-strength materials are expensive, which increases costs.

[0005] One of the objects of the present invention, which was conceived in light of the above-mentioned problems, is to provide a helical gear and a reducer including the helical gear, which are capable of improving breakage performance while suppressing increases in size and costs. However, in addition to this object, another object of the present invention is to achieve effects derived from the configurations shown in the "Description of Embodiments" below, which cannot be obtained with conventional techniques. [Means for solving the problem]

[0006] (1) Disclosure The helical gear is a helical gear serving as a planetary gear that meshes with the ring gear and sun gear of a planetary gear mechanism. The helical gear comprises a helical tooth portion formed by helical tooth traces on the outer cylindrical surface of a cylindrical rim, and a lightening portion formed by recessing an area of ​​one end face of the rim in the axial direction, the area being a predetermined value or less from the axis center, toward the other end face. a shaft hole that is bored coaxially with the shaft center and has a hollow cylindrical shape with a radius smaller than the predetermined value, and into which a carrier pin of the planetary gear mechanism is rotatably inserted; The ratio of the thickness of the rim minus the thickness of the lightening portion to the tooth thickness of the helical tooth portion is defined as a first ratio, and the ratio of the recess dimension to the overall axial length of the rim is defined as a second ratio, and the relationship between the first ratio and both end points of the range of the second ratio is given by the following formula: P= a m- b P= c n- d (where P is the first percentage [%], m is one end point [%], n is the other end point [%]) [The values ​​of a, b, c, and d included in the above formula are determined as follows: The tooth root stress generated at both axial ends of the helical tooth portion due to meshing between the sun gear and the ring gear is the first tooth root stress. The tooth root stress generated in the axial center of the helical tooth portion due to the meshing of the sun gear and the ring gear is the second tooth root stress. The tooth root stress generated in the axial center of the helical tooth portion due to being supported by the carrier pin is the third tooth root stress. When the first ratio is 19.0[%], and the relationship between the second ratio [%] and the maximum values ​​of the first tooth root stress, the second tooth root stress, and the third tooth root stress for the second ratio is graphed, the range of the second ratio in which the maximum tooth root stress is 1.1 times or less of the minimum value of the maximum tooth root stress in the graph is defined as R. 1 ~R 2 Let's say. When the first ratio is 56.2% and the relationship between the second ratio [%] and the maximum values ​​of the first tooth root stress, the second tooth root stress, and the third tooth root stress for the second ratio is graphed, the range of the second ratio in which the maximum tooth root stress is 1.1 times or less of the minimum value of the maximum tooth root stress in the graph is defined as R. 3 ~R 4 Let's say. When the first ratio is 103.8[%], and the relationship between the second ratio [%] and the maximum values ​​of the first tooth root stress, the second tooth root stress, and the third tooth root stress for the second ratio is graphed, the range of the second ratio in which the maximum tooth root stress is 1.1 times or less of the minimum value of the maximum tooth root stress in the graph is defined as R. 5 ~R 6 Let's say. In a plane graph with the first ratio as the vertical axis and the second ratio as the horizontal axis, three coordinates (R 1 ,19.0),(R 3 ,56.2),(R 5 ,103.8) is approximated as a straight line, the slope of the line is a and the intercept of the line is b. In a plane graph with the first ratio as the vertical axis and the second ratio as the horizontal axis, three coordinates (R 2 ,19.0),(R 4 ,56.2),(R 6 , 103.8) is approximated as a straight line, the slope of the line is c and the intercept of the line is d.

[0007] (2) Regarding (1) above, it is preferable that in the formula, a=12.628, b=25.78, c=9.8605, and d=88.24. ( 3 )the above( 2 ), the first ratio is preferably within the range of 19.0 to 103.8%. In this case, the second ratio is preferably within the range of at least 3.6 to 19.3%. ( 4 )the above( 2 )or( 3 ), the second ratio is preferably within the range of 6.4 to 15.0%.

[0008] If the first ratio is 19.0%, the second ratio is preferably within the range of 3.6 to 10.7%. If the first ratio is 56.2%, the second ratio is preferably within the range of 6.4 to 15.0%. If the first ratio is 103.8%, the second ratio is preferably within the range of 10.7 to 19.3%.

[0009] ( 5 ) (1) to ( 4 ) It is preferable that the recessed portion is provided on each of one end face and the other end face of the rim in the axial direction, and the recess dimension on the one end face is the same as the recess dimension on the other end face.

[0010] ( 6) Above ( 1 ) or (5) In the present invention, it is preferable that the rim has a sliding contact portion that is protruded toward the opposite side from the other end face in an annular area where the distance to the axis center exceeds the predetermined value on one end face in the axial direction of the rim.

[0011] (7) The disclosed reducer is 1 ) ~ (6) Eitherand the planetary gear mechanism. The aforementioned The transmission includes an input shaft connected to the sun gear, and an output shaft connected to a carrier having the carrier pin. [Effects of the Invention]

[0012] The disclosed helical gear and reducer can improve breakage performance while suppressing increases in size and costs. [Brief explanation of the drawings]

