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Dynamics analysis of noncircular planetary gears. (English) Zbl 07899927

Summary: Noncircular planetary gear has simple structure and wide application, but its dynamics research is still blank. Therefore, this paper designs and establishes a 3–4 noncircular planetary gear model, and takes a deep dive into its dynamic characteristics. Firstly, the torsional vibration mechanical model of noncircular planetary gear is established, and the key factors in the planetary gear system are fully considered, such as time-varying meshing stiffness, backlash, meshing damping and excitation frequency. These factors have an important impact on the vibration characteristics of the system. Then, the vibration differential equation of the system is established, and the vibration characteristics of the system under different parameter conditions are analyzed. The results show that the noncircular planetary gear system with large damping and appropriate stiffness can maintain a more stable operating state at a larger excitation frequency. In addition, shortening the acceleration time of the system can effectively reduce the damage caused by the unstable state to the system. These findings provide a solid theoretical basis for the subsequent optimization and analysis of noncircular planetary gears.

MSC:

70E55 Dynamics of multibody systems
70K50 Bifurcations and instability for nonlinear problems in mechanics
70K55 Transition to stochasticity (chaotic behavior) for nonlinear problems in mechanics
Full Text: DOI

References:

[1] Ao, M.; Yu, G.; Wang, L., Optimization synthesis of hybrid six-bar mechanism with noncircular gear constraints, J Mech Des, 145, 6, Article 064502 pp., 2023
[2] Lee, J.; Yoon, S. H.; Kim, C., Experimental surrogate-based design optimization of wing geometry and structure for flap wing micro air vehicles, Aerosp Sci Technol, 123, Article 107451 pp., 2022
[3] Mundo, D., Geometric design of a planetary gear train with non-circular gears, Mech Mach Theory, 41, 4, 456-472, 2006 · Zbl 1143.70333
[4] Liu, J.; Yu, G.; Tong, Z., Design and experimental study of a planetary gearing mechanism based on twice unequal amplitude transmission ratio, Int J Agric Biol Eng, 15, 1, 155-163, 2022
[5] Addomine, M.; Figliolini, G.; Pennestri, E., A landmark in the history of non-circular gears design: the mechanical masterpiece of Dondi’s astrarium, Mech Mach Theory, 122, 219-232, 2018
[6] Zhang, X.; Fan, S., Synthesis of the steepest rotation pitch curve design for noncircular gear, Mech Mach Theory, 102, 16-35, 2016
[7] Zheng, F.; Guo, X. D.; Zhang, M. D., Non-uniform flank rolling measurement for shaped noncircular gears, Measurement, 116, 207-215, 2018
[8] Han, X.; He, C.; Zheng, F., Transmission performance evaluation of non-circular spur bevel gear based on a novel isochronal measurement method, Mech Mach Theory, 185, Article 105329 pp., 2023
[9] Mo, S.; Zhang, Y. X., Nonlinear vibration and primary resonance analysis of non-orthogonal face gear-rotor-bearing system, Nonlinear Dyn, 108, 3367-3389, 2022
[10] Mo, S.; Wang, L.; Hu, Q., Coupling failure dynamics of tooth surface morphology and wear based on fractal theory, Nonlinear Dyn, 112, 1, 175-195, 2024
[11] Mo, S.; Zhang, T.; Jin, G. G., Analytical investigation on load sharing characteristics of herringbone planetary gear train with flexible support and floating sun gear, Mech Mach Theory, 144, 2, 1-27, 2020
[12] Mo, S.; Li, Y.; Wang, D., An analytical method for the meshing characteristics of asymmetric helical gears with tooth modifications, Mech Mach Theory, 185, Article 105321 pp., 2023
[13] Mo, S.; Luo, B.; Song, W., Geometry design and tooth contact analysis of non-orthogonal asymmetric helical face gear drives, Mech Mach Theory, 173, Article 104831 pp., 2022
