TH5632C 型立式加工中心曲面加工计算机辅助编程
|
摘要
本文以实现在小型三坐标二联动立式加工中心TH5632C上加工曲面的计算机辅助编程为目的。对于二轴联动的数控加工中心，实现加工曲面的方式一般是采用球头铣刀，通过把曲面剖切成平行于某轴的平面曲线，再用直线、圆弧、抛物线去拟合该平面曲线，最终对每一条曲线加工集合成曲面。
结合国内外的应用现状，论文综合分析了在数控加工中，用直线段及圆弧段来拟合和逼近非圆曲线及列表曲线的常用处理方法及算法，在此基础上，对于平面非圆曲线的加工预处理，提出用等误差直线逼近非圆曲线的近似算法——逐点逼近法、伸缩步长法；而对于列表曲线的加工预处理，则先采用累加弦长三次参数样条曲线拟合列表曲线，再以双圆弧来逼近三次参数样条曲线，最终求得列表曲线的节点坐标。在满足加工精度和实时性要求的条件下，本文采用C语言实现上述算法。
论文的开始对数控编程中数值计算的内容和要求作了简要介绍，其中节点坐标数据的计算是数值计算中最烦琐、最复杂的计算。逼近误差δ≤δ_允以及加工实时性要求是针对任何平面轮廓曲线寻找其最佳的节点算法的重要依据和必要条件。
用直线段逼近非圆曲线的算法总体来说有以下三种，即：等间距法—使每段逼近直线在X轴上的投影相等；等弦长法—使每段逼近直线的长度相等；等误差法—使每段逼近直线与轮廓曲线的最大误差相等。本文用C语言实现了以上算法的计算机程序，该程序可完成抛物线，椭圆和双曲线三种常用曲线的计算机插补节点计算，同时给出使用说明。
用圆弧段逼近非圆曲线，目前常用的方法有曲率圆法，三点圆法和相切圆法等。本文主要探讨采用双圆弧法逼近非圆曲线，并给出其算法流程。
对于列表曲线，本文采用三次参数样条函数对列表曲线进行第一次拟合，然后用双圆弧样条进行第二次逼近的算法，并用C语言结合实例给出了计算程序和计算结果。
本文还通过旋转曲面零件的数控加工实践，对二坐标联动加工时直线插补步长、行距及球刀半径的选择进行了探讨。
The thesis aims to design the computer-aided program for the curved face machining based on the small three coordinate axes vertical machine center. In the two axes linked numerical control machine center, the spherical cutter is firstly used to subdivide the curved face to a plane curve that is parallel to one axis. Then the line, the arc and the parabola are adopted to form a fitted curve. Finally, the curved face is aggregated by each curve.
Based on the analysis of the present domestic and overseas situation, the thesis discusses the normal techniques and arithmetic of fitting and approaching non-circularity curves and tabulate curves by line and arc in the numerical control milling. For the pretreatment of the plane non-circularity curve, the thesis then points out the approximate arithmetic of non-circularity curve, namely the point-to-point approaching and the flexible steps method, by using equal error line approaching. While for the pretreatment of the tabulate curves, the first step is to approach tabulate curves with accumulating cube parameter style curves. Then the double-arc is adopted to fit the cube parameter style curve. Finally the coordinate of nodes on the tabulate curve is calculated. Meeting the requirement of cut accuracy and real-time control, the thesis aims at achieving the above algorithm with C Language. Meanwhile, the summary of the advantages and disadvantages of each the algorithm lays the foundation for its implement
ation in the numerical control system and plotting system.
Therefore, the thesis has been organized in the following way.
Firstly, it will summarize the contents and requirements of numerical computation in the numerical program, in which the calculation of nodes coordination may be the most complicated. The approaching error δ≤δ允 and the real-time control are important and necessary during the selection of optimum nodes algorithm for configuration.
There are three algorithms in the approaching non-circularity curve with line, namely the equal interval algorithm, the equal arc algorithm and the equal error algorithm. In the thesis, the computer programs of these algorithms will be realized with C Language. Furthermore, these programs can realize the computer interpolate nodes algorithm of three normal curves, including parabola, ellipse and
hyperbola.
