Grey Relation Evaluation and Truth Value Fusion of Rolling Bearing Multisource Residual Stress

Abstract

Bearing ring residual stress test data obtained by µ-360 s residual stress analyzer have the characteristics of unknown probability distribution and limited samples. For this problem, this study introduces the uncertainty and proposes a grey relation method to estimate the true value of the bearing ring residual stress. Based on poor information theory (incomplete and insufficient information for the characteristic presented in the subject investigated) and by fusing the membership function method, maximum membership method, rolling mean method, and bootstrap method, the true value sequence of the residual stress is obtained. On this basis, true value fusion is implemented again using the grey bootstrap method, and the estimated true value of the residual stress for the bearing ring was obtained. The results show that the residual stresses of bearing rings are fused by multiple methods, and the overall estimated true value of the residual stress of the bearing ring is −578 MPa. Owing to different processing techniques, the true value of the residual stress varies in different parts of the ring as follows: −918 MPa on the large end surface of the ring, −673 MPa on the small end face of the ring, −228 MPa at the vertical test point on the outer surface of the ring, and −231 MPa at the parallel test point on the outer surface of the ring. The error between the estimated true value obtained using the grey relation method and that obtained through the fusion of multiple methods is generally 10% or less, thereby confirming the effectiveness of the grey relation method.