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.
Highlights
Ball bearings can be considered as the system consisting of inner ring, outer ring, cage and rolling elements which have themselves geometrical precision
There must be the connection between the geometrical precision of elements and the running accuracy of the bearing, but this connection can be difficultly expressed by mathematical formula
The geometrical precisions of elements and the running accuracy of bearing follow the regularities of distribution which can be obtained with statistical analysis
Summary
Ball bearings can be considered as the system consisting of inner ring, outer ring, cage and rolling elements which have themselves geometrical precision. The delivered and mapped relation between the joint distribution of the running accuracy and the multivariate distribution of the element geometrical precision can be constructed by Copula function. General estimation of distribution algorithm can’t construct appropriate joint multivariate distribution function which can designate relativity between marginal univariant distribution function and multivariate joint distribution function. Li Lihong et al.: Copula Estimation Method of the Running Accuracy of Ball Bearing to distribution estimation with less operation and can preferably expressed distribution situation of dominant group [17]. Statistics method can be adopted to analyzing the distribution feature of elements geometrical precision of bearings and the dependence relation between the running accuracy of bearings and multivariate distribution of elements. The running accuracy of bearings can be estimated by constructing the mathematic model between the running accuracy and elements geometrical precision before assembly
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