There are also three algorithms in the approaching non-circularity curve with arc, namely the circum flexion algorithm, the three-point circle method and the tangency circle algorithm. In the thesis, the double-arc algorithm and its flowchart will be mainly discussed in approaching non-circularity curve.
For the tabulate curve, the cube parameter style curve will be firstly adopted to fit the curve. Then the double-arc style curve will be implemented. The computer program and the running results with C Language will be included in this section based on examples.
Finally, the thesis will discuss the selection of step length, string space and radius of spherical cutter in the three coordinate axes and two axes linked machining center based on the practice of NC machining for revolution surface parts.
结合国内外的应用现状，论文综合分析了在数控加工中，用直线段及圆弧段来拟合和逼近非圆曲线及列表曲线的常用处理方法及算法，在此基础上，对于平面非圆曲线的加工预处理，提出用等误差直线逼近非圆曲线的近似算法——逐点逼近法、伸缩步长法；而对于列表曲线的加工预处理，则先采用累加弦长三次参数样条曲线拟合列表曲线，再以双圆弧来逼近三次参数样条曲线，最终求得列表曲线的节点坐标。在满足加工精度和实时性要求的条件下，本文采用C语言实现上述算法。
论文的开始对数控编程中数值计算的内容和要求作了简要介绍，其中节点坐标数据的计算是数值计算中最烦琐、最复杂的计算。逼近误差δ≤δ_允以及加工实时性要求是针对任何平面轮廓曲线寻找其最佳的节点算法的重要依据和必要条件。
用直线段逼近非圆曲线的算法总体来说有以下三种，即：等间距法—使每段逼近直线在X轴上的投影相等；等弦长法—使每段逼近直线的长度相等；等误差法—使每段逼近直线与轮廓曲线的最大误差相等。本文用C语言实现了以上算法的计算机程序，该程序可完成抛物线，椭圆和双曲线三种常用曲线的计算机插补节点计算，同时给出使用说明。
用圆弧段逼近非圆曲线，目前常用的方法有曲率圆法，三点圆法和相切圆法等。本文主要探讨采用双圆弧法逼近非圆曲线，并给出其算法流程。
对于列表曲线，本文采用三次参数样条函数对列表曲线进行第一次拟合，然后用双圆弧样条进行第二次逼近的算法，并用C语言结合实例给出了计算程序和计算结果。
本文还通过旋转曲面零件的数控加工实践，对二坐标联动加工时直线插补步长、行距及球刀半径的选择进行了探讨。
The thesis aims to design the computer-aided program for the curved face machining based on the small three coordinate axes vertical machine center. In the two axes linked numerical control machine center, the spherical cutter is firstly used to subdivide the curved face to a plane curve that is parallel to one axis. Then the line, the arc and the parabola are adopted to form a fitted curve. Finally, the curved face is aggregated by each curve.
Based on the analysis of the present domestic and overseas situation, the thesis discusses the normal techniques and arithmetic of fitting and approaching non-circularity curves and tabulate curves by line and arc in the numerical control milling. For the pretreatment of the plane non-circularity curve, the thesis then points out the approximate arithmetic of non-circularity curve, namely the point-to-point approaching and the flexible steps method, by using equal error line approaching. While for the pretreatment of the tabulate curves, the first step is to approach tabulate curves with accumulating cube parameter style curves. Then the double-arc is adopted to fit the cube parameter style curve. Finally the coordinate of nodes on the tabulate curve is calculated. Meeting the requirement of cut accuracy and real-time control, the thesis aims at achieving the above algorithm with C Language. Meanwhile, the summary of the advantages and disadvantages of each the algorithm lays the foundation for its implement
ation in the numerical control system and plotting system.
Therefore, the thesis has been organized in the following way.
Firstly, it will summarize the contents and requirements of numerical computation in the numerical program, in which the calculation of nodes coordination may be the most complicated. The approaching error δ≤δ允 and the real-time control are important and necessary during the selection of optimum nodes algorithm for configuration.
There are three algorithms in the approaching non-circularity curve with line, namely the equal interval algorithm, the equal arc algorithm and the equal error algorithm. In the thesis, the computer programs of these algorithms will be realized with C Language. Furthermore, these programs can realize the computer interpolate nodes algorithm of three normal curves, including parabola, ellipse and
hyperbola.
