A New Algorithm to Solve Meshing-In Impact Considering the Measured Pitch Error and to Investigate its Influence on the Dynamic Characteristics of a Gear System

  • Fang GuoEmail author
  • Zong-De Fang
Regular Paper


To study the actual changing rule of the meshing-in impact considering the measured pitch error and the effect on the dynamic characteristics of a gear system, this paper presents a new algorithm to calculate the meshing-in impact considering the measured pitch error. Based on the tooth contact analysis and loaded tooth contact analysis considering the measured pitch error, the algorithm can determine the exact original position where each mating tooth pair comes into contact in the process of gear transmission. Furthermore, we consider the meshing-in impact as dynamic excitation and simulate the dynamic response of the gear system with or without this excitation. The simulation result is expressed in time and frequency domains, phase plane plots and Poincaré maps. By using the wavelet packet transformation, the impact feature is extracted from the vibration response of the gear system.


Meshing-in impact Measured pitch error Original position coming into contact Dynamic response 



The authors would like to thank the National Science Foundation of China for financially supporting this research under the Grant No. 51375384.


  1. 1.
    Wang, Q. B., & Zhang, Y. M. (2015). A model for analyzing stiffness and stress in a helical gear pair with tooth profile errors. Journal of Vibration and Control, 23(2), 20–23.Google Scholar
  2. 2.
    Lin, T. J., & He, Z. H. (2017). Analytical method for coupled transmission error of helical gear system with machining error, assembly errors and tooth modifications. Mechanical Systems and Signal Processing, 91, 167–182.CrossRefGoogle Scholar
  3. 3.
    Kang, M. R., & Kahraman, A. (2015). An experimental and theoretical study of the dynamic behavior of double-helical gear sets. Journal of Sound and Vibration, 350, 11–29.CrossRefGoogle Scholar
  4. 4.
    Yu, W., Mechefske, C. K., & Timusk, M. (2017). The dynamic coupling behavior of a cylindrical geared rotor system subjected to gear eccentricities. Mechanism and Machine Theory, 107, 105–122.CrossRefGoogle Scholar
  5. 5.
    Liu, Y. F., Lai, J. B., Dong, P., & Xu, X. Y. (2017). Dynamic analysis of helical planetary gear sets under combined force and moment loading. Shock and Vibration, 2017(3), 1–13.Google Scholar
  6. 6.
    Wang, Y. Z., Liu, Y., Tang, W., & Liu, P. (2017). Parametric finite element modeling and tooth contact analysis of spur and helical gears including profile and lead modifications. Engineering Computations, 34(8), 2877–2898.CrossRefGoogle Scholar
  7. 7.
    Yang, Y., Wang, X. R., Wang, M. K., Li, H., & Dai, Y. P. (2017). Dynamic behaviors of helical geared multishaft rotor systems by modal synthesis. Proceedings of the Institution of Mechanical Engineers Part C: Journal of Mechanical, 231(8), 1410–1426.Google Scholar
  8. 8.
    Clarke, A., Jamali, H. U., Sharif, K. J., Evans, H. P., Frazer, R., & Shaw, B. (2017). Effect of profile errors on lubrication performance of helical gears. Tribology International, 111, 184–191.CrossRefGoogle Scholar
  9. 9.
    Shi, W., Park, H. C., Na, S., Song, J., Ma, S., & Kim, C. W. (2014). Dynamic analysis of three-dimensional drivetrain system of wind turbine. International Journal of Precision Engineering and Manufacturing, 15(7), 1351–1357.CrossRefGoogle Scholar
  10. 10.
    Sun, W., Li, X., & Wei, J. (2018). An approximate solution method of dynamic reliability for wind turbine gear transmission with parameters of uncertain distribution type. International Journal of Precision Engineering and Manufacturing, 19(6), 849–857.CrossRefGoogle Scholar
