Analysis On The Performance Reliability Of Rolling Bearings Based On Poor Information

Reliability is used to describe the ability of products to perform specific functions during the service period,which is an important index to evaluate the performances of rolling bearings.Performance continuity reliability is used to describe the ability of products to maintain the optimal performance state to run.The performance continuity reliability of rolling bearings changes,which will affect the run state of mechanical system.So it has great academic and application value to study the performance reliability and performance continuity reliability of rolling bearings.The classical statistical theory is generally based on known probability distributions to analyze and study reliability problems,which has certain limitations.Poor information system theory has become one of the hot topics in the field of scientific research since it is used to solve the reliability problems of small samples with unknown probability distributions.So this paper applies poor information system theory to study the performance reliability and performance continuity reliability of rolling bearings under the condition of poor information.A new concept is proposed for performance continuity reliability of rolling bearings,and a model for evaluating performance continuity reliability is established based on maximum entropy principle to calculate failure degree of performance of rolling bearings.According to performance data during optimal operation performance time of rolling bearings,the sufficient sample data is obtained using bootstrap resampling method.The maximum entropy principle is applied to build probability density functions of sample data,and the confidence intervals of random variables of performance are obtained according to small probability event principle.The frequency of performance sample data outside the confidence interval is obtained by using Poisson counting principle.The performance continuity relative reliability of rolling bearings in the future is calculated,and the failure degree of rolling bearings maintaining optimal performance situation can be predicted.The experiments show that the model can be used without setting performance thresholds in advance and any prior information on probability density functions of samples.A hierarchical bootstrap maximum entropy evaluation model is proposed to analyze the life reliability of rolling bearings under the condition of small samples without any prior information.Adequate sample data is obtained by using bootstrap method to re-sample the current zero-failure data samples.Based on maximum entropy method,different Lagrange multipliers can be obtained by changing the number of samples.In order to get the interval estimation values of Lagrange multipliers,the bootstrap method is used again to re-sample the small sample data of Lagrange multipliers.The probability density functions and reliability functions are achieved by carrying on permutation and combination for the upper and lower limit values of each Lagrange multiplier,so the interval estimation values of reliability functions can be gained using minimum uncertainty principle.Experimental investigation shows that the hierarchical bootstrap maximum entropy evaluation model can effectively solve the reliability evaluation problem for zero-failure data of small samples with known or unknown probability distributions.New concepts including variation probability,variation speed and variation acceleration,are proposed and a reliability prediction model is established to predict the inherent variation tendency of vibration performance reliability of rolling bearings based on the maximum entropy principle and Poisson process.The maximum entropy principle is applied to calculate the probability density function of sample data in the intrinsic sequence.According to Poisson process,variation number and variation frequency of performance data outside the confidence interval of intrinsic sequence are achieved for time series subdivided.Variation speed and variation acceleration of rolling bearing vibration performance are calculated by discrimination processing for time.The rolling bearing SKF6205 is used as an example to illustrate the applications of maximum entropy principle and Poisson process in analyzing variation process.Experimental investigation shows that the variation probability of reliability presents a nonlinear increase trend with the increase of wear diameter,which can be divided into initial running stage,normal performance degradation stage and performance deterioration stage.Moreover,the reliability prediction model can be used to analyze variation process of reliability under the condition of poor information,which is proven to be a useful supplement for available reliability theories.A mathematical model is established to evaluate the performance continuity reliability by combining maximum entropy principle with Bayesian principle.The probability density function of data sample is calculated using maximum entropy principle during the optimal time for the vibration performance of rolling bearings,which is considered as the prior sample information.Maximum entropy principle is applied again to calculate probability density functions used as the current sample information for data samples of different time series.According to Bayesian principle,the posterior sample information is obtained for the data samples of time series.The vibration performance continuity relative reliability of rolling bearing is calculated to predict the failure degree of rolling bearing maintaining the optimal vibration performance state.The deep groove ball bearing SKF6205 is used as an example to perform an experiment investigation,which shows that the bearing should be maintained or replaced before the wear diameter of the inner ring groove reaches 0.75 mm.The performance continuity reliability evaluation model has no requirements for the probability density functions of data samples,and the calculated values are in accordance with theoretical analysis values basically.This paper makes full use of the advantages of the poor information system theory,which uses different mathematical methods to fuse,analyzing and evaluating the performance reliability and performance continuity reliability of rolling bearings to solve the problems of reliability evaluation on small sample data with unknown probability distributions under the condition of poor information.The research on this topic makes a useful supplement for existing reliability theories,which has important application value for the practical problems in engineering.