Abstract: Aiming at evaluation of sphericity form error in cartesian coordinates, an evaluation algorithm of sphericity error by using the minimum circumscribed sphere (MCS) is introduced. In order to evaluate sphericity error accurately, a 3D model of measuring and computing based on cartesian coordinates is established, and geometric curved surface character of circumscribed sphere is studied. As a result, the theory of using geometrical symmetry of intersecting chord to quickly evaluate sphericity error is obtained. The evaluation entia of “2+1”,“3+1”,“4+1”modes for MCS by intersecting chord relation is constructed. The virtual center location produced through intersecting chord twice can determine the position of evaluation point accurately, which means making the evaluation more accurate and reliable. The analysis data and results indicate that the algorithm has high computing speed and evaluating precision, thus providing a new strategy and means for sphericity form error evaluation.

Key words: Cartesian coordinates, Intersecting chord, Minimum circumscribed sphere evaluation, Sphericity error