Copula Estimation Method of the Running Accuracy of Ball Bearing

Abstract

The bearing is an assembly consisting of multiple elements and its performance is shown mainly as its running accuracy which is influenced by many factors including its elements' geometrical precision. The influence of elements geometrical precision on bearing running accuracy is joint effect when multiple elements are assembled together. So there must be dependent relationships between bearing running accuracy and the joint action of multiple elements. Such relationship was very complicated and difficultly described by mathematical formula. But, the elements' geometrical precision follow statistics law, and so, statistics can be applied to analyzing elements' dimension distribution law and construct joint distribution function. The copula function can be introduced to establish the transmit relationships that join the running accuracy to multiple elements geometrical precision. Based on the copula estimation of distribution algorithm, the mathematic modeling of the radial and face run out distribution of the bearing and elements dimension precision distribution can be built to forecast bearings running accuracy.