Abstract：A new algorithm for circularity based on fast search for the center of a circle is proposed, according to the definition of roundness of ISO 1101-1983. Through the established mathematical model and algorithm flow, two concentric circles and the center of the circle are quickly searched and found. First, use the least squares method to fit the center of the circle. Then, the moving direction of the circle center is determined according to the farthest point and the closest point from the circle center. The next circle center is searched according to the set step value and the center movement direction. Finally, iterative calculations are performed several times until the roundness meets the requirements. The experimental results show that the roundness calculation error of the proposed algorithm is less than 1μm, and the calculation efficiency is increased by 10 times, compared with the area search method. It can meet the needs of engineering applications.
盛东良,詹剑良,朱丹. 一种基于快速搜索圆心的圆度新算法[J]. 计量学报, 2022, 43(6): 724-728.
SHENG Dong-liang,ZHAN Jian-liang,ZHU Dan. A New Algorithm for Circularity Based on Fast Searching the Center. Acta Metrologica Sinica, 2022, 43(6): 724-728.
［1］ISO 1101-1983. Technical drawings; Geometrical tolerancing; Tolerancing of form, orientation, location, and run out; Generalities, definitions, symbols, indications on drawing ［S］.
［2］Choi W, Kurfess T R, Cagan J. Sampling uncertainty in coordinate measurement data analysis ［J］. Precision Engineering, 1998, 22 (3): 153-163.
［3］Murthy T S R, Abdin S Z. Minimum zone evaluation of surfaces ［J］. International Journal of Machine Tool Design & Research, 1980, 20 (2): 123-136.
［4］Murthy T S R. A comparison of different algorithms for circularity evaluation ［J］. Precision Engineering, 1986,8 (1): 19-23.
［5］Yeralan S, Ventura J A. Computerized roundness inspection ［J］. International Journal of Production Research, 1988, 26 (12): 1921-1935.
［6］Ventura J A, Yeralan S. The minimax center estimation problem for automated roundness inspection ［J］. European Journal of Operational Research, 1989, 41 (1): 64-72.
［7］Lai K, Wang J. A Computational geometry approach to geometric tolerancing［C］//Proceedings of the 16th North American Manufacturing Research Conference. Champaign, Illinois, USA,1988: 376-379.
［8］Le V B, Lee D T. Out-of-roundness problem revisited ［J］. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1991, 13 (3): 217-223.
［9］Huang J. An exact solution for the roundness evaluation problems ［J］. Precision Engineering, 1999, 23 (1): 2-8.
［10］Huang J. A new strategy for circularity problems ［J］. Precision Engineering, 2001, 25 (4): 301-308.
［11］岳武陵, 吴勇. 基于仿增量算法的圆度误差快速准确评定 ［J］. 机械工程学报, 2008, 44 (1): 87-91.
Yue W L, Wu Y. Fast and accurate evaluation of roundness error based on simulation incremental algorithm ［J］. Chinese Journal of Mechanical Engineering, 2008, 44 (1): 87-91.
［12］黄富贵, 郑育. 基于区域搜索的圆度误差评定方法 ［J］. 计量学报, 2008, 29 (2): 117-119.
Huang F G, Zheng Y J. A method for roundness error evaluation based on area hunting ［J］. Acta Metrologica Sinica, 2008, 29 (2): 117-119.
［13］雷贤卿, 畅为航, 薛玉君, 等. 圆度误差的网格搜索算法 ［J］. 仪器仪表学报, 2008,29 (11):2324-2329.
Lei X Q, Chang W H, Xue Y J, et al. Evaluation of roundness error based on mesh search algorithm ［J］. Chinese Journal of Scientific Instrument, 2008, 29 (11): 2324-2329.
［14］王灿, 许本胜, 黄美发. 区域搜索下圆度误差快速精密评定 ［J］. 制造业自动化, 2015, 37 (11): 94-96.
Wang C, Xu B S, Huang M F. The raipd precision evaluation of roundness based on area hunting ［J］. Manufacturing Automation, 2015, 37 (11): 94-96.
［15］张春阳, 雷贤卿, 李济顺, 等. 基于几何优化的圆度误差评定算法 ［J］. 机械工程学报, 2010, 46 (12):8-12.
Zhang C Y, Lei X Q, Li J S, et al. Method for roundness error evaluation based on geometry optimization ［J］. Journal of Mechanical Engineering, 2010, 46 (12): 8-12.
［16］黄富贵, 董兆鹏. 圆度误差评定的线性化处理方法 ［J］. 华侨大学学报, 2011, 32 (5): 492-494.
Huang F G, Dong Z P. Linearization Method of Roundness Error Evaluation Based on Principle of Measuring Coordinate ［J］. Journal of Huaqiao University, 2011, 32 (5): 492-494.
［17］申翠香, 张晓宇. 基于量子遗传算法的圆度误差测量研究 ［J］. 计量学报, 2018, 39 (2): 242-245.
Shen C X, Zhang X Y. Detecting Roundness Error Based on Quantum Genetic Algorithm ［J］. Acta Metrologica Sinica, 2018, 39 (2): 242-245.
2022, Vol. 43 
