Flexspline and harmonic drive
The flexible wheel's cap-shaped structure with optimized radius and thickness ratios in the flange and cylindrical portions addresses stress concentration issues, improving structural stability and lifespan in harmonic reducers.
Patent Information
- Application Number
- TW115202417
- Authority / Receiving Office
- TW · TW
- Patent Type
- Utility models
- Current Assignee / Owner
- Priority Date
- 2025-06-25
- Filing Date
- 2026-03-19
- Publication Date
- 2026-07-11
- Estimated Expiration
- 2036-03-18
AI Technical Summary
Conventional flexible wheels in harmonic reducers suffer from stress concentration, affecting structural stability and component lifespan.
A flexible wheel with a cap-shaped structure featuring specific radius ratios and thickness relationships in its flange and cylindrical portions, along with a smooth connection, reduces stress concentration by optimizing the flexible gear design.
The optimized design effectively reduces maximum stress by 3% to 4%, enhancing structural performance and longevity of the flexible gear.
Smart Images

Figure IMG-2_DRAW_115202417-A0305-14-0001-1 
Figure IMG-2_DRAW_115202417-A0305-14-0002-2 
Figure IMG-2_DRAW_115202417-A0305-14-0003-3
Abstract
Description
Flexible gear and harmonic reducer FLEXSPLINE AND HARMONIC DRIVE Technical Field
[0001] This disclosure relates to a flexible gear and harmonic reducer, and more particularly to a flexible gear and harmonic reducer with a cap-shaped structure. Prior Technology
[0002] Generally speaking, a harmonic reducer includes a flexible wheel, a rigid wheel, and a waveform generator. The waveform generator is driven to rotate by a motor. The flexible wheel deforms due to its elasticity and disengages from the meshing part of the rigid wheel, thereby generating a small number of misaligned teeth for speed reduction. It is widely used in various fields.
[0003] However, conventional flexible wheels are prone to stress concentration, which can affect structural stability and component lifespan, so there is still room for improvement. Summary of the Invention
[0004] To address the aforementioned issues, this disclosure provides a flexible gear and harmonic reducer, which, through structural configuration, can reduce stress concentration in the flexible gear and improve structural performance.
[0005] According to one embodiment of this disclosure, a flexible wheel is provided, comprising a cylindrical portion and a flange portion. The cylindrical portion has an inner surface surrounding a through hole. The flange portion is connected to one end of the cylindrical portion and protrudes outward in a radial direction. The flange portion is recessed near the cylindrical portion to form a bottom wall and an inner side wall. The bottom wall is connected to the cylindrical portion and is parallel to the radial direction, and the inner side wall is connected to the bottom wall and is parallel to an axial direction. The bottom wall surface facing the cylindrical portion includes a first arc segment and a second arc segment connected together. A first radius of curvature of the first arc segment is different from a second radius of curvature of the second arc segment, and the first arc segment and the second arc segment have a boundary line. A first radial distance D1 is between the inner side wall and the inner surface, and a second radial distance D2 is between the inner side wall and the boundary line, satisfying the relationship 5.75 ≤ D1 / D2 ≤ 6.10.
[0006] According to the aforementioned embodiment of the flexible wheel, the first distance D1 and the second distance D2 can satisfy the relationship D1 / D2=6.
[0007] According to the aforementioned embodiment of the flexible wheel, the minimum thickness of the bottom wall along the axial direction can be T1. The flexible wheel further includes a smooth portion connected between the bottom wall of the cylindrical portion and the flange portion. The connection thickness of the smooth portion and the bottom wall along the axial direction is T2, which satisfies the relationship 1.42≤T2 / T1≤1.82.
[0008] According to the aforementioned embodiment of the flexible wheel, the minimum thickness T1 and the connection thickness T2 can satisfy the relationship T2 / T1=1.6.
[0009] The flexible wheel according to the above embodiment may further include a plurality of locking holes, which extend axially through the flange portion.
[0010] According to another embodiment of this disclosure, a harmonic reducer is provided, comprising a flexible wheel, a rigid wheel, and a waveform generator. The flexible wheel includes a cylindrical portion and a flange portion. The cylindrical portion has an inner surface surrounding a through hole. The flange portion is connected to one end of the cylindrical portion and protrudes radially outward. The flange portion is recessed near the cylindrical portion to form a bottom wall and an inner side wall. The bottom wall is connected to the cylindrical portion and parallel to the radial direction, and the inner side wall is connected to the bottom wall and parallel to an axial direction. The bottom wall surface facing the cylindrical portion includes a first arc segment and a second arc segment connected together. A first radius of curvature of the first arc segment is different from a second radius of curvature of the second arc segment, and the first arc segment and the second arc segment have a boundary line. A first radial distance D1 is between the inner side wall and the inner surface, and a second radial distance D2 is between the inner side wall and the boundary line, satisfying the relationship 5.75 ≤ D1 / D2 ≤ 6.10. The rigid wheel is sleeved on the cylindrical portion. The waveform generator includes a shaft insert through a hole.
