Non-linear Dynamic Feature of Multi-freedom Gear System Subjected to Internal and External Excitation

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Journal of Vibration and Shock ›› 2016, Vol. 35 ›› Issue (13) : 153-159.

XIANG Ling JIA Yi LI Yuanyuan FENG Xiaoran GAO Xueyuan DI Weiwei

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Abstract

Based on the period-enlargement method, a six-degree-of freedom nonlinear dynamic model of a spur gear pair was developed with rectangular-wave mesh stiffness, backlash, sliding friction and other no-linear factors. Periodic terms in the dynamic equations were expanded by Fourier series and numerical integration was used to investigate the influences of the system parameters including rotation speed and supporting stiffness on the bifurcation features of the system. The Poincaré maps, bifurcation diagrams, FFT spectrum and the largest Lyapunov exponents were achieved to systematically analyze the effect of supporting stiffness on gear system . It was shown that the system goes into chaos motion after several ‘frequency hopping’ with the increase of exciting frequency. Besides, as the supporting stiffness is improved, the number of such “frequency hopping” increases accordingly. Also, the regions of exciting frequency corresponding to chaos motion decrease and move backward, in other words, the system enters into later chaotic motion due to the larger supporting stiffness. Moreover, the roads to chaos become diverse, in addition to quasi-periodic route, there also exists intermittent, catastrophic route and the non-typical ‘5T-periodic motion - phase-locked - unsteady attractor - chaos’ route. Finally, with the increase of supporting stiffness, the resonance of the system at w/2(w is the exciting frequency) could enhance and the dynamic meshing force increases accordingly, but the DMF in some chaotic regions decreases gradually. And the gear system exhibits a change of ‘double-side impact motion - single-side impact motion - no impact motion’.

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spur gear pair / nonlinear dynamics / friction / backlash / supporting stiffness

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XIANG Ling JIA Yi LI Yuanyuan FENG Xiaoran GAO Xueyuan DI Weiwei . 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

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