支承轴承作用下齿轮系统动力学分析

Dynamic Analysis of Spur Gear System Considering Back-Up Bearings

基于牛顿动力学原理,建立了非线性直齿齿轮副系统数学模型,在Matlab软件环境中采用四阶Runge-Kutta方法求解数值解,分析了齿轮系统启动时支承轴承的支承刚度,支承阻尼对直齿齿轮系统中齿轮位移振动,齿轮相对位置变化以及齿轮动态传递误差的动力学影响。结果表明,主动轮与从动轮的相对位移在中、高频区的位移振动随齿轮轴承支承刚度增加而增强,且振动频率从低频向中高频偏移。增大支承阻尼能减缓齿轮啮合时沿啮合线方向的相对位移振动,改善低频区的传动效果。轴承支承刚度的增加使齿轮动态传递误差振动加剧,影响齿轮转动精度;支承阻尼变化不影响齿轮动态传递误差的振动频率,只改变振动幅值。

Based on the Newtonian dynamics principle,a mathematical model for nonlinear spur gear pair system was established,and a algorithm program was designed and the numerical solution was obtained based on the fourth order Runge- Kutta method in the software environment of Matlab. Influences on gear displacement,gear relative displacement and gear dynamic transmission error arousing by supporting stiffness and damping from back-up bearings are analyzed. The results show that the relative displacement of the driving wheel and driven wheel in the middle and high frequency vibration displacement increases with the rise of gear bearing stiffness,and vibration frequency shifts from low frequency to high one.The gear relative displacement vibration gets gentle in low frequency domain along the gear mesh direction while the bearing damping increases. The increase in bearing stiffness makes a damage not only to gear dynamic transmission error but also precision of gear transmission. Bearing damping changes will not affect the vibration frequency of the gear dynamic transmission error,only a small influence on amplitude value.