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Research on pitch error phase matching of herringbone star gear system considering multi-tooth with different backlash

含多齿不同间隙的人字星型齿轮系统的齿距误差相位匹配研究

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Abstract

Pitch error is inevitable in gear machining, and it will aggravate the vibration and noise of the herringbone star gear train (HSGT). Although the machining accuracy is limited, the dynamic performance of the system can be further improved by appropriately combining the error phases. In this work, according to the periodicity of the pitch error and its influence on the backlash, the different backlash formed by the meshing tooth pairs during the transmission is deduced, then the meshing state and error excitation force of each tooth pair are considered, respectively. A new dynamic model of HSGT considering multi-tooth with different backlash under the influence of pitch error is established, and the reliability of the model is verified by the vibration experiment of the gearbox. Based on the proposed model, the influence mechanism of the error phase adjustment on two-sides of the herringbone center gear on the load-sharing performance is analyzed, and the optimal error phase combination of three parallel star gears is explored. When the pitch error value is constant, this research can guide the error phases combination of each herringbone gear in the HSGT, thereby reducing the vibration and improving the load-sharing performance of the system.

摘要

在加工过程中, 齿轮不可避免地会产生齿距误差, 这会加剧人字星型齿轮系统(HSGT)的振动和噪声. 尽管加工精度是有限的, 但通过适当的组合误差相位可以进一步提高系统的动态性能. 本工作中, 根据齿距误差的周期性及其对间隙的影响, 推导了传动过程中啮合齿对形成的不同齿隙, 然后分别考虑各齿对的啮合状态和误差激振力. 建立了在齿距误差影响下含有多齿不同间隙的HSGT动力学模型, 并通过齿轮箱振动实验验证了该模型的可靠性. 基于该模型分析了人字中心齿轮两侧误差相位的调整对均载性能的影响机理, 探索了三个平行星型齿轮最优的误差相位组合. 当齿距误差值一定时, 本研究可以指导HSGT中各人字齿轮误差相位的组合, 从而减少振动, 提高系统的均载性能.

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References

  1. J. Shi, X. Gou, and L. Zhu, Generation mechanism and evolution of five-state meshing behavior of a spur gear system considering gear-tooth time-varying contact characteristics, Nonlinear Dyn. 106, 2035 (2021).

    Article  Google Scholar 

  2. X. F. Gou, H. Wang, L. Y. Zhu, H. B. Que, J. F. Shi, and Z. F. Li, Modeling and analyzing of torsional dynamics for helical gear pair considered double and three teeth drive-side meshing, Meccanica 56, 2935 (2021).

    Article  MathSciNet  Google Scholar 

  3. L. Xiang, Y. Zhang, N. Gao, A. Hu, and J. Xing, Nonlinear dynamics of a multistage gear transmission system with multi-clearance, Int. J. Bifurcation Chaos 28, 1850034 (2018).

    Article  MathSciNet  Google Scholar 

  4. J. Chen, W. Li, G. Xin, L. Sheng, S. Jiang, and M. Li, Nonlinear dynamic characteristics analysis and chaos control of a gear transmission system in a shearer under temperature effects, Proc. Inst. Mech. Eng. Part C-J. Mech. Eng. Sci. 233, 5691 (2019).

    Article  Google Scholar 

  5. S. Wang, and R. Zhu, Nonlinear dynamic analysis of GTF gearbox under friction excitation with vibration characteristics recognition and control in frequency domain, Mech. Syst. Signal Process. 151, 107373 (2021).

    Article  Google Scholar 

  6. S. Mo, Y. Zhang, Y. Song, W. Song, and Y. Huang, Nonlinear vibration and primary resonance analysis of non-orthogonal face gear-rotor-bearing system, Nonlinear Dyn. 108, 3367 (2022).

    Article  Google Scholar 

  7. Y. Yi, K. Huang, Y. Xiong, and M. Sang, Nonlinear dynamic modelling and analysis for a spur gear system with time-varying pressure angle and gear backlash, Mech. Syst. Signal Process. 132, 18 (2019).

    Article  Google Scholar 

  8. H. Liu, C. Zhang, C. L. Xiang, and C. Wang, Tooth profile modification based on lateral- torsional-rocking coupled nonlinear dynamic model of gear system, Mech. Mach. Theor. 105, 606 (2016).

    Article  Google Scholar 

  9. K. Huang, Y. Xiong, T. Wang, and Q. Chen, Research on the dynamic response of high-contact-ratio spur gears influenced by surface roughness under EHL condition, Appl. Surf. Sci. 392, 8 (2017).

