摘要
在数控加工中,通常用小线段表达刀位轨迹,会导致刀位点庞大且轨迹不平滑。基于Akima曲线具有光顺连接且端点连接处保证G1以上连续,将刀位点拟合成Akima样条曲线,提出了Akima刀位轨迹的递推式拟合算法。该算法可概述为:在刀位点数大于三个的前提下拟合首段Akima样条曲线,保留并延用段末刀位点的切线矢量以保证拟合曲线的凸凹性,然后以该段段末点为下一段的起点,在相邻刀位点间利用弧长参数化计算下一个刀位点的切线矢量,进而生成一段Akima样条。同样延用该段段末刀位点的切线矢量并作为下一段的起点,在相邻刀位点间以递推式拟合生成Akima样条曲线,以此循环至终点。利用UG软件生成了内含388个刀位点的文字模型,通过Matlab编程和仿真实验,以拟合曲线总弧长为评价参数,验证了算法的有效性。
In NC machining,tool-path was usually expressed by short-line segment,which could result in the magnititude of the cutter location（CL） points whose trajectory was unsmooth. The CL points were fitted into Akima spline curve with its advantages of smooth junction and the node points for over G1-continuity,thus the Akima algorithm for tool-path with recursion curve-fitting is proposed. The algorithm can be summarized：the first Akima spline curve,in the condition of outnumbering three CL points,is fitting and the tangent vector of the end CL point of the segment is preserved and followed to ensure the concavity and the convexity of the fitting curve,then the end point is regarded as the start one of the next segment,and the tangent vector of the next CL point will be calculated by the the arc-length parameterization between the adjoining point,then the Akima spline can be produced. The tangent vector of the end one of the very segment,in the same way,will continue to be used as the start point of the next one,so the Akima spline curve will be generated via the recursion curve-fitting between the adjacent CL point,as the circle to the end. The model of the characteristic sole（consists of 388 CL points） is generated by ultilizing UG software. Meanwhile,the number of the final fitting segments and the arc-length of the fitting curve,through Matlab programming and simulation experiment,are used as the evaluating parameters to validate the effectiveness of the algorithm.
作者
周鹏
吴继春
周会成
杨世平
李明富
刘金刚
ZHOU Peng WU Ji-chun ZHOU Hui~cheng YANG Shi-ping LI Ming-fu LIU Jin-gang(The Engineering Center of Ministry of Education of Complex Trajectory Processing Technology and Equip- ment, Xiangtan University, Xiangtan Hunan 411105, China The Research Center of Engineering Technology of National Numerical Control System, Huazhong University of Science and Technology, Wuhan 430074,China)
出处
《组合机床与自动化加工技术》
北大核心
2017年第9期27-30,共4页
Modular Machine Tool & Automatic Manufacturing Technique
基金
国家自然科学基金项目资助(51575210
51575466
51475402)
省自然联合基金(2017JJ4053)
省教育厅创新平台(17K091)
关键词
小线段
Akima算法
弧长参数
递推式拟合
short-line segment
Akima algorithm
arc-length parameterization
recursion curve-fitting
