Abstract
Based on Hertz contact deformation theory, the load distribution of roller and bearing load can be obtained with the consideration of rotating speed and TRB clearance. Furthermore, The TRB load model were introduced into the established dynamic model of helical gear system which includes time varying meshing stiffness(TVMS) of helical gear pair, comprehensive transmission error, gear backlash and bearing mounting style. Dynamic differential equations were solved by Runge–Kutta method. The effect of rotating speed, TRB clearance on the bearing load and dynamic behavior of system were investigated. Results show that input rotating speed and TRB clearance have significant influence on the gear system dynamic behavior. The increase of rotating speed could bring the system into nT-periodic motion, chaotic motion, nT-periodic motion, quasi-periodic motion and chaotic motion. And with the increase of TRB clearance, the system undergoes nT-periodic motion, quasi-periodic motion, and chaotic motion. When the rotating speed is 1000 r/min ~ 2700 r/min, 3200 r/min ~ 4900 r/min or the TRB clearance is less than 5 mm, the system is in nT-periodic motion. When the rotating speed is 4900 r/min ~ 6000 r/min or the TRB clearance is between 5 and 10 mm, the system displays quasi-periodic motion form. When the rotating speed is 2700 r/min ~ 3200 r/min or bigger than 6000 r/min or the bearing clearance exceeds 10 mm, the system is in chaotic motion.
Similar content being viewed by others
Data availability
The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.
References
Zantopulos, H.: The radial and axial stiffnesses of tapered roller bearings under combined load. (1996)
Tong, V.C., Hong, S.W.: Characteristics of tapered roller bearing subjected to combined radial and moment loads. Int. J. Precis. Eng. Manuf.-Green Technol. 1, 323–328 (2014)
Yang, L., Xu, T.: Characteristics of high speed tapered roller bearing considering combined loads[C]//2017 Prognostics and System Health Management Conference (PHM-Harbin). IEEE: pp. 1–7. (2017)
Zhang, H., Shi, W., Liu, G., et al.: A method to solve the stiffness of double-row tapered roller bearing. Math. Probl. Eng. (2019). https://doi.org/10.1155/2019/1857931
Dong, J.J., Cao, P.Y., Wang, J.W.: Influence of torque load on internal load distribution of tapered roller bearings. J. Phys.: Conf. Ser IOP Publ. 1314(1), 012095 (2019)
Yang, D., Wang, X.: Time-varying stiffness analysis of double-row tapered roller bearing based on the mapping structure of bearing stiffness matrix. Acta. Mech. Sin. 38(11), 522030 (2022)
Jiang, Z., Huang, X., Zhu, H., et al.: A new method for contact characteristic analysis of the tapered roller bearing in wind turbine main shaft. Eng. Fail. Anal. 141, 106729 (2022)
Li, Y., Gao, Y.: Internal load distribution of single-row tapered roller bearings doubly supporting main shaft of wind turbine. Adv. Mech. Eng. 14(5), 16878132221098896 (2022)
Zhou, S., Song, G., Sun, M., et al.: Nonlinear dynamic analysis for high speed gear-rotor-bearing system of the large scale wind turbine. J. Vibroeng. 17(8), 4560–4574 (2015)
Zhou, S., Song, G., Ren, Z., et al.: Nonlinear dynamic analysis of coupled gear-rotor-bearing system with the effect of internal and external excitations. Chin. J. Mech. Eng. 29(2), 281–292 (2016)
Yin, M., Chen, G., Su, H.: Theoretical and experimental studies on dynamics of double-helical gear system supported by journal bearings. Adv. Mech. Eng. 8(5), 1687814016646977 (2016)
Bai, H., Song, C., Zhu, C., et al.: Dynamic analysis of gear–shaft–bearing coupled system considering bearing waviness defect. J. Comput. Nonlinear Dyn. 15(1), 011008 (2020)
Bai, H., Song, C., Zhu, C., et al.: Dynamic modeling and analysis of helical gear-shaft-bearing coupled system. J. Theor. Appl. Mech. (2020). https://doi.org/10.15632/jtam-pl/122334
Liu, X., Liu, D., Hu, X.: Influence of the bearing thermal deformation on nonlinear dynamic characteristics of an electric drive helical gear system. Sensors 21(1), 309 (2021)
Chen, Y.C., Cheng, X.F., Choi, S.T.: Dynamic analysis of a helical geared rotor-bearing system with composite rotating shafts. Aircr. Eng. Aerosp. Technol. 93(10), 1699–1708 (2021)
