汇流传动齿轮系统分岔与混沌研究

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In order to investigate the influences of backlash atc.nonlinear factors on a gear system featuring confluence transmission, considering the effects of backlash,transmission error,time-varying mesh stiffness and layout parameters,a non-linear dynamic model of a three-gear system with two gear pairs was built.Starting from mesh stiffness＇s phase difference,excitation frequency and load ratio,the influence of each parameter on the gear system＇s dynamic characteristics were studied.In order to judge the periodic motion and chaos behavior,Poincare mapping,spectral analysis and Lyapunov index based on chaotic time series were adopted.With changing of system parameters,such as,frequency ratio and load ratio,the left-right gear pairs showed complex nonlinear dynamic behaviors of coexist of same periodic motion,coexist of different periodic motion,double period bifurcation and chaos.为研究齿轮系统中侧隙等非线性因素对汇流传动齿轮系统的影响,考虑齿侧间隙、传动误差、时变啮合刚度和布局参数的影响,建立了含有两个齿轮副的三齿轮系统动力学模型。分别从啮合刚度的相位差、激励频率和载荷比三个方面出发,研究了各个参数的变化对齿轮系统动态特性的影响。为了判别周期运动和混沌行为,采用了庞加莱映射、频谱分析和基于混沌时间序列的lyapunov指数分析手段。结果表明,在改变诸如频率比、载荷比等一系列系统参数的情况下,左右齿轮副表现出同周期运动并存、不同周期运动并存、倍周期分岔、混沌等丰富的非线性动力学行为。