Minimum zone fitting and error evaluation for arc correction type convex contour of bearing roller

Abstract

The minimum zone fitting and error evaluation for the arc-modified convex contour of a bearing roller have important applications for consistency detection and quantificational research of the elastohydrodynamic lubrication of a bearing roller. Based on the definition of the shape error and the geometric characteristics of the arc corrected roller convexity line of the bearing, a new fitting and error evaluation method for the total convexity contour of a bearing roller is presented. First, the reference cutoff points of the arc segment and straight line are determined based on the curvature difference of each measurement point. Then, the measuring points on both sides of the two reference cutoff points are selected as auxiliary cutoff points for arc fitting. The fitting error is obtained based on the minimum area method. Finally, a series of tangent equations are obtained based on the tangent principle between a line and two arcs, and the straightness error is determined by calculating the distances between the measuring points and the tangents. The example results show that an arc-modified convex contour can be fitted, and its global error can be evaluated effectively and precisely using the presented method. This study also provides a new idea for the minimum zone fitting of multi-segment curves along a plane.