非平面运动球式自动平衡装置稳定性分析  

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

作　　者：罗建[1] 谭青[1] 江波[1] 

机构地区：[1]中南大学机电工程学院,长沙410083

出　　处：《噪声与振动控制》2016年第2期21-26,共6页Noise and Vibration Control

摘　　要：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。In the actual production, since imbalance moment is acting on the high-speed rotor, the whole shaft will produce a spatial motion, which can lead to non-plane motion of the rotor. In this paper, based on the Lagrange equation and Newton’s law, a mathematical model of the ball-type automatic balancer device with non-plane motion was established. In order to obtain the possible stable solution of the mathematical model, perturbation method and Rolls-Hurwitz criterion were adopted to analyze the stability of the system. Through this analysis, it was found that there exists the stable solution for the automatic balancer device in the cases of one ball or two balls. And the vibration of the system under different condition can be obtained. The device has stable solutions at over-critical speed, and it can also counterpoise the unbalanced force under certain conditions to reduce the vibration.

关 键 词：振动与波 非平面运动 球式自动平衡装置 数学模型 稳定性分析 稳定解 

分 类 号：TH113.1[机械工程—机械设计及理论]