[0013] [Figure 1] 1 is a cross-sectional view showing the configuration of a reducer according to an embodiment of the present invention; [Figure 2] FIG. 2 is a skeleton diagram of a compound planetary gear mechanism incorporated in the reducer of FIG. 1. [Figure 3] FIG. 3 is a front view of the planetary gear mechanism in FIG. 2. [Figure 4] FIG. 4 is a perspective view of a helical gear applied to the planetary gear mechanism of FIG. 3. [Figure 5] FIG. 5 is a cross-sectional view of the helical gear of FIG. 4. [Figure 6] 1 is a graph showing the relationship between the thickness reduction rate and the tooth root stress of a helical gear. [Figure 7] 1 is a graph showing the relationship between the thickness reduction rate and the maximum tooth root stress of a helical gear. [Figure 8] FIG. 2 is a perspective view of the first carrier of FIG. 1. [Figure 9] 2A and 2B are cross-sectional views of the main part of the first carrier of FIG. 1 (enlarged view of A in FIG. 1). [Figure 10] 2 is a cross-sectional view of the locking portion of FIG. 1 (cross-sectional view taken along line B of FIG. 1). [Figure 11] 10 is a table showing the simulation results of CAE analysis of the relationship between the second ratio and the tooth root stress, with the first ratio fixed at 19.0%. [Figure 12] 12 is a graph showing the relationship between the second ratio and the tooth root stress shown in FIG. 11. [Figure 13] 12 is a graph showing the relationship between the second ratio and the maximum tooth root stress shown in FIG. 11. [Figure 14]10 is a table showing the simulation results of CAE analysis of the relationship between the second ratio and the tooth root stress, with the first ratio fixed at 56.2%. [Figure 15] 15 is a graph showing the relationship between the second ratio and the tooth root stress shown in FIG. 14. [Figure 16] 15 is a graph showing the relationship between the second ratio and the maximum tooth root stress shown in FIG. 14. [Figure 17] 10 is a table showing the simulation results of CAE analysis of the relationship between the second ratio and the tooth root stress, with the first ratio fixed at 103.8%. [Figure 18] 18 is a graph showing the relationship between the second ratio and the tooth root stress shown in FIG. 17. [Figure 19] 18 is a graph showing the relationship between the second ratio and the maximum tooth root stress shown in FIG. 17. [Figure 20] 10 is a graph showing the relationship between a first ratio and a second ratio. DETAILED DESCRIPTION OF THE INVENTION

[0014] [1. Configuration] Hereinafter, a helical gear and a reducer 7 including a helical gear will be described as an embodiment. FIG. 1 is a cross-sectional view showing the configuration of a reducer 7 incorporating a helical gear. This reducer 7 is a transmission that reduces the speed of the rotational driving force of, for example, a motor 6 to increase torque. The driving force generated by the motor 6 is input to the reducer 7 via an input shaft 17, and after being changed in speed (decelerated) inside the reducer 7, is output from an output shaft 27. A plurality of gears are interposed in the power transmission path from the input shaft 17 to the output shaft 27. The example shown in FIG. 1 is a reducer 7 incorporating a two-stage compound planetary gear mechanism that combines a first planetary gear mechanism 10 and a second planetary gear mechanism 20.

[0015] The first planetary gear mechanism 10 and the second planetary gear mechanism 20 are housed inside a gear housing 8 and a cover 9 formed to surround the outer periphery of the reducer 7. The gear housing 8 is formed, for example, in the shape of a hollow cylinder with both the bottom and top sides open. The gear housing 8 shown in FIG. 1 has an open end face on the right side of the page, and a truncated conical (tapered) cover 9 is attached to the opening. The gear housing 8 and the cover 9 are locked to each other via a locking portion 40 provided in at least one location (multiple locations if necessary).

[0016] The gear housing 8 shown in FIG. 1 has an inclined portion formed in a truncated cone shape (tapered) at its left end on the page. A hole is formed in the center of the inclined portion (the top surface of the truncated cone) through which the input shaft 17, which is the rotating shaft of the motor 6, is inserted. The motor 6 (shown in outline by a dashed line) is attached to the gear housing 8 so as to cover this hole. Furthermore, a cover 9 is attached to the gear housing 8 shown in FIG. 1 at its right end on the page. A hole is formed in the center of the cover 9 (the top surface of the truncated cone) through which the output shaft 27 is inserted. The input shaft 17 and the output shaft 27 are arranged coaxially with the center axis C of the gear housing 8.

[0017] FIG. 2 is a skeleton diagram of the compound planetary gear mechanism built into the reducer 7. The first planetary gear mechanism 10 is provided with a first sun gear 11, a first planetary gear 12, a first ring gear 13, and a first carrier 14. The first sun gear 11 is an external gear connected to (or formed integrally with) the input shaft 17. The first ring gear 13 is an internal gear formed on (or fixed to) the inner circumferential surface of the gear housing 8. The first planetary gear 12 is an external gear interposed between the first sun gear 11 and the first ring gear 13, and meshes with both gears. The tooth traces formed on each of the gears 11 to 13 are helical, and the first sun gear 11 and the first planetary gear 12 are also called external helical gears, and the first ring gear 13 is also called an internal helical gear.

[0018] 3 is a front view showing the first planetary gear mechanism 10 provided with four first planetary gears 12. The number of first planetary gears 12 can be set arbitrarily and may be one or two or more. The center of the first planetary gear 12 is rotatably supported by a first carrier pin 15 fixed to the first carrier 14. The first planetary gear 12 is rotatable (can rotate) around an axis D of the first carrier pin 15.

[0019] As shown in FIGS. 1 to 3, a first carrier shaft 16 that is coaxial with the input shaft 17 is formed (or fixed) on first carrier 14. First carrier 14 is rotatable about first carrier shaft 16 (i.e., about central axis C). This allows first planetary gear 12 to revolve around central axis C. First carrier shaft 16 also functions as an output shaft that outputs the rotational driving force that has been changed in speed by first planetary gear mechanism 10. Here, the number of teeth of first sun gear 11 is defined as Z1, and the number of teeth of first ring gear 13 is defined as Z2. When first sun gear 11 is rotationally driven with first ring gear 13 fixed, the reduction ratio of the rotational speed output from first carrier shaft 16 (the angular velocity ratio of first carrier shaft 16 to input shaft 17) is Z1 / (Z1+Z2).

[0020] As shown in FIGS. 1 and 2, the second planetary gear mechanism 20 includes a second sun gear 21, a second planetary gear 22, a second ring gear 23, and a second carrier 24. The second sun gear 21 is an external gear having a larger diameter than the first sun gear 11, and is connected to (or formed integrally with) the first carrier shaft 16. In this embodiment, the first carrier shaft 16 also functions as an input shaft that inputs a rotational driving force to the second planetary gear mechanism 20. The second ring gear 23 is an internal gear having a larger diameter than the first ring gear 13, and is formed (or fixed) on the inner circumferential surface of the gear housing 8. The second planetary gear 22 is an external gear interposed between the second sun gear 21 and the second ring gear 23, and meshes with both gears. Each of the gears 21 to 23 included in the second planetary gear mechanism 20 is also a helical gear.

