Since 1963
ARTICLE
Global behaviors of parameterized solution domain and basins of attraction of star herringbone gear transmission system
1
School of Mechanical and Electrical Engineering, Xi’an Polytechnic University, Xi’an, China
2
State Key Laboratory for Strength and Vibration of Mechanical Structures, Xi’an Jiaotong University, Xi’an, China
Submission date: 2024-03-12
Final revision date: 2025-01-11
Acceptance date: 2025-01-22
Online publication date: 2025-04-22
Publication date: 2025-05-01
Corresponding author
Journal of Theoretical and Applied Mechanics 2025;63(2):289-306
KEYWORDS
time-varying meshing stiffnessparameterized solution domainbasin of attractionjoint probability density functionstochasticity
TOPICS
ABSTRACT
The analysis of global behaviors is quite essential for the prediction of the potential dynamical vibration of the geared system. A novel meshing stiffness formula approximated to rectangular wave was proposed utilizing an odd harmonic superposition, the distribution maps of the parameterized solution domain and basin of attraction of the star herringbone gear transmission system were calculated containing various periodic regions and then validated. The analysis of the joint probability density indicates that transformations occurred on the portrait structure of attractors during the evolution into chaos. In addition, with discretization techniques and cell mapping methodology, the two-dimensional parameterized solution domain, as well as overall distributions of periodic and chaotic domains hidden in the basins of attraction were identified. Subsequently, the stochasticity of the damping ratio produced in normal distribution is analyzed, which presents that the attractor will experience perturbations before reaching a steady-state, while the periodicity of the attractor is significantly weakened. By the comparison of evolution behaviors, the distributions of periodic basin of attraction have little variations, but it caused some scattered periodic cells which mixed in the original domains, resulting in the deterioration of the steady-state to the system.
REFERENCES (20)
1.
Arian, G. & Taghvaei, S. (2021). Dynamic analysis and chaos control of spur gear transmission system with idler. European Journal of Mechanics – A/Solids, 87, Article 104229. https://doi.org/10.1016/j.euro....
2.
Dreeben, T.D. & Pope, S.B. (1998). Probability density function/Monte Carlo simulation of near-wall turbulent flows. Journal of Fluid Mechanics, 357, 141–166. https://doi.org/10.1017/S00221....
3.
Farshidianfar, A. & Saghafi, A. (2014). Global bifurcation and chaos analysis in nonlinear vibration of spur gear systems. Nonlinear Dynamics, 75(4), 783–806. https://doi.org/10.1007/s11071....
4.
Gou, X.F., Zhu, L.Y., & Chen, D.L. (2015). Bifurcation and chaos analysis of spur gear pair in two-parameter plane. Nonlinear Dynamics, 79(3), 2225–2235. https://doi.org/10.1007/s11071....
5.
Gyebrószki, G. & Csernák, G. (2017). Clustered Simple Cell Mapping: An extension to the Simple Cell Mapping method. Communications in Nonlinear Science and Numerical Simulation, 42, 607–622. https://doi.org/10.1016/j.cnsn....
6.
Hong, J., Yang, Z.F., Sun, B., Song, Z., & Ma, Y. (2022). Influence of local rotary inertia on the dynamic properties of rotor systems (in Chinese). Journal of Aerospace Power, 37(4), 673–683. http://doi.org/10.13224/j.cnki....
7.
Koh, D., Anderson, R.L., & Bermejo-Moreno, I. (2021). Cell-mapping orbit search for mission design at ocean worlds using parallel computing. The Journal of the Astronautical Sciences, 68(1), 172–196. https://doi.org/10.1007/s40295....
8.
Li, Z.G., Jiang, J., Li, J., Hong, L., & Li, M. (2018). A subdomain synthesis method for global analysis of nonlinear dynamical systems based on cell mapping. Nonlinear Dynamics, 95(1), 715–726. https://doi.org/10.1007/s11071....
9.
Lin, H., Hong, L., & Liu, X. (2021). Global characteristics of solution domain and attraction domain in power split gear transmission parameter space (in Chinese). Journal of Vibration Engineering, 34(2), 235–242.
10.
Ma, S.C., Ning, X., & Wang, L. (2020). Dynamic analysis of stochastic friction systems using the generalized cell mapping method. Computer Modeling in Engineering & Sciences, 122(1), 49–59. https://doi.org/10.32604/cmes.....
11.
Marafona, J.D.M., Carneiro, G.N., Marques, P.M.T., Martins, R.C., António C.C., & Seabra, J.H.O. (2024). Gear design optimization: Stiffness versus dynamics. Mechanism and Machine Theory, 191, Article 105503. https://doi.org/10.1016/j.mech....
12.
Mo, S., Zhang, Y., Luo, B., Bao, H., Cen, G., & Huang, Y. (2022). The global behavior evolution of non-orthogonal face gear-bearing transmission system. Mechanism and Machine Theory, 175, Article 104969. https://doi.org/10.1016/j.mech....
13.
Saghafi, A. & Farshidianfar, A. (2016). An analytical study of controlling chaotic dynamics in a spur gear system. Mechanism and Machine Theory, 96(Part 1), 179–191. https://doi.org/10.1016/j.mech....
14.
Tang, J.Y., Xiong, X.B., & Chen S.Y. (2011). Analysis of global character of single degree of freedom nonlinear gear system based on digraph cell mapping method (in Chinese). Journal of Mechanical Engineering, 47(5), 59–65.
15.
Tang, X., Bao, H.Y., Lu, F.X., & Jin, G. (2020). Nonlinear dynamic analysis of planetary gear train system with meshing beyond pitch point. Transactions of Nanjing University of Aeronautics and Astronautics, 37(6), 884–897.
16.
Wang, S.Y. & Zhu, R.P. (2020). Nonlinear torsional dynamics of star gearing transmission system of GTF gearbox. Shock and Vibration, 2020(1), Article 6206418. https://doi.org/10.1155/2020/6....
17.
Wang, X., Jiang, J., Hong, L., Zhao, A. & Sun, J.Q. (2023). Radial basis function neural networks solution for stationary probability density function of nonlinear stochastic systems. Probabilistic Engineering Mechanics, 71, Article 103408. https://doi.org/10.1016/j.prob....
18.
Xiang, L., Deng, Z.Q., & Hu, A.J. (2020). Dynamical analysis of planetary gear transmission system under support stiffness effects. International Journal of Bifurcation and Chaos, 30(6), Article 2050080. https://doi.org/10.1142/S02181....
19.
Yue, X.L., Xu, Y., Xu, W., & Sun, J.Q. (2019). Probabilistic response of dynamical systems based on the global attractor with the compatible cell mapping method. Physica A: Statistical Mechanics and its Applications, 516, 509–519. https://doi.org/10.1016/j.phys....
20.
Zhang, W., Han, B.B., Li, X., Sun, J.Q., & Ding, Q. (2019). Multiple-objective design optimization of squirrel cage for squeeze film damper by using cell mapping method and experimental validation. Mechanism and Machine Theory, 132, 66–79. https://doi.org/10.1016/j.mech....
| eISSN: | 2543-6309 |
| ISSN: | 1429-2955 |
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