On the basis of the classical two degree of freedom (2-DOF) rotor-bearing system, the stochastic dynamic equations are solved and the dynamic reliability of the rotor’s positioning precision is examined in this paper. Firstly, the stochastic dynamic equations are converted to several deterministic dynamic equations by orthogonal polynomial approximation method. The contact uncertainty coefficient is described by Bernoulli distribution and the instantaneous contact probability of the ball-inner race contact of the rolling bearing is obtained. Then the state function of the system is defined and the statistical fourth moment method is adopted to determine the first four moments of the system response and state function. Edgeworth series technique is used to approach the cumulative distribution function (CDF) of the maximum displacement of the response and the system state function. Different parameters effects on the characteristics of the responses and the reliability of the system are investigated. The comparisons of the results obtained from the Monte Carlo simulation (MCS), the previous study and the present study illustrate the effectiveness of the study.

在经典的两自由度（2-DOF）转子轴承系统的基础上，求解了随机动力学方程，并研究了转子定位精度的动态可靠性。首先，通过正交多项式逼近法将随机动力学方程转化为几个确定性动力学方程。接触不确定性系数由伯努利分布描述，并获得滚动轴承的滚珠内圈接触的瞬时接触概率。然后定义系统的状态函数，并采用统计第四矩方法确定系统响应和状态函数的前四个矩。Edgeworth级数技术用于响应的最大位移的累积分布函数（CDF）和系统状态函数。研究了不同参数对响应特性和系统可靠性的影响。从蒙特卡洛模拟（MCS），先前的研究和本研究获得的结果的比较说明了该研究的有效性。