Bifurcation Characteristics of Split Torque-Combine Power Gear Transmission under Meshing Parameter Excitation
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摘要: 为研究分扭-并车齿轮传动系统非线性分岔特性，建立了含多间隙的分扭-并车齿轮系统非线性动力学模型，引入高斯消元技术和广义相对位移变量消除了系统的刚体位移，并对动力学方程组实施了量纲一化处理。综合考虑啮合频率、齿侧间隙、综合传动误差和阻尼比等激励下的分岔通道，借助分岔图、Poincaré截面和Lyapunov指数等手段对系统的分岔行为进行了定性和定量表征。结果表明啮合频率增大时系统发生逆向倍周期分岔，分岔点位置受齿侧间隙影响显著；齿侧间隙和综合传动误差变化下混沌域内均出现短暂周期窗口；阻尼对倍周期分岔运动存在抑制作用，其结果对该类齿轮系统动力学设计具有参考价值。
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关键词:
- 分扭-并车齿轮传动 /
- Poincaré截面 /
- Lyapunov指数 /
- 分岔 /
- 混沌
Abstract: In order to investigate the nonlinear bifurcation characteristics of a split torque-combine power gear transmission, the nonlinear dynamic model of the split torque-combine power gear transmission with multiple backlashes is formulated; the rigid body displacements in dynamic equations are eliminated by adopting the Gaussian elimination technique as well as generalized relative displacement variation; dynamic equations are solved non-dimensionally. Bifurcation route under the excitation of meshing frequency, backlash, general transmission error and damping ratio are taken into account; qualitative and quantitative characteristics of bifurcation behavior are investigated by using a bifurcation diagram, the Poincaré section and the Lyapunov exponent. The investigation results show that an inverse period doubling bifurcation occurs when the meshing frequency increases; the bifurcation node is significantly affected by backlash; transient periodic windows take place inside the chaotic regions when a backlash or general transmission error varies; damping has a restraining effect on the period doubling bifurcation evolution. -
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