Minimum zone evaluation of sphericity deviation based on the intersecting chord method in Cartesian coordinate system

• Intersecting chord method is proposed to realize the minimum zone evaluation of sphericity deviation.
• The virtual centre generated by the intersecting chords simplifies the model structure of sphericity deviation and reduces the modelling difficulty.
• The MZSP based on the intersecting chord method provides a favourable solution for the evaluation of sphericity deviation.

Along with the developments of manufacturing and machining technology, spherical parts with high-precision are widely applied to many industrial fields. The high-quality spherical parts depend not only on the design and machining techniques but also on the adopted measurement and evaluation approaches. This paper focuses on the minimum zone evaluation model of sphericity deviation in Cartesian coordinate system. A new method, i.e. intersecting chord method, is proposed to solve the problem of constructing 3 + 2 and 2 + 3 models of the minimum zone reference spheres (MZSP). The modelling method employs intersecting chords rather than characteristic points to construct the geometrical structure of evaluation model. Hence, the efficiency of processing data is improved without compromising the accuracy of deviation evaluation. In the modelling process, the two concentric spheres of minimum zone model are simplified as an intersecting chords structure, the virtual centre generated by the intersecting chords can be used to judge whether the searched object is the maximum object or not, which decrease the positioning error of the minimum zone centre and reduce the difficulty of constructing models. To test and verify the performances of intersecting chord method, two experiments are performed to confirm the effectiveness of the proposed method, and the results indicate that the proposed method is more trustworthy against accuracy and computation time than other methods required to achieve the same results.