    Article  Google Scholar 

  10. J. Chen, R. Zhu, W. Chen, M. Li, X. Yin, and G. Dai, Nonlinear dynamic modeling and analysis of helical gear system with time-varying backlash caused by mixed modification, Nonlinear Dyn. 111, 1193 (2023).

    Article  Google Scholar 

  11. K. Feng, J. C. Ji, Q. Ni, and M. Beer, A review of vibration-based gear wear monitoring and prediction techniques, Mech. Syst. Signal Process. 182, 109605 (2023).

    Article  Google Scholar 

  12. K. Feng, P. Borghesani, W. A. Smith, R. B. Randall, Z. Y. Chin, J. Ren, and Z. Peng, Vibration-based updating of wear prediction for spur gears, Wear 426–427, 1410 (2019).

    Article  Google Scholar 

  13. A. Fernández-del-Rincón, M. Iglesias, A. de-Juan, A. Diez-Ibarbia, P. García, and F. Viadero, Gear transmission dynamics: Effects of index and run out errors, Appl. Acoust. 108, 63 (2016).

    Article  Google Scholar 

  14. X. Liu, Z. Fang, X. Yin, N. Zhao, Y. Shen, and H. Guo, A novel calculation method of long period pinion axial displacement and meshing impact force for double helical gear considering asymmetry error, Mech. Mach. Theor. 171, 104775 (2022).

    Article  Google Scholar 

  15. C. Wang, Impact of load-sharing on dynamic characteristics of herringbone gears, J. Vib. Control 29, 4059 (2023).

    Article  MathSciNet  Google Scholar 

  16. F. Guo, and Z. D. Fang, 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, Int. J. Precis. Eng. Manuf. 20, 395 (2019).

    Article  Google Scholar 

  17. S. Chen, and J. Tang, Effects of staggering and pitch error on the dynamic response of a double-helical gear set, J. Vib. Control 23, 1844 (2017).

    Article  MathSciNet  Google Scholar 

  18. B. Yuan, G. Liu, and L. Liu, Quasi-static characteristics and vibration responses analysis of helical geared rotor system with random cumulative pitch deviations, Appl. Sci. 10, 4403 (2020).

    Article  Google Scholar 

  19. J. Hong, D. Talbot, and A. Kahraman, Effects of tooth indexing errors on load distribution and tooth load sharing of splines under combined loading conditions, J. Mech. Des. 137, 032601 (2015).

    Article  Google Scholar 

  20. P. Liu, L. Zhu, X. Gou, J. Shi, and G. Jin, Modeling and analyzing of nonlinear dynamics for spur gear pair with pitch deviation under multi-state meshing, Mech. Mach. Theor. 163, 104378 (2021).

    Article  Google Scholar 

  21. S. Mo, Y. Li, B. Luo, L. Wang, H. Bao, G. Cen, and Y. Huang, Research on the meshing characteristics of asymmetric gears considering the tooth profile deviation, Mech. Mach. Theor. 175, 104926 (2022).

    Article  Google Scholar 

  22. S. Mo, B. Luo, W. Song, Y. Zhang, G. Cen, and H. Bao, Geometry design and tooth contact analysis of non-orthogonal asymmetric helical face gear drives, Mech. Mach. Theor. 173, 104831 (2022).

    Article  Google Scholar 

  23. S. Wang, and R. Zhu, Modeling and theoretical investigation of nonlinear torsional characteristics for double-helical star gearing system in GTF gearbox, J. Vib. Eng. Technol. 10, 193 (2022).

    Article  Google Scholar 

  24. F. Ren, A. Li, G. Shi, X. Wu, and N. Wang, The effects of the planet-gear manufacturing eccentric errors on the dynamic properties for herringbone planetary gears, Appl. Sci. 10, 1060 (2020).

    Article  Google Scholar 

  25. P. Sondkar, and A. Kahraman, A dynamic model of a double-helical planetary gear set, Mech. Mach. Theor. 70, 157 (2013).

    Article  Google Scholar 

  26. M. R. Kang, and A. Kahraman, An experimental and theoretical study of quasi-static behavior of double-helical gear sets, J. Mech. Des. 143, 043401 (2021).

    Article  Google Scholar 

  27. J. Liu, Y. Xu, Y. Shao, H. Xiao, and H. Li, The effect of a localized fault in the planet bearing on vibrations of a planetary gear set, J. Strain Anal. Eng. Des. 53, 313 (2018).

