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Sensitivity of Spline Self-excited Vibration to Structure Parameters

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Proceedings of the 11th IFToMM International Conference on Rotordynamics (IFToMM 2023)

Part of the book series: Mechanisms and Machine Science ((Mechan. Machine Science,volume 140))

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Abstract

Many aviation splines have to work in grease-lubricated or non-lubricated environments because of structural, weight and space restrictions. When a spline rotor system works at speeds above the critical speed, a poor lubrication or a specific misalignment will lead the spline in such a rotor experiencing self-excited vibration. In this paper, a constant stiffness and time-varying damping model is established for the spline coupling used in helicopter tail transmission shaft system. A multi-degree-of-freedom model for helicopter tail transmission shaft system is developed according to Timoshenko beam theory and lumped-mass method. The coupled differential equations are solved using Newmark-β method. According to the magnitude of low-frequency component, the self-excited vibration sensitivities to critical system parameters (i.e., spline tooth number, modulus, pressure angle and tooth width) are investigated for splines used in helicopter tail transmission shaft system. This study provides a reference for the mechanism research and suppression of the self-excited vibration of splines encountered in helicopter tail transmission shaft system.

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References

  1. Fu, C.G., Zheng, D.P., Ou, Y.X., Zhou, S.J., Zhao, X.M.: Aeroengine Design Manual, vol. 19. Aviation Industry Press, Beijing, China (2001)

    Google Scholar 

  2. Zhao, G., Zhao, X.Y., Qian, L.T., Yuan, Y.B., Ma, S., Guo, M.: A review of aviation spline research. Lubricants 11(1), 1–20 (2023)

    Google Scholar 

  3. Wang, Y.L., Zhao, G., Sun, X.C., Li, S.X.: Review on research of aviation spline. Aeronaut. Manuf. Technol. 3, 91–100 (2017)

    Google Scholar 

  4. Walton, J., Artiles, A., Lund, J., Dill, J., Zorzi, E.: Internal rotor friction instability. NASA Report, MTI-88TR39 (1990)

    Google Scholar 

  5. Williams, R., Trent, R.: The effect of nonlinear asymmetric supports on turbine engine rotor stability. SAE Trans. 79, 1010–1020 (1970)

    Google Scholar 

  6. Marmol, R.A., Smalley, A.J., Tecza, J.A.: Spline coupling induced nonsynchronous rotor vibrations. J. Mech. Des. 102(1), 168–176 (1980)

    Google Scholar 

  7. Marmol, R.A.: Engine rotor dynamics, synchronous and nonsynchronous whirl control. Army Research and Technology Labs Report, USARTL-TR-79-2 (1979)

    Google Scholar 

  8. Roger Ku, C.P., Walton, J.F., Lund, J.W.: Dynamic coefficients of axial spline couplings in high-speed rotating machinery. J. Vib. Acoust. 116(3), 250–256 (1994). https://doi.org/10.1115/1.2930421

    Article  Google Scholar 

  9. Park, S.K.: Determination of loose spline coupling coefficients of rotor bearing systems in turbomachinery. PhD Thesis, Texas A&M University, Texas, USA (1991)

    Google Scholar 

  10. Zhu, H., Chen, W., Zhu, R., Gao, J., Liao, M.: Modelling and dynamic analysis of spline-connected multi-span rotor system. Meccanica 55(6), 1413–1433 (2020). https://doi.org/10.1007/s11012-020-01163-9

    Article  MathSciNet  Google Scholar 

  11. Brommundt, E., Kramer, E.: Instability and self-excitation caused by a gear coupling in a simple rotor system. Forsch Ingenieurwesen-Eng. Res. 70(1), 25–37 (2005)

    Article  Google Scholar 

  12. GAO, T.: Research on the stability of spline connected rotor system. Master’s Thesis, Shanghai Jiao Tong University, Shanghai, China (2016)

    Google Scholar 

  13. Zhao, G., Liu, Z.S., Chen, F.: Influences of spline coupling on stability of rotor-bearing system. J. Vib. Eng. 22(3), 280–286 (2009)

    Google Scholar 

  14. Zhao, G., Long, X., Ge, C.F., Liu, Z.S.: Study on stability of rotor-bearing systems with different types of coupling. In: Proceedings of the 9th National Symposium on Rotor Dynamics ROTDYN’ 2010, Guiyang, China (2010)

    Google Scholar 

  15. Kang, L.X., Cao, Y.H., Mei, Q.: Dynamic instability of helicopter transmission rotating shafts with spline coupling. J. Beijing Univ. Aeronaut. Astronaut. 36(6), 645–649 (2010)

    Google Scholar 

  16. Li, Y.J., Zhao, G., Wu, X.S., Li, J., Yuan, W., Mei, Q.: Summary of research on self-excited vibration of aviation spline-rotor system. Acta Aeronautica et Astronautica Sinica 43(08), 21–35 (2022)

    Google Scholar 

  17. Wang, T., Wang, L., Liao, M.F.: Stability analysis of rotor with spline coupling. Aeroengine 47(03), 66–71 (2021)

    Google Scholar 

  18. Wang, T., Wang, Y.K., Liu, M.R., Zhong, Z.C.: Stability analysis of rotor with a spline coupling. In: 2022 International Symposium on Aerospace Engineering and Systems, China (2022)

    Google Scholar 

  19. Huang, J.B., Liao, M.F., Liu, Q.Y., Xue, Y.G., Wang, S.J., Zhou, X.: Experiment study on vibration stability of rotor system with spline connection structure. J. Propul. Technol. 43(02), 275–285 (2022)

    Google Scholar 

  20. Zhao, G.: Study on coupled dynamics of rotor-coupling-bearing-isolator system. PhD. Thesis, Harbin Institute of Technology, Harbin, China (2009)

    Google Scholar 

  21. Lin, H.H., Lundberg, G.: Prediction of gear dynamics using fast Fourier transform of static transmission error. Mech. Struct. Mach. 21(2), 237–260 (1993)

    Article  Google Scholar 

Download references

Acknowledgement

The authors gratefully acknowledge the support provided by the National Natural Science Foundation of China (No. 12172073) and National Science and Technology major projects (779608000000200007).

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Correspondence to Yunbo Yuan .

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Li, Y., Zhao, G., Zhang, Z., Yuan, Y., Li, J., Wang, Y. (2024). Sensitivity of Spline Self-excited Vibration to Structure Parameters. In: Chu, F., Qin, Z. (eds) Proceedings of the 11th IFToMM International Conference on Rotordynamics. IFToMM 2023. Mechanisms and Machine Science, vol 140. Springer, Cham. https://doi.org/10.1007/978-3-031-40459-7_8

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  • DOI: https://doi.org/10.1007/978-3-031-40459-7_8

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-40458-0

  • Online ISBN: 978-3-031-40459-7

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