Sphericity error united evaluation using particle swarm optimization technique

Spheres are widely used in many engineering applications and spherical geometric errors have a serious effect on the performance of mechanical parts. There are three methods commonly used to evaluate sphericity error. They are: minimum zone sphere (MZS) method, minimum circumscribed sphere (MCS) method and maximum inscribed sphere (MIS) method. In this paper, Particle swarm optimization (PSO) inspired by bird flocking and human social relations is proposed to implement the above three sphericity errors evaluation simultaneously. Particles adjust their velocity according to the individual´s best position ever found and the best position of all particles. Then, examples are presented to illustrate the effectiveness of the proposed method. Finally, the experimental results evaluated by different methods confirm that the proposed method can find the optimal solutions of the three methods. In comparison with existing evaluation methods, the algorithm is not only easier to implement and there are fewer parameters to adjustt, but also it unifies the three kinds of sphericity error evaluation. Also, it overcomes the drawback of Least Square Method (LSM) that does not guarantee the minimum zone solution specified in the ISO (1101) standard and can result in overestimation of form tolerances and the rejection of good parts.