基于最少圆覆盖的短电弧加工数学模型研究  

Research on Mathematic Model of Short Arc Machining Based on Minimal Circle Coverage

作　　者：杨炳煜 徐雷 龚光富 顾正 蔡岳[1,2] 王恩良 宫婧[1,2] 孙知信[1,2] YANG Bingyu;XU Lei;GONG Guangfu;GU Zheng;CAI Yue;WANG Enliang;GONG Jing;SUN Zhixin(Post Big Data Technology and Application Engineering Research Center of Jiangsu Province,Nanjing University of Posts and Telecommunications,Nanjing,Jiangsu 210003,China;Post Industry Technology Research and Development Center of the State Posts Bureau,Internet of Things Technology,Nanjing University of Posts and Telecommunications,Nanjing,Jiangsu 210009,China;Anhui Yougu Express Intelligent Technology Co.Ltd.,Wuhu,Anhui 241399,China)

机构地区：[1]南京邮电大学江苏省邮政大数据技术与应用工程研究中心,江苏南京210003 [2]南京邮电大学国家邮政局邮政行业技术研发中心(物联网技术),江苏南京210009 [3]安徽邮谷快递智能科技有限公司,安徽芜湖241399

出　　处：《数学建模及其应用》2022年第4期13-23,共11页Mathematical Modeling and Its Applications

基　　金：国家自然科学基金(62272239,61972208)。

摘　　要：在工业上,使用短电弧加工处理物体的表面,达到消除锈蚀、光洁物体等目的,使其可以被进一步加工成为成品零件.为了节约能源,需要使用最少的短电弧覆盖某个物体表面,这就引申出二维平面上的有界集的覆盖问题.本文将该问题抽象为给定一种要求寻找最少覆盖集数量的圆形有界闭集的覆盖问题,并分析了所需小圆数量与大小圆半径比例的关系.本文还通过增加缺失项的思想设计了动态偏移最小圆覆盖算法并分析了在加工中误差对覆盖问题的影响,对任意给定的大圆和小圆进行模拟覆盖实验,并使用两种模型总结出基于半径比-最少数量与半径比-最大面积利用率两套经验公式,并经过验证,曲线拟合效果较好.本实验为覆盖问题提供了一种切实可行的求解方法.In industry, short electrical arc machining is used to treat the surface of an object to eliminate rust and treat the surface so that it can be further processed into finished parts. In order to save energy, it is necessary to use the least short arc to cover the surface of an object, which leads to the coverage problem of bounded sets on a two-dimensional plane. In this paper, this problem is abstracted as a coverage problem that requires finding the minimum number of circular bounded closed sets, and analyzes the relationship between the required number of small circles and the ratio of the radius of the large and small circles. This paper also designed a dynamic offset minimum circle coverage algorithm by adding missing items and analyzed the influence of errors on the coverage problem during processing. Simulated coverage experiments were performed on any given large circle and small circle, and two models were used to summarize Two sets of empirical formulas based on radius ratio-minimum number and radius ratio-maximum area utilization ratio were developed, and after verification, the curve fitting effect is better. This experiment provides a practical solution to the coverage problem.

关 键 词：短电弧加工 欧式空间 有界闭集覆盖问题 圆覆盖问题 动态偏移最小圆覆盖算法 二次回归 非线性最小二乘法求解 

分 类 号：TP391.9[自动化与计算机技术—计算机应用技术]