含万向铰偏斜旋转轴的组合共振及其稳定性分析

基于欧拉方程推导出了含万向铰偏斜旋转轴的横向振动模型,利用多尺度方法对该模型进行求解,得出了该偏斜系统可能出现的多种共振模式,进而对含万向铰偏斜轴系横向振动和型组合共振、差型组合共振进行稳定性分析,并对该类偏斜系统横向振动和型组合共振响应进行数值计算与仿真,检验所得稳定性理论分析结果。研究表明:对于和型组合共振而言,其稳定性边界与输入扭矩T0、支撑轴承安装位置l、轴承刚度Kx2和Ky2等因素有关;当轴承安装位置距万向铰中心较近或者轴承弹簧刚度系数较小时,系统在频率(ω10+ω20)/2附近产生和型组合共振的区域减小,即能够抑制系统和型组合共振的产生。该研究可为偏斜轴系振动与噪声抑制提供理论支持。

The stability analysis on combination resonance of misaligned rotary shafts driven through a universal joint

The lateral vibration model of the system is deduced in virtue of Euler Eqautions,and the combination resonance modes are presented by multi-scale method,then the stability condition and stability map about combination resonance of sum type are analyzed.At last,the lateral vibration response of the system is simulated numerically by Runge-Kutta Method in order to validate the theoretical stability results.The results indicate the stability boundary of sum type combination resonance is related to the factors such as input torque T 0,the bearing position l and spring constant of support bearing K x2,K y2,.The position l or spring constant decreasing leads to the resonance instability domain diminishing.The conclusion provides an academic foundation for analyzing vibration and noise of misaligned rotary shafts.