Skip to main content
SpringerLink
Log in

Deformation analysis of the flexspline of harmonic drive gears considering the driving speed effect using laser sensors

  • Article
  • Published:
Science China Technological Sciences Aims and scope Submit manuscript

Abstract

Accurate description of the elastic deformation of the flexspline is the foundation for optimization design of the structure and conjugate profiles of the harmonic drive gear. This paper proposed an experimental method to investigate the effect of the driving speed on the deformation characteristics of the flexspline. First, an experimental apparatus that integrates a special-fabricated micro-displacement platform and a pair of laser displacement sensors is developed, and the radial displacement of the flexspline is measured in vertical and horizontal directions. Next, the deformation analyses of the flexspline at different driving speeds are performed with our method and the conventional method, and the comparison results reveal that the radial displacement of the flexspline is actually composed of both harmonic and random components, and the amplitude decreases and tends to zero with the increase of the driving speed, especially near the closed end of the flexspline. Last, the mechanisms of the inherent multi-frequency and amplitude attenuation characteristics of the radial displacement of the flexspline are discussed. It is indicated that the impact and friction existing in the flexible bearing of the wave generator is likely responsible for the existence of the random component, and the assumption of linear distribution of the flexspline deformation along the rotating axis is invalid under high speed condition. Our research promotes the further study on the contact-impact problem of the flexible bearing of the wave generator and the transfer characteristic of the elastic deformation of the flexspline.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Ma D H, Wu J N, Yan S Z. A method for detection and quantification of meshing characteristics of harmonic drive gears using computer vision. Sci China Tech Sci, 2016, 59: 1305–1319

    Article  Google Scholar 

  2. Zhao J L, Yan S Z, Wu J N, et al. Thermodynamic analysis of a space station remote manipulator with a harmonic drive that considers an integrated thermal protection layer. Sci China Tech Sci, 2015, 58: 1884–1893

    Article  Google Scholar 

  3. Liu G J, Liu Y G, Zhang H W, et al. The kapvik robotic mast: An innovative onboard robotic arm for planetary exploration rovers. IEEE Robot Automat Mag, 2015, 22: 34–44

    Article  Google Scholar 

  4. Dong H M. Study on kinematics and meshing characteristic of harmonic gear drives based on the deformation function of the flexspline. Dissertation for the Doctoral Degree. Dalian: Dalian University of Technology, 2008

    Google Scholar 

  5. Liu C J, Chen L J, Wei C. Deformation and stress analysis of flexspline in harmonic drive based on finite element method. Int J Sci, 2015, 2: 96–100

    Google Scholar 

  6. León D, Arzola N, Tovar A. Statistical analysis of the influence of tooth geometry in the performance of a harmonic drive. J Braz Soc Mech Sci Eng, 2015, 37: 723–735

    Article  Google Scholar 

  7. Chen X, Liu Y, Xing J, et al. A novel method based on mechanical analysis for the stretch of the neutral line of the flexspline cup of a harmonic drive. Mech Mach Theory, 2014, 76: 1–19

    Article  Google Scholar 

  8. Zu L, Yin A, Sun Y, et al. Deformation analysis and simulation of the cup-shaped flexspline for harmonic drive using in aerocrafts. Int J Comput Theory Eng, 2016, 8: 512–516

    Article  Google Scholar 

  9. Chen X, Liu Y, Xing J, et al. The parametric design of double-circular-arc tooth profile and its influence on the functional backlash of harmonic drive. Mech Mach Theory, 2014, 73: 1–24

    Article  Google Scholar 

  10. Gao H, Zhuang H, Li Z, et al. Optimization and experimental research on a new-type short cylindrical cup-shaped harmonic reducer. J Cent South Univ, 2012, 19: 1869–1882

    Article  Google Scholar 

  11. Kayabasi O, Erzincanli F. Shape optimization of tooth profile of a flexspline for a harmonic drive by finite element modelling. Mater Des, 2007, 28: 441–447

    Article  Google Scholar 

  12. Liu W Z, Zhang N R, Zhang C L, et al. Finite element calculation and analysis on the column-shaped flexspline of harmonic drive (in Chinese). J Mech Eng, 2006, 42: 52–57

    Google Scholar 

  13. Chen X X, Liu Y S, Xing J Z, et al. Neutral line stretch of flexspline in harmonic driver (in Chinese). J Mech Eng, 2014, 50: 189–196

    Article  Google Scholar 

  14. Ivanov M N. The Harmonic Drive. Beijing: Defense Industry Press, 1987. 1–70

    Google Scholar 

  15. Shen W M, Ye Q T. Theory and Design of Harmonic Drive. Beijing: China Machine Press, 1985. 1–81

    Google Scholar 

  16. Liu T L, You B D, Wang P X, et al. Heat-structure coupling analysis of harmonic drive under different thermal loading. Int J Control Autom, 2015, 8: 201–210

