Skip to main content
SpringerLink
Log in

Dynamic Characteristics of the Multistage Planetary Gear Transmission System Based on a Stochastic Load

  • Regular Paper
  • Published:
International Journal of Precision Engineering and Manufacturing Aims and scope Submit manuscript

Abstract

Multistage planetary gear transmission has a large speed ratio, compact structure and large load capacity in engineering practice. However, its vibration affects the performance and reliability of the transmission, especially under a stochastic load condition with different dynamic characteristics. In this context, the dynamic behavior of a four-stage planetary gear transmission system is investigated using the lumped-parameter model. First, the translation-torsion dynamics model of the multistage planetary gear transmission system is established. Then, the natural frequency and the effect of meshing stiffness and component mass on the natural frequency are investigated. Further, the dynamics equation of the planetary gear transmission system is solved by the Runge–Kutta method, and the damped dynamic response with an equivalent load and the dynamic responses with stochastic loads are analyzed. Notably, the displacement amplitude increases with the increment of the stochastic load. In addition, the frequency domain response under 50%, 75%, 100% and 120% of the equivalent torque are studied. Lastly, a test rig is built for a yaw drive in a wind turbine with the four-stage planetary gear transmission system, and the vibration of the ring gear of the second stage and output shaft are tested with 50%, 75%, 100% and 120% of equivalent load. The experiment results verify the correctness of the theoretical dynamic model of the multistage planetary gear transmission system.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

References

  1. Ambarisha, V. K., & Parker, R. G. (2007). Nonlinear dynamics of planetary gears using analytical and finite element models. Journal of Sound and Vibration, 302(3), 577–595. https://doi.org/10.1016/j.jsv.2006.11.028

    Article  Google Scholar 

  2. Mohammed, O. D., Rantatalo, M., & Aidanpää, J.-O. (2015). Dynamic modelling of a one-stage spur gear system and vibration-based tooth crack detection analysis. Mechanical Systems and Signal Processing, 54–55, 293–305. https://doi.org/10.1016/j.ymssp.2014.09.001

    Article  Google Scholar 

  3. Sun, T., & Hu, H. (2003). Nonlinear dynamics of a planetary gear system with multiple clearances. Mechanism and Machine Theory, 38(12), 1371–1390. https://doi.org/10.1016/S0094-114X(03)00093-4

    Article  MATH  Google Scholar 

  4. Eritenel, T., & Parker, R. G. (2009). Modal properties of three-dimensional helical planetary gears. Journal of Sound and Vibration, 325(1–2), 397–420. https://doi.org/10.1016/j.jsv.2009.03.002

    Article  Google Scholar 

  5. Manarikkal, I., Elasha, F., Laila, D. S., & Mba, D. (2019). Dynamic modelling of planetary gearboxes with cracked tooth using vibrational analysis. In A. Fernandez Del Rincon, F. Viadero Rueda, F. Chaari, R. Zimroz, & M. Haddar (Eds.), Advances in condition monitoring of machinery in non-stationary operations (Vol. 15, pp. 240–249). Cham: Springer International Publishing. https://doi.org/10.1007/978-3-030-11220-2_25

  6. Hu, C., Shen, C., Peng, R., & Chen, R. (2017). Dynamics analysis of the pitch control reducer for MW wind turbine. Journal of Vibroengineering, 19(8), 5842–5857. https://doi.org/10.21595/jve.2017.19146

  7. Yang, J., & Yang, P. (2013). Random vibration analysis of planetary gear trains. Journal of Vibration and Acoustics, 135(2), 021005. https://doi.org/10.1115/1.4023053

    Article  Google Scholar 

  8. Hasnijeh, S. G., Poursina, M., Leira, B. J., Karimpour, H., & Chai, W. (2019). Stochastic dynamics of a nonlinear time-varying spur gear model using an adaptive time-stepping path integration method. Journal of Sound and Vibration, 447, 170–185. https://doi.org/10.1016/j.jsv.2019.02.001

    Article  Google Scholar 

  9. Fang, Y., Liang, X., & Zuo, M. J. (2018). Effects of friction and stochastic load on transient characteristics of a spur gear pair. Nonlinear Dynamics, 93(2), 599–609. https://doi.org/10.1007/s11071-018-4212-3

    Article  Google Scholar 

  10. Feki, M. S., Chaari, F., Abbes, M. S., Viadero, F., del Rincon, A. Fdez., & Haddar, M. (2013). Dynamic analysis of planetary gear transmission under time varying loading conditions. In F. Viadero & M. Ceccarelli (Eds.), New trends in mechanism and machine science (Vol. 7, pp. 311–318). Dordrecht: Springer Netherlands. https://doi.org/10.1007/978-94-007-4902-3_33

  11. Chen, H., Fan, J., Jing, S., & Wang, X. (2019). Probabilistic design optimization of wind turbine gear transmission system based on dynamic reliability. Journal of Mechanical Science and Technology, 33(2), 579–589. https://doi.org/10.1007/s12206-019-0112-9

