Information-poor Experimental Analysis On The Reliability Of Mechanical Products

With the rapid development of industrial technology, an increasing number of attention has been paid to the evaluation of the reliability of mechanical products. In the meanwhile, the limitations of conventional evaluation methods and empirical value formulas of reliability are gradually exposed, which makes the study on reliability models becomes more and more important. The existing findings have indicated that the prior information about probability distributions and variation trends of performance data of mechanical products is relatively poor, belonging to the category of information-poor system. As a result, how to make effective experimental analyses on the reliability of mechanical products in the case of poor information is the problem we are concentrated on and dedicated to solve in the paper.1 Studying the time series of the rolling bearing vibration acceleration, the Poisson method is proposed in the paper to identify the variation process of the rolling bearing vibration performance. Based on the Poisson process, the cumulative failure probability function is established and experimental analyses with poor information are conducted with the time series of vibration acceleration of four rolling bearings in the same size under four kinds of different running conditions. The investigation results have shown that the cumulative failure probability value obtained in an evaluation cycle can truly reveal the current variation states and degrees of the rolling bearing vibration performance under a given threshold value, therefore, through continuous evaluations, the variation process of the rolling bearing vibration performance can be effectively identified.2 Based on the time series of the rolling bearing vibration information, the concept of variation intensity is defined, and via the organic fusion of the grey bootstrap principle and the Poisson process, the grey bootstrap Poisson forecasting method is put forward in the paper. Experimental investigations on the reliability of bearing vibration as a time series have proved that the variation states of the performance reliability can be truly described by the “reliability curve in deck chair shape” and predicted values are in very good accordance with test values, with a maximum absolute error value of 0.068 and a maximum relative error value of 14.5%. Hence, the grey bootstrap Poisson method can be used to effectively predict the variation states of bearing vibration performance as a time series.3 In view of the failure data along with poor information, the reliability analysis method of mechanical products is presented. According to the expected empirical value formula of reliability, the expected empirical value vector of failure data can be obtained; discrete failure frequency vector of lifetime data is inferred by the expected empirical value vector(i.e. statistical histogram is obtained); based on the intervalmapping Newton iteration method, the maximum entropy probability density function is established, the failure probability distribution function is gained by integration, and then the estimated true value function of reliability is acquired. Studies on simulation cases and experimental cases have proved the method proposed is not only able to evaluate the reliability with a known distribution but effective and feasible in the reliability assessment under the condition of failure data without any priori information about the possibility distribution.By means of the Poisson process, the organic fusion of the grey bootstrap principle and the Poisson process, and the effective fusion of the expected empirical formula of reliability and the maximum entropy principle, the three methods for performance reliability analyses of mechanical products proposed in the paper can break through the restriction of the existing theories and the defects of statistical analysis methods, and help to discover the performance failure timely and to take corresponding measures, which provides scientific basis for the safety and reliable operation of the system, thus having important theoretical significance and application values.