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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。
Based on the Euler equation, the transverse vibration model with universal joint swivel axis is deduced, and the multi-scale method is used to solve the model. Many possible resonance modes of the system are obtained, The transverse vibration and the combined resonance of combined axis and the differential combined resonance are analyzed. The transverse vibration and the combined resonance response of this type of deflection system are numerically calculated and simulated, and the theoretical analysis results of the obtained stability are tested. The results show that the stability boundary is related to the input torque T0, the bearing mounting position l, bearing stiffness Kx2 and Ky2 for the combined resonance. When the bearing mounting position is closer to the center of the universal joint or the bearing spring stiffness When the coefficient is small, the area where the system produces the sum-type combination resonance near the frequency (ω10 + ω20) / 2 decreases, that is, the system and the type combination resonance can be suppressed from being generated. This study can provide theoretical support for skew axis vibration and noise suppression.