CN113339477A - Optimization method of high-strength flexible gear torsional curved surface, flexible gear and harmonic reducer - Google Patents
Optimization method of high-strength flexible gear torsional curved surface, flexible gear and harmonic reducer Download PDFInfo
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- CN113339477A CN113339477A CN202110620369.2A CN202110620369A CN113339477A CN 113339477 A CN113339477 A CN 113339477A CN 202110620369 A CN202110620369 A CN 202110620369A CN 113339477 A CN113339477 A CN 113339477A
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
- F16H—GEARING
- F16H49/00—Other gearings
- F16H49/001—Wave gearings, e.g. harmonic drive transmissions
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
- F16H—GEARING
- F16H55/00—Elements with teeth or friction surfaces for conveying motion; Worms, pulleys or sheaves for gearing mechanisms
- F16H55/02—Toothed members; Worms
- F16H55/17—Toothed wheels
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Abstract
The invention relates to an optimization method of a high-strength flexible gear torsional curved surface, a flexible gear and a harmonic reducer.A curvature radius of the torsional curved surface is calculated, the flexible gear comprises a gear ring section and a flange section, the gear ring section is superposed with a central shaft of the flange section, and the gear ring section is connected with the flange section through a smooth curve transition section; the smooth curve transition section is obtained by the optimization method, the smooth curve transition section is in continuous smooth transition with the gear ring section and the flange section, and the curvature radius of the smooth curve transition section is larger than 1/4 of the meshing radius of the flexible gear. The harmonic reducer comprises the flexible gear. The invention increases the rigidity of the flexible gear, improves the vibration performance of the flexible gear, avoids the stress concentration at a certain position of the flexible gear, is beneficial to prolonging the service life of the flexible gear and is beneficial to improving the reliability of the harmonic reducer.
Description
Technical Field
The invention relates to the technical field of harmonic gear reducers, in particular to a flexible gear with a large curvature radius curve profile and a harmonic reducer.
Background
The harmonic reducer has the unique advantages of high bearing capacity, large transmission ratio, small volume, stable transmission, high transmission precision and the like, so that the harmonic reducer is widely applied to the industries of electronics, aerospace, aviation, robots and the like.
The harmonic reducer is mainly composed of three basic components, namely a rigid gear, a flexible gear and a wave generator, and the transmission of the harmonic reducer is realized by the meshing transmission of the flexible gear and the teeth of the rigid gear through the elastic deformation of the flexible gear. Referring to fig. 1, the flange of the flexible gear is vertically connected with the cylinder wall, because the wave generator struts the two ends of the flexible gear, the flexible gear is continuously deformed by the continuous rotation of the wave generator, and the stress concentration of the connecting part of the cylinder wall and the flange is realized while the gear ring is continuously deformed, the connecting part is designed to be a fillet in the prior art, so that the stress concentration is prevented by dispersing the stress, and meanwhile, the appearance is attractive and the hand feeling is comfortable. However, the stress at the position of the flexible gear is large, the problem of stress concentration cannot be solved by a common fillet, the wall thickness of the position is very thin, the rigid promotion of the flexible gear is limited, the normal use of the harmonic reducer is influenced and the maintenance cost of the harmonic reducer is increased due to the fact that the common flexible gear is broken at the position.
Disclosure of Invention
Therefore, the technical problem to be solved by the invention is to overcome the defect that the right-angle connection between the gear ring section and the flange section is easy to damage in the working process of the flexible gear in the prior art, and provide an optimization method of a high-strength flexible gear torsional curved surface, the flexible gear and a harmonic reducer, so that the stress is prevented from being concentrated on the torsional curved surface, and the rigidity of the flexible gear is improved.
In order to solve the technical problem, the invention provides an optimization method of a high-strength flexible gear torsional curved surface, which comprises the following steps:
determining the positions of a flexible gear ring section and a flange section;
calculating the limit curvature radius of the circular arc smoothly connecting the two ends according to the distance of the vertical lines of the two opposite ends of the gear ring section and the flange section to obtain the minimum curvature radius of the torsional curved surface connecting the gear ring section and the flange section;
designing a connecting curved surface according to the curvature radius, and fitting smooth connecting surfaces between two ends of the connecting curved surface and the end parts of the gear ring section and the flange section;
and combining the connecting surface obtained in the step with the connecting curved surface to form a torsional curved surface for connecting the gear ring section and the flange section.
In one embodiment of the invention, the curve profile formed by the torsional curved surface, the ring gear segment and the flange segment together satisfies a cubic spline interpolation function.
