基于Hausdorff距离的圆锥曲线变步长高精度逼近  

High Accuracy Approximation of Conic with Variable Step Size Based on Hausdorff Distance

作　　者：王健 褚皓宇 张亚欧[3] 赵万生[3] WANG Jian;CHU Haoyu;ZHANG Yaou;ZHAO Wansheng(Nanjing Engineering Institute of Aircraft Systems,AVIC,Nanjing 211100,China;Shanghai Aerospace Control Technology Institute,Shanghai 201108,China;School of Mechanical Engineering,Shanghai Jiao Tong University,Shanghai 200240,China)

机构地区：[1]中国航空工业集团公司金城南京机电液压工程研究中心,江苏南京211100 [2]上海航天控制技术研究所,上海201108 [3]上海交通大学机械与动力工程学院,上海200240

出　　处：《电加工与模具》2025年第S1期81-87,共7页Electromachining & Mould

基　　金：国家自然科学基金项目(52175426)。

摘　　要：具有圆锥曲线边界及型腔的零部件被广泛应用于模具、齿轮制造等工业领域。人们常在CAM系统中采用直线段逼近曲线后生成刀具轨迹。然而,直线逼近达到较高精度时所需的直线段长度较小且数量庞大,易造成机床冲击且加工效率较低。为此,提出了一种基于Hausdorff距离的变步长高精度逼近算法。通过仿真实验对比现有逼近方法,证明所提算法可在保证加工精度的基础上显著提升最小逼近曲线长度、降低加工代码数量。实际加工结果还表明,所提算法可大幅提升固定周期抬刀情况下的电火花成形加工效率。Parts with conic boundaries are widely used in aerospace,mold and die,and gear industries.Short linear segments to approximate curve boundaries for generating machining code are commonly used in computer aided manufacturing(CAM)systems.To achieve the specified approximation accuracy,enormous number of extreme short linear segments are required,resulting in a large number of G01 codes and low machining efficiency.To address this issue,this paper proposes a high accuracy approximation approach,which selects the type of approximate curve according to the geometric characteristics of the curve at the discrete point and adjusts the approximate curve length adaptively on the basis of the Hasudorff distance between the approximate and the original curve,namely Hasudorff-distance-based approximation(HDA).The performance of the HAD is evaluated by solving some typical approximation tasks and the results are compare with those by other approximation methods.Comparison results show that HAD significantly outperforms other counterpart methods in terms of the minimum approximation curve length and approximation error.Experimental outcomes validate that the introduced HDA method markedly enhances the machining efficiency of die-sinking EDM when employing a tool jumping strategy with a constant period.

关 键 词：圆锥曲线逼近 HAUSDORFF距离 变步长 CAM系统 

分 类 号：TG669[金属学及工艺—金属切削加工及机床]