[0021] The center of the second planetary gear 22 is rotatably supported by a second carrier pin 25 fixed to the second carrier 24. The second planetary gear 22 is rotatable (can rotate) around the axis of the second carrier pin 25. A second carrier shaft 26 that is coaxial with the input shaft 17 is formed (or fixed) on the second carrier 24. The second carrier 24 is rotatable around the second carrier shaft 26 (i.e., around the central axis C). This allows the second planetary gear 22 to revolve around the central axis C. An output shaft 27 that is coaxial with the input shaft 17 is connected to (or formed integrally with) the second carrier shaft 26.

[0022] Second carrier shaft 26 functions as an output shaft that outputs the rotational driving force whose speed is changed by second planetary gear mechanism 20. Here, the number of teeth of second sun gear 21 is Z3, and the number of teeth of second ring gear 23 is Z4. When second sun gear 21 is rotationally driven with second ring gear 23 fixed, the reduction ratio of the rotational speed output from second carrier shaft 26 (angular velocity ratio of second carrier shaft 26 to first carrier shaft 16) is Z3 / (Z3+Z4). Furthermore, the reduction ratio of output shaft 27 to input shaft 17 is Z1 / {Z1+(Z1+Z2)Z4}.

[0023] FIG. 4 is a perspective view of the first planetary gear 12 (helical gear). The first planetary gear 12 is a helical gear with helical tooth traces formed on the outer cylindrical surface of a cylindrical rim 1, and has a helical tooth portion 2. The helical tooth portion 2 is a portion of the outer cylindrical surface of the rim 1 where the helical tooth traces are formed. The tooth thickness of the helical tooth portion 2 (the thickness of the tooth portion at the pitch diameter of the gear) is J. The first planetary gear 12 is drilled with a shaft hole 4 into which a first carrier pin 15 is rotatably inserted. The shaft hole 4 is a hollow cylindrical hole, and its center is coaxial with the axis D of the first carrier pin 15. The meshing ratio of the first planetary gear 12 is set to be at least greater than 1.

[0024] One axial end face of the rim 1 is provided with a lightening portion 3 that is recessed toward the other end face. The lightening portion 3 is a circular area on one axial end face of the rim 1 that is recessed toward the other end face, with the distance to the axis D being equal to or less than a predetermined value. This lightening portion 3 is provided on at least one of both end faces of the rim 1. Preferably, lightening portions 3 are provided on both end faces. The shape of the lightening portion 3 on one end face may be different from the shape of the lightening portion 3 on the other end face, but more preferably, the lightening portion 3 on one end face and the lightening portion 3 on the other end face have the same shape. Furthermore, the circular area in which the lightening portion 3 is formed is at least larger than the shaft hole 4. When the radius of the area in which the lightening portion 3 is formed is a predetermined value, the radius of the shaft hole 4 is smaller than the predetermined value (the radius of the lightening portion 3).

[0025] FIG. 5 is a cross-sectional view of the first planetary gear 12 (helical gear) taken along a plane passing through the axis D. The ratio P is defined as the rim thickness G minus the recessed thickness H (counterbore diameter) of the recessed portion 3 relative to the tooth thickness J of the helical tooth portion 2. It is expressed as "P = (GH) / J." When the ratio P is 56.2%, the recessed dimension F of the recessed portion 3 in the axial direction is set within a range of 4 to 22% of the overall axial dimension E of the rim 1. Preferably, the recessed dimension F is set within a range of 7 to 17% of the overall dimension E. The recessed portion 3 has a side portion 31 formed on the inner circumferential surface of a cylinder centered on the axis D, and a bottom portion 32 formed on a plane perpendicular to the axis D. The same applies to the open end of the side portion 31.

[0026] Here, the dimension from the tooth bottom of the helical tooth portion 2 to the cylindrical surface of the shaft hole 4 is defined as the rim thickness G (rim thickness). The dimension obtained by subtracting the radius of the shaft hole 4 from the predetermined value of the lightening portion 3 is defined as the lightening thickness H. These rim thicknesses G and H are shown as examples in Figure 5. When the ratio P = 56.2 [%], the lightening thickness H is preferably set to at least one-third of the rim thickness G, and more preferably at least half of the rim thickness G. Increasing the lightening thickness H reduces the root stress of the helical tooth portion 2.

[0027] 6 and 7 are diagrams illustrating the simulation results of CAE (Computer Aided Engineering) analysis when the ratio P is 56.2%. Using a computer and software for CAE analysis, the inventors investigated how various tooth root stresses change when the shape of the first planetary gear 12 (helical gear) is changed. FIG. 6 is a graph showing the relationship between the ratio (percentage) of the recess dimension F to the overall axial dimension E of the rim 1 and the tooth root stress of the helical tooth portion 2 for the first planetary gear 12. The vertical axis represents the tooth root stress expressed as a percentage, with the maximum value of the tooth root stress when the recess dimension F is 0 (in other words, the tooth root stress when the ratio of the recess dimension F to the overall axial dimension E of the rim 1 is 0) being set to 100%. Three types of tooth root stress are considered here. The first tooth root stress is the tooth root stress generated at both axial ends of the helical tooth portion 2 due to the meshing between the first sun gear 11 and the first ring gear 13. The second tooth root stress is the tooth root stress generated at the axial center of the helical tooth portion 2 due to the meshing between the first sun gear 11 and the first ring gear 13. The third tooth root stress is the tooth root stress generated at the axial center of the helical tooth portion 2 due to support by the first carrier pin 15. The magnitude of each tooth root stress changes according to the recess dimension F of the lightening portion 3, in other words, according to the ratio of the recess dimension F to the overall length dimension E.

[0028] The first tooth root stress decreases as the recess dimension F increases, as shown by the black circles and thick solid line in Fig. 6. On the other hand, the second tooth root stress increases as the recess dimension F increases, as shown by the black triangles and dashed line in Fig. 6. The same is true for the third tooth root stress, which also increases as the recess dimension F increases, as shown by the black squares and two-dot chain line in Fig. 6. The value of each tooth root stress changes almost linearly with the ratio of the recess dimension F to the overall length dimension E.

