Skip to main content
SpringerLink
Log in

A semi-analytical method of time-varying mesh stiffness in concentric face gear split-torque transmission system

  • Original Article
  • Published:
Journal of Mechanical Science and Technology Aims and scope Submit manuscript

Abstract

Concentric face gear split-torque transmission system (CFGSTTS) has great applied value in the field of aeronautical transmission due to the characteristic of high integration. Mesh stiffness, as one of the most primary sources of vibration, is vitally important for the dynamic performances of gear transmission system. The existing finite element method (FEM) and analytical method (AM) are not suitable for tackling the mesh stiffness calculation of closed-loop multi-branch system such as CFGSTTS. Thus, a semi-analytical method (SAM) is presented and verified, which combines the high precision of FEM with the high efficiency of AM. Additionally, the differences between the mesh stiffness of independent face gear drive and that of the same gear pair in CFGSTTS under accordant load is researched by applying SAM. The influence rules of distribution angle and load condition on the mesh stiffness of gear pairs considering system structure are also studied. Results demonstrate that the mesh stiffness of gear pairs in CFGSTTS is time-varying and tends to be consistent with each other by adjusting load parameters.

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

Similar content being viewed by others

References

  1. P. Marques, R. Martins and J. Seabra, Analytical load sharing and mesh stiffness model for spur/helical and internal/external gears-Towards constant mesh stiffness gear design, Mechanism and Machine Theory, 113 (2017) 126–140.

    Article  Google Scholar 

  2. C. G. Cooley, C. Liu, X. Dai and R. G. Parker, Gear tooth mesh stiffness: A comparison of calculation approaches, Mechanism and Machine Theory, 105 (2016) 540–553.

    Article  Google Scholar 

  3. Y. Guo and R. G. Parker, Analytical determination of back-side contact gear mesh stiffness, Mechanism and Machine Theory, 78 (2014) 263–271.

    Article  Google Scholar 

  4. C. Xie, L. Hua, J. Lan, X. Han, X. Wan and X. Xiong, Improved analytical models for mesh stiffness and load sharing ratio of spur gears considering structure coupling effect, Mechanical Systems and Signal Processing, 111 (2018) 331–347.

    Article  Google Scholar 

  5. N. L. Pedersen and M. F. Jargensen, On gear tooth stiffness evaluation, Computers and Structures, 135 (2014) 109–117.

    Article  Google Scholar 

  6. L. Chang, G. Liu and L. Wu, A robust model for determining the mesh stiffness of cylindrical gears, Mechanism and Machine Theory, 87 (2015) 93–114.

    Article  Google Scholar 

  7. J. Zhan, M. Fard and R. Jazar, A CAD-FEM-QSA integration technique for determining the time-varying meshing stiffness of gear pairs, Measurement, 100 (2017) 139–149.

    Article  Google Scholar 

  8. M. B. Sanchez, M. Pleguezuelos and J. I. Pedrero, Approximate equations for the meshing stiffness and the load sharing ratio of spur gears including hertzian effects, Mechanism and Machine Theory, 109 (2017) 231–249.

    Article  Google Scholar 

  9. Q. Wang, B. Zhao, Y. Fu, X. Kong and H. Ma, An improved time-varying mesh stiffness model for helical gear pairs considering axial mesh force component, Mechanical Systems and Signal Processing, 106 (2018) 413–429.

    Article  Google Scholar 

  10. G. I. Sheveleva, A. E. Volkov and V. I. Medvedev, Algorithms for analysis of meshing and contact of spiral bevel gears, Mechanism and Machine Theory, 42 (2007) 198–215.

    Article  Google Scholar 

  11. V. I. Medvedev, A. E. Volkov, M. A. Volosova and O. E. Zubelevich, Mathematical model and algorithm for contact stress analysis of gears with multi-pair contact, Mechanism and Machine Theory, 86 (2015) 156–171.

    Article  Google Scholar 

  12. A. F. Rincon, F. Viadero, M. Iglesias, P. Garcia, A. de-Juan and R. Sancibrian, A model for the study of meshing stiffness in spur gear transmissions, Mechanism and Machine Theory, 61 (2013) 30–58.

    Article  Google Scholar 

  13. A. Saxena, A. Parey and M. Chouksey, Time varying mesh stiffness calculation of spur gear pair considering sliding friction and spalling defects, Engineering Failure Analysis, 70 (2016) 200–211.

    Article  Google Scholar 

  14. L. Cui, H. Zhai and F. Zhang, Research on the meshing stiffness and vibration response of cracked gears based on the universal equation of gear profile, Mechanism and Machine Theory, 94 (2015) 80–95.

    Article  Google Scholar 

  15. J. G. Verma, S. Kumar and P. K. Kankar, Crack growth modeling in spur gear tooth and its effect on mesh stiffness using extended finite element method, Engineering Failure Analysis, 94 (2018) 109–120.

    Article  Google Scholar 

  16. Q. Wang, K. Chen, B. Zhao, H. Ma and X. Kong, An analytical-finite-element method for calculating mesh stiffness of spur gear pairs with complicated foundation and crack, Engineering Failure Analysis, 94 (2018) 339–353.

    Article  Google Scholar 

  17. Z. Chen, W. Zhai, Y. Shao, K. Wang and G. Sun, Analytical model for mesh stiffness calculation of spur gear pair with non-uniformly distributed tooth root crack, Engineering Failure Analysis, 66 (2016) 502–514.