The invention also provides a flexible gear, which comprises a gear ring section and a flange section, wherein the gear ring section is superposed with the central axis of the flange section, and the gear ring section is connected with the flange section through a smooth curve transition section;
the smooth curve transition section is obtained according to the optimization method, continuous smooth transition is conducted among the smooth curve transition section, the gear ring section and the flange section, and the curvature radius of the smooth curve transition section is larger than 1/4 of the meshing radius of the flexible gear.
In one embodiment of the present invention, one end of the smooth curved transition section is provided with a first straight line section connected with the flange section.
In one embodiment of the invention, the length of the first straight line segment is less than half the height of the smooth curved transition segment.
In one embodiment of the invention, the first straight line segment and the smooth curved transition segment have the same thickness.
In one embodiment of the invention, the other end of the smooth curved transition section is provided with a second straight line section connected with the gear ring section.
In one embodiment of the invention, the length of the second straight segment is less than 1/3 for the total length of the smooth curved transition and ring gear segment.
In one embodiment of the invention, the second straight line section is conical with the same inner diameter as the gear ring section, and the thickness of the second straight line section gradually increases along the circular arc transition section to the gear ring section.
In one embodiment of the invention, the outer ring of the second straight line section is inclined to the gear ring section by 0-3 degrees along the circular arc transition section, a second transition section is arranged between the second straight line section and the gear ring section, the inner diameter of the second transition section is the same as that of the gear ring section, and the outer ring of the second transition section is in an arc shape which is concave towards the inner ring.
In one embodiment of the invention, the ring gear section, the smooth curved transition section and the flange section are integrally formed.
The invention also provides a harmonic reducer, which comprises the flexible gear.
Compared with the prior art, the technical scheme of the invention has the following advantages:
the optimization method of the invention determines the minimum transition curvature of the high-strength flexible gear, and is convenient for designing the transition curved surface of the flexible gear;
according to the flexible gear, the smooth curve transition section with the large curvature radius is arranged, so that the rigidity of the flexible gear is increased, the vibration performance of the flexible gear is improved, stress concentration at a certain position of the flexible gear is avoided, and the service life of the flexible gear is prolonged;
the harmonic reducer provided by the invention adopts the flexible gear, is simple in structure and high in feasibility, and is beneficial to improving the reliability of the harmonic reducer.
Drawings
In order that the present disclosure may be more readily and clearly understood, reference is now made to the following detailed description of the embodiments of the present disclosure taken in conjunction with the accompanying drawings, in which
FIG. 1 is a prior art flexspline configuration;
FIG. 2 is a flexspline structure of the present invention;
FIG. 3 is an enlarged view of the structure of region A in FIG. 2;
fig. 4 is an enlarged view of the structure of region B in fig. 3.
The specification reference numbers indicate: 1. a flexible gear; 11. a smooth curve transition section; 12. a ring gear section; 13. A first straight line segment; 14. a second straight line segment; 15. a second transition section; 20. a flange section.
Detailed Description
The present invention is further described below in conjunction with the following figures and specific examples so that those skilled in the art may better understand the present invention and practice it, but the examples are not intended to limit the present invention.
In the invention, in the process of twisting the thin-wall cylinder surrounded by the twisted curved surfaces, the section vertical to the rotation center is pure shear, and the relative twisting angle of two end surfaces is as follows:
Φ＝Tl/GIp (1)
wherein IpIs a poleThe moment of inertia, for a hollow shaft,
Iρ＝π(D4-d4)/32 (2)
wherein D is the outer diameter of the hollow shaft and D is the inner diameter of the hollow shaft.
The shear forces experienced during shaft torsion are:
τmax＝T/Wt (3)
wherein T is torque, WtIs the torsional section coefficient.
For a hollow shaft:
Wt＝π(D4-d4)/16D (4)
according to the formulas (1) and (3), the larger the polar inertia moment is, the smaller the torsion angle is, the larger the torsion section coefficient is, and the smaller the shearing force is applied during torsion, and according to the formulas (2) and (4), the larger the radius of the hollow shaft is, the larger the polar inertia moment and the torsion section coefficient is, and the smaller the torsion angle and the shearing force are, when the thickness of the hollow shaft is not changed. Therefore, the right-angle torsion positions of the original connection gear ring section and the flange section in the flexible gear are set to be curved surfaces, so that the radius of the hollow shaft is continuously and smoothly increased, and in order to ensure the rapid curvature change of the torsion curved surface and ensure the smooth transition of all parts, the torsion curved surface is determined by adopting the following steps:
determining the positions of a flexible gear ring section and a flange section; in actual production, the sizes of the flange section and the gear ring section can be determined according to customer requirements, and the positions of the flexible gear ring section and the flange section can be determined at the moment.