[0029] As shown in Figure 6, if the ratio of recess dimension F to overall length dimension E is too small, the first tooth dedendum stress will be excessive. On the other hand, if the ratio of recess dimension F to overall length dimension E is too large, the third tooth dedendum stress will be excessive. Therefore, it is important to set the ratio of recess dimension F to overall length dimension E within an appropriate range. This prevents a situation in which any of the three tooth dedendum stresses becomes excessively large. can Compared to when there is no cutout 3, The maximum tooth root stress among the three types of tooth root stress is About 20% degree cutting It can be reduced.

[0030] FIG. 7 is an approximate curve illustrating the relationship between the ratio of recess dimension F to overall length dimension E (horizontal axis) and the maximum tooth root stress (maximum tooth root stress, vertical axis) among the three types of tooth root stress shown in FIG. 6 . According to the inventor's calculations, when ratio P is 56.2%, the range of F ratio at which the maximum tooth root stress value is equal to or less than predetermined value X is 4 to 22%. X is a smaller value than when no recessed portion 3 is provided (i.e., recess dimension F is 0). Therefore, by setting the F ratio within this range, the maximum tooth root stress is kept equal to or less than predetermined value X, thereby improving the strength of the gear. Furthermore, the range of F ratio at which the maximum tooth root stress value is equal to or less than second predetermined value Y, which is smaller than predetermined value X, is 7 to 17%. Therefore, by setting the F ratio within this range, the maximum tooth root stress is kept equal to or less than second predetermined value Y, thereby further improving the strength of the gear.

[0031] As shown in FIG. 5, one axial end face of the rim 1 is provided with a sliding contact portion 5 that protrudes outward from the helical end face 28, which is the axial end face of the helical tooth portion 2. The sliding contact portion 5 is a portion of one axial end face of the rim 1 that is formed by protruding toward the opposite side (outward) from the other end face in an annular area whose distance to the axis D exceeds a predetermined value (the radius of the lightening portion 3). This sliding contact portion 5 is provided on at least one of both end faces of the rim 1. Preferably, sliding contact portions 5 are provided on both end faces. The shape of the sliding contact portion 5 on one end face side may be different from the shape of the sliding contact portion 5 on the other end face side, but more preferably, the sliding contact portion 5 on one end face side and the sliding contact portion 5 on the other end face side have the same shape.

[0032] The sliding contact portion 5 is provided with a first surface portion 51 and a second surface portion 52. The first surface portion 51 is a portion formed in a flat plane perpendicular to the axis D. The first surface portion 51 is provided so as to come into surface contact with another member whose position is fixed, such as the gear housing 8 or the cover 9. The second surface portion 52 is a portion formed in a cylindrical surface shape so as to connect the first surface portion 51 and the helical tooth end surface 28. By supporting the first surface portion 51 on another member, displacement or movement of the first planetary gear 12 in the axial direction is prevented.

[0033] 1, the member that comes into surface contact with the first surface portion 51 only needs to support at least a portion of the first surface portion 51, and does not need to simultaneously support the entire surface of the first surface portion 51. Furthermore, although the overall length dimension E shown in FIG. 5 indicates the distance between the first surface portion 51 on one end face side and the first surface portion 51 on the other end face side, the overall length dimension E may also be the distance between the helical tooth end surface 28 on one end face side and the helical tooth end surface 28 on the other end face side. When the sliding contact portion 5 is formed on only one side, the overall length dimension E may also be the distance between the first surface portion 51 on one end face side and the helical tooth end surface 28 on the other end face side.

[0034] Fig. 8 is a perspective view of the first carrier 14 of the first planetary gear mechanism 10 shown in Fig. 3. The first carrier 14 is provided with a disk portion 18 formed in a disk shape perpendicular to the central axis C, cylindrical first carrier pins 15 erected on one side of the plate surface of the disk portion 18, and a cylindrical first carrier shaft 16 erected on the other side of the plate surface of the disk portion 18. The number of first carrier pins 15 is four so as to correspond to the four first planetary gears 12.

[0035] 9(A) and 9(B) are cross-sectional views (enlarged views of A in FIG. 1) illustrating the shape of the base end of the first carrier pin 15. The first carrier pin 15 receives force from the first planetary gear 12, generating stress. The area near the base end, where stress is particularly likely to concentrate, is formed as an arc in a cross section passing through the axis D. To mitigate stress concentration, it is desirable to increase the radius of curvature r as much as possible. Therefore, the shape of the base end of the first carrier pin 15 is formed so that the central angle θ is 90° or less in a cross section passing through the axis D. For example, the shape is formed so that the arc is approximately 30°. As an example, the diameter of the first planetary gear 12 is φ10 and the diameter of the four first carrier pins 15 is φ5. The central angle θ of the arc constituting the cross section of the base end of the first carrier pin 15 is set, for example, within a range of 20 to 50°, preferably within a range of 25 to 35°, and more preferably 30°.

[0036] Here, if the base end portion is designed as an arc with a central angle θ of 90°, the radius of curvature r of the arc has an upper limit of approximately 2.5 in order to prevent interference between the first carrier pins 15. Furthermore, if the radius of curvature r of the arc is set larger than this (for example, to approximately r20.0), it becomes necessary to space the first carrier pins 15 apart, which increases the size of the first planetary gear mechanism 10. On the other hand, by setting the central angle θ of the arc to approximately 30°, it becomes unnecessary to space the first carrier pins 15 apart even when the radius of curvature r is set large (for example, to approximately r20.0), and this makes it easy to downsize the first planetary gear mechanism 10.

[0037] 9(A), the upper end of the arc forming the base end of the first carrier pin 15 may be smoothly connected to the cylindrical surface of the first carrier pin 15, and the lower end of the arc may be connected to the disk portion 18 by a smooth curve (for example, an arc with a smaller radius of curvature or a spline curve). Furthermore, since the larger the radius of curvature r, the more likely stress is to be concentrated at the lower end of the arc, the phase (position relative to the center) of the arc forming the base end of the first carrier pin 15 may be shifted as shown in FIG.

