线性连续系统的动态与渐变耦合可靠性分析

机械设备的零部件通常承载着动态载荷,且由于制造的不确定性致使几何元素的尺寸、形状以及相互位置具有随机性,同时多于80%的零部件都是由于某些量的劣化导致渐变失效,因此,开展动态与渐变耦合可靠性研究对于机械行业的发展具有极为重要的意义。研究随机参数线性连续系统遭受强度劣化和承受动态载荷时的可靠性问题。根据线性连续系统的随机动力学理论获得随机响应的计算公式,由此建立随机交变应力的计算模型。采用一随机变量描述初始强度的不确定性,利用非平稳Gamma过程描述强度劣化量的演变过程。在此基础上构建线性连续系统的动态与渐变耦合状态函数和可靠度表达式。应用提出的方法分析轴扭转振动系统的动态与渐变耦合可靠性,将当量正态化法和设计验算点法相结合以估算动态与渐变耦合可靠度,采用中心差分方法分析该可靠度的敏感性。利用数值实例验证提出方法的实用性和有效性。结果表明,提出的动态与渐变耦合可靠性分析方法能够有效解决随机参数线性连续系统遭受强度劣化和承受动态载荷时的可靠性分析问题。

Dynamic and Gradual Coupling Reliability Analysis of Linear and Continuous System

It is very important for the development of machinery industry to investigate the dynamic and gradual coupling reliability.This reason is that the part of mechanical equipment bears a dynamic load generally,has the random size,form and relative position of its geometrical elements due to the stochastic propriety of manufacturing process and more than 80% of the parts are subjected to gradual failure because of the deterioration of some parameters.The reliability problem of the linear and continuous system which bears dynamic load,is subjected to gradual failure due to strength deterioration and has several random parameters would be studied in this paper.According to the random dynamics theory of the linear and continuous system,the stochastic response is formulated and the stochastic alternating stress model is given.The uncertainty of the original strength and the evolution process of the strength deterioration are described by a random variable and a non-stationary Gamma process respectively.Then,the dynamic and gradual coupling state function and reliability of the linear and continuous system are modeled.The proposed reliability analysis method is employed to analyze the dynamic and gradual coupling reliability of the shaft torsional vibration system.The equivalent normalization and design checking point method are jointed to estimate the dynamic and gradual coupling reliability and the central difference method is used to analyze the reliability sensitivity.The practicality and validity of the proposed method are demonstrated by a numerical example.The results show that the presented dynamic and gradual coupling reliability analysis method could solve the reliability problem of t the linear and continuous system which bears dynamic load,is subjected to gradual failure due to strength deterioration and has several random parameters.