Calculating the limit curvature radius of the circular arc smoothly connecting the two ends according to the distance of the vertical lines of the two opposite ends of the gear ring section and the flange section to obtain the minimum curvature radius of the torsional curved surface connecting the gear ring section and the flange section; when the distances between the two ends of the section of the torsional curved surface in the X direction and the Y direction are equal, the radius of the hollow shaft can be continuously and smoothly increased by adopting circular arc connection, and meanwhile, the convenience of design is ensured. The radius is the minimum curvature radius of the torsional curved surface, and the other limit is that two ends of the curved surface are connected through a straight line, but at the moment, the connecting line is an oblique line, and smooth transition between the connecting line and two ends of the torsional curved surface cannot be realized.
In addition, because the distances between the two ends of the section of the torsional curved surface in the X direction and the Y direction are not equal under the common condition, the circular arc can not realize the connection of the two ends of the section, so that a connecting curved surface is designed according to the curvature radius, and the smooth connecting surfaces between the two ends of the connecting curved surface and the end parts of the gear ring section and the flange section are fitted; so that smooth curved surfaces are formed between the two ends of the torsional curved surface and the gear ring section and the flange section.
Combining the connecting surface obtained in the above steps with the connecting curved surface to form a torsional curved surface connecting the gear ring section and the flange section.
By utilizing computer software, the standard flexible gear and the flexible gear obtained by the method are subjected to simulation analysis respectively, so that the torsional rigidity of the flexible gear designed according to the invention is improved by more than 30%, and the performance is improved by 10 times in a quadruple rated overload test.
As the preferred embodiment of the invention, the curve profile formed by the torsional curved surface, the gear ring segment and the flange segment meets the cubic spline interpolation function, and the smooth transition of the torsional curved surface is ensured.
Referring to fig. 2 and 3, the structure of the high-strength flexible gear of the present invention is schematically shown. The flexible gear 1 comprises a gear ring section 12 and a flange section 20, wherein the gear ring section 12 is overlapped with the central axis of the flange section 20, the gear ring section 12 is connected with the flange section 20 through a smooth curve transition section 11, and the smooth curve transition section is obtained according to the optimization method. And the circumferential stress of the flexible gear is uniform when the gear ring section 12 drives the flange section 20 to synchronously rotate. The gear ring section 12 and the flange section 20 are connected through the smooth curve transition section 11, so that the diameter of a cylinder at the transition position of the gear ring section 12 and the flange section 20 is continuously and smoothly increased, stress concentration is reduced, fatigue stress is reduced, and the service life of the flexible gear 1 is prolonged. In this embodiment, the gear ring section 12, the smooth curve transition section 11 and the flange section 20 are integrally formed, and the molecules in the flexible gear 1 formed under the same condition are uniformly distributed, so that the phenomenon that the molecules are disordered at the joint to cause stress concentration at the joint and influence the quality of the flexible gear 1 is avoided.
Furthermore, the smooth curve transition section 11, the gear ring section 12 and the flange section 20 are in continuous smooth transition, so that local stress surge caused by section size surge is avoided. Meanwhile, 1/4 that the curvature radius R of the smooth curve transition section 11 is larger than the meshing radius of the flexible gear 1 is obtained according to finite element analysis by combining the size parameter and the thickness of the smooth curve transition section 11 with the flexible gear load. By arranging the smooth curve transition section 11 with large curvature, the stress transmission range is enlarged, stress concentration is avoided, the rigidity of the flexible gear 1 is improved, and the service life of the flexible gear 1 is further prolonged. Meanwhile, the smooth curve transition section 11 is arc-shaped and has internal stress along the radial direction, so that the vibration along the radial direction can be improved, the working stability is further improved, and the service life of the flexible gear 1 is prolonged.
