旋转机械随机参数动力响应的概率密度分析方法研究

发布时间：2018-01-03 20:09

本文关键词：旋转机械随机参数动力响应的概率密度分析方法研究　出处：《河南工业大学》2012年硕士论文　论文类型：学位论文

【摘要】：随机参数转子动力学问题正在受到越来越多国内学者的关注，已经成为转子系统线性和非线性动力学问题之后的重要研究课题。但以往的研究多以求得随机参数结构反应的数值特征值为目标，从全面反映随机结构反应的概率信息的角度考察，这仅是对随机结构反应的一种较为宏观的把握，更为精细化的反映是对随机参数结构反应概率密度的把握。本文以随机摄动Riccati传递矩阵法导出的随机参数转子系统动力学响应与随机参数变量之间的函数关系式为基础，研究了通过数值积分方法获得了随机参数转子系统动力响应的概率密度的方法。主要研究内容和成果如下： 1.研究了在已知随机参数变量联合概率密度情况下的转子系统动力学响应的概率分布的计算方法，运用二次型、雅克比行列式及概率的相关知识，导出了用数值积分法计算动力响应概率密度的关键公式。 2.以MATLAB7.0为平台，开发了基于摄动Riccati传递矩阵法的随机参数转子系统动力响应概率密度计算程序。 3.基于该方法，以实验室的具有随机可控电磁支撑的Bentley转子为模型，计算分析了两个随机参数变量转子系统动力学响应的概率密度，并与Monte Carlo模拟方法对比。结果表明：当变异系数较小时，该分析方法具有很高的计算精度，且较随机模拟方法具有计算量小、速度快的优点；随着变异系数的增大，，该方法的精度有一定的下降；当变异系数达到0.30时，仍然保持着较高的精度（在10%以内），能够满足工程实际的需要。 4.以锅炉给水泵转子为例，研究了两端轴承的四个主刚度参数随机变化情况下的转子系统动力响应的概率密度，并与Monte Carlo模拟方法对比。通过这个工程实例，说明了该方法的精度和实用性。
[Abstract]:The problem of rotor dynamics with random parameters is attracting more and more attention from domestic scholars. It has become an important research topic after the linear and nonlinear dynamic problems of rotor systems, but most of the previous studies are aimed at finding the numerical eigenvalues of the structural responses of random parameters. From the point of view of reflecting the probability information of stochastic structural response, this is only a macroscopic grasp of stochastic structural response. The more detailed reflection is the grasp of the probability density of the random parameter structure response. In this paper, the dynamic response of the stochastic parameter rotor system derived by the stochastic perturbation Riccati transfer matrix method and the random parameter variable. Is based on the functional relationship of. The probability density of the dynamic response of a stochastic parameter rotor system is obtained by numerical integration method. The main contents and results are as follows: 1. The method of calculating the probability distribution of dynamic response of rotor system under the condition of joint probability density of known random parameter variables is studied, and the knowledge of quadratic form, Jacobian determinant and probability is used. The key formulas for calculating the probability density of dynamic response by numerical integration method are derived. 2. Based on the perturbed Riccati transfer matrix method, a program for calculating the probability density of the dynamic response of a stochastic parameter rotor system is developed on the platform of MATLAB7.0. 3. Based on this method, the probability density of dynamic response of two random parameter variable rotor systems is calculated and analyzed using the Bentley rotor with controlled electromagnetic support in the laboratory as the model. Compared with the Monte Carlo simulation method, the results show that the analysis method has high accuracy and less computational complexity than the random simulation method when the coefficient of variation is small. The advantage of speed; With the increase of the coefficient of variation, the precision of the method decreases to a certain extent. When the coefficient of variation reaches 0. 30, the accuracy is still high (less than 10%), which can meet the need of engineering practice. 4. Taking the boiler feedwater pump rotor as an example, the probability density of the dynamic response of the rotor system under the random variation of the four main stiffness parameters of the two ends bearings is studied. The method is compared with Monte Carlo simulation method. The accuracy and practicability of the method are illustrated by an engineering example.
【学位授予单位】：河南工业大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：TH113

【参考文献】