Load Sharing Performance of Herringbone Planetary Gear System with Flexible Pin

  • Chang-lu Wang
  • Jing WeiEmail author
  • Zi-heng Wu
  • Long Lu
  • Hao Gao
Regular Paper


To study the load distribution mechanism of the power-split transmission, and improve the carrying capacity of the herringbone star gear transmission system, the dynamic model of the planetary gear system for a geared turbofan engine with the flexible pin was established based on the node finite element method. The model considered the comprehensive influence of meshing error, time-varying meshing stiffness, bearing supporting stiffness and meshing phase. The dynamic load sharing performance of the system were studied in the equivalent meshing error, and the influence of the error incentives and structure of pins on the load sharing characteristics was analyzed. The results indicate that the vibration track of the center gears deviates from the origin because of the eccentricity error. The load sharing performance of the system can be improved by improving gears’ manufacturing precision. Moreover, the influence of manufacturing errors is larger than that of assembling errors. The flexible pin improved by Montestruc has the best load sharing performance among the four types of pin models designed in the study. The load sharing performance declines with an increase of in input speed and a decrease in input power.


Load sharing Flexible pin Herringbone gears Planetary gear system Gear dynamics 

List of Symbols


The shearing stiffness


The axial compressive stiffness


The equivalent stiffness of gears’ body deformation


The Hertz contacting stiffness


The pressure angle of the sun gear


The helix angle of the sun gear


Location phase angle of the mth star gear


The overall mass matrixes of the system


The overall stiffness matrixes of the system


The overall damping matrixes of the system


The overall displacement vector of shafting nodes


The bending stiffness



This study was supported by the National Natural Science Foundation of China (51775058) and the pre-research project of civil aircraft of Ministry of industry and information technology of China (MJZ-2016-D-33). The authors would also like to acknowledge the support from the project No. 2018CDJDCD0001 supported by the Fundamental Research Funds for the Central Universities as well as Fujian Provincial Major Program for Industries and Universities’ Cooperation (2017H6019).


  1. 1.
    Ma, P., & Botman, M. (1985). Load sharing in a planetary gear stage in the presence of gear errors and misalignment. Journal of Mechanical Design,107(1), 4–10.Google Scholar
  2. 2.
    Kahraman, A. (1994). Load sharing characteristics of planetary transmissions. Mechanism and Machine Theory,29(8), 1151–1165.MathSciNetCrossRefGoogle Scholar
  3. 3.
    Bodas, A., & Kahraman, A. (2004). Influence of carrier and gear manufacturing errors on the static load sharing behavior of planetary gear sets. JSME International Journal Series C-Mechanical Systems Machine Elements and Manufacturing,47(3), 908–915.CrossRefGoogle Scholar
  4. 4.
    Singh, A. (2003). Application of a system level model to study the planetary load sharing behavior. In Proceedings of the ASME 2003 international design engineering technical conferences and computers and information in engineering conference (pp. 469–476).CrossRefGoogle Scholar
  5. 5.
    Montestruc, A. N. (2011). Influence of planet pin stiffness on load sharing in planetary gear drives. Journal of Mechanical Design,133(1), 014501.CrossRefGoogle Scholar
  6. 6.
    Zhu, C., Xu, X., & Wang, H. (2011). Modal prediction and sensitivity analysis of wind-turbine planetary gear system with flexible planet pin. Journal of Computational and Theoretical Nanoscience,4(3), 1219–1224.Google Scholar
  7. 7.
    Zhu, C., Xu, X., Liu, H., Luo, T., & Zhai, H. (2014). Research on dynamical characteristics of wind turbine gearboxes with flexible pins. Renewable Energy,68(7), 724–732.CrossRefGoogle Scholar
  8. 8.
    Ren, F., Qin, D., Lim, T. C., & Lyu, S. (2014). Study on dynamic characteristics and load sharing of a herringbone planetary gear with manufacturing errors. International Journal of Precision Engineering and Manufacturing,15(9), 1925–1934.CrossRefGoogle Scholar
  9. 9.
    Sun, W., Li, X., Wei, J., Zhang, A., Ding, X., & Hu, X. (2015). A study on load-sharing structure of multi-stage planetary transmission system. Journal of Mechanical Science and Technology,29(4), 1501–1511.CrossRefGoogle Scholar
  10. 10.
    Mo, S., Zhang, Y., & Wu, Q. (2015). Research on multiple-split load sharing of two-stage star gearing system in consideration of displacement compatibility. Mechanism and Machine Theory,88, 1–15.CrossRefGoogle Scholar
  11. 11.
    Mo, S., & Zhang, Y. (2015). Spiral bevel gear true tooth surface precise modeling and experiments studies based on machining adjustment parameters. Proceedings of the Institution of Mechanical Engineers Part C-Journal of Mechanical Engineering Science,229, 14.Google Scholar
  12. 12.
    Hicks, R. J. (1967). Load equalizing means for planetary pinions. U.S.Patent No. 3,303,713Google Scholar
  13. 13.
    Fox G. P., Jallat E. (2006). Epicyclic gear system. U.S. Patent No. 6,994,651Google Scholar
  14. 14.
    Stringer, D. B. (2008). Geared rotor dynamic methodologies for advancing prognostic modeling capabilities in rotary-wing transmission systems. Virginia: University of Virginia.Google Scholar
  15. 15.
    Lin, C. H., & Tsao, T. P. (2002). Depressing the torque vibrations of turbine blades using virtual inertia. Electric Power Systems Research,61(1), 23–32.CrossRefGoogle Scholar
  16. 16.
    Wei, J., Zhang, A., Qin, D., Lim, T. C., Shu, R., Lin, X., et al. (2017). A coupling dynamics analysis method for a multistage planetary gear system. Mechanism and Machine Theory,110, 27–49.CrossRefGoogle Scholar
  17. 17.
    Chen, Z., Shao, Y., & Lim, T. C. (2012). Non-linear dynamic simulation of gear response under the idling condition. International Journal of Automotive Technology,13(4), 541–552.CrossRefGoogle Scholar
  18. 18.
    Parker, R. G., Lin, J. (2003). Mesh phasing relationships in planetary and epicyclic gears. In Proceedings of the ASME 2003 international design engineering technical conferences and computers and information in engineering conference (pp. 525–534).Google Scholar
  19. 19.
    Liew, H. V., & Lim, T. C. (2005). Analysis of time-varying rolling element bearing characteristics. Journal of Sound and Vibration,283(3), 1163–1179.CrossRefGoogle Scholar
  20. 20.
    Zhong, W., & Cai, Z. (2000). Precise integration method for LQG optimal measurement feedback control problem. Applied Mathematics and Mechanics (English Edition),21(12), 1417–1422.CrossRefGoogle Scholar

Copyright information

© Korean Society for Precision Engineering 2019

Authors and Affiliations

  1. 1.Institute of Beautiful China DevelopmentSanming UniversitySanmingChina
  2. 2.State Key Laboratory of Mechanical TransmissionChongqing UniversityChongqingChina

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