Bifurcation &amp; impact characteristics of a single-stage gear train in a two-parameter plane

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Journal of Vibration and Shock ›› 2018, Vol. 37 ›› Issue (13) : 218-223.

Bifurcation & impact characteristics of a single-stage gear train in a two-parameter plane

TIAN Ya-ping1，Chu Yan-Dong2，Rao Xiao-Bo1

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Abstract

In order to analyze effects of multi-parameter coupling on bifurcation & impact characteristics of a nonlinear gear system，in a plane with 2 parameters of time-varying stiffness amplitude coefficient and dimensionless rotating speed, the bifurcation/impact diagram of a single-stage gear train was obtained using Poincaré-Newton-Floquet (PNF) method and the extended algorithm. The regions of periodic motion, quasi-periodic motion, chaotic motion and mesh impact type were determined in the diagram. The dynamic behaviors of graze bifurcation, double-period bifurcation, upheaval bifurcation, amplitude jump, Hopf bifurcation and the bifurcation transition law were found in the diagram. The validity of the proposed method was verified with 3D/2D bifurcation diagram, Poincaré map one and phase one simulated with Runge-Kutta numerical method. The stable region for single period motion with non-shock of parametric coupling and matching was found in the two-parameter plane. The results provided a reference for structural design and optimization of gear systems.

Key words

single-stage gear train / nonlinear vibration / bifurcation / PNF numerical method / two-parameter plane

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TIAN Ya-ping1，Chu Yan-Dong2，Rao Xiao-Bo1. Bifurcation & impact characteristics of a single-stage gear train in a two-parameter plane[J]. Journal of Vibration and Shock, 2018, 37(13): 218-223

References

[1] Kahraman A, Singh R. Non-linear Dynamics of a Spur Gear pair[J]. Journal of Sound and Vibration, 1990, 142(1):49-75.
[2] Vinayak H, Singh R, Padmanabhan C. Linear Dynamic Analysis of Multi-mesh Transmissions Containing External Rigid Gears[J]. Journal of Sound and Vibration, 1995,185(1):1-32.
[3] 刘晓宁, 王三民, 沈允文. 三自由度齿轮传动系统的非线性振动分析[J]. 机械科学与技术, 2004, 23(10): 59-61.
LIU Xiao-ning, Wang San-min, SHEN Yun-wen. Nonlinear vibrations of 3-DOF geared rotor-bearing system [J]. Mechanical Science and technology for aerospace engineering, 2004,23 (10):59-61.
[4] 苟向锋,陈代林. 三自由度齿轮传动系统的分岔与混沌研究[J]. 机械科学与技术, 2014, 33(2): 199-203.
GOU Xiang-feng, Chen Dai-lin. Research on bifurcation and chaos of 3-DOF gear transmission system [J]. Mechanical Science and techanology for aerospace engineering, 2014, 33(2): 199-203.
[5] 王晓笋，巫世晶，周旭辉，等. 含磨损故障的齿轮传动系统非线性动力学特性[J]. 振动与冲击, 2013,3(16):37-43+69.
WANG Xiao-sun, Wu Shi-jing, Zhou Xu-hui, et al. Nonlinear dynmaics analysis of gear transmission system with wear fault[J]. Journal of Vibration and shock, 2013, 3(16):37-43+69.
[6] Luo Yue-gang, Ren Zhao-hui, Ma Hui. Stability of periodic motion on the rotor- bearing system with coupling faults of crack and rub-impact [J]. Journal of Mechanical Science and Technology, 2007, 21:860-864.
[7] Han Qing-kai. Periodic motions of a dual-disk rotor system with rub-impact at fixed limiter [J]. Proc. JMSE, Part C: Journal of Mechanical Engineering Science, 2008, 222(C10): 1935-1946.
[8] Han Qing-kai. Periodic motion stability of a dual-disk rotor system with rub-impact at fixed limiter [J]. Vibro-Impact Dynamics of Ocean System, LANCM, 2009,44:105-109.
[9] 李同杰，朱如鹏，鲍和云，等. 行星齿轮传动系的周期运动及其稳定性[J]. 振动工程学报,2013,26(6):815-822.
LI Tong-jie, zhu Ru-peng, Bao He-yun, et al. coexisting periodic solutions and their stability of a nonlinear planetary gear train[J]. Journal of Vibration Engineering, 2013, 26(6):815-822.
[10] Gou Xiang-Feng，Zhu Ling-Yun，Chen Dai-lin. Bifurcation and chaos analysis of spur gear pair in two-parameter plane [J]. Nonlinear Dynamic, 2015, 79:2225-2235.
[11] 苟向锋，陈代林. 双参变量下齿轮-转子系统扭转振动特性分析[J].工程力学,2014,31（11）：211-217.
GUO Xiang-feng, Chen Dai-lin. Dynamic analysis on torsional vibration of gear-rotor system in two parameters plane[J]. Engineering mechanics, 2014，31（11）：211―217.
[12] 胡海岩. 应用非线性动力学[M]. 北京：航空工业出版社，2000.
HU Hai-yan. Application of nonlinear dynamics [M]. Beijing: Aviation industry press, 2000.
[13] 韩清凯,于涛,王德友,等. 故障转子系统的非线性振动分析与诊断方法[M]. 北京:科学出版社,2010.
HAN Qing-kai, Yu Tao, Wang De-you, et al. The nonlinear rotor system vibration analysis and fault diagnosis method [M]. Beijing: Science Press, 2010.
[14] 李润方, 王建军. 齿轮系统动力学-振动、冲击、噪声[M]. 科学出版社, 1997.
LI Run-fang, Wang Jian-jun. Gear system dynamics vibration, shock and noise [M]. Science press: 1997.