Effect of Supporting Damping on Nonlinear Dynamics of Multi-freedom Gear System

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Journal of Vibration and Shock ›› 2017, Vol. 36 ›› Issue (19) : 139-144.

Xiang Ling, Gao Xueyuan, Zhang Lijia, Jia Yi

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Abstract

Based on the period-enlargement method, a six-degree-of freedom nonlinear dynamic model with rectangular-wave mesh stiffness, backlash, sliding friction and other nonlinear factors of a spur gear pair is established. The numerical integration method is applied to solve the response of the system. The bifurcation diagrams, Poincaré maps, FFT spectrum and the largest Lyapunov exponents are used to systematically analyze the effect of supporting damping on gear system. The results shows that the chaotic attractor and chaotic domain would decrease gradually and even degenerate to stable periodic motion as the supporting damping is improved, resulting in the complexity of the bifurcation characteristic of the gear system. Moreover, the resonance of the system at w/2(w is the exciting frequency) would be weakened. Finally, support damping have an important effect on the meshing state of gear system and could make the system exhibit a change from double-side impact motion to single-side impact motion.

Key words

gear pair / nonlinear dynamics / friction / backlash / supporting damping

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Xiang Ling, Gao Xueyuan, Zhang Lijia, Jia Yi. Effect of Supporting Damping on Nonlinear Dynamics of Multi-freedom Gear System[J]. Journal of Vibration and Shock, 2017, 36(19): 139-144

References

[1] Vaishya M, Singh R. Analysis of periodically varying gear mesh systems with coulomb friction using Floquet theory[J]. Journal of Sound and Vibration, 2001, 243(3)：525-545.
[2] Moradi H, Salarieh H. Analysis of nonlinear oscillations in spur gear pairs with approximated modelling of backlash nonlinearity[J]. Mechanism & Machine Theory, 2012, 51(5):14-31.
[3] Wang J, Zheng J, Yang A. An Analytical Study of Bifurcation and Chaos in a Spur Gear Pair with Sliding Friction[J]. Procedia Engineering, 2012, 31(16):563–570.
[4] Li S, Kahraman A. A tribo-dynamic model of a spur gear pair[J]. Journal of Sound & Vibration, 2013, 332(20):4963–4978.
[5] 程欧, 苟向锋. 多自由度齿轮系统非线性动力学分析[J]. 噪声与振动控制, 2015, 35(6):31-35.
CHENG Ou, GOU Xiangfeng. Nonlinear Dynamics Analysis of a Multi-DOF Gear System[J]. Noise and Vibration Control, 2015, 35(6):31-35.
[6] 李应刚, 陈天宁, 王小鹏等. 外部动态激励作用下齿轮系统非线性动力学特性[J]. 西安交通大学学报, 2014, 48(1):101-105.
LI Yinggang, CHEN Tianning, WANG Xiaopeng et al. Non-Linear Dynamics of Spur Gear Pair under External Periodic Excitation[J]. Journal of Xi'an Jiaotong University, 2014, 48(1):101-105.
[7] 张慧博, 王然, 陈子坤, 等. 考虑多间隙耦合关系的齿轮系统非线性动力学分析[J]. Journal of Vibration and Shock, 2015, 34(8):144-150.
ZHANG Huibo, WANG Ran, CHEN Zikun, et al. Nonlinear dynamic analysis of a gear-rotor system with coupled multi-clearance[J]. Journal of Vibration and Shock, 2015, 34(8):144-150.
[8] 王树国, 张艳波, 刘文亮等. 多间隙二级齿轮非线性振动分岔特性研究[J]. 应用数学和力学, 2016, 37(2)：173-181.
WANG Shuguo, ZHANG Yanbo, Liu Wenliang, et al. Nonlinear vibration bifurcation characteristics of multi-clearance 2-stage gear systems[J]. Applied Mathematics and Mechanics, 2016, 37(2):173-181.
[9] 盛冬平，朱如鹏，陆凤霞等. 多间隙弯扭耦合齿轮非线性振动的分岔特性研究[J]. 振动与冲击, 2014，33（19）：116-122.
SHENG Dongping, ZHU Rupeng, LU Fengxia, et al. Bifurcation characteristics of bending torsional coupled gear nonlinear vibration with multi-clearance[J]. Journal of Vibration and Shock, 2014, 33(19):116-122.
[10] 向玲, 贾轶, 李媛媛, 等. 内外激励作用下多自由度齿轮系统的非线性动力学特性[J]. 振动与冲击, 2016, 35(13): 153-159.
XIANG Ling, JIA Yi, LI Yuanyuan, et al. Non-linear Dynamic Feature of Multi-freedom Gear System Subjected to Internal and External Excitation[J]. Journal of Vibration and Shock, 2016, 35(13): 153-159.
[11] Tang J, Chen S, Zhou C. An improved nonlinear dynamic model of gear transmission[C]//ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2007: 577-583.
[12] Gill-Jeong C. Nonlinear behavior analysis of spur gear pairs with a one-way clutch[J]. Journal of Sound and Vibration, 2007, 304(s 1–2):18-30.
[13] Walha L, Fakhfakh T, Haddar M. Nonlinear dynamics of a two-stage gear system with mesh stiffness fluctuation, bearing flexibility and backlash[J]. Mechanism & Machine Theory, 2009, 44(5):1058-1069.