Minimum Circumscribed Circle and Maximum Inscribed Circle of Roundness Deviation Evaluation with Intersecting Chord Method

Along with the development of precision machining technology, the quality of cylinder surfaces has become the primary factor in deciding whether the quality of parts meets the requirements of high performance or not. In precision machining of cylinders, the measurement and evaluation of roundness deviation is an indispensable component to quantify form tolerance. This paper focuses on the modeling method of roundness deviation. A new modeling method of an evaluation model, i.e., the intersecting chord method, is proposed to address the minimum circumscribed circle (MCCI) and maximum inscribed circle (MICI) in the evaluation of roundness deviation. The method depends on the geometric structure of the intersecting chords, and the chord is used as the main element of modeling rather than as the characteristic point as in earlier methods. Therefore, the virtual center produced by the structure of intersecting chords can accurately locate the endpoint positions of characteristic chords and the center of the reference circle. The modeling process with intersecting chords does not determine the search direction and step size in each iteration, which can reduce the number of iterations and mitigate the difficulty in modeling. Finally, these theoretical studies are verified through comparative verifications and experiments, and the results show that the intersecting chord method can not only quickly construct the MCCI and MICI models but also accurately quantify roundness deviation.