Multi-objective Optimization Design Method Of Accelerated Degradation Test For Motorized Spindle With Uncertain Model

CNC machine tools are the basis of value generation in the manufacturing industry and the key support point of the rise of the industry.For a country,the position of the equipment manufacturing industry in the international division of labor plays an "anchoring" role.The reliability of motorized spindle,as a key functional component of CNC machine tool,largely affects the reliability of CNC machine tool.Therefore,the topic that how to evaluate and improve the reliability of motorized spindles has attracted the high attention of scholars and machine tool enterprises.For high-reliability and long-life motorized spindle,it is difficult to accurately evaluate its reliability within the allowed time through traditional reliability life tests.However,with the operation of the motorized spindle,its key performance indicators will gradually degrade,and the accumulation of such performance degradation will gradually lead to its functional degradation and eventually to failure.Accelerated degradation test(ADT)technology can be adopted to increase the degradation rate of motorized spindle by using the accelerated stress which is higher than the normal stress.Then,the degradation model of the key performance indicator can be established by collecting the degradation information during the degradation process.Finally,the reliability level of the product can be efficiently evaluated.Considering the strict limitation of the test time and cost in engineering practice,how to carry out the accelerated degradation test under limited conditions,get the valid test data,and accurately evaluate the reliability of product are the study goals of the optimization design of ADT.A reasonable assumption of the degradation model is an important prerequisite to ensure the accuracy of the optimized results of ADT.However,it is difficult to define the most suitable degradation model to describe the degradation process of product due to its randomness and complexity.Besides that,the optimized results are different under different model assumptions.Therefore,it is necessary to carry out the research on the optimization design of ADT under the condition of model uncertainty.In addition,due to the complex working conditions of the motorized spindle and huge amount of test requirements,the single optimization objective used in the existing optimization methods cannot meet actual engineering needs.Besides,the optimized test plans under different optimization objectives are different and even contradictory.How to obtain the optimal test plan that balances multiple optimization objectives under the limited test time and cost is an urgent problem to be solved.Therefore,with the support of the National Natural Science Foundation of China and the National Science and Technology Major Project,this paper uses the motorized spindle as the research object to study the optimization design method of ADT considering the uncertainty of the degradation model,multi-objective optimization design methods of ADT,and the reliability evaluation method based on ADT data.It provides scientific and effective support for designing the reliability of the motorized spindle.The main study work of this paper includes:(1)The structure and function of the motorized spindle are analyzed.On this basis,the fault analysis is carried out based on the field fault data to determine the main characteristic indicator that reflects the performance degradation of the motorized spindle,which will be used for monitoring and analyzing in ADT.The reliability test device of the motorized spindle is built,and the diagnostic test of the motorized spindle is also carried out.To determine the highest stress level allowed in ADT,the failure mechanism consistency test of the motorized spindle is carried out according to the diagnostic test data.(2)The optimization design method is studied for ADT considering the uncertainty of the degradation model.Firstly,the ADT optimization models are established based on the Wiener process,the Gamma process and the inverse Gaussian process respectively,and the rationality and necessity of considering the uncertainty of the degradation model are verified through comparison and analysis.Secondly,the optimization design method of ADT considering the uncertainty of degradation model is proposed.The weights of candidate models are determined based on the Akaike information criterion,and the combination forecasting method is adopted to construct the optimization objective function.Then,taking the test sample size,the measurement interval and the number of measurements under each stress level as design variables,the optimization model of ADT considering the uncertainty of the degradation model is established under the constraint of pre-set test budget.The self-adaptive search algorithm is proposed to solve the optimization model.It adjusts the search step size dynamically according to the feedback of the change degree of the optimization objective function,which improves the search efficiency,avoids falling into the local search and ensures the optimization effect.(3)Considering the uncertainty of the degradation model,the multi-objective optimization design method of ADT based on the game theory is proposed.Taking the test sample size,the measurement interval and the number of measurements under each stress level as design variables,the optimization model is established to improve the prediction accuracy of mean time to failure(MTTF),the estimation accuracy of model parameters,and the robustness of model parameter deviations under the constraint of pre-set test budget.Based on the game theory,the multi-objective optimization model is transformed into a cooperative game problem.The fuzzy clustering method is used to calculate the strategy space owned by each game player,and the profit function of the game party is constructed based on the collusion and cooperation model.Finally,the multi-objective optimization model is solved and the comprehensive optimal test plan that balances multiple optimization objectives is obtained.(4)The simulation evaluation method of ADT is proposed based on Monte Carlo method.The asymptotic variance of the estimated MTTF under the normal stress,the determinant value of Fisher information matrix of the model parameters,and the relative ratio of the asymptotic variance before and after the fluctuation of the model parameters are used as the indexes to evaluate the test plan.The average value of each evaluation index is used to check the accuracy of the test plan,and the standard deviation of each evaluation index is used to check the stability of the test plan.Meanwhile,aiming at the problem that the maximum likelihood estimator of accelerated degradation model parameters is biased in the case of small amount of samples,the method of correcting the model parameter estimator is proposed based on simulated test data.It uses the ratio of the median of the maximum likelihood estimator of the model parameters to the true value to measure the degree of deviation of the parameter estimator.The model parameter estimator is corrected through the partial ratio coefficient,thereby improving the estimation accuracy of model parameters and the final reliability evaluation result.(5)Based on the above study on the optimization design method of ADT,the optimal ADT plan is determined for the motorized spindle.Relying on the motorized spindle reliability test device,the ADT is carried out on motorized spindles of a domestic CNC machine tool.Based on the proposed statistical analysis method and the reliability evaluation method,the test data are preprocessed by using variational mode decomposition,and the parameters of three candidate models,Wiener process,Gamma process and inverse Gaussian process are estimated by maximum likelihood estimation method.Finally,the reliability evaluation result of the motorized spindle is obtained considering the uncertainty of the degradation model.In addition,the reliability evaluation software for motorized spindle is designed and developed,which integrates the three modules of the preprocessing the accelerated degradation test data,establishing of the accelerated degradation model and reliability evaluation.By using this software,the reliability evaluation of the motorized spindle can be realized efficiently and accurately.