Intersecting chord method for minimum zone evaluation of roundness deviation using Cartesian coordinate data

• The intersecting chord method is used to realize the minimum zone model of roundness deviation.
• The position of minimum zone centre is determined by intersecting chords.
• Computational efficiency of modelling process is greatly improved.

Minimum zone evaluation of roundness deviation is a very important and complex problem in precision measurement. Along with the continuous development of precision machining technology, it has become an increasingly prominent issue of how to quickly and accurately evaluate the minimum zone roundness deviation from a large number of coordinate data. In this paper, an intersecting chord method is first proposed to realize the minimum zone model of roundness deviation with coordinate data. The new modelling method uses the crossing relationship of chords to construct the intersecting structure and the 2 + 2 evaluation model of the minimum zone roundness deviation, which can not only accurately determine the position of minimum zone centre but also greatly improve the computational efficiency of modelling process. Using the related chords and their extreme points to generate a virtual centre, this may reduce the deviation between the intersecting chords structure and the centre of the minimum zone evaluation. The proposed method makes use of the geometric relationship of chords, so the minimum zone roundness deviation can be obtained without the optimal method or the point-by-point method. The validation test of the proposed method is designed to analyze a coordinate dataset published in other literature. Comparing the proposed method with the published method, it is easy to show that the relative error between two results is less than 0.4%. Finally, an experiment is also given to indicate that the calculation accuracy and the evaluation efficiency of the proposed method achieve a satisfactory conclusion.