    Article  Google Scholar 

  17. Xiang Q, Yin Z. Investigation of temperature effect on stress of flexspline. Appl Math Mech Eng Ed, 2014, 35: 791–798

    Article  MathSciNet  Google Scholar 

  18. Zou C, Tao T, Jiang G D, et al. Deformation and stress analysis of short flexspline in the harmonic drive system with load. In: Proceedings of IEEE International Conference on Mechatronics and Automation. Takamatsu, 2013. 676–680

    Google Scholar 

  19. Dong H M, Wang D L. Elastic deformation characteristic of the flexspline in harmonic drive. In: Proceedings of ASME/IFToMM International Conference on Reconfigurable Mechanisms and Robots. London, 2009. 363–369

    Google Scholar 

  20. Zhao J L, Yan S Z. Coupling vibration analysis for harmonic drive in joint and flexible arm undergoing large range motion. In: Proceedings of International Symposium on Flexible Automation. Cleveland, 2016. 442–449

    Google Scholar 

  21. Chen X X, Lin S Z, Xing J Z, et al. Assembly model of harmonic gear based on elastic component deformation (in Chinese). Comput Integr Manuf Syst, 2011, 17: 338–343

    Google Scholar 

  22. Chen X X, Lin S Z, Xing J Z. The investigation of elongation of the neutral line in harmonic drive. In: Proceedings of International Conference on Computer Design and Applications. Qinhuangdao, 2010. 383–386

    Google Scholar 

  23. Ostapski W, Mukha I. Stress state analysis of harmonic drive elements by FEM. Bull Pol Acad Sci Tech Sci, 2007, 55: 115–123

    MATH  Google Scholar 

  24. Gao H B, Li Z G, Deng Z Q. Sensitivity analysis of cup-shaped flexible gear parameters to its stress based on ANSYS (in Chinese). J Mech Eng, 2010, 46: 1–7

    Article  Google Scholar 

  25. Ostapski W. Analysis of the stress state in the harmonic drive generator-flexspline system in relation to selected structural parameters and manufacturing deviations. Bull Polish Acad Sci Tech Sci, 2010, 58: 683–698

    MATH  Google Scholar 

  26. Fan Y G, Cao B H. Technical Manual of The Harmonic Drive. Beijing: Defense Industry Press, 1995. 1–21

    Google Scholar 

  27. Li Q F, Cheng K, Zhong J. Study on deformation and deformation force of flexible gear of harmonic wave gear transmission (in Chinese). Mech Desig, 2008, 25: 48–50

    Google Scholar 

  28. Zhang H, Ahmad S, Liu G. Modeling of torsional compliance and hysteresis behaviors in harmonic drives. IEEE-ASME T Mech, 2015, 20: 178–185

    Article  Google Scholar 

  29. Tuttle T D. Understanding and modeling the behavior of a harmonic drive gear transmission. Dissertation for the Master Degree. Cambridge: Massachusetts Institute of Technology, 1992

    Google Scholar 

  30. Dong H, Wang D, Ting K L. Kinematic effect of the compliant cup in harmonic drives. J Mech Des, 2011, 133: 051004

    Article  Google Scholar 

  31. Wu Z, Huang N E. Ensemble empirical mode decomposition: A noise-assisted data analysis method. Adv Adapt Data Anal, 2009, 01: 1–41

    Article  Google Scholar 

  32. Zhao B H, Liu Z S, Song C L, et al. Mechanics analysis on flexible thin wall bearing in harmonic transmission (in Chinese). Bearing, 2002, 10: 1–3

    Google Scholar 

  33. Le K X, Shen Y W. Deformation state of the flexspline considering the clearance in the harmonic drive (in Chinese). Gear, 1990, 14: 1–4

    Google Scholar 

  34. Guan J, Wang J X, Han Y F, et al. Analysis on mixed lubrication of harmonic reducer flexible bearing (in Chinese). Tribology, 2016, 36: 153–160

    Google Scholar 

  35. Lu Q H, Liang Y, Fan Y X, et al. Research on tooth profile interference based on meshing simulation of harmonic drive (in Chinese). J Syst simul, 2009, 21: 6317–6320

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. State Key Laboratory of Tribology, Department of Mechanical Engineering, Tsinghua University, Beijing, 100084, China

    DongHui Ma, JiaNing Wu, Tao Liu & ShaoZe Yan

Authors
  1. DongHui Ma
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. JiaNing Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Tao Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. ShaoZe Yan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to ShaoZe Yan.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ma, D., Wu, J., Liu, T. et al. Deformation analysis of the flexspline of harmonic drive gears considering the driving speed effect using laser sensors. Sci. China Technol. Sci. 60, 1175–1187 (2017). https://doi.org/10.1007/s11431-016-9060-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11431-016-9060-y

Keywords

Search

Navigation