Dynamic Prediction for Accuracy Maintaining Reliability of Superprecision Rolling Bearing in Service

Abstract

A dynamic prediction method for accuracy maintaining reliability (AMR) of superprecision rolling bearings (SPRBs) in service is proposed by effectively fusing chaos theory and grey system theory and applying stochastic processes. In this paper, the time series of a vibration signal is used to characterize the state information for SPRB, and four runtime data points can be predicted in the future, which depends on four chaotic forecasting models to preprocess the time series. Using the grey bootstrap method and sampling from the four runtime data, a large amount of generated data (GD) are gained to analyze the changes in information on bearing service accuracy. Then, using a predefined accuracy threshold to match the Poisson count for the GD, the estimated value of variation intensity is obtained. Subsequently, with the help of the Poisson process, the dynamic evolution process is forecast in real time for AMR of the SPRB for each step in the future. Finally, according to a novel concept for maintaining relative reliability in an SPRB, the failure degree of a bearing maintaining an optimum accuracy status (BMOAS) is effectively described. Experimental investigation shows that multiple chaotic forecasting methods are accurate and feasible with all relative errors below 15%; the reliability of each step in the future can truly be described, and the prediction results for AMR over the same subseries show good consistency; dynamic monitoring of the health status of SPRB can be realized by the degree to which a BMOAS fails.

Evaluation of Dynamic Uncertainty of Rolling Bearing Vibration Performance

“…If the vibration time series has chaotic characteristics, then suppose that X(M) is the center trajectory (viz., the trajectory of prediction started or the phase space trajectory at the end), L the reference trajectories similar to the center trajectory, and X(M l ) the lth reference trajectory. e weighted zero-order local prediction method, first-order local prediction method, weighted first-order local prediction method, and improved weighted first-order local prediction method are used to reconstruct the phase space as follows [31].…”

“…where p(w) is the probability density function of the data series Y B . rough the maximum entropy principle [31], the optimal estimation of the density function based on sample information can be obtained, and the main idea of maximum entropy is that the solution is the most "unbiased" among all feasible solutions, as follows:…”

“…According to the grey model GM (1, 1) [31], suppose the first-order accumulated generating operator (1-AGO) of V β is given by…”

Dynamic Evaluation of the Degradation Process of Vibration Performance for Machine Tool Spindle Bearings

“…In summary, the model realizes on-line monitoring of the degradation process of OVPS, which can give timely feedback so as to take preventive and remedial measures before the failure of OVPS for MTSB. Compared to the method in the Reference [8], the vibration threshold does not need to be set manually. Compared to other AI prediction methods, it does not require training on vibration signals, and the adjustment process of parameter is also omitted.…”

“…When analyzing the degradation process of bearings, the mathematical statistical methods generally assume that the amount of data are limited, and then extract characteristic parameters of bearings [8][9][10]. Based on the vibration signal collected, Ye et al [11] used the maximum entropy method to calculate the PDF of bearings, which was regarded as degradation characteristics.…”