Song, C., Bai, H., Zhu, C., et al.: Computational investigation of off-sized bearing rollers on dynamics for hypoid gear-shaft-bearing coupled system. Mech. Mach. Theory 156, 104177 (2021)
Huang, F., Wang, X., Fu, H., et al.: Nonlinear vibration characteristics of gear-rotor-bearing system. J. Phys.: Conf. Ser. IOP Publ. 2229(1), 012002 (2022)
Gou, X., Zhu, L., Qi, C.: Bifurcation and chaos analysis of a gear-rotor-bearing system. J. Theor. Appl. Mech. (2018). https://doi.org/10.15632/jtam-pl.56.3.585
Liu, Z., Li, F., Jing, B.: Coupled vibration analysis of a bevel geared rotor-bearing system[m]//advances in asset management and condition monitoring: COMADEM 2019, pp. 233–249. Springer International Publishing, Cham (2020)
Zhou, S., Song, G., Sun, M., et al.: Nonlinear dynamic response analysis on gear-rotor-bearing transmission system. J. Vib. Control 24(9), 1632–1651 (2018)
Sun, Z., Chen, S., Hu, Z., et al.: Vibration response analysis of a gear-rotor-bearing system considering steady-state temperature. Nonlinear Dyn. 107, 477–493 (2022)
Wang, S., Zhu, R.: Modeling and theoretical investigation of nonlinear torsional characteristics for double-helical star gearing system in GTF gearbox. J. Vib. Eng. Technol. 10(1), 193–209 (2022)
Yan, B.S., Li, R.Y., Liu, C.H.: Dynamic analysis on the bend-torsion-shaft-pendulum coupling vibration model of helical gear. Appl. Mech. Mater. Trans. Tech. Publ Ltd 851, 273–278 (2016)
Wang, X., Kang, B.: Effect of gear backlash function on the dynamics characteristic of helical gear. J Mech. Transm. 39, 17–23 (2015)
Song, X.: Nonlinear dynamics analysis of flexible rotor bearing system with helical-gear. China Mech. Eng. 24(11), 1484 (2013)
Chen, X., Miao, Y.Y., Yang, W., et al.: Nonlinear dynamic characteristics analysis of a gear transmission system with multiple clearances based on finite element method. J. Vib. Shock 29(2), 46–49 (2010)
Chang, Q., Hou, L., Sun, Z., et al.: Nonlinear modeling of helical gear pair with friction force and frictional torque. Wseas Trans. Appl. Theor. Mech. 9(1), 264–274 (2014)
Yavuz, S.D., Saribay, Z.B., Cigeroglu, E.: Nonlinear dynamic analysis of a drivetrain composed of spur, helical and spiral bevel gears. Nonlinear Dyn. 100(4), 3145–3170 (2020)
Jin, B., Bian, Y., Liu, X., et al.: Dynamic modeling and nonlinear analysis of a spur gear system considering a nonuniformly distributed meshing force. Appl. Sci. 12(23), 12270 (2022)
Tong, V.C., Hong, S.W.: Characteristics of tapered roller bearing with geometric error. Int. J. Precis. Eng. Manuf. 16, 2709–2716 (2015)
Luo, J., Luo, T.: Analysis calculation and application of rolling bearing. China Machine Press, Beijing (2009)
Wan, Z., Cao, H., Zi, Y., et al.: Mesh stiffness calculation using an accumulated integral potential energy method and dynamic analysis of helical gears. Mech. Mach. Theory 92, 447–463 (2015)
Sainsot, P., Velex, P., Duverger, O.: Contribution of gear body to tooth deflections—a new bidimensional analytical formula. J. Mech. Des. 126(4), 748–752 (2004)
Jingyue, W., Sheng, G., Jia-Qiang, E.: Study on the mathematical model of non-linear air spring. J. Mech. Des. 36(6), 20–24 (2019)
Oke, W.A., Khulief, Y.A.: Vibration analysis of composite pipes using the finite element method with B-spline wavelets. J. Mech. Sci. Technol. 30, 623–635 (2016)
He Weidong, Lu., Xinhui, Y.W.: Torsional rigidity calculation of RV reducer based on equivalent model. J. Mech. Transm 37(09), 38–41 (2013). ((in Chinese))
Liu, J., Zhao, W., Liu, W.: Frequency and vibration characteristics of high-speed gear-rotor-bearing system with tooth root crack considering compound dynamic backlash. Shock. Vib. 2019, 1–19 (2019)
Acknowledgements
This work is supported by the National Natural Science Foundation of China (Grant No. 52275061).
Funding
National Natural Science Foundation of China, No. 52275061.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interests
The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this paper.
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.
About this article
Cite this article
Che, X., Zhu, R. Nonlinear dynamic analysis of helical gear-rotor-bearing coupled system based on bearing load calculation with TRB clearance. Nonlinear Dyn 111, 17787–17807 (2023). https://doi.org/10.1007/s11071-023-08826-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11071-023-08826-8