    Article  Google Scholar 

  28. J. Wei, A. Zhang, D. Qin, T. C. Lim, R. Shu, X. Lin, and F. Meng, A coupling dynamics analysis method for a multistage planetary gear system, Mech. Mach. Theor. 110, 27 (2017).

    Article  Google Scholar 

  29. C. Hu, G. Geng, and P. D. Spanos, Stochastic dynamic load-sharing analysis of the closed differential planetary transmission gear system by the Monte Carlo method, Mech. Mach. Theor. 165, 104420 (2021).

    Article  Google Scholar 

  30. S. Mo, T. Zhang, G. Jin, X. Cao, and H. Gao, Analytical investigation on load sharing characteristics of herringbone planetary gear train with flexible support and floating sun gear, Mech. Mach. Theor. 144, 103670 (2020).

    Article  Google Scholar 

  31. C. Wang, J. Wei, Z. Wu, L. Lu, and H. Gao, Load sharing performance of herringbone planetary gear system with flexible pin, Int. J. Precis. Eng. Manuf. 20, 2155 (2019).

    Article  Google Scholar 

  32. F. Curà, and A. Mura, Theoretical and numerical evaluation of tilting moment in crowned teeth splined couplings, Meccanica 53, 413 (2018).

    Article  Google Scholar 

  33. Y. Guan, Z. Fang, X. Yang, and G. Chen, Tooth contact analysis of crown gear coupling with misalignment, Mech. Mach. Theor. 126, 295 (2018).

    Article  Google Scholar 

  34. H. Dong, H. Zhang, X. Zhao, and L. Duan, Study on the load-sharing characteristics of face-gear four-branching split-torque transmission system, Adv. Mech. Eng. 13, 168781402110099 (2021).

    Article  Google Scholar 

  35. J. G. Kim, Y. J. Park, S. D. Lee, J. Oh, J. H. Kim, and G. H. Lee, Influence of the carrier pinhole position errors on the load sharing of a planetary gear train, Int. J. Precis. Eng. Manuf. 19, 537 (2018).

    Article  Google Scholar 

  36. S. Mo, Z. Yue, Z. Feng, L. Shi, Z. Zou, and H. Dang, Analytical investigation on load-sharing characteristics for multi-power face gear split flow system, Proc. Insti. Mech. Eng. Part C-J. Mech. Eng. Sci. 234, 676 (2020).

    Article  Google Scholar 

  37. C. Zhang, P. Cao, R. Zhu, W. Chen, and D. Wang, Dynamic modeling and analysis of the spline joint-flexible coupling-rotor system with misalignment, J. Sound Vib. 554, 117696 (2023).

    Article  Google Scholar 

  38. R. E. Spears, and S. R. Jensen, Approach for selection of Rayleigh damping parameters used for time history analysis, J. Press. Vessel Tech. 134, 061801 (2012).

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 52275061).

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Authors and Affiliations

  1. National Key Laboratory of Science and Technology on Helicopter Transmission, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China

    Jiajun Chen  (陈家俊), Rupeng Zhu  (朱如鹏), Weifang Chen  (陈蔚芳) & Miaomiao Li  (李苗苗)

  2. 703 Research Institute, China Shipbuilding Industry Corporation, Harbin, 150000, China

    Xunmin Yin  (尹逊民)

  3. School of Energy Science and Engineering, Harbin Institute of Technology, Harbin, 150000, China

    Xiaoxu Zhang  (张晓旭)

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  1. Jiajun Chen  (陈家俊)
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  3. Weifang Chen  (陈蔚芳)
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  4. Miaomiao Li  (李苗苗)
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  6. Xiaoxu Zhang  (张晓旭)
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Contributions

Author contributions Jiajun Chen carried out specific research, built the mathematical model and analyzed it, and wrote the original draft. Rupeng Zhu formulated overarching research goals and supported the development and design of methodology. Weifang Chen and Miaomiao Li performed the experimental verification work and supported the writing of the original draft. Xunmin Yin received financial support for this research, and supervised the execution of research activities. Xiaoxu Zhang reviewed and edited the writing, and supported the translation.

Corresponding author

Correspondence to Rupeng Zhu  (朱如鹏).

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Conflict of interest On behalf of all authors, the corresponding author states that there is no conflict of interest.

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Chen, J., Zhu, R., Chen, W. et al. Research on pitch error phase matching of herringbone star gear system considering multi-tooth with different backlash. Acta Mech. Sin. 40, 523331 (2024). https://doi.org/10.1007/s10409-023-23331-x

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