基于不同Poincaré截面的齿轮啮合接触冲击分析

Contact impact analysis of gear meshing based on different Poincaré maps

为保证齿轮系统在啮合接触过程中稳定运行,基于含间隙单自由度直齿圆柱齿轮系统的非线性动力学模型,构建不同Poincaré截面。用延续算法和变步长4阶Runge-Kutta法对系统在不同激励频率和扭矩下的动力学特征进行仿真,得到系统关于周期激励、齿面啮合、齿背接触和脱啮运动的n-p-q-r运动规律,利用分岔图、最大Lyapunov指数图、相图和Poincaré映射图研究了系统的分岔和混沌特性。结果表明:当其他参数取定的情况下,频率取值为[0.5,0.607]∪[2.12,2.5]以及扭矩取值为[0.064,0.164 7]时,齿轮的传动最为平稳。

In order to ensure a stable operation of the gear system in the engagement process,different Poincarémaps are established based on the nonlinear dynamic model of unidirectional spur gear system with clearance.The difference dynamic behaviors about frequency and torsion are researched by the continuation method and 4 order variable step-size Runge-Kutta method,n-p-q-r motion of the system representing exciting cycle,tooth surface meshing,tooth backside contact and unmeshing in the meshing process is got.The bifurcation diagram,the top Lyapunov exponent,phase diagram and Poincarémaps are used to study the bifurcation and chaotic characteristics of the system.The results show that when other parameters are fixed,the transmission of the gear was the most stable with the frequency value in[0.5,0.607]∪[2.12,2.5]and the torque value in[0.064,0.164 7].