    Article  Google Scholar 

  18. Y. Luo, N. Baddour and M. Liang, A shape-independent approach to modelling gear tooth spalls for time varying mesh stiffness evaluation of a spur gear pair, Mechanical Systems and Signal Processing, 120 (2019) 836–852.

    Article  Google Scholar 

  19. Y. Luo, N. Baddour, G. Han, F. Jiang and M. Liang, Evaluation of the time-varying mesh stiffness for gears with tooth spalls with curved-bottom features, Engineering Failure Analysis, 92 (2018) 430–442.

    Article  Google Scholar 

  20. H. Ma, X. Pang, R. Feng, J. Zeng and B. Wen, Improved time-varying mesh stiffness model of cracked spur gears, Engineering Failure Analysis, 55 (2015) 271–287.

    Article  Google Scholar 

  21. O. D. Mohammed, M. Rantatalo and J. Aidanpaa, Improving mesh stiffness calculation of cracked gears for the purpose of vibration-based fault analysis, Engineering Failure Analysis, 34 (SI) (2013) 235–251.

    Google Scholar 

  22. N. K. Raghuwanshi and A. Parey, Experimental measurement of spur gear mesh stiffness using digital image correlation technique, Measurement, 111 (2017) 93–104.

    Article  Google Scholar 

  23. J. Dong, J. Tang and Z. Hu, Investigation of assembly, power direction and load sharing in concentric face gear split-torque transmission system, Meccanica, 54 (14) (2019) 2485–2506.

    Article  Google Scholar 

  24. F. L. Litvin, A. Fuentes, Q. Fan and R. F. Handschuh, Computerized design, simulation of meshing, and contact and stress analysis of face-milled formate generated spiral bevel gears, Mechanism and Machine Theory, 37 (5) (2002) 441–459.

    Article  Google Scholar 

  25. F. L. Litvin, I. G. Perez, A. Fuentes, D. Vecchiato, B. D. Hansen and D. Binney, Design, generation and stress analysis of face-gear drive with helical pinion, Computer Methods in Applied Mechanics and Engineering, 194 (36-38) (2005) 3870–3901.

    MATH  Google Scholar 

  26. F. L. Litvin, D. Vecchiato, E. Gurovich, A. Fuentes, I. G. Perez, K. Hayasaka and K. Yukishima, Computerized developments in design, generation, simulation of meshing, and stress analysis of gear drives, Meccanica, 40 (3) (2005) 291–324.

    Article  Google Scholar 

  27. F. L. Litvin, A. Nava, Q. Fan and A. Fuentes, New geometry of face worm gear drives with conical and cylindrical worms: generation, simulation of meshing, and stress analysis, Computer Methods in Applied Mechanics and Engineering, 191 (27-28) (2002) 3035–3054.

    Article  Google Scholar 

  28. F. L. Litvin, Gear Geometry and Applied Theory, 1th Ed., PTR Prentice Hall, Englevood Cliffs, USA (1994).

    MATH  Google Scholar 

  29. ISO Standard 6336-1:2006, Calculation of Load Capacity of Spur and Helical Gears-Part 1: Basic Principles, Introduction and General Influence Factors, International Organization for Standardization, Geneva, Switzerland (2006).

Download references

Acknowledgments

The authors gratefully acknowledge the support of the National Key Research and Development Program of China through grant No. 2017YFB1300702. The authors gratefully acknowledge the support of the National Natural Science Foundation of China (NSFC) through grants No.51535012, U1604255, and the support of the Key Research and Development Project of Hunan province through grant No. 2016JC2001.

Author information

Authors and Affiliations

  1. Light Alloy Research Institute, Central South University, Changsha, 410083, China

    Jianxiong Dong

  2. State Key Laboratory of High Performance Complex Manufacturing, Central South University, Changsha, 410083, China

    Jianxiong Dong, Jinyuan Tang & Zehua Hu

  3. School of Mechanical and Electrical Engineering, Central South University, Changsha, 410083, China

    Jinyuan Tang & Zehua Hu

  4. School of Aeronautics and Astronautics, Central South University, Changsha, 410083, China

    Yi Wang

Authors
  1. Jianxiong Dong
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jinyuan Tang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zehua Hu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yi Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Jinyuan Tang or Yi Wang.

Additional information

Recommended by Editor No-cheol Park

Jianxiong Dong received his M.S. in School of Mechanical and Electrical Engineering at Central South University, China in 2015. He received his B.S. in School of Mechanical and Electrical Engineering at Central South University, China in 2012. He is an Ph.D. candidate in Central South University. His research interests include dynamic, vibration, tooth contact analysis, finite element analysis in gear systems.

Jinyuan Tang is a Professor in School of Mechanical and Electrical Engineering and State Key Laboratory of High Performance Complex Manufacturing of Central South University, Changsha, PR China. His research includes dynamics, design and manufacturing of the gears including face gear and bevel gear, the tooth surface strengthening and gear modification, and machine design.

Zehua Hu received his Ph.D. in School of Mechanical and Electrical Engineering at Central South University, China in 2019. He received his M.S. in School of Mechanical and Electrical Engineering at Central South University, China in 2014. His research interests include gear dynamic, vibration, gear design.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Dong, J., Tang, J., Hu, Z. et al. A semi-analytical method of time-varying mesh stiffness in concentric face gear split-torque transmission system. J Mech Sci Technol 34, 589–602 (2020). https://doi.org/10.1007/s12206-020-0107-6

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12206-020-0107-6

Keywords

Search

Navigation