Reliability Modeling Of NC Machine Tools Considering Working Conditions And Testing Period Design

NC machine tools is a complex mechanical-electrical-hydraulic system. The reliability problem of NC machine tools has been paid much attention as basic manufacturing equipment in equipment manufacturing industry and national defense modernization.Compared with foreign advanced NC machine tools, domestic NC machine tools, especially the domestic high-end NC machine tools, have smaller gaps in terms of accuracy and function, but, larger gap in terms of reliability, which makes domestic NC machine tools have low market share, high-end NC machine tools rely on import, and has seriously restricted the development of equipment manufacturing industry and national defense modernization. Therefore, it is urgent to improve the reliability of domestic NC machine tools. Establishing the reliability model of NC machine tools is the important foundation for reliability evaluation, reliability design, and reliability growth of NC machine tools. Many experts and scholars have established the reliability models of NC machine tools from different perspectives, for example, fault information processing, distribution model, test types, parameter estimation, and maintenance and so on, to improve the accuracy of NC machine tools reliability assessment. However, most of the reliability modeling of NC machine tools is limited by the fault information, and have not considered the influence of working conditions on the reliability of NC machine tools. Researches show that, the product will show different reliability levels under different working conditions or environment. It is well known that NC machine tools are used in various industries and regions, and the processing tasks are often different. Therefore, ignoring working conditions and environment will result in a large bias in reliability evaluation. In order to improve reliability evaluation's accuracy, it is an urgent problem that how to establish the reliability model of NC machine tools accurately considering the working conditions.Under the support of the state key science and technology projects the domestic NC machine tools are taken as the research objects. In combination with the differences of working conditions, the process and methods of collecting fault information and working condition information in the field reliability test of domestic NC machine tools are analyzed.The reliability of NC machine tools under different working conditions are modeled and evaluated. The interval estimation method of reliability of NC machine tool is studied. The testing period of NC machine tools under Fixed-time censoring test is designed, and thespecific examples are given respectively.The detail works are as follows:(1) The reliability research status of NC machine tools at home and abroad is analyzed,and the methods of reliability evaluation of NC machine tools considering working conditions and testing period design are put forward combined with the practical engineering requirements.(2) The types of working conditions of NC machine tools are summarized, and the collection and recording process of the working conditions of NC machine tools are established. The corresponding identifications between fault information and working conditions are designed to make them correspond to each other exactly. The premise of the field reliability test of NC machine tools is that the normal production of the user can not be affected, and so force measuring device cannot be installed on NC machine tools. Then the cutting parameters obtained by the field reliability test are used to calculate cutting force based on the empirical formula. The number of tool changing is obtained by technological procedure of parts or field observation test method. Finally, the reliability of NC machine tools is evaluated under Fixed-time censoring test, which has not considered working conditions.(3) For traditional reliability evaluation methods do not consider the working conditions' effects on reliability, there is a great error in the result of a traditional method compared with the actual value. A new reliability evaluation model of NC machine tools is proposed based on the Cox proportional hazards model, which describes the mathematical relation between the working condition and the reliability level of NC machine tools. Firstly,the coefficients of working condition covariates in the new reliability evaluation model are estimated by the partial likelihood estimation method; secondly, the working condition covariates which have no effects on the reliability of NC machine tools are eliminated by the likelihood ratio test; and then parameters of the baseline failure rate function are estimated by the maximum likelihood estimation method; Thus the reliability evaluation model of NC machine tool is obtained under different working conditions and the reliability level of NC machine tools is obtained. Case study shows that the proposed method could establish the relation between the working condition covariates and the reliability level of NC machine tools, and the influence laws of cutting force, the number of tool changing, environment temperature and cutting fluid on the reliability of NC machine tools are analyzed combined with case study.(4) Firstly, the existing interval estimation methods of the reliability parameters of NCmachine tools are analyzed. A larger error will be induced due to the lack of time-censored data in the re-sampling process when parametric Bootstrap method is applied to estimate the confidence interval of a reliability index of NC machine tools, and aiming at this problem, a Bootstrap method fully utilizing the time-censored data of the NC machine tools was proposed. The relation between the complete and time-censored data in the time-censored test of NC machine tools is analyzed, and the Bootstrap samples are generated based on this relation, solving the problem that the time-censored data can't be utilized in the Bootstrap's re-sampling process. The reliability parameters' point estimators are obtained by the maximum likelihood estimation and the Newton-Raphson. The bias-correction and accelerated method is used to decrease Biased error caused by the maximum likelihood, and then the confidence intervals are estimated. The coverage rate of interval estimations obtained by simulation test method is taken as evaluation index to verify the merits of interval estimations obtained by each method. In combination with a real case, the principle of specifying the length of test time T and the number of the initially generated complete datum k are discussed and proved.(5) Aiming at the problem that the difficulty in determining testing period for assessing NC machine tool's reliability increases the testing cost or decreases the assessment accuracy,a method of determining testing period is presented based on Bootstrap re-sampling. This method uses the change rate of interval estimate width of MTBF as the criterion for determining the testing period, and uses the history fault information of the tested machine tool as the research object. The upper and lower bounds of the reliability intervals estimate for different testing period are fitted by Power function, which obtained by the Bootstrap re-sampling method, and the goodness of fit test is carried out. The model of change rate for interval estimate width of MTBF is established by the derivative of fitting function, and the testing period was obtained. Three factors influencing the testing period, the number of machine tools, shape parameter and confidence level, are analyzed in combination with the real case.The main innovations of this paper are as follows:(1) A new reliability modeling model of NC machine tools considering working conditions is proposed, which can describe the mathematical relation between the working conditions and the reliability level of NC machine tools. The proposed model overcomes the shortcomings of traditional reliability modeling methods without considering the influence of working conditions on the reliability of NC machine tools, which provides the basis for reliability improvement design of NC machine tool.(2) A larger error will be induced due to the lack of time-censored data in the re-sampling process when parametric Bootstrap method is applied to estimate the confidence interval of a reliability index of NC machine tools, and aiming at this problem, a Bootstrap method fully utilizing the time-censored data of the NC machine tools was proposed, which reduces the error of interval estimation of the traditional Bootstrap method. Aiming at the problem that general interval estimation method cannot be used, because there are two variables, TBF(Time Between Failures) and working condition, in the proposed model, an interval estimation method for the Reliability modeling of NC machine tools considering working conditions is proposed.(3) A new method to determine the testing period is proposed based on Bootstrap re-sampling, which solves the problem that the reliability testing period cannot be reasonably determined.The proposed method uses the change rate of interval estimate width of MTBF as the criterion to determine the test period.