Abstract: To tackle the problem of quantitative analysis of inherent characteristics of gear-rotor systems which lacked sufficient information to build an accurate probability model,an uncertainty quantification method based on interval random moment technology was proposed.Rayleigh quotient formula was firstly introduced to derive the approximate solution of the natural frequency of gear-rotor systems with random interval mixed variables.Then,the interval variables were expressed as the distribution parameters of random variables,and the uncertainty modeling was carried out with the established random variables.Combined with Taylor expansion of multi-dimensional interval random functions and ordered moment method,the expressions of the mean and variance of the natural frequency of the gear-rotor system were derived.Furthermore,the upper and lower bounds of the mean and variance were obtained according to the fundamental algebraic operations and interval budget rule,and the influence law of random and interval variables on the natural frequency of the system was analyzed through the fluctuation of the upper and lower bounds and the concavity and convexity of the function curve.A numerical example of a gear-rotor system was used to verify the correctness and effectiveness of the proposed method.

Key words: interval random moment technology, uncertainty quantification, approximate solution, natural frequency, gear-rotor systems

摘要： 针对缺乏足够信息构建精确概率模型的齿轮—转子机构系统固有特性量化分析问题,提出基于区间随机阶矩技术的不确定性量化方法。引入瑞利商公式,推导了含随机区间混合变量的齿轮—转子系统固有频率的近似解;将区间变量表示为随机变量分布参数的形式,以随机变量进行不确定性建模,并结合多维区间随机函数泰勒展开技术和随机变量函数阶矩法,推导了齿轮—转子系统固有频率的均值和方差的表达式;根据四则运算和区间预算法获得均值和方差的上下界,并通过上下界波动量与函数曲线的凹凸性分析随机和区间变量对系统固有频率的影响规律。最后应用齿轮—转子机构系统数值案例验证了所提方法的正确性和有效性。

关键词: 区间随机阶矩法, 不确定性量化, 近似解, 固有频率, 齿轮—转子系统