Reliability Index And Its Solution Method Based On AFOSM Sample Conversion

There are naturally various types of uncertainties in machine design,namely material characteristics,geometric properties and imposed loads.The combination of these uncertainties in machinery ultimately leads to uncertainty in mechanical failure.While pursuing low cost and light weight,machine design should also pursue the reliability of the designed machine.Therefore,the accurate calculation of mechanical reliability becomes a critical issue.A lot of work has been done in solving nonlinear performance function,but there are few ways to coordinate accuracy and computational cost.Therefore,a new reliability index and its solution method are proposed in this paper to solve the reliability.Taking two numerical examples as examples,the optimal values of parameters under two basic variables and three basic variables are given,and the performance is compared with other algorithms.A cantilever tube in mechanics of materials and an existing domestic RV reducer are taken as application case,a set of relatively complete mechanical reliability solution technical scheme is proposed.The main work of the paper is as follows:(1)The concept of regional equivalent of conversion index is proposed.The classical reliability algorithm in probabilistic reliability model is systematically studied and introduced.The regional equivalent of conversion index used to describe the failure region is proposed,and its solution method is explained.(2)The expression of regional equivalent of conversion index is deduced.The expression of regional equivalent of conversion index is deduced from two perspectives of graphic description and integral infinitesimal,and the mapping relationship between regional equivalent of conversion index and failure rate is established when the number of basic variables is 2,3,4,and the mapping relationship is analyzed.(3)The optimal value of parameters was obtained by example analysis.Through two numerical examples,the influence of sampling parameters on the relative error of reliability is obtained,the reasons are analyzed,and the optimized parameter values under different dimensions are given.Two numerical examples of parameter analysis and a mechanical example of cantilever tube are compared with the traditional classical algorithm,and the proposed algorithm is proved to have certain advantages in efficiency and precision.(4)Reliability analysis of cycloid gear mechanism.Taking a certain type of RV reducer made in China as the research object,a three-dimensional mathematical model and finite element simulation model are established for the cycloidal pin gear mechanism,a key part of the second stage transmission mechanism.A series of sample points are generated by experimental design method according to four key geometric parameters,and the response surface was constructed after simulation.Based on the BP neural network,the limit state function of the RV reducer is fitted,and the AFOSM sampling conversion method was used to solve the problem,and the validity of the method for solving practical problems is verified.In this paper,regional equivalent conversion index is proposed based on the traditional advanced first order and second moment,which solves the reliability by sampling instead of searching for the most probable point,effectively improving the solution efficiency and stability under certain circumstances,which has certain engineering application value.