[0038] For example, in the example shown in FIG. 9(A), the upper end of the arc is located in the 9 o'clock direction (horizontal direction from the center to the left) relative to the center of the dashed circle. In contrast, in the example shown in FIG. 9(B), the upper end of the arc is located in the 8 o'clock direction (downward and left direction from the center) relative to the center of the dashed circle. As such, the normal direction of the upper end of the arc forming the base end of the first carrier pin 15 may be set parallel to the disk portion 18 (horizontal direction in the figure), or may be set in a non-parallel, oblique direction. However, it is preferable that the boundary between the cylindrical surface of the first carrier pin 15 and the upper end of the arc be smoothly connected by an arc with a smaller radius of curvature, a spline curve, or the like. The same applies to the boundary between the disk portion 18 and the lower end of the arc.

[0039] In addition, since the upper side of the arc forming the base end of the first carrier pin 15 is subjected to a larger stress than the lower side, the angle θ A is the angle θ B Set it larger than (θ A >θ B It is preferable to set the angle θ A 9(B), is the angle between the line segment connecting the upper end of the arc forming the base end of the first carrier pin 15 to the center of the arc and the cylindrical surface of the first carrier pin 15. Also, angle θ B is the angle formed by the line segment connecting the lower end of the arc forming the base end of the first carrier pin 15 to the center of the arc and the plate surface of the disk portion 18 in FIG. 9(B).

[0040] 10 is a cross-sectional view (cross-sectional view B in FIG. 1) of the locking portion 40 in FIG. 1. The locking portions 40 are provided, for example, at multiple locations and are arranged at predetermined intervals in the circumferential direction of the gear housing 8 and the cover 9. The locking portions 40 are each provided with a claw 41 that protrudes from the gear housing 8 side and a claw receiver 43 that is recessed into the cover 9 side. As shown in FIG. 1, by moving the gear housing 8 toward the cover 9 along the central axis C, the claw 41 is fitted into the inside of the claw receiver 43, and the concave and convex shapes engage with each other. This allows the gear housing 8 and the cover 9 to be locked together.

[0041] In the cross section of the locking portion 40 shown in FIG. 10 , claw end faces 42 are provided at both circumferential ends of the claw 41. Correspondingly, claw receiving end faces 44 are provided at both circumferential ends of the claw receiver 43. The claw receiving end faces 44 are formed to be sized to be in surface contact with the entire surface of the claw end face 42. In other words, the claws 41 and the claw receiver 43 are shaped so that the radially outer surface of the claw 41 is located more inward than the radially outer surface of the claw receiver 43. With this structure, for example, when the gear housing 8 attempts to rotate around the central axis C, the claw end faces 42 come into full collision with the claw receiving end faces 44 (there is no offset collision). This prevents the claws 41 from opening and jumping out of the claw receiver 43 (disengagement), making it easier to maintain the engagement between the gear housing 8 and the cover 9.

[0042] When the claw end surfaces 42 protrude radially outward relative to the end surfaces of the claw receivers 43, even if the protruding portion is only a portion of the claw end surfaces 42, an offset collision (partial collision) of the claw end surfaces 42 may generate a radially outward force on the claws 41, causing the claws 41 to open and protrude outside the claw receivers 43. In contrast, as shown in Figure 10, by configuring the claw end surfaces 42 to fit inside the claw receivers 43, the claws 41 are less likely to protrude outward.

[0043] [2.Analysis results] 11 to 20 are diagrams illustrating the simulation results of the CAE analysis according to the above-described embodiment. The inventors used a computer and software for CAE analysis to study how various tooth root stresses change when the shape of the first planetary gear 12 (helical gear) is changed. Here, the ratio P of the value obtained by subtracting the cutout thickness H (counterbore diameter) of the cutout portion 3 from the rim thickness G to the tooth thickness J of the helical tooth portion 2 is defined as a first ratio P. Furthermore, the ratio F of the recessed dimension in the axial direction of the cutout portion 3 to the overall axial dimension E of the rim 1 is defined as a second ratio Q. In other words, Q = F / E.

[0044] It should be noted that the analysis conditions (e.g., mesh size, number of meshes, mesh shape, etc. of the analysis structure) for the simulation results shown in Figures 11 to 20 are slightly different from the analysis conditions for the simulation results shown in Figures 6 and 7. Therefore, it should be noted that the simulation results shown in Figures 11 to 20 do not necessarily completely match the simulation results shown in Figures 6 and 7. It should also be noted that when interpreting the simulation results shown in Figures 6, 7, and 11 to 20, one should strive to understand the technical features and characteristics derived from each analysis result, without being caught up in differences or discrepancies in minor matters (specific numerical values, graph shapes, etc.).

[0045] 11 is a table showing the simulation results when the first percentage P is fixed at 19.0% and the second percentage Q of the recess dimension F in the axial direction of the lightening portion 3 is changed within the range of 3.6 to 12.1%. The analysis conditions are: rim thickness G is 1.69 mm, lightening thickness H (counterbore diameter) is 1.49 mm, tooth thickness J is 1.05 mm, tooth width of the helical tooth portion 2 is 7.0 mm, and input torque is 2.0 Nm.

[0046] Figure 12 is a graph showing the behavior of the three types of tooth root stresses [MPa] shown in Figure 11 versus the second ratio Q [%]. The black circles and thick solid lines in the figure represent the first tooth root stress and its approximate curve. Similarly, the black triangles and dashed lines represent the second tooth root stress and its approximate curve, and the black squares and two-dot chain lines represent the third tooth root stress and its approximate curve. These graphs show that the first tooth root stress is relatively large in the region where the second ratio Q is relatively small, while both the second and third tooth root stresses are relatively large in the region where the second ratio Q is relatively large.

