| The spindle is an essential key functional component of CNC machine tools,and its reliability level has an important impact on the reliability of the machine tool as a whole.When establishing the spindle reliability model,it often relies on the failure data obtained from early tests,field tests or bench tests as samples.However,with the development of technology,the reliability level of key functional components,especially electric spindles,has improved greatly,and it is difficult to obtain a large amount of failure data in a short period of time,and a situation of small samples of failure data has emerged.If the classical mathematical method is used to deal with such data,it is inevitable that the results are inaccurate.Therefore,it is very important and practical to study a reliability assessment method for small sample data.In this paper,the reliability assessment of electric spindles when the failure data is insufficient is solved by considering the environmental factors under the framework of Bayesian method,and the work is as follows:(1)Analyze the shortcomings of the traditional FMECA(Failure Mode,Effects,and Criticality Analysis)method.In view of the problem of a small number of evaluation factors and unclear evaluation criteria,the number of evaluation factors is refined and increased.Evaluation factors such as functional structure complexity are added to the traditional method.The best-worst method,data envelopment analysis method,and FMECA analysis method are combined to obtain a new RPN calculation method.The validity of the new method is verified through examples.(2)Development of a reliability assessment model for electric spindles.The two-parameter Weibull distribution model is used as the reliability assessment model for electric spindles.Based on the Bayesian approach,the prior distribution is determined and the posterior distribution is obtained as the key elements and the specific steps are introduced.The Mean Time Between Failures(MTBF)was selected as the reliability evaluation index for electric spindles,and the relevant formula for calculating MTBF using Weibull parameters was derived.(3)Determination of the prior distribution of Weibull parameters.By refer encing electric spindles similar to the target model with sufficient failure data,the concept of environmental factors introduced from the aerospace field was c ombined with expert judgment to compare the reliability levels between the tar get and historical products.The time function values of the reference historicalproduct at specific percentiles were used as a basis for expert judgment,and the weight of expert judgment was determined using the Analytic Hierarchy Pr ocess.The final expert judgment result was obtained by weighted scoring,and the prior distribution of the Weibull distribution was mathematically derived fro m the expert judgement.(4)To calculate the posterior distribution of the Weibull parameters,the approximate interval method of discretizing continuous quantities in the field of mathematics and the Bayesian analysis software Open BUGS were used.The approximate interval method was implemented in MATLAB to obtain the MTBF of the target electric spindle;The Open BUGS software was also used to provide the corresponding BUGS model and parameter simulation process,complete parameter estimation,and obtain MTBF values by inputting into relevant formulas to calculate reliability indicators.And the whole set of processes in this paper is applied to QT software development tools to develop an application software for Windows system,which can be promoted and applied in similar industrial environment in the future. |
