A simple unified branch-and-bound algorithm for minimum zone circularity and sphericity errors

Zheng, Y.

doi:10.1088/1361-6501/ab4d1d

Cited by 11 publications

(8 citation statements)

References 34 publications

(37 reference statements)

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“…However, the ISO and ASME standards lack explicit methodologies for implementing the minimum zone criterion [ 23 , 24 , 25 ]. Furthermore, evaluating this dataset based on the minimum zone criterion involves non-differentiable and unconstrained problems [ 26 , 27 , 28 ]. Meeting the requirements for speed, accuracy, and robustness in the HSR manufacturing process presents a significant challenge for algorithms that evaluate sphericity error based on the minimum zone criterion.…”

Section: Introductionmentioning

confidence: 99%

An Adaptive Multi-Population Approach for Sphericity Error Evaluation in the Manufacture of Hemispherical Shell Resonators

Zhao,

Cui,

Bian

et al. 2024

Sensors

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The performance of a hemispherical resonant gyroscope (HRG) is directly affected by the sphericity error of the thin-walled spherical shell of the hemispherical shell resonator (HSR). In the production process of the HSRs, high-speed, high-accuracy, and high-robustness requirements are necessary for evaluating sphericity errors. We designed a sphericity error evaluation method based on the minimum zone criterion with an adaptive number of subpopulations. The method utilizes the global optimal solution and the subpopulations’ optimal solution to guide the search, initializes the subpopulations through clustering, and dynamically eliminates inferior subpopulations. Simulation experiments demonstrate that the algorithm exhibits excellent evaluation accuracy when processing simulation datasets with different sphericity errors, radii, and numbers of sampling points. The uncertainty of the results reached the order of 10−9 mm. When processing up to 6000 simulation datasets, the algorithm’s solution deviation from the ideal sphericity error remained around −3 × 10−9 mm. And the sphericity error evaluation was completed within 1 s on average. Additionally, comparison experiments further confirmed the evaluation accuracy of the algorithm. In the HSR sample measurement experiments, our algorithm improved the sphericity error assessment accuracy of the HSR’s inner and outer contour sampling datasets by 17% and 4%, compared with the results given by the coordinate measuring machine. The experiment results demonstrated that the algorithm meets the requirements of sphericity error assessment in the manufacturing process of the HSRs and has the potential to be widely used in the future.

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Section: Introductionmentioning

confidence: 99%

An Adaptive Multi-Population Approach for Sphericity Error Evaluation in the Manufacture of Hemispherical Shell Resonators

Zhao,

Cui,

Bian

et al. 2024

Sensors

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“…According to the standards set by the American Society of Mechanical Engineers (ASME) and the International Organization for Standardization (ISO) [6,7], the processing of datasets can be executed by applying four distinct criteria: the least squares criterion, the minimum circumscribed criterion, the maximum inscribed criterion, and the minimum zone criterion. The minimum zone criterion is the general default criterion for evaluating the sphericity error [8][9][10]. The aforementioned criterion enables the acquisition of a unique minimum sphericity error, and it is also the arbitration method when there is inconsistency in the evaluation of the sphericity error.…”

Section: Introductionmentioning

confidence: 99%

A Novel Approach for High-Precision Evaluation of Sphericity Errors Using Computational Geometric Method and Differential Evolution Algorithm

Zhao,

Cui,

Wang

et al. 2023

Applied Sciences

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The sphericity error is a critical form and position tolerance for spheres. We explored the distribution of sphericity errors within the solution space to achieve a high-precision evaluation using the minimum zone criteria. Within local solution spaces, we propose treating the evaluation of sphericity errors as a unimodal function optimization task. And computational geometric methods are employed to achieve highly accurate solutions within the local solution spaces. Subsequently, we integrated the computational geometric method with the differential evolution algorithm (DE algorithm). By centering on individual population members of the DE algorithm, we partitioned the local solution spaces and utilized the best solutions within them to optimize the population. With the gradual convergence of the DE algorithm, we successfully achieved the high-precision resolution of sphericity errors. The experimental results demonstrate a significant order-of-magnitude improvement in precision compared to traditional algorithms in the field of sphericity error evaluation, with uncertainty levels reaching magnitudes of 10−14 mm. Moreover, this method enhances the accuracy of sphericity error evaluation by approximately 10% for three-coordinate measuring machines. Additionally, we conducted ablation experiments to validate the effectiveness of the proposed computational geometric method. In summary, this approach enables the high-precision evaluation of sphericity errors and provides a practical methodology for applying ultra-precision spheres in precision engineering.

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“…Rossi and Lanzetta [13] proposed a exhaustive mesh based approach to find the MZC. Zheng [14] presents a branch and bound algorithm to compute the minimum zone circularity. Huang et al [15] propose a MZC algorithm by integrating a bidirectional search of unequal probability and offset movement mechanism.…”

Section: Introductionmentioning

confidence: 99%

New accurate algorithms of circularity evaluation

Zhuo¹,

Geng²,

Zhong³

et al. 2022

Meas. Sci. Technol.

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The minimum circumscribed circle (MCC), maximum inscribed circle (MIC), and minimum zone circle (MZC) methods for circularity evaluation are difficult to execute due to the lack of specific rules in mathematics, especially the MZC. New accurate algorithms have been proposed to realize the MIC, MCC and MZC evaluation methods. First, the diameter criterion and acute triangle criterion of control points defining the MIC or MCC are presented. The definition of the crossing sector structure is introduced in the minimum zone criterion and transformed into an angular relationship of control points, making it easy to identify the MZC. Then the key points of the algorithms are presented in details including the initial circle or the initial region, centre moving direction, minimum step size and updating rules of control points. Flow charts are provided to make the algorithm producible. Finally, four cases are selected to demonstrate the advantages of the algorithms. The results show that the proposed MZC algorithm is more general than that in the published reference. Compared to the traditional ergodic searching algorithms, the efficiency of the new algorithm for the MIC, the MCC and the MZC evaluations of circularity can be improved by 100% when the point set increases to 100 and above.

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A simple unified branch-and-bound algorithm for minimum zone circularity and sphericity errors

Cited by 11 publications

References 34 publications

An Adaptive Multi-Population Approach for Sphericity Error Evaluation in the Manufacture of Hemispherical Shell Resonators

An Adaptive Multi-Population Approach for Sphericity Error Evaluation in the Manufacture of Hemispherical Shell Resonators

A Novel Approach for High-Precision Evaluation of Sphericity Errors Using Computational Geometric Method and Differential Evolution Algorithm

New accurate algorithms of circularity evaluation

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