Tooth contact analysis with latent error of double circular-arc spiral bevel gears for industrial robot joint nutation drive

  • Zheng Lin
  • Ligang YaoEmail author
  • Jun Zhang
  • Tongke Su
  • Kunjing Chen
Technical Paper


The influence of the cone vertex error and tilt error on the tooth contact trace of double circular-arc spiral bevel gears for industrial robot joint nutation drive has been studied in this paper. According to the meshing relationship between double circular-arc spiral bevel gear and crown gear, the meshing coordinate systems with latent error parameters of cone vertex error and tilt error were established, and the tooth profile equations of external and internal spiral bevel gears were deduced. According to the meshing equation and coordinate transformation, the contact trace equation of the tooth surface was established, and the influence of different latent error values on the location of the contact trace was solved and analyzed. The finite element loading contact simulation of the double circular-arc spiral bevel gears with different latent error values was carried out. The results of the simulation analysis and numerical analysis were basically consistent. The latent errors would cause noise and vibration of industrial robot joint nutation drive and affect the service life of double circular-arc spiral bevel gears.


Industrial robot joint Nutation drive Tooth contact Latent error Spiral bevel gear Double circular arc 



This work was supported by the National Natural Science Foundation of China [Grant No. 51775114], the program of Fujian Provincial Industrial Robot Basic Components Technology Research and Development Center [Grant No. 2014H21010011] and the program of Fujian Provincial Young and Middle-aged Teacher Education and Scientific Research [Grant No. JAT160510].


  1. 1.
    Uzuka K, Enomoto I, Suzumori K (2009) Comparative assessment of several nutation motor types. Trans Mechatron 14(1):82–91CrossRefGoogle Scholar
  2. 2.
    Gu B, Yao LG, Wei GW et al (2006) The analysis and modeling for nutation drives with double circular-arc helical bevel gears. Mater Sci Forum 505–507:949–954CrossRefGoogle Scholar
  3. 3.
    Elu P, Kemper Y (1980) Performance of a nutating traction drive. Am Soc Mech Eng 80:63–80Google Scholar
  4. 4.
    Kemper Y (1981) The nutating traction drive. J Eng Power Trans ASME 103(1):154–157CrossRefGoogle Scholar
  5. 5.
    Uzuka K, Enomoto I, Suzumori K (2006) Development of nutation motors (1st report, driving principle and basic characteristics of pneumatic nutation motor). Trans Jpn Soc Mech Eng 72(4):1194–1199CrossRefGoogle Scholar
  6. 6.
    Uzuka K, Enomoto I, Suzumori K (2007) Development of nutation motors (4th report, development of small-sized and high torque pneumatic nutation motor by the OFW type bevel gears and principle of lever). Trans Jpn Soc Mech Eng 73(6):1731–1737CrossRefGoogle Scholar
  7. 7.
    He SJ (2007) Theoretical study on the rolling cone output mechanism of nutation gear. Coal mine Mach 28:55–57Google Scholar
  8. 8.
    He SJ, Zhao Q (1997) Analysis of profile in cycloid nutation gear. J Mech Transm 21(4):8–11Google Scholar
  9. 9.
    Yao LG, Gu B, Huang SJ et al (2010) Mathematical modeling and simulation of the external and internal double circular-arc spiral bevel gears for the nutation drive. J Mech Des ASME 132(2):021008.1-10CrossRefGoogle Scholar
  10. 10.
    Lin Z, Yao LG, Huang SJ (2010) Transmission ratio analysis and controllable tooth profile modeling for the nutation drive with double circular-arc external and internal spiral bevel gears. Adv Mater Res 97–101:3128–3134CrossRefGoogle Scholar
  11. 11.
    Lin Z, Yao LG (2013) Mathematical model and 3d modeling of involute spiral bevel gears for nutation drive. Adv Mater Res 694:503–506CrossRefGoogle Scholar
  12. 12.
    Lin Z, Yao LG (2012) General mathematical model of internal meshing spiral bevel gears for nutation drive. Appl Mech Mater 101–102:708–712Google Scholar
  13. 13.
    Zhang J, Yao LG, Huang SJ et al (2015) Accurate modeling of tooth profile of double arc spiral bevel gears. Mech Manuf Eng 1:119–124CrossRefGoogle Scholar
  14. 14.
    Cai YW, Yao LG, Xie ZY et al (2017) Influence analysis of system parameters on characteristics of the nutation drive with double circular arc spiral bevel gears. Forsch Ingenieurwes 81(2–3):125–133CrossRefGoogle Scholar
  15. 15.
    Litvin FL (1995) Computer design and generation of low-noise helical gears with modified surface technology. Trans ASME 117:125–134Google Scholar
  16. 16.
    Litvin FL, Fuentes A, Fan Q et al (2002) Handschuh: Computerized design, simulation of meshing, and contact and stress analysis of face-milled formate generated helical bevel gears. Mech Mach Theory 37:441–459CrossRefGoogle Scholar
  17. 17.
    Litvin FL, Ignacio GP, Fuentes A et al (2005) Design, generation and stress analysis of face-gear drive with helical pinion. Comput Methods Appl Mech Eng 194(36):3870–3901CrossRefGoogle Scholar
  18. 18.
    Ignacio GP, Fuentes A (2017) Implementation of a finite element model for gear stress analysis based on tie-surface constraints and its validation through the Hertz’s theory. ASME J Mech Des 140(2):023301-13Google Scholar
  19. 19.
    Huang CH, Wen SZ, Li RF et al (1996) Preliminary design tool LLTCA for spiral bevel and hypoid gears. J Tsinghua Univ (Sci Technol) 36(04):48–53Google Scholar
  20. 20.
    Fang ZD (1998) Model and approach for loaded tooth contact analysis (LTCA) of gear drives. J Mech Transm 22(2):1–3Google Scholar
  21. 21.
    Deng XZ, Fang ZD, Yang HB (2001) Calculation on tooth surface contact stress course of hypoid gears. China Mech Eng 12(12):1362–1364Google Scholar
  22. 22.
    Wu BL, Shao JH (1999) Investigation on load distributions among contact bearings of double circular arc helical gears. J Aerosp Power 14(3):297–300Google Scholar

Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2019

Authors and Affiliations

  • Zheng Lin
    • 1
    • 2
  • Ligang Yao
    • 2
    Email author
  • Jun Zhang
    • 2
  • Tongke Su
    • 2
  • Kunjing Chen
    • 1
  1. 1.College of Mechanical and Electrical EngineeringWuyi UniversityWuyishanChina
  2. 2.School of Mechanical Engineering and AutomationFuzhou UniversityFuzhouChina

Personalised recommendations