A simple asymptotic search method for estimation of minimum zone sphericity error

With the rapid development of micromachining technology, sphericity errors have become an important factor that determines product quality; thus, it is critical to establish an algorithm to estimate sphericity errors effectively and accurately. In this paper, an asymptotic search method based on the minimum zone sphere (MZS) is proposed to estimate sphericity errors. A least square sphere center is used as the initial reference center through establishing a search sphere model to gradually approach the MZS center. Then, a quasi-MZS center is determined. According to the definition and geometric structure of the minimum zone sphere, five control points dominating the homocentric spheres are searched. As a result, the MZS center and the sphericity error are obtained. Both simulation experiments and data from the literature are utilized to verify the feasibility and performance. The results indicate that the proposed method is reliable and can estimate sphericity errors efficiently and accurately.