[14] Mo, S.; Liu, Y. H.; Huang, X., Nonlinear vibration and super harmonic resonance analysis of wind power planetary gear system, Nonlinear Dyn, 2024, doi.org/10.1007/s11071-023-09268-y
[15] Zhang, X.; Zhong, J. X.; Li, W., Nonlinear dynamic analysis of high-speed gear pair with wear fault and tooth contact temperature for a wind turbine gearbox, Mech Mach Theory, 173, Article 104840 pp., 2022
[16] Xia, H.; Meng, F. S.; Zhang, X., Nonlinear dynamics analysis of gear system considering time-varying meshing stiffness and backlash with fractal characteristics, Nonlinear Dyn, 111, 14851-14877, 2023
[17] Zheng, X.; Luo, W.; Hu, Y., Study on the mesh stiffness and nonlinear dynamics accounting for centrifugal effect of high-speed spur gears, Mech Mach Theory, 170, Article 104686 pp., 2022
[18] Shi, J. F.; Gou, X. F.; Jin, W. Y., Multi meshing-state and disengaging-proportion analyses of a gear-bearing system considering deterministic random excitation based on nonlinear dynamics, J Sound Vib, 544, Article 117360 pp., 2023
[19] Alimoradzadeh, M.; Tornabene, F.; Esfarjani, S. M.; Dimitri, R., Finite strain-based theory for the superharmonic and subharmonic resonance of beams resting on a nonlinear viscoelastic foundation in thermal conditions, and subjected to a moving mass loading, Int J Non Linear Mech, 148, Article 104271 pp., 2023
[20] Zheng, X.; Hu, Y.; He, Z.; Xiao, Y.; Zhang, X., On the extended tooth contact and nonlinear dynamics for spur gears—An analytical model, Mech Mach Theory, 175, Article 104958 pp., 2022
[21] Wang, M.-Q.; Ma, W.-L.; Li, Y., Dynamic analysis of piecewise nonlinear systems with fractional differential delay feedback control, Chaos Solit Frac, 164, Article 112624 pp., 2022 · Zbl 1508.93113
[22] Luo, W.; Qiao, B.; Shen, Z., Investigation on the influence of spalling defects on the dynamic performance of planetary gear sets with sliding friction, Tribol Int, 154, Article 106639 pp., 2021
[23] Lai, J.; Liu, Y.; Xu, X., Dynamic modeling and analysis of Ravigneaux planetary gear set with unloaded floating ring gear, Mech Mach Theory, 170, Article 104696 pp., 2022
[24] Wang, S.; Zhu, R., Research on dynamics and failure mechanism of herringbone planetary gearbox in wind turbine under gear surface pitting, Eng Fail Anal, 146, Article 107130 pp., 2023
[25] Zhang, C.; Wei, J.; Peng, B., Investigation of dynamic similarity of gear transmission system considering machining error distortion: theoretical analysis and experiments, Mech Mach Theory, 172, Article 104803 pp., 2022
[26] Pedrero, J. I.; Pleguezuelos, M.; Sánchez, M. B., Influence of meshing stiffness on load distribution between planets of planetary gear drives, Mech Mach Theory, 170, Article 104718 pp., 2022
[27] Molaie, M.; Samani, F. S.; Zippo, A., Spiral bevel gears: nonlinear dynamic model based on accurate static stiffness evaluation, J Sound Vib, 544, Article 117395 pp., 2023
[28] Xue, S.; Howard, I.; Wang, C., Dynamic modelling of the gear system under non-stationary conditions using the iterative convergence of the tooth mesh stiffness, Eng Fail Anal, 131, Article 105908 pp., 2022
[29] Hu, A. J.; Liu, S. X.; Xiang, L., Dynamic modeling and analysis of multistage planetary gear system considering tooth crack fault, Eng Fail Anal, 137, Article 106408 pp., 2022
[30] Hu, Z.; Liu, W.; Chen, S., Dynamic modeling and analysis of thin-webbed spur gear pair, Thin-Wall Struct, 183, Article 110386 pp., 2023
[31] Shi, J.; Gou, X.; Zhu, L., Five-state engaging model and dynamics of gear-rotor-bearing system based on time-varying contact analysis considering gear temperature and lubrication, Appl Math Model, 112, 47-77, 2022 · Zbl 1505.70008
[32] Dai, H.; Wang, Y.; Luo, S., Dynamic modeling and vibration analysis of planetary gear sets concerning mesh phasing modulation, Mech Syst Signal Process, 200, Article 110557 pp., 2023
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