Error Evaluation of the Crown Profile of Logarithmic Generatrix Roller

Abstract

In order to realize the accurate assessment of the profile error of the crown of the bearing roller, according to the geometric characteristics and the definition of the shape error of the contour element of the logarithmic bus-type roller, based on the principle of least squares, the least squares piece-wise fitting and error evaluation method of the logarithmic bus-type (combined form of the two-segment logarithmic curve) bearing roller crown profile are studied. Firstly, the three-point method is used to determine the curvature of the discrete data points of the convexity curve, and the boundary point of the two logarithmic curves is determined by the curvature difference method. Secondly, the measuring points adjacent to both sides of the dividing point are selected as auxiliary dividing points; the auxiliary dividing points and the corresponding logarithmic curve segment measuring points are fitted together to fit a series of least squares curves and calculate the corresponding errors. Through comparison and judgment, the least square error of the logarithmic bus-type roller profile is finally determined. Finally, through comparison and judgment, the least square error of the logarithmic bus-type roller profile is finally determined. The example results show that the total error of the logarithmic bus-type roller crown profile curve is 0.0071mm. The method in this paper can effectively realize the fitting and error evaluation of the bearing crown profile error, and it also verifies that the logarithmic prime line can reduce the stress concentration and improve the service life of the bearing.