[0011] According to the aforementioned embodiment of the harmonic reducer, the first distance D1 and the second distance D2 can satisfy the relationship D1 / D2=6.
[0012] According to the aforementioned embodiment of the harmonic reducer, the minimum thickness of the bottom wall along the axial direction can be T1, and the flexible wheel further includes a smooth portion connected between the bottom wall of the cylindrical portion and the flange portion. The connection thickness of the smooth portion and the bottom wall along the axial direction is T2, which satisfies the relationship 1.42≤T2 / T1≤1.82.
[0013] According to the aforementioned embodiment of the harmonic reducer, the cylindrical portion may include an adjacent front section and a rear section, the front section being connected to the smooth portion, and the rear section being used to engage with the rigid wheel portion.
[0014] The harmonic reducer according to the aforementioned embodiment may further include a crossed roller bearing, which is sleeved on the cylindrical portion and located between the flange portion and the rigid wheel. Simple Explanation of the Diagram
[0015] Figure 1 shows a perspective view of a harmonic reducer according to one embodiment of the present disclosure; Figure 2 shows an exploded view of the harmonic reducer of the embodiment in Figure 1; Figure 3 shows a cross-sectional schematic diagram of the harmonic reducer of the embodiment in Figure 1; Figure 4 shows a cross-sectional schematic diagram of a flexure of the harmonic reducer in the embodiment of Figure 1; Figure 5 shows the relationship between the maximum stress and the ratios of the first and second distances; and Figure 6 shows the relationship between maximum stress and minimum thickness. Implementation
[0016] The embodiments of this disclosure will now be described with reference to the drawings. For clarity, many practical details will be described in the following description. However, the reader should understand that these practical details should not be used to limit this disclosure. That is, these practical details are not essential in some embodiments of this disclosure. Furthermore, for the sake of simplicity, some conventional structures and elements will be shown in the drawings in a simple schematic manner; and repeated elements may be represented by the same or similar designations.
[0017] Furthermore, the terms "first," "second," and "third" used in this article are merely used to describe different components or parts, and do not impose any restrictions on the components / parts themselves. Therefore, the first component / part can also be referred to as the second component / part. Moreover, the combinations of components / parts / mechanisms / modules in this article are not combinations generally known, conventional, or conventional in this field. Whether the components / parts / mechanisms / modules themselves are conventional cannot be used to determine whether their combination relationships are easily accomplished by those with ordinary knowledge in the technical field.
[0018] Please refer to Figures 1 through 4, wherein Figure 1 shows a perspective view of a harmonic reducer 10 according to an embodiment of the present disclosure, Figure 2 shows an exploded view of the harmonic reducer 10 of the embodiment in Figure 1, Figure 3 shows a cross-sectional view of the harmonic reducer 10 of the embodiment in Figure 1, and Figure 4 shows a cross-sectional view of a flexible wheel 100 of the harmonic reducer 10 of the embodiment in Figure 1. The harmonic reducer 10 includes a flexible wheel 100, which includes a cylindrical portion 110 and a flange portion 120.
[0019] The cylindrical portion 110 has an inner surface (not shown) surrounding a through hole 130. A flange portion 120 is connected to one end of the cylindrical portion 110 and protrudes outward in a radial direction. The flange portion 120 is recessed adjacent to the cylindrical portion 110 to form a bottom wall 122 and an inner side wall 121. The bottom wall 122 is connected to the cylindrical portion 110 and is parallel to the radial direction, and the inner side wall 121 is connected to the bottom wall 122 and is parallel to an axial direction X1. The bottom wall surface (not shown) of the bottom wall 122 facing the cylindrical portion 110 includes a first arc segment 122a and a second arc segment 122b connected to each other. A first radius of curvature of the first arc segment 122a is different from a second radius of curvature of the second arc segment 122b, and the first arc segment 122a and the second arc segment 122b have a boundary line L1. Among them, the first radial distance between the inner wall 121 and the inner surface is D1, and the second radial distance between the inner wall 121 and the boundary line L1 is D2, which satisfies the relationship 5.75≤D1 / D2≤6.10.
[0020] Therefore, when the relationship 5.75≤D1 / D2≤6.10 is satisfied, the maximum stress can be effectively reduced.
[0021] Specifically, the flange portion 120 and the cylindrical portion 110 are orthogonally connected to form a cap-shaped structure. The flange portion 120 can be divided into an inner section and an outer section 124 radially. The inner section is adjacent to the cylindrical portion 110 and is recessed relative to the outer section 124, so the outer section 124 can be relatively higher to form a step difference. The flexible wheel 100 may further include a plurality of locking holes 150, which can penetrate the flange portion 120 along the axial direction X1, especially penetrating the outer section 124 of the flange portion 120, and are arranged in a ring.
