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转子动平衡的方法已为人熟知,但理论分析文章很少。本文根据力学原理,推导出转子不平衡质量和轴承振动振幅值的数学关系式。由于数学上求解困难性,文章根据实际允许的降维范围,约束了轴承在X和Z方向上的运动,因此问题归结为求解垂直于轴线X的Y方向振动与转子不平衡质量的关系式。本文利用矢量和复数的关系,求解了Y方向振动的微分方程式。最后讨论了约束Z方向运动时转子陀螺力矩的影响程度,虽以汽轮发电机为例,但理论也适用于一般刚性转子的动平衡分析。
The method of rotor balancing is well known, but there are few theoretical analysis articles. Based on the mechanics principle, this paper deduces the mathematical relation between rotor unbalance quality and bearing vibration amplitude. Due to the difficulty in solving math problems, the paper constrains the bearing movement in the X and Z directions according to the actual allowable dimension reduction. Therefore, the problem can be attributed to solving the relationship between the Y-direction vibration perpendicular to the axis X and the rotor unbalance mass. In this paper, by using the relation between vector and complex number, the differential equation of Y-direction vibration is solved. Finally, the influence degree of rotor gyroscopic torque when constraining Z-direction motion is discussed. Although the example of turbine generator is used, the theory is also applicable to the dynamic balance analysis of a general rigid rotor.