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This paper reports an improved method that integrates a bidirectional search of unequal probability and an offset movement mechanism (BSOM) to evaluate the minimum zone roundness (MZR) with high speed and accuracy. The centre and roundness of a least-squares circle are first solved to construct an original search zone, and the initial candidate points of the minimum zone circle centre are configured. A bidirectional search of unequal probability that considers the subsequent points either toward or away from the current best candidate point is designed to enhance the global search ability. Considering the candidate points at different located positions have different effects on convergence characteristics, the search area is divided into two sections based on the average distance between the current best candidate point and the other candidate points, and different forward and backward search probabilities are configured. An adaptive offset movement mechanism is integrated to generate new candidate points for the next generation. The effectiveness of the proposed method is experimentally verified using datasets from previous studies. The configurations of BSOM parameters and influence of the distribution and number of data points on evaluation accuracy and efficiency are analyzed. The experimental examples and comparison results demonstrate the excellent convergence performance of the proposed method, which reaches the global optimum faster than previous methods. Across six different datasets, only 0.0095 s–0.0282 s is required when the average distance D  ⩽  1.0  ×  10−7 mm as the iteration convergence condition, and the standard deviation of the MZR is less than 5.3777  ×  10−9 mm, while the search parameters are set as P1  =  0.6, P2  =  0.95, and b  =  0.6. The proposed approach is expected to be suitable for on-line evaluation of roundness error.

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This study proposes a high speed and accurate evaluation method for minimum zone roundness (MZR) using an optimal solution guidance algorithm (OSGA). The least-square center and roundness determine an original search zone, then the initial candidate points are configured as the centers of a minimum zone circle (MZC). To enhance the global search ability, subsequent candidate points follow the current optimal candidate points. The best three current candidate points jointly generate the new candidate points for the next iteration. In addition, a dynamic search zone updating strategy is proposed to achieve fast convergence of the optimal solution. The width of the search zone varies with the number of iterations required to achieve this rapid convergence. The effectiveness and performance of the proposed method are validated using datasets from previous studies. The proposed OSGA achieves excellent convergence performance, and reaches the global optimal solutions more quickly than previous methods. Across four different datasets, the termination condition is satisfied in only 0.0031-0.0058 s, the optimal solutions are obtained within 5-15 iterations, and the standard deviation of the MZR is less than 5.8276 × 10 −6 mm. The proposed method is also expected to extend to rapid and high-precision evaluation of cylindricity or straightness.

Aiming to develop a more effective circularity evaluation method that satisfies the definition of a particular reference circle criterion, this paper proposes a strategy to determine the minimum circumscribed circle (MCC) and maximum inscribed circle (MIC) using the subzone division approach. The whole circumference zone space that encloses all the sampling data points is divided into different subzones to determine the target candidate feature points, which are used for constructing the MCC or MIC. The first feature point of the MCC/MIC is evaluated according to the farthest/nearest distance from the center of the least squares circle (LSC) within the whole circumference subzone. Subzone with a 120° central angle is designated in the direction of the first feature point that is mapped about the center of the LSC. The second candidate feature point is constrained and determined within this subzone. The third subzone, which contains the third feature point, is formed in the direction of the first and second feature points that are mapped about the center of the LSC. The mathematical model of the MCC or MIC is then constructed using these three feature points. Experimental examples (using five different datasets) and a comparison with previous studies demonstrate that the proposed method yields the exact solution for the MIC and MCC in only 1–2 iterations.