[0022] As shown in Figure 4, the bottom wall 122 and the inner wall 121 can be surrounded to define a recessed annular groove 123 located on the inner section. The orientation of the annular groove 123 is opposite to the extension direction of the cylindrical portion 110. The surface of the bottom wall 122 located on the left side of Figure 4 can be defined as the bottom wall surface. It is not planar but concave and includes a first arc segment 122a and a second arc segment 122b. The first arc segment 122a is closer to the outer section 124, and the second arc segment 122b is closer to the cylindrical portion 110. The first arc segment 122a and the second arc segment 122b are both part of an arc surface. Because the first radius of curvature of the first arc segment 122a is different from the second radius of curvature of the second arc segment 122b, the first arc segment 122a and the second arc segment 122b are not smoothly connected to the same spherical surface but form a boundary line L1 between them. The boundary line L1 is a loop, and is represented as a point in Figure 4 due to the cross-sectional relationship.
[0023] Because the first arc segment 122a and the second arc segment 122b are discontinuous surfaces and relatively thin, the boundary line L1 is prone to stress concentration and damage. Therefore, by making the first distance D1 and the second distance D2 satisfy the relationship 5.75≤D1 / D2≤6.10, the maximum stress can be reduced.
[0024] Furthermore, the minimum thickness of the bottom wall 122 along the axial direction X1 can be T1. The flexible wheel 100 may further include a smooth portion 140 connecting the bottom wall 122 of the cylindrical portion 110 and the flange portion 120. The connection thickness (not shown) of the smooth portion 140 and the bottom wall 122 along the axial direction X1 is T2, satisfying the relationship 1.42≤T2 / T1≤1.82. As shown in Figure 4, one of the locations of the second arc segment 122b has a minimum thickness T1, that is, the thickness at this location is thinner than at other locations. Therefore, by satisfying 1.42≤T2 / T1≤1.82, the maximum stress can also be effectively reduced.
[0025] Please refer to Figures 5 and 6, and also to Figure 4. Figure 5 shows the relationship between the maximum stress and the ratios of the first distance D1 and the second distance D2, and Figure 6 shows the relationship between the maximum stress and the minimum thickness T1. In this embodiment, the first distance D1 can be, for example, 10.47 mm, the minimum thickness T1 is 0.25 mm, and the connection thickness T2 is 0.4 mm. Assuming that D1 / D2 is changed by adjusting the second distance D2 to satisfy 5.75 ≤ D1 / D2 ≤ 6.10, and particularly to satisfy the relationship D1 / D2 = 6, the maximum stress can be reduced. Furthermore, if D1 / D2 is limited to between 5.22 or 6, and the minimum thickness T1 is adjusted to change T2 / T1 to satisfy 1.42 ≤ T2 / T1 ≤ 1.82, and particularly to satisfy the relationship T2 / T1 = 1.6, the maximum stress can be reduced. This can reduce the maximum stress by 3% to 4%, particularly from 223 MPa to 215 MPa, thereby reducing stress concentration.
[0026] As shown in Figure 4, the cylindrical portion 110 may include an adjacent front section 111 and a rear section (not shown). The front section 111 is connected to the smooth portion 140, and the radial thickness of the front section 111 is equal to the radial thickness of the smooth portion 140. That is, the front section 111 of the cylindrical portion 110 is connected to the smooth portion 140 and has the same thickness. The rear section may include a plurality of teeth 112, and the rear section is used to correspond to the internal teeth 310 of a rigid wheel 300 (details of which will be described later).
[0027] Please refer to Figures 2 and 3. The harmonic reducer 10 may further include a rigid wheel 300 and a waveform generator 200. The rigid wheel 300 is sleeved on the cylindrical part 110, and the waveform generator 200 includes a shaft 210 inserted into the through hole 130.
[0028] Specifically, the rigid wheel 300 may be hollow annular and correspond to the teeth 112 of the cylindrical portion 110. The rigid wheel 300 includes several internal teeth 310, which can mesh with the teeth 112 on the rear section when fitted onto the cylindrical portion 110. The waveform generator 200 may further include a ball bearing 220, which is fitted onto the shaft 210 and includes an inner ring that rotates with the shaft 210. When the waveform generator 200 is inserted into the through hole 130, the outer ring of the ball bearing 220 can correspond to the inner side of the rear section.
[0029] The harmonic reducer 10 may further include a crossed roller bearing 400, which may be sleeved on the cylindrical portion 110 and located between the flange portion 120 and the rigid wheel 300. The crossed roller bearing 400 may include a plurality of threaded holes and locking holes 150 corresponding to each other, so that the crossed roller bearing 400 and the flexible wheel 100 can be locked with screws.