[0047] Figure 13 graphs the relationship between the second ratio Q [%] in Figure 11 and the maximum values [MPa] of the first, second, and third root stresses with respect to the second ratio Q. The black circles and thick solid lines in the figure indicate the maximum root stress and the approximate curve. Here, let the minimum value (bottom value) of the maximum root stress in this graph be R. The range of the second ratio Q in which the maximum root stress is smaller than the value Z obtained by multiplying the minimum value R by a predetermined coefficient K is a range in which each of the first, second, and third root stresses does not become excessively large and is comprehensively small. The minimum value R in Figure 13 is 13.0 [MPa]. Also, as a result of the inventor's intensive study, it has been found that excellent effects can be obtained if the increase in the maximum root stress with respect to the minimum value R is within 10% (K ≤ 1.1). When the predetermined coefficient K is 1.1, the value Z becomes 14.3 [MPa]. Extracting the range of the second ratio Q in which the maximum root stress is less than or equal to the value Z gives approximately 3.6 to 10.7 [%]. The specific value of the predetermined coefficient K can be arbitrarily set, but it is set, for example, within the range of 1.0 < K ≤ 1.5.

[0048] Figure 14 is a table showing the simulation results when the first ratio P is fixed at 56.2 [%] and the concave dimension F in the axial direction of the relief portion 3 is changed within the range where the second ratio Q is 5.0 to 15.0 [%]. The analysis conditions are that the rim thickness G is 1.69 [mm], the relief thickness H (drill diameter) is 1.1 [mm], the tooth thickness J is 1.05 [mm], the tooth width of the helical tooth portion 2 is 7.0 [mm], and the input torque is 2.0 [Nm].

[0049] Figure 15 graphs the behavior of the three types of root stresses [MPa] shown in Figure 14 with respect to the second ratio Q [%]. The black circles and thick solid lines in the figure indicate the first root stress and the approximate curve. Similarly, the black triangles and broken lines indicate the second root stress and the approximate curve, and the black squares and two-dot chain lines indicate the third root stress and the approximate curve. From these graphs, it can be seen that in the region where the second ratio Q is relatively small, the first root stress becomes relatively large, while in the region where the second ratio Q is relatively large, the third root stress becomes relatively large. Also, when the first ratio P is 56.2 [%], it can be seen that there is little need to consider the second root stress when examining the maximum root stress.

[0050] Figure 16 is a graph showing the relationship between the second percentage Q [%] in Figure 14 and the maximum values ​​[MPa] of the first, second, and third root stresses for that second percentage Q. The black circles and thick solid lines in the figure represent the maximum root stress and an approximate curve. The minimum value R in Figure 16 is 15.2 [MPa]. When the predetermined coefficient K is 1.1, the value Z is 16.72 [MPa]. The range of the second percentage Q where the maximum root stress is equal to or less than the value Z is extracted, and is approximately 6.4 to 15.0 [%].

[0051] 17 is a table showing the simulation results when the first proportion P is fixed at 103.8% and the second proportion Q of the axial recess dimension F of the lightening portion 3 is changed within the range of 6.4 to 23.6%. The analysis conditions are: rim thickness G is 1.69 mm, lightening thickness H (counterbore diameter) is 1.49 mm, tooth thickness J is 1.05 mm, tooth width of the helical tooth portion 2 is 7.0 mm, and input torque is 2.0 Nm.

[0052] Figure 18 is a graph showing the behavior of the three types of tooth root stresses [MPa] shown in Figure 17 versus the second percentage Q [%]. The black circles and thick solid lines in the figure represent the first tooth root stress and its approximate curve. Similarly, the black triangles and dashed lines represent the second tooth root stress and its approximate curve, and the black squares and two-dot chain lines represent the third tooth root stress and its approximate curve. These graphs show that the first tooth root stress is relatively large in the region where the second percentage Q is relatively small, while the third tooth root stress is relatively large in the region where the second percentage Q is relatively large. It can also be seen that even when the first percentage P is 103.8 [%], there is little need to consider the second tooth root stress when determining the maximum tooth root stress.

[0053] FIG. 19 graphs the relationship between the second ratio Q [%] in FIG. 17 and the maximum values [MPa] of the first, second, and third root stresses with respect to the second ratio Q. The black circles and thick solid line in the figure indicate the maximum root stress and the approximate curve. The minimum value R in FIG. 19 is 14.6 [MPa]. Also, when a predetermined coefficient K is 1.1, the value Z becomes 16.06 [MPa]. When extracting the range of the second ratio Q for which the maximum root stress is below the value Z, it is approximately 10.7 to 19.3 [%].

[0054] FIG. 20 graphs the relationship between the range of the second ratio Q extracted from each of FIGS. 13, 16, and 19 and the first ratio P. The black circles and black triangles in FIG. 20 represent both ends of the range of the second ratio Q. Here, let the smaller of these two ends be m and the other be n (m < n). The range of the second ratio Q is such that as the first ratio P increases, both ends m and n that define the range of the second ratio Q both move in the increasing direction. That is, it can be seen that the preferred range of the second ratio Q varies according to the first ratio P.

[0055] When linearly approximating the coordinates of each of the ends m and n, the following approximate equations representing the relationship between the first ratio P and both ends m and n of the range of the second ratio Q are obtained. P = 12.628m - 25.78 P = 9.8605n - 88.24 (where P: first ratio [%], m: one end [%], n: the other end [%])

[0056] From the above approximate equations, it can be seen that as the first ratio P increases, the range of the second ratio Q expands. The graph for end m is shown as a thick solid line in FIG. 20, and the graph for end n is shown as a dashed line. The range sandwiched between the thick solid line and the dashed line in FIG. 20 is the preferred range of the first ratio P and the second ratio Q. In FIG. 20, the range where the black circles and black triangles exist is in the range of 19.0 to 103.8 [%] for the first ratio P and within the range of 2 to 22 [%] for the second ratio Q.

[0057] In addition, in a coordinate system that expresses the relationship between the first ratio P and the second ratio Q, such as that shown in Figure 20, the area that shows a preferable combination of the first ratio P and the second ratio Q can be defined as a rectangular area that satisfies the following four inequalities (Equations A to D). [Formula A] P≦aQ-b [Formula B] P≧cQ-d [Formula C] P≧e [Formula D] P≦f (where P: first ratio [%], Q: second ratio [%], a>c>0, f>e≧0)

[0058] 20 corresponds to the case where a = 12.628, b = 25.78, c = 9.8605, and d = 88.24. If the upper and lower limits of the first ratio P are set within the range in which the black circles and black triangles exist, then e = 19.0 and f = 103.8. However, the upper and lower limits of the first ratio P are not limited to these values, and the values ​​of e and f can be set arbitrarily as long as at least f > e ≥ 0 is satisfied.

