摘要
在考虑齿轮副时变啮合刚度、齿面摩擦、齿侧间隙及辐板刚度和阻尼的情况下，建立了齿轮传动系统的三维非线性动力学模型。根据啮合点位置推导出啮合刚度、齿面摩擦系数与时间的关系，并考虑了齿轮动载荷在各齿轮副之间的实际分配情况。针对强非线性变微分方程组求解困难的问题，提出了利用添加方程组维数的方法将变系数微分方程组转化成常微分方程组，并采用4~5阶自适应变步长的龙格库塔法求解微分方程组的数值解。系统地分析了辐板刚度、阻尼以及齿面摩擦对齿轮副和辐板振动性能的影响，为更深入研究齿轮的阻尼减振提供了理论基础和研究方向。
Abstract
A three-dimensional nonlinear dynamic model for gear transmission system is developed considering the time-varying meshing stiffness, tooth surface friction and backlash. Based on the contact point place, we deduced the expression of time-varying meshing stiffness and tooth surface friction coefficient about time, considering the dynamic distribution of load. It is difficult to solve the strongly non-linear variant differential equation, so a method is proposed which change the variant differential equation to ordinary differential equation using increase the dimension of differential equations. And the numerical solution of differential equations is obtained using 4 to 5 order adaptive variable steps Runge-Kutta method. The effects of teeth surface friction and web damping and stiffness on the nonlinear dynamic of gear is analysis systematically, and it provides a theoretical basis and directions of research for in-depth study of the gear transmission system.
关键词
齿面摩擦 /
时变刚度 /
辐板 /
非线性变微分方程 /
龙格库塔法
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Key words
teeth surface friction /
time-varying meshing stiffness /
web /
non-linear invariant differential equation /
Runge-Kutta
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古成中;吴新跃; 张文群.
辐板刚度、阻尼及齿面摩擦对齿轮振动特性的影响[J]. 振动与冲击, 2011, 30(9): 178-183
GU Cheng-zhong; WU Xin-yue; ZHANG Wen-qun.
Effects of teeth surface friction and web damping and stiffness on the nonlinear dynamic of gear transmission[J]. Journal of Vibration and Shock, 2011, 30(9): 178-183
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