Bending stress analysis of eccentric straight and helical curve-face gear pair

  • Chao LinEmail author
  • Wenjie Wei
  • Shuang Wang
  • Xiguang Xia
  • Qingkun Xin


As a new type of gear transmission developed in recent years, curve-face gear transmission has not appeared before. In order to solve the problem of root bending strength of the eccentric straight and helical curve face gear, a calculating method of the tooth root bending strength was proposed. According to the principle of space meshing, differential geometry and design of machinery, the parametric equations of pitch curve was obtained, the pressure angle and the contact ratio in the meshing process were derived. The plane equivalent pitch curve was obtained, and the formula for calculating the equivalent tooth form factor and the equivalent stress correction factor was acquired. The calculation method of the bending strength of the gear pair was established, and the influence of the basic structural parameters on the bending stress was also analyzed in detail. The position of the stress hazard of the eccentric curve-face gear was determined. Through the finite element analysis and transmission experiment, the accuracy of the calculation method of strength of the gear pair was verified.


Straight curve face gear Helical curve face gear Non-circle gear rack Bending stress 



  1. Cai, Z.: Study on the time-varying meshing design and characteristics analysis of curve-face gear drive. Chongqing University (2017). (in Chinese)Google Scholar
  2. Cai, Z., Lin, C.: Design and analysis of cleaning mechanism for an intermittent screw-driven pipeline robot. J. Mech. Sci. Technol. 31(2), 911–921 (2017). CrossRefGoogle Scholar
  3. Cao, X.: Error detection and analysis method for curve-face gear. Chongqing University (2015). (in Chinese) Google Scholar
  4. Cheng, D.X.: Handbook of Mechanical Design. China Industry Press, Beijing (2008). (in Chinese) Google Scholar
  5. Fan, Y.: Machining methods of orthogonal variable transmission ratio curve-face gear. Chongqing University (2015). (in Chinese)Google Scholar
  6. He, C., Lin, C.: Analysis of loaded characteristics of helical curve face gear. Mech. Mach. Theory 115, 267–282 (2017). CrossRefGoogle Scholar
  7. Huang, C.: Tooth root bending strength analysis and experimental study of curve-face gear. Chongqing University (2017). (in Chinese)Google Scholar
  8. Lin, C., Liu, Y.: Characteristic analysis and application of composite motion curve-face gear pair. J. Braz. Soc. Mech. Sci. Eng. 38(6), 1797–1804 (2016). CrossRefGoogle Scholar
  9. Lin, C., Nie, L.: Strength calculation method of eccentric-high order elliptical bevel gear pair. J. Mech. Eng. 49(05), 47–54 (2013). (in Chinese) CrossRefGoogle Scholar
  10. Lin, C., Wu, X.: Calculation and analysis of contact ratio of helical curve-face gear pair. J. Braz. Soc. Mech. Sci. Eng. 39(6), 2269–2278 (2017). CrossRefGoogle Scholar
  11. Lin, C., Zeng, D.: Design, generation and tooth width analysis of helical curve-face gear. J. Adv. Mech. Des. Syst. Manuf. 9(5), M66 (2015). MathSciNetCrossRefGoogle Scholar
  12. Lin, C., Gong, H., Nie, N.: Geometry design, three-dimensional modeling and kinematic analysis of orthogonal fluctuating gear ratio face gear drive. Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci. 227(4), 779–793 (2012). CrossRefGoogle Scholar
  13. Lin, C., Zhao, X., Zeng, D.: Constructing principle and design of curved-face gear coupling. J. Central South Univ. (Science and Technology) 47(11), 3707–3714 (2016). (in Chinese) CrossRefGoogle Scholar
  14. Lin, C., Wu, X., Wei, Y.: Design and characteristic analysis of eccentric helical curve-face gear. J. Adv. Mech. Des. Syst. Manuf. (2017). CrossRefGoogle Scholar
  15. Lin, C., He, C., Hu, Y.: Analysis on the kinematical characteristics of compound motion curve-face gear pair. Mech. Mach. Theory 128, 298–313 (2018). CrossRefGoogle Scholar
  16. Wang, Y., Lin, C.: Bending stress analysis of orthogonal curve-face gear. J. Adv. Mech. Des. Syst. Manuf. 10(1), JAMDSM0015 (2016). CrossRefGoogle Scholar
  17. Wang, Z., Liu, R., Lin, J.C., et al.: Optimized face gear and its bending stress analysis. Adv. Mater. Res. 381, 5 (2011). CrossRefGoogle Scholar
  18. Wang, Y., Wu, C., Gong, K., et al.: Loaded tooth contact analysis of orthogonal face-gear drives. Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci. 226(9), 2309–2319 (2012). CrossRefGoogle Scholar
  19. Zhao, X.: Analysis of characteristics of double curve-face gear piston pump composite transmission. Chongqing University (2016). (in Chinese)Google Scholar
  20. Zhou, C., Huang, F., Han, X., et al.: An elastic–plastic asperity contact model and its application for micro-contact analysis of gear tooth profiles. Int. J. Mech. Mater. Des. 13(3), 335–345 (2017). CrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  • Chao Lin
    • 1
    Email author
  • Wenjie Wei
    • 1
  • Shuang Wang
    • 1
  • Xiguang Xia
    • 1
  • Qingkun Xin
    • 2
  1. 1.State Key Laboratory of Mechanical TransmissionChongqing UniversityChongqingChina
  2. 2.China North Vehicle Research InstituteBeijingChina

Personalised recommendations