连续短线段拐角加工路径平滑算法  

Smoothing algorithm for continuous short line segment corner machining paths

作　　者：张剑飞[1] 续娇 ZHANG Jianfei;XU Jiao(School of Computer and Control Engineering,Qiqihar University,Qiqihar 161006,China)

机构地区：[1]齐齐哈尔大学计算机与控制工程学院,黑龙江齐齐哈尔161006

出　　处：《高师理科学刊》2024年第7期52-57,共6页Journal of Science of Teachers＇College and University

基　　金：黑龙江省教育厅基本科研业务专项(145209806);齐齐哈尔市科技计划重点项目(ZDGG-202203)。

摘　　要：数控机床在处理连续拐角路径时,由于存在大量短线段的转接关系,常导致全局路径不连续和不平滑问题.针对该问题,提出了一种最大曲率和最短路径长度约束的路径拐角优化方法.首先,应用曲线曲率与角度之间的映射关系,以齿轮轮廓轨迹为模型,求得平均转角下的最短路径长度,以及五阶样条拟合曲线的最大曲率;然后,通过约束最大曲率和最短路径长度对离散数据点进行插值;最后,采用德布尔三角递推方法再次进行三阶样条曲线拟合,从而获得约束下的平滑拐角路径.实验表明,所提出的方法精度误差在5 mm以内,最大曲率值降低了20%以上,同时B-Spline曲线满足C2连续性,能够有效提高车床的加工效率.When dealing with continuous corner paths on CNC machine tools,the transit relationship of a large number of short segments leads to global path discontinuity and non-smoothness problems,for which a path corner optimization method with maximum curvature and shortest path length constraints is proposed.To address this,the mapping relationship between curve curvature and angle is applied,using the gear profile trajectory as a model to determine the shortest path length under average turning angles and the maximum curvature of a fifth-order spline-fitted curve.Subsequently,interpolation of discrete data points is performed while constraining the maximum curvature and shortest path length.Finally,the De Boor′s recursive triangular method is employed for a second cubic spline curve fitting,resulting in a smooth corner path under the specified constraints.Experimental results demonstrate that the accuracy error of the proposed method is within 5 mm,the curvature maximum is reduced by more than 20%,and the B-Spline curve satisfies C2 continuity at the same time,which can effectively improve the machining efficiency of the lathe.

关 键 词：B-SPLINE 拐角优化 最大曲率 几何连续性 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]