    Article  Google Scholar 

  12. Hammami, A., Fernandez Del Rincon, A., Chaari, F., Santamaria, M. I., Viadero Rueda, F., & Haddar, M. (2016). Effects of variable loading conditions on the dynamic behaviour of planetary gear with power recirculation. Measurement, 94, 306–315. https://doi.org/10.1016/j.measurement.2016.07.083

    Article  Google Scholar 

  13. Concli, F., Cortese, L., Vidoni, R., Nalli, F., & Carabin, G. (2018). A mixed FEM and lumped-parameter dynamic model for evaluating the modal properties of planetary gearboxes. Journal of Mechanical Science and Technology, 32(7), 3047–3056. https://doi.org/10.1007/s12206-018-0607-9

    Article  Google Scholar 

  14. Karray, M., Feki, N., Chaari, F., & Haddar, M. (2014). Modal analysis of helical planetary gear train coupled to bevel gear. In M. S. Abbes, J.-Y. Choley, F. Chaari, A. Jarraya, & M. Haddar (Eds.), Mechatronic systems: Theory and applications (pp. 149–158). Cham: Springer International Publishing. https://doi.org/10.1007/978-3-319-07170-1_14

  15. Mo, S., Zhang, Y., Wu, Q., Houjoh, H., & Matsumura, S. (2016). Research on natural characteristics of double-helical star gearing system for GTF aero-engine. Mechanism and Machine Theory, 106, 166–189. https://doi.org/10.1016/j.mechmachtheory.2016.09.001

    Article  Google Scholar 

  16. Zhai, H., Zhu, C., Song, C., Liu, H., Li, G., & Ma, F. (2015). Dynamic modeling and analysis for transmission system of high-power wind turbine gearbox. Journal of Mechanical Science and Technology, 29(10), 4073–4082. https://doi.org/10.1007/s12206-015-0901-8

    Article  Google Scholar 

  17. Liu, C., Qin, D., & Liao, Y. (2017). Dynamic modeling and analysis of high-speed planetary gear including centrifugal force. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 39(10), 3769–3778. https://doi.org/10.1007/s40430-017-0783-z

    Article  Google Scholar 

  18. Xiang, L., Gao, N., & Hu, A. (2018). Dynamic analysis of a planetary gear system with multiple nonlinear parameters. Journal of Computational and Applied Mathematics, 327, 325–340. https://doi.org/10.1016/j.cam.2017.06.021

    Article  MathSciNet  MATH  Google Scholar 

  19. Kahraman, A. (2001). Free torsional vibration characteristics of compound planetary gear sets. Mechanism and Machine Theory, 36(8), 953–971. https://doi.org/10.1016/S0094-114X(01)00033-7

    Article  MATH  Google Scholar 

  20. Sun, Z. M., Shen, Y. W., & Li, S. Y. (2001). A study on torsional vibrations in an encased differential gear train. Journal of Aerospace Power, 16(2), 163–166. https://doi.org/10.13224/j.cnki.jasp.2001.02.014

  21. Xiang, L., Zhang, Y., Gao, N., Hu, A., & Xing, J. (2018). Nonlinear dynamics of a multistage gear transmission system with multi-clearance. International Journal of Bifurcation and Chaos, 28(03), 1850034. https://doi.org/10.1142/S0218127418500347

    Article  MathSciNet  MATH  Google Scholar 

  22. Wan, K. Y. (2004). Dynamic analysis of planetary gear transmission system (Master). Nanjing University of Aeronautics and Astronautics.

    Google Scholar 

  23. Xiao, Z. M., Qin, D. T., Wang, J. H., Wu, W. H., & Chen, L. F. (2010). Study on torsional dynamics of 3-stage planetary gears of main reducer used in driving cutterhead of shield tunnelling machine. China Mechanical Engineering, 21(18), 2176.

    Google Scholar 

  24. Maatar, M., & Velex, P. (1996). An analytical expression for the time-varying contact length in perfect cylindrical gears: some possible applications in gear dynamics. Journal of Mechanical Design, 118(4), 586–589. https://doi.org/10.1115/1.2826933

    Article  Google Scholar 

Download references

Acknowledgements

This research is grateful for the financial support from the National Natural Science Foundation of China (51705442, 52075465), China Scholarship Council (201908430286), the Natural Science Foundation of Hunan Province of China (2021JJ30676), and the Scientific and Technological Achievements Transformation and Industrialization Plan of Hunan Province (2019GK4025). It is also grateful to the referees whose comments were helpful in the revision of this paper. The authors have no relevant financial or non-financial interests to disclose.

Author information

Authors and Affiliations

  1. School of Mechanical Engineering and Mechanics, Xiangtan University, Xiangtan, 411105, China

    Congfang Hu, Gaode Geng, Xianxian Liu, Shiping Yang & Xinzi Tang

Authors
  1. Congfang Hu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Gaode Geng
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Xianxian Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Shiping Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Xinzi Tang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xinzi Tang.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hu, C., Geng, G., Liu, X. et al. Dynamic Characteristics of the Multistage Planetary Gear Transmission System Based on a Stochastic Load. Int. J. Precis. Eng. Manuf. 24, 657–669 (2023). https://doi.org/10.1007/s12541-022-00743-x

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12541-022-00743-x

Keywords

Search

Navigation