Method for sphericity error evaluation using geometry optimization searching algorithm

• A method for sphericity error evaluation using Geometry Optimization Searching Algorithm (GOSA) is a new sphericity evaluation method.
• The algorithm is no requirement to the distribution of the measure points, and can realize error evaluation to the spherical surface and the spherical cap.
• The algorithm is simple, intuitive and easy to program, and it has the commonality, better astringency and stability.

According to geometrical characteristics of the sphericity error, a new evaluation algorithm for sphericity error based on geometry optimization searching method has been presented. First, the reference point is established and the initial error is calculated by using the measured points, Second, a regular hexahedron of side length f is collocated by taking the reference point as datum point, and the maximum difference of the radius of all measured points are calculated by regarding each vertex of the hexahedron as the centre of the measured spherical surface. Third, the reference point or side length of the hexahedron is changed by comparing the initial error and the maximum difference of the radius. Step by step, the sphericity error value of corresponding evaluation method (including Minimum Zone Sphere method (MZS), Minimum Circumscribed Sphere method (MCS) and Maximum Inscribed Sphere method (MIS)) are obtained. The principle and the steps of using the algorithm to solve the sphericity error are described in detail and the mathematical formula and program flowchart are given. The experimental results show that the sphericity error can be evaluated effectively and exactly with this algorithm.