非平面运动球式自动平衡装置稳定性分析

在实际生产工作中,高速运动转子由于受到不平衡力矩作用,会使整个转轴产生空间转动,这种转动使得转子产生非平面运动。采用拉格朗日方程和牛顿定律,建立一种非平面运动球式自动平衡装置数学模型;通过摄动法和劳斯-霍尔维茨判据对其可能使系统稳定的解进行分析,得出该自动平衡装置分别在1个球和2个球的情况下存在能够使系统稳定的解以及系统在不同条件下振动情况。该装置在过临界转速下存在稳定点,在一定条件下能对不平衡力进行平衡,达到减振目的。

Stability Analysis of Ball-type Automatic Balancer Devices with Non-plane Motion

In the actual production, as imbalance moment was acting on high-speed rotor, the whole shaft produced a space motion, which led to non-plane motion of the rotor. By using the Lagrange equation and Newton’s law, a mathematical model of ball-type automatic balancers device with non-plane motion had been established. In order to analyze the possible solution of the mathematical model which would make the system stable , perturbation method and Rolls - Hurwitz criterion had been adopted. After this kind of analysis, there is solution which can make the system stable when the automatic balancers device is at the situation of one ball or two balls. And the vibration of system under different condition can be obtained. The device has solutions which can make the system stable at critical speed, and it can also counterpoise unbalanced force under certain conditions, in order to achieve the purpose of vibration.