In the invention, the smooth curve transition section 11 is in smooth transition with the gear ring section 12 and the flange section 20, the smooth curve transition section 11 is 1/4 circular arcs, and D is in the process that the smooth curve transition section 11 is in transition from the gear ring section 12 to the flange section 204-d4The value of (D) is continuously increased, i.e. the torsional section resistance coefficient is continuously increased, and at the same time, because the radius of the smooth curve transition section 11 is larger, the difference between the values of D and D is wider, i.e. the torsional section resistance coefficient of the smooth curve transition section 11 is larger than that of the transition section with smaller radius. The torsion resistance of the flexible gear 1 is improved, the stress concentration of the flexible gear 1 during elastic deformation is dispersed, the rigidity and the stability of the flexible gear 1 are improved, and the performance of the flexible gear 1 is improved under the condition that the wall thickness of the flexible gear 1 is not changed. With specific reference to table 1:
further, in order to facilitate the connection between the smooth curve transition section 11 and the gear ring section 12, i.e. the flange section 20, a first straight line section 13 connected with the flange section 20 is arranged at one end of the smooth curve transition section 11. The smooth curve transition section 11 is connected with the flange section 20 through the first straight line section 13, the transition from the flange section 20 to the arc transition section is completed, and the flange section 20 and the smooth curve transition section 11 can be effectively connected. The first straight line segment 13 is therefore the same thickness as the smooth curved transition 11. Therefore, the uniformity of the distribution of molecules in the structure at the joint of the first straight line section 13 and the smooth curve transition section 11 is effectively ensured, the uniformity of the overall stress is further ensured, and the stress concentration at the joint is avoided. In this embodiment, in order to avoid the stress concentration on the first straight line segment 13 and damage to the first straight line segment 13, the length H of the first straight line segment 13 is set to be less than half of the height H of the smooth curve transition segment 11. The height of the arc-shaped transition section is the distance between the minimum inner diameter of the arc-shaped transition section and the connection position of the first straight line section 13 and the flange section 20. Because the length h of the first straight line section 13 is short, most of the torsion generated in the rotation process of the flexible gear 1 is borne by the smooth curve transition section 11, and the smooth curve transition section 11 has good torsion resistance and rigidity, the torsion transmitted to the first straight line section 13 is not enough to damage the first straight line section 13, and the service life of the flexible gear 1 is prolonged.
Referring to fig. 3 and 4, further, the other end of the smooth curved transition section 11 is provided with a second straight line section 14 connected with the ring gear section 12. The second straight section 14 provides an operative connection of the arcuate transition section to the ring gear section 12. The length L of the second straight section 14 is less than 1/3 of the total length L of the smooth curved transition section 12 and the ring gear section 12. The second straight section 14 of shorter length, on the one hand, leaves sufficient space for the smooth curved transition 11 to be arranged and, on the other hand, avoids stress concentrations in the second straight section 14. When the flexible gear 1 rotates, the torsion is quickly transmitted to the smooth curve transition section 11 from the second straight line section 14, the second straight line section 14 cannot be subjected to overlarge torsion, the smooth curve transition section 11 has good torsion resistance and rigidity, and the stress concentration on the smooth curve transition section 11 can be avoided, so that the service life of the flexible gear 1 is prolonged. In this embodiment, since the thickness of the smooth curve transition section 11 is smaller than that of the ring gear section 12, in order to ensure smooth transition between the smooth curve transition section 11 and the ring gear section 12, the second straight section 14 is a cone with the same inner diameter as that of the ring gear section 12, and the thickness of the second straight section 14 gradually increases from the circular arc transition section to the ring gear section 12. Because the smooth curved transition section 11 is an 1/4 circle, in order to ensure the smooth connection between the second straight-line section 14 and the smooth curved transition section 11, the taper of the second straight-line section 14 cannot be too large, so that the outer ring of the second straight-line section 14 is inclined to the gear ring section 12 by 0-3 degrees along the circular arc transition section, that is, the taper angle α of the second straight-line section 14 is 0-3 degrees. At this time, a certain difference still exists between the thickness of the end of the second straight line section 14 and the gear ring section 12, so a second transition section 15 is arranged between the second straight line section 14 and the gear ring section 12, the inner diameter of the second transition section 15 is the same as that of the gear ring section 12, and the outer ring of the second transition section 15 is in an arc shape which is concave towards the inner ring. By utilizing the relation that the arc can be tangent to the straight line, the second straight line section 14 and the second transition section 15 are in smooth transition, and meanwhile, the included angle between the second transition section 15 and the gear ring section 12 is large and is approximate to smooth transition, so that the stress concentration caused by size sudden change is avoided, and the service life of the flexible gear 1 is prolonged.
The invention also provides a harmonic reducer comprising a flexspline 1 according to any one of the preceding claims. Through setting up smooth curve changeover portion 11 of big curvature radius, improved the intensity of flexbile gear 1, weakened the deflection that flexbile gear 1 transmitted from ring gear section 12 to flange section 20 for the deformation of smooth curve changeover portion 11 reduces, improves flexbile gear 1 life.
It should be understood that the above examples are only for clarity of illustration and are not intended to limit the embodiments. Other variations and modifications will be apparent to persons skilled in the art in light of the above description. And are neither required nor exhaustive of all embodiments. And obvious variations or modifications therefrom are within the scope of the invention.