[0059] [3. Actions and Effects] (1) A helical gear (first planetary gear 12) as an embodiment is provided with a helical tooth portion 2 formed by helical tooth traces on the outer cylindrical surface of a cylindrical rim 1, and a lightening portion 3 formed by recessing an area of ​​one axial end face of the rim 1 where the distance to the axis D is equal to or less than a predetermined value toward the other end face. In the above helical gear, the ratio of the value obtained by subtracting the lightening thickness H of the lightening portion 3 from the thickness G of the rim 1 to the tooth thickness J of the helical tooth portion 2 is defined as a first ratio P, and the ratio of the recess dimension F to the overall axial length E of the rim 1 is defined as a second ratio Q. Also, as shown in FIG. 20 , the relationship between the end point m of the range of the first ratio P and the second ratio Q is given by the mathematical formula "P = 12.628m - 25.78," and the relationship between the end point n of the range of the first ratio P and the second ratio Q is given by the mathematical formula "P = 9.8605n - 88.24."

[0060] With this configuration, the first to third tooth root stresses To prevent either of these from becoming excessively largeThis makes it possible to easily determine the range of the second ratio Q in which the first ratio P is set, thereby reducing the root stress occurring in the helical tooth portion 2. Furthermore, the above-mentioned formula makes it possible to clearly define the relationship between the first ratio P and the second ratio Q, thereby more reliably reducing the root stress occurring in the helical tooth portion 2.

[0061] (2) As shown in Figures 11 to 20, it has been confirmed that the tooth root stress generated in the helical tooth portion 2 can be reduced when the first ratio P is in the range of 19.0 to 103.8 [%]. Therefore, it is preferable that the first ratio P is in the range of 19.0 to 103.8 [%]. Alternatively, the first percentage P may be set within a range of 19.0 to 103.8% and the second percentage Q may be set within a range of 3.6 to 19.3%. With this configuration, a good combination of the first percentage P and the second percentage Q can be more reliably achieved, as shown in FIG. (3) As shown in Figures 11 to 20, it has been confirmed that when the second ratio Q is in the range of 6.4 to 15.0%, the tooth root stress generated in the helical tooth portion 2 can be reduced. Therefore, it is preferable that the second ratio Q is in the range of 6.4 to 15.0%.

[0062] In a coordinate system in which the relationship between the first proportion P and the second proportion Q is expressed, the area representing the combination of the first proportion P and the second proportion Q may be defined as a rectangular area that satisfies the following four inequalities (Equations A to D). [Formula A] P≦aQ-b [Formula B] P≧cQ-d [Formula C] P≧e [Formula D] P≦f (where P: first ratio [%], Q: second ratio [%], a>c>0, f>e≧0) In this configuration as well, the relationship between the first rate P and the second rate Q can be clearly defined, and the tooth root stress occurring in the helical tooth portion 2 can be reduced more reliably.

[0063] When the first percentage P is 19.0%, the second percentage Q is preferably in the range of 3.6 to 10.7%, which ensures that the maximum tooth root stress is equal to or less than the value Z (for example, 14.3 MPa), as shown in Fig. 13. Furthermore, when the first percentage P is 56.2%, it is preferable that the second percentage Q be within the range of 6.4 to 15.0%, which ensures that the maximum tooth root stress is equal to or less than the value Z (for example, equal to or less than 16.72 MPa), as shown in Fig. 16. Furthermore, when the first percentage P is 103.8%, it is preferable that the second percentage Q is within the range of 10.7 to 19.3%, which ensures that the maximum tooth root stress is equal to or less than the value Z (for example, equal to or less than 16.06 MPa), as shown in Fig. 19.

[0064] (4) In the helical gear (first planetary gear 12) of the embodiment, a lightening hole 3 is provided on both end surfaces of the rim 1. These two lightening holes 3 preferably have the same shape, and the recess dimension F on one end surface is the same as the recess dimension F on the other end surface. With this configuration, the tooth root stress can be reduced evenly on both end surfaces of the gear, further improving breakage resistance.

[0065] (5) The helical gear as an embodiment is the first planetary gear 12 of the first planetary gear mechanism 10, and is provided with a shaft hole 4 into which a first carrier pin 15 is rotatably inserted. The shaft hole 4 is bored into a hollow cylindrical shape that is coaxial with the axis D and has a radius smaller than a predetermined value (the radius of the lightening portion 3). With this configuration, as shown by the thick solid line in Fig. 6, it is possible to reduce the tooth root stress at both axial ends of the first planetary gear 12, and further improve breakage resistance.

[0066] (6) The helical gear (first planetary gear 12) of the embodiment is provided with a sliding contact portion 5, which is formed by projecting an annular area of ​​one axial end face of the rim 1, where the distance to the axis D exceeds a predetermined value (the radius of the lightening portion 3), toward the opposite side from the other end face. The sliding contact portion 5 functions as a receiving surface to prevent the tooth end face from directly rubbing against the surface on the thrust direction side when the helical gear moves in the thrust direction. This allows the performance of the first planetary gear 12 to be maintained for a long period of time, improving product quality.

[0067] (7) The reducer 7 as an embodiment includes the above-mentioned helical gear (first planetary gear 12), an input shaft 17, and an output shaft (first carrier shaft 16). The input shaft 17 is connected to the first sun gear 11 in the first planetary gear mechanism 10. The first carrier shaft 16, which is the output shaft, is connected to the first carrier 14 to which the first carrier pin 15 that supports the first planetary gear 12 is attached. With this configuration, the breakage performance of the first planetary gear 12 built into the reducer 7 can be improved, and the quality of the reducer 7 can be improved.

