Performance Analysis of Harmonic Drive Based on Different Tooth Thickness Modification Methods

Abstract

In order to eliminate the meshing interference between the flexspline and circular spline after the taper deformation of the flexspline, the radial deformation difference method, major and minor axis fitting method, and ellipse fitting method are used to modify the tooth thickness of the flexspline and analyze the performance indexes such as the assembly stress, transmission error, and fatigue life. Firstly, the conjugate tooth profile is solved based on the quadruple-circular-arc tooth profile and modified kinematic method. Then, based on the finite element radial deformation of the flexspline, the principle and characteristics of three modification methods are analyzed, and the modification amount of each section of the flexspline tooth is calculated. Finally, the influence of the three modification methods on the performance of the harmonic drive is compared. The results show that the radial deformation difference method can initially determine the modification amount. The minimum static assembly stress is 406. 22 MPa by the major and minor axis fitting method. The ellipse fitting method has the best dynamic performance, small transmission error fluctuation, a peak-to-peak value of 3. 060", and a maximum fatigue life of 107. 558 cycles.

Keywords

harmonic drive / taper deformation / flexspline / quadruple-circular-arc tooth profile / tooth thickness modification

References

[1] MUSSER C. Strain wave gearing:US2906143[P]. 1959-09-29.

[2] PATEL D M, JIVANI R G, PANDYA V A. Harmonic drive design & application:a review[J]. Global Research and Development Journal for Engineering, 2015, 1(1):34.

[3] YANG P, ZHANG L Y, WANG C L, et al. Summary of re-search status on harmonic gear driving technology[J]. Journal of Mechanical Transmission, 2005, 29(3):69-72. (in Chinese)

[4] FENG F, WANG W, TANG L N, et al. Application and development trends of the space harmonic reducer with high precision[J]. Journal of Mechanical Transmission, 2014, 38(10):98-107. (in Chinese)

[5] HUANG X, HE W J, FU Y X. Summery of precision speed reducer of industrial robots[J]. Journal of Machine Tool & Hydraulics, 2015, 43(13):1-6. (in Chinese)

[6] ISHIKAWA S. Wave gear device:US8215205B2[P]. 2012-07-10.

[7] RAVIOLA A, DE MARTIN A, GUIDA R, et al. Harmonic drive gear failures in industrial robots applications:an overview[J]. PHM Society European Conference, 2021, 6(1):11.

[8] ROUTH B. Design aspects of harmonic drive gear and performance improvement of its by problems identification:a review[J]. AIP Conference Proceedings, 2018, 1943(1):020016.

[9] CHEN X X, LIU Y S, XING J Z, et al. The parametric design of double-circular-arc tooth profile and its influence on the functional backlash of harmonic drive[J]. Mechanism and Machine Theory, 2014, 73:1-24.

[10] TANG T, LI J Y, WANG J X, et al. Double-circular-arc tooth profile design and parametric analysis on the comprehensive performance of the harmonic drive[J]. Proceedings of the Institution of Mechanical Engineers, Part J:Journal of Engineering Tribology, 2022, 236(3):480-498.

[11] HUANG J Z, XU J H, QIAN N. Investigation on high contact ratio harmonic two-dimensional tooth profile design based on mid-point meshing method[J]. Journal of Mechanical Science and Technology, 2023, 37(2):835-850.

[12] ISHIKAWA S, KANAGAWA Y, KIYOSAWA Y, et al. Wave gear drive with continues meshing,high ratcheting torque tooth profile:US7694607[P]. 2010-04-13.

[13] YANG C B, MA H L, ZHANG T, et al. Calculation of tooth thickness errors and its adjustment on meshing backlash of harmonic drive[J]. International Journal of Precision Engineering and Manufacturing, 2023, 24(2):289-301.

[14] ZENG X Y, LI J Y, WANG J X, et al. Design and modification of harmonic double circular arc tooth profile based on finite element method[J]. Journal of Zhejiang University(Engineering Science), 2021, 55(8):1548-1557. (in Chinese)

[15] JIANG Q Q, GONG A, LI X F, et al. Influence of radial deformation of cam on profile modification in harmonic drive[J]. Journal of Mechanical Transmission, 2019, 43(6):1-5. (in Chinese)

[16] SONG C S, ZHU F H, LI X Z, et al. Three-dimensional conjugate tooth surface design and contact analysis of harmonic drive with double-circular-arc tooth profile[J]. Chinese Journal of Mechanical Engineering, 2023, 36(1):83.

[17] CHENG Y H, CHEN Y C. A general mathematical modeling and finite element analysis of a strain wave gear possessing a double-circular-arc-with-a-common-tangent profile[J]. Proceedings of the Institution of Mechanical Engineers, Part C:Journal of Mechanical Engineering Science, 2023, 237(1):223-236.

[18] HUANG B, LOU J Q, CENG G J, et al. Tooth profile modification and experimental study of double circular arc flexsplines in harmonic reducers[J]. Journal of Mechanical Transmission, 2023, 47(11):108-116. (in Chinese)

[19] WANG J X, YUAN P, TAN C L, et al. Spatial tooth profile design of harmonic drive by rack approximation method[J]. Journal of Jilin University(Engineering and Technology Edition), 2017, 47(4):1121-1129. (in Chinese)

[20] ZHANG Y D L. Spatial tooth profile design and meshing characteristics study of flexspline in harmonic reducer[D]. Shanghai: Donghua University, 2022. (in Chinese)

[21] LÜ H Z, JIANG Y, YOU J, et al. Dynamic design and transmission performance analysis based on CF/PEEK composite for short flexspline harmonic drive[J]. Journal of Mechanical Science and Technology, 2024, 38(6):2885-2899.

[22] LIU T Q, ZHANG G X, ZHANG T, et al. A fast life prediction method for hard metals under multiaxial high-cycle fatigue loading[J]. Journal of Chongqing University, 2023, 46(3):94-102. (in Chinese)