[0030] The waveform generator 200 can be connected to a motor (not shown) to drive the waveform generator 200. The waveform generator 200 can then cause the flexible wheel 100 to deform elastically and drive the rigid wheel 300 to rotate, thereby achieving a deceleration effect.
[0031] Although this disclosure has been presented above with reference to embodiments, it is not intended to limit this disclosure. Anyone skilled in the art may make various modifications and refinements without departing from the spirit and scope of this disclosure. Therefore, the scope of protection of this disclosure shall be determined by the appended claims.
[0032] 10: Harmonic reducer 100: Flexible Wheel 110: Cylinder section 111: Front Section 112: Teeth 120: Flange portion 121: Inner wall 122: Bottom wall 122a: First arc segment 122b: Second arc segment 123: Annular groove 124: Lateral segment 130: piercing 140: Smooth Part 150: Keyhole 200: Waveform Generator 210: Shaft 220: Ball bearing 300: Steel Wheel 310: Internal teeth 400: Crossed Roller Bearing D1: First Distance D2: Second distance L1: Boundary Line T1: Minimum thickness T2: Connection Thickness X1: Axial direction
Claims
1. A flexible wheel, comprising: a cylindrical portion having an inner surface surrounding a perforation; and a flange portion connected to one end of the cylindrical portion and projecting radially outward, the flange portion being recessed adjacent to the cylindrical portion to form a bottom wall and an inner side wall, the bottom wall being connected to the cylindrical portion and parallel to the radial direction, and the inner side wall being connected to the bottom wall and parallel to an axial direction; wherein... The bottom wall surface facing the cylinder includes a first arc segment and a second arc segment connected together. The first arc segment has a first radius of curvature different from the second arc segment, and the first arc segment and the second arc segment have a boundary line. The first distance between the inner wall and the inner surface along the radial direction is D1, and the second distance between the inner wall and the boundary line along the radial direction is D2, satisfying the relationship 5.75≤D1 / D2≤6.
10.
2. The flexible wheel as described in claim 1, wherein the first distance D1 and the second distance D2 further satisfy the relationship D1 / D2=6.
3. The flexible wheel as described in claim 1, wherein the minimum thickness of the bottom wall along the axial direction is T1, the flexible wheel further includes a smooth portion connecting the bottom wall of the cylindrical portion and the flange portion, and a connection thickness of the smooth portion and the bottom wall along the axial direction at a connection point is T2, satisfying the relationship 1.42≤T2 / T1≤1.
82.
4. The flexible wheel as described in claim 3, wherein the minimum thickness T1 and the connection thickness T2 further satisfy the relationship T2 / T1=1.
6.
5. The flexible wheel as described in claim 1 further includes a plurality of locking holes that extend through the flange along the axial direction.
6. A harmonic reducer, comprising: a flexible gear, including: a cylindrical portion having an inner surface surrounding a perforation; and a flange portion connected to one end of the cylindrical portion and projecting outward in a radial direction, the flange portion being recessed adjacent to the cylindrical portion to form a bottom wall and an inner side wall, the bottom wall being connected to the cylindrical portion and parallel to the radial direction, and the inner side wall being connected to the bottom wall and parallel to an axial direction; wherein, The bottom wall surface facing the cylindrical portion includes a first arc segment and a second arc segment connected together. A first radius of curvature of the first arc segment is different from a second radius of curvature of the second arc segment, and the first arc segment and the second arc segment have a boundary line. A first radial distance D1 is between the inner wall and the inner surface, and a second radial distance D2 is between the inner wall and the boundary line, satisfying the relationship 5.75≤D1 / D2≤6.10; a rigid wheel is sleeved on the cylindrical portion; and a waveform generator includes a shaft inserted into the through hole.
7. The harmonic reducer as described in claim 6, wherein the first distance D1 and the second distance D2 further satisfy the relationship D1 / D2=6.
8. The harmonic reducer as claimed in claim 6, wherein the minimum thickness of the bottom wall along the axial direction is T1, the flexible wheel further includes a smooth portion connecting the bottom wall of the cylindrical portion and the flange portion, and a connection thickness of the smooth portion and the bottom wall along the axial direction at a connection point is T2, satisfying the relationship 1.42≤T2 / T1≤1.
82.
9. The harmonic reducer as claimed in claim 8, wherein the cylindrical portion includes an adjacent front section and a rear section, the front section being connected to the smooth portion and the rear section being used to engage with the rigid wheel portion.
10. The harmonic reducer as claimed in claim 9 further includes a crossed roller bearing sleeved on the cylindrical portion and located between the flange portion and the rigid wheel.