Evaluation of Three-Dimensional Shape of Steel Ball by Spherical Harmonic Function

Abstract

In the previous report, it was shown that harmonic analysis results on the three-dimensional shape of a steel ball obtained by use of spherical functions gave good evaluations of characteristics of steel balls used in a bearing assembly. However, this type of analysis is inadequate for evaluating the shape of the ball geometrically. In this paper, first, the possibility of three-dimensional geometrical evaluation by spherical harmonic analysis is described. The 'reference direction' is defined as the index for directivity of each order of the spherical component and has no relationship with the coordinates for measurement. This 'reference direction' or the value of each spherical component for which this direction is obtained, is utilized to illustrate and evaluate the spherical shape of the steel ball. Second, the method for estimating the three-dimensional shape of the steel ball by two-dimensional measurement is explained (e. g., a roundness meter). Mean Fourier coefficients of cross-sectional forms of the steel ball are theoretically calculated, and the correlation between this value and the harmonic analysis result obtained through the use of the spherical functions is obtained.