Claims (12)
1. The optimization method of the high-strength flexible gear torsional curved surface is characterized by comprising the following steps:
determining the positions of a flexible gear ring section and a flange section;
calculating the limit curvature radius of the circular arc smoothly connecting the two ends according to the distance of the vertical lines of the two opposite ends of the gear ring section and the flange section to obtain the minimum curvature radius of the torsional curved surface connecting the gear ring section and the flange section;
designing a connecting curved surface according to the curvature radius, and fitting smooth connecting surfaces between two ends of the connecting curved surface and the end parts of the gear ring section and the flange section;
and combining the connecting surface obtained in the step with the connecting curved surface to form a torsional curved surface for connecting the gear ring section and the flange section.
2. The method for optimizing the torsional curved surface of the high-strength flexible gear according to claim 1, wherein a curve profile formed by the torsional curved surface, the gear ring segment and the flange segment meets a cubic spline interpolation function.
3. A flexible gear is characterized by comprising a gear ring section and a flange section, wherein the gear ring section is superposed with the central axis of the flange section, and the gear ring section is connected with the flange section through a smooth curve transition section;
the smooth curved transition section is obtained according to the optimization method of claim 1 or 2, the smooth curved transition section is continuously and smoothly transited with the gear ring section and the flange section, and the curvature radius of the smooth curved transition section is larger than 1/4 of the meshing radius of the flexible gear.
4. The flexspline of claim 3, wherein the smooth curved transition section is provided at one end with a first straight segment connected to the flange section.
5. The flexspline of claim 4, wherein the length of the first straight segment is less than half the height of the smooth curved transition.
6. The flexspline of claim 4, wherein the first straight line segment and the smooth curved transition segment are the same thickness.
7. The flexspline of claim 3, wherein the smooth curved transition section is provided at the other end with a second straight section connected to the ring gear section.
8. The flexspline of claim 7, wherein the second linear segment has a length less than 1/3 of the total length of the smooth curved transition segment and the ring gear segment.
9. The flexspline of claim 7, wherein the second linear section is tapered with an inner diameter equal to the ring gear section, and the thickness of the second linear section increases along the circular arc transition section toward the ring gear section.
10. The flexspline of claim 7, wherein the outer ring of the second straight section is inclined to the gear ring section by 0-3 ° along the circular arc transition section, a second transition section is provided between the second straight section and the gear ring section, the inner diameter of the second transition section is the same as that of the gear ring section, and the outer ring of the second transition section is in an arc shape concave to the inner ring.
11. The flexspline of claim 3, wherein the ring gear segment, the smooth curved transition segment and the flange segment are integrally formed.
12. A harmonic reducer comprising a flexspline according to any of claims 3 to 11.
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| CN202110620369.2A CN113339477A (en) | 2021-06-03 | 2021-06-03 | Optimization method of high-strength flexible gear torsional curved surface, flexible gear and harmonic reducer |
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| CN202110620369.2A CN113339477A (en) | 2021-06-03 | 2021-06-03 | Optimization method of high-strength flexible gear torsional curved surface, flexible gear and harmonic reducer |
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Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| EP0514829A2 (en) * | 1991-05-20 | 1992-11-25 | Harmonic Drive Systems Inc. | Cup-type harmonic drive having a short, flexible cup member |
| CN104747660A (en) * | 2015-04-14 | 2015-07-01 | 上海鑫君传动科技有限公司 | Harmonic reducer structure for extending service life |
| CN107676456A (en) * | 2017-08-31 | 2018-02-09 | 成都瑞迪机械科技有限公司 | long-life harmonic speed reducer |
| CN109578551A (en) * | 2018-12-06 | 2019-04-05 | 北京工业大学 | A kind of harmonic reducer flexible wheel cup body based on continuous transition curve |
-
2021
- 2021-06-03 CN CN202110620369.2A patent/CN113339477A/en active Pending
Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| EP0514829A2 (en) * | 1991-05-20 | 1992-11-25 | Harmonic Drive Systems Inc. | Cup-type harmonic drive having a short, flexible cup member |
| CN104747660A (en) * | 2015-04-14 | 2015-07-01 | 上海鑫君传动科技有限公司 | Harmonic reducer structure for extending service life |
| CN107676456A (en) * | 2017-08-31 | 2018-02-09 | 成都瑞迪机械科技有限公司 | long-life harmonic speed reducer |
| CN109578551A (en) * | 2018-12-06 | 2019-04-05 | 北京工业大学 | A kind of harmonic reducer flexible wheel cup body based on continuous transition curve |
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