Two-step Extremum Response Surface Method of reliability analysis on flexible mechanism

摘要

To improve the precision and efficiency of reliability analysis of flexible mechanism, Two-step Extremum Response Surface Method (TERSM) of reliability analysis is proposed. Dynamics differential equations of the flexible mechanism were established by using the integrated modal method and the flexible multi-body system dynamics method. By using the Monte Carlo Method (MCM), the random sample values of the input dynamic parameters were obtained and dynamics differential equations were solved for each random sample value which revealed the responses of their displacement, speed and acceleration in certain time domain. On this basis, dynamic stresses and deflections were obtained. By taking the extremum values of the stresses and the deflections as output responses and the random sample values of dynamic parameters as input quantities, Extremum Response Surface functions (ERSF) were established. Taking maximum and minimum values of output extremum responses as parts of the sampling points, the coefficients of ERSF were solved. Definite expressions of ERSF were obtained to analyze the reliability of flexible mechanism. The comparison with various other methods shows that this method has greatly improved the computational speed while keeping acceptable computational accuracy, TERSM is proved to be a high precision and high efficiency in dynamic reliability analysis of flexible mechanism, and this method has opened up an effective way for reliability optimization of flexible mechanism.