中文摘要：

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。

英文摘要：

The mathematical model of the single-ball-type automatic balancer with eccentric raceway is established on the use of Alembert principle. And the mathematical model of the system has been converted by using the harmonic balance method, and analyzed the steady state response and the perturbation equation for the system. Based on this, the influence of eccentric raceway on the single-ball automatic balancer＇ s perfectly balanced state stability have been studied. Studies have shown that：under the overcritical rotating speed, when the raceway eccentricity is less than a critical value, it is stable of the single-ball automatic balancer＇ s perfectly balanced state ; when the raceway eccentricity is over the critical value, there will be instability of single-ball automatic balancer＇ s perfectly balanced state.