Estimation of sphericity by means of statistical processing for roundness of spherical parts

Abstract In the industrial standard of “balls for rolling bearings,” deviation from spherical form (sphericity) is defined as follows. It is usually determined by numerically evaluating the ball profiles, in two or three equatorial planes at 90° to each other, and recording them on a polar chart. Furthermore, the standard indicates that the minimum circumscribed circle method is relatively simple and generally satisfactory for ball profiles, and the method is also based on the assumption that two or three equatorial profiles at 90° to each other are a good indication of the deviation from spherical form. The measurement method for three-dimensional (3-D) spherical profiles is two-dimensional (2-D), because a practical (3-D) measuring system for spherical forms remains to be developed. This is another important problem. Using the method recommended in the standard, the deviation value is significantly underestimated, because the major part of the 3-D surface is not measured. Verification of the above-mentioned assumption is also difficult in general. If numerous measurements of 2-D profiles are performed, the degree of underestimation decreases. However, this requires much time and labor. In this study, a 3-D deviation value from spherical form is calculated from a few 2-D roundness values obtained using a general roundness measuring system with a statistical technique. Furthermore, an appropriate number of measuring cross sections necessary to estimate the sphericity with high reliability are presented.