内外激励作用下多自由度齿轮系统的非线性动力学特性

向玲,贾轶,李媛媛,冯晓冉, 高雪媛,邸薇薇

振动与冲击 ›› 2016, Vol. 35 ›› Issue (13) : 153-159.

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振动与冲击 ›› 2016, Vol. 35 ›› Issue (13) : 153-159.
论文

内外激励作用下多自由度齿轮系统的非线性动力学特性

  • 向玲 ,贾轶 ,李媛媛 ,冯晓冉, 高雪媛,邸薇薇
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Non-linear Dynamic Feature of Multi-freedom Gear System Subjected to Internal and External Excitation

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

采用周期扩大法,建立了齿轮副的六自由度非线性动力学模型,模型考虑了齿轮副间的时变啮合刚度、齿侧间隙、齿面摩擦等非线性因素;对模型中的相关周期项作傅里叶级数展开,并采用数值积分方法研究六自由度齿轮传动系统的运动随转速、支撑刚度的分岔特性。结合poincaré截面图、分岔图、FFT频谱及最大Lyapunov指数图,系统地分析了支撑刚度对齿轮系统的影响。结果发现,随着激励频率的提高,系统经过多次跳跃进入混沌,提高支撑刚度会使系统的跳跃点数目增加,并且使系统的混沌区减小且整体后移,致使系统推迟进入混沌;再者会使系统通向混沌的道路多样化,除了拟周期通道之外,还出现了激变性、阵发性的混沌道路及“周期5—拟周期—锁相—不稳定吸引子—混沌”的非常规混沌道路。另外支撑刚度的提高会使系统的1/2次谐振加强,致使谐振频率下的动态啮合力(DMF)增大,但会使一些混沌区的DMF逐渐减小,并且使啮合轮齿经历“双边冲击—单边冲击—无冲击”的状态变化。

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’. 

 

关键词

齿轮副 / 非线性动力学 / 摩擦 / 间隙 / 支撑刚度

Key words

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

引用本文

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向玲,贾轶,李媛媛,冯晓冉, 高雪媛,邸薇薇. 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 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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