  11. 11.
    Parker, R. G., Vijayakar, S. M., & Imajo, T. (2000). Non-linear dynamic response of a spur gear pair: Modeling and experimental comparisons. Journal of Sound and Vibration, 237(3), 435–455.CrossRefGoogle Scholar
  12. 12.
    Theodossiades, S., & Natsiavas, S. (2000). Non-linear dynamics of gear-pair systems with periodic stiffness and backlish. Journal of Sound and Vibration, 229(2), 287–310.CrossRefGoogle Scholar
  13. 13.
    Seireg, A., & Houser, D. R. (1970). Evaluation of dynamic factors for spur and helical gears. ASME Journal of Engineering for Industry, 92(2), 504–514.CrossRefGoogle Scholar
  14. 14.
    Munro, R. G., Morrish, L., & Palmer, D. (1999). Gear transmission error outside the normal path of contact due to corner and top contact. Proceedings of the Institution of Mechanical Engineers Part C: Journal Of Mechanical, 213(4), 389–400.Google Scholar
  15. 15.
    Zhou, C. J., Tang, J. Y., & Zhong, Z. H. (2008). Corner contact and impact friction of gear drive. Chinese Journal of Mechanical Engineering, 44(3), 75–81 (in Chinese).CrossRefGoogle Scholar
  16. 16.
    Zhou, C. J., & Chen, S. Y. (2014). Modeling and calculation of impact friction caused by corner contact in gear transmission. Chinese Journal of Mechanical Engineering, 27(5), 958–964.MathSciNetCrossRefGoogle Scholar
  17. 17.
    Zhou, C. J., Zhang, C., & Tang, J. Y. (2014). Modeling and calculation of impact of mesh-out at corner contact in gear drive. Journal of Aerospace Power, 29(5), 1205–1210 (in Chinese).Google Scholar
  18. 18.
    Tang, J. Y., Liu, X., & Dai, J. (2007). Study on corner contact shock of gear transmission by ANSYS/LS-DYNA software. Journal of Vibration and Shock, 26(9), 40–50 (in Chinese).Google Scholar
  19. 19.
    Tang, J. Y., Zhou, W., & Chen, S. Y. (2011). Contact-impact analysis of gear transmission system. Chinese Journal of Mechanical Engineering, 47(7), 22–30 (in Chinese).CrossRefGoogle Scholar
  20. 20.
    Lin, T. J., Li, R. F., Guo, X. D., & Wang, L. H. (2003). 3D nonlinear impact characteristics analysis for hypoid gearing with backlash. China Mechanical Engineering, 14(9), 727–730 (in Chinese).Google Scholar
  21. 21.
    Lin, T. J., Ou, H., & Li, R. F. (2007). A finite element method for 3D static and dynamic contact/impact analysis of gear drives. Computer Methods in Applied Mechanics and Engineering, 196, 1716–1728.CrossRefzbMATHGoogle Scholar
  22. 22.
    Xie, H. D., Zhou, Z. Y., Xia, W., Qiu, C., & Zhang, W. (2005). Numerical study on meshing impact of helical gear. Journal of Mechanical Transmission, 29(3), 6–9 (in Chinese).Google Scholar
  23. 23.
    Imin, R., & Geni, M. (2014). Stress analysis of gear meshing impact based on SPH method. Mathematical Problems in Engineering, 2014(4), 1–7.MathSciNetCrossRefGoogle Scholar
  24. 24.
    Litvin, F. L., & Fuentes, A. (2004). Gear geometry and applied theory (2nd ed.). Cambridge: Cambridge University Press.CrossRefzbMATHGoogle Scholar
  25. 25.
    Fang, Z. D. (1998). Model and approach for loaded tooth contact analysis (LTCA) of gear drives. Mechanical Transmission, 22(2), 1–3, 16 (in Chinese).Google Scholar
  26. 26.
    Deng, X. Z., Feng, Z. D., Ren, D. F., & Wei, B. Y. (2002). Study on contact ratio of spiral bevel gears and influence of pitch error. Journal of Aerospace Power, 17(2), 268–272 (in Chinese).Google Scholar

Copyright information

© Korean Society for Precision Engineering 2019

Authors and Affiliations

  1. 1.School of Mechanical EngineeringNorthwestern Polytechnical UniversityXi’anPeople’s Republic of China

Personalised recommendations