利用达朗伯原理建立单球自动平衡装置在滚道偏心下的数学模型,并利用谐波平衡法对该数学模型进行转换,分析单球自动平衡装置的稳态响应及其扰动方程,在此基础上研究滚道偏心对单球自动平衡装置完全平衡状态稳定性的影响.研究表明:过临界转速下,滚道偏心距小于某一临界值时,单球自动平衡装置的完全平衡状态是稳定的;滚道偏心距超过该临界值时,单球自动平衡装置的完全平衡状态会变得不稳定.

The Matlab code is used very often in numerical simulation of ball-type automatic balancers. But the results are neither intuitive nor interactive. In this paper, a new dynamic simulation system with VB platform was designed. The mathematical model of the ball-type automatic balancers was solved numerically using Runge-Kutta method. The simulation results show that the system enables interactive visualization and intuition of the simulation results and realizes the dynamic presentation of the state of dynamic motion of the balls. The simulation results obtained by the numerical simulation system of the ball-type automatic balancers are consistent with those of the self-synchronization theory. The amplitude of the unbalanced rotor is reduced effectively.

There are many factors which influence the vibration reduction effect of the ball-type automatic balancer when it is operating at the over-critical speed. In this paper, the mathematical model of the ball-type automatic balancer with installation eccentricity is established and the numerical simulation is done using the parameters determined by the experimental testing. Influence of the installation eccentricity on the vibration reduction effect of the ball-type automatic balancer is analyzed. The results show that the smaller the installation eccentricity is, the better the vibration reduction effect is. Within a certain range, improving the accuracy of the rotor's processing and installation can significantly raise the vibration reduction effect for the ball-type automatic balancer. But over high accuracy of processing and installation may not be necessary since it does not help too much for improving the vibration reduction effect further. Result of the analysis may have application significance for vibration reduction of ball-type automatic balancers.