[0068] [4. Other] The above-described embodiments are merely illustrative and are not intended to exclude various modifications or applications of techniques not explicitly described in the present embodiments. Each configuration of the present embodiments can be modified in various ways without departing from the spirit of the present embodiments. Furthermore, each configuration of the present embodiments can be selected as needed, or can be appropriately combined with various configurations included in known techniques.

[0069] In the above embodiment, first planetary gear 12 has been described in detail as an example of a helical gear, but the structure of the helical gear of the present invention can also be applied to other gears. For example, the helical gear structure shown in FIGS. 4 and 5 may be applied to second planetary gear 22 of second planetary gear mechanism 20. Alternatively, a similar structure may be applied to first sun gear 11 or second sun gear 21. In addition, while the above embodiment illustrates reducer 7 to which the helical gear of the present invention is applied, the device to which the helical gear of the present invention is applied is not limited to this, and the helical gear of the present invention can be applied to various power transmission devices, such as gear motors, cycloid reducers, and transmissions (gear boxes). [Explanation of symbols]

[0070] 1 rim 2 helical teeth 3. Hollowed-out section 4 shaft holes 5 Sliding part 6 motors 7 Reducer 8 Gear housing 9 Cover 10 First planetary gear mechanism 11 First sun gear 12 First planetary gear (helical gear) 13 First ring gear 14 First Carrier 15 First carrier pin 16 First carrier shaft (output shaft, input shaft) 17 Input shaft 18 Disc Section 20 Second planetary gear mechanism 21 Second sun gear 22 Second planetary gear 23 Second ring gear 24 Second Career 25 Second carrier pin 26 Second carrier axis 27 Output shaft 28 Beveled tooth end face 31 Side part 32 Bottom part 40 Locking part 41 Nails 42 Claw end surface 43 Claw holder 44 Claw receiving end surface 51 First page 52 Second surface part C center axis D axis center E Overall length F recess dimensions G Rim Thickness H Cutout thickness (counterbore diameter) r radius of curvature θ central angle J tooth thickness K is a given coefficient P First Proportion Q Second ratio R Minimum value of maximum tooth root stress (bottom value) Z: The minimum value R multiplied by a predetermined coefficient K m One end point defining the range of the second ratio n The other endpoint defining the range of the second ratio

Claims

1. A helical gear as a planetary gear that meshes with the ring gear and sun gear of a planetary gear mechanism, a helical tooth portion formed on an outer cylindrical surface of the cylindrical rim in the shape of a helical winding; a recessed portion formed by recessing an area of ​​one end face of the rim in the axial direction, the area being such that the distance to the axis of the rim is equal to or less than a predetermined value, toward the other end face; a shaft hole that is bored into a hollow cylindrical shape coaxial with the shaft center and has a radius smaller than the predetermined value, and into which a carrier pin of the planetary gear mechanism is rotatably inserted, The ratio of the thickness of the rim to the tooth thickness of the helical tooth portion minus the thickness of the lightening portion is defined as a first ratio, and the ratio of the recess dimension to the overall axial length of the rim is defined as a second ratio, The relationship between the first ratio and the end points of the range of the second ratio is given by the following formula: A helical gear characterized by: P = a m - b P = cn-d (where P is the first percentage [%], m is one end point [%], and n is the other end point [%]) [The values ​​of a, b, c, and d included in the above formula are determined as follows: The tooth root stress generated at both axial ends of the helical tooth portion due to meshing between the sun gear and the ring gear is the first tooth root stress. The tooth root stress generated in the axial center portion of the helical tooth portion due to meshing between the sun gear and the ring gear is the second tooth root stress. The tooth root stress generated at the axial center of the helical tooth portion due to being supported by the carrier pin is the third tooth root stress. - Assuming that the first ratio is 19.0 [%], when the relationship between the second ratio [%] and the maximum values ​​of the first tooth root stress, the second tooth root stress, and the third tooth root stress for the second ratio is graphed, the range of the second ratio in which the maximum tooth root stress is 1.1 times or less of the minimum value of the maximum tooth root stress in the graph is defined as R 1 to R 2 . - Assuming that the first ratio is 56.2 [%], when the relationship between the second ratio [%] and the maximum values ​​of the first tooth root stress, the second tooth root stress, and the third tooth root stress for the second ratio is graphed, the range of the second ratio in which the maximum tooth root stress is 1.1 times or less of the minimum value of the maximum tooth root stress in the graph is defined as R3 to R4. - Assuming that the first ratio is 103.8 [%], when the relationship between the second ratio [%] and the maximum values ​​of the first tooth root stress, the second tooth root stress, and the third tooth root stress for the second ratio is graphed, the range of the second ratio in which the maximum tooth root stress is 1.1 times or less of the minimum value of the maximum tooth root stress in the graph is defined as R5 to R6. In a plane graph with the first ratio on the vertical axis and the second ratio on the horizontal axis, when the three coordinates (R 1 , 19.0), (R 3 , 56.2), and (R 5 , 103.8) are linearly approximated, the slope of the line is a and the intercept of the line is b. In a plane graph with the first ratio on the vertical axis and the second ratio on the horizontal axis, when the three coordinates (R 2 , 19.0), (R 4 , 56.2), and (R 6 , 103.8) are linearly approximated, the slope of the line is c and the intercept of the line is d.

2. In the formula, a = 12.628, b = 25.78, c = 9.8605, d = 88.24 2. The helical gear according to claim 1, wherein:

3. The first ratio is within a range of 19.0 to 103.8%.

3. The helical gear according to claim 2, wherein:

4. The second ratio is within a range of 6.4 to 15.0%.

3. The helical gear according to claim 2, wherein:

5. the hollowed-out portion is provided on each of one end surface and the other end surface of the rim in the axial direction, The recess dimensions on the one end surface are the same as the recess dimensions on the other end surface.

2. The helical gear according to claim 1, wherein:

6. a sliding contact portion that is projected toward the opposite side from the other end face of the rim in an annular area where the distance to the axis center exceeds the predetermined value on one end face of the rim in the axial direction; 2. The helical gear according to claim 1, wherein:

7. A helical gear according to any one of claims 1 to 6; an input shaft connected to the sun gear of the planetary gear mechanism; an output shaft connected to a carrier having the carrier pin.

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