There are also three algorithms in the approaching non-circularity curve with arc, namely the circum flexion algorithm, the three-point circle method and the tangency circle algorithm. In the thesis, the double-arc algorithm and its flowchart will be mainly discussed in approaching non-circularity curve.
For the tabulate curve, the cube parameter style curve will be firstly adopted to fit the curve. Then the double-arc style curve will be implemented. The computer program and the running results with C Language will be included in this section based on examples.
Finally, the thesis will discuss the selection of step length, string space and radius of spherical cutter in the three coordinate axes and two axes linked machining center based on the practice of NC machining for revolution surface parts.
引文
[1] 毕承恩、丁乃建等编著．现代数控机床上、下册．北京：机械工业出版社．出版年：1991
[2] 《实用数控加工技术》编委会编．实用数控加工技术．北京：兵器工业出版社．出版年：1995
[3] 王爱玲、沈全兴等主编．现代数控编程技术及应用．北京：国防工业出版社．出版年：2002
[4] 刘雄伟等编著．数控加工理论及编程技术．第二版．北京：机械工业出版社．出版年：1994[]
[5] 唐建主编．数控加工及程序编制基础．北京：机械工业出版社．出版年：2000
[6] 《加工中心应用与维修》编委会编．加工中心应用与维修．北京：机械工业出版社．出版年：1992
[7] 曾小慧．吴明华．周济．戴同．数控加工教学仿真系统的设计与开发．组合机床与自动化加工技术．1996．NO．12
[8] 吴祖育．秦鹏飞主编．数控机床．北京：机械工业出版社．出版年：1994．
[9] 温宝俊、唐文献等编著．数控机床加工程序编制及设计制造一体化．中国标准出版社．出版年：1998
[10] 唐浩强编著．C程序设计．清华大学出版社．出版年：1997
[11] Jani Shan. Survey of CAD/feature Based Process and NC Programming Techniques. Computer_Aided Engineering Journal. 1991. No.4
[12] 李浙昆、樊瑜瑾、杨晓京、任伟．NC加工刀具轨迹设计中的几个优化问题．机械设计与制造．1999．NO．4
[13] Kunwoo Li et al. Generation of toolpath with selection of proper tools for rough cutting process. Computer_Aided design. 1994. Vol.26
[14] Suh 、Ys et al. Nc milling tool path generation for arbitrary pockets definded by sculptured surfaces.. Computer_Aided design. 1990. Vol.22
[15] 寇有顺、倪亚萍等编著．数控机床编程．北京理工大学出版社．出版年：1996
[16] 王强如、李兰友编著．C语言绘图与计算机仿真技术．北京航空航天大学
出版社．出版年：1996
[17] 葛研军、王启义．数控铣床图像编程与仿真系统的研究．制造技术与机床．1998．NO．4
[18] 赵良才、范牧昌等编．数控机床程序编制．镇江航泊学院出版社．出版年：1999
[19] L C.C. A new approach to CNC tool path generation. Computer_Aided design. 1998.30(8)
[20] Lee Y S、Chang T C. Application of computational geometry optimizing 2.5D or 3D NC surface machining. Computers in Industry. 1995.26
[21] Park S.C、Chio B.K. Tool-path planning for direction-parallel area milling. Computer Aided Design. 2000 (32)
[22] Presson H. NC machining of arbitrary shaped pockets. Computer Aided Design. 1978.10(3)
[23] Guyder M.K. Automating the optimization of 2-1/2 axis milling. Computer Aided Design. 1990. Vol.15
[24] Cox J.J. Space-filling curves in tool-path application. Computer Aided Design. 1994. Vol.26
[25] Lambergts C.A.H. An efficient automatic tool-path generator for 2.5D free-form pockets. Computer in Industry. 1998. Vol.29
[26] 于华主编．数控机床的编程及实例．北京．机械工业出版社．出版年：1996
[27] 阮世勋、张建峰、雷运青．基于双圆弧法精确加工母线为非圆曲线工件．机械加工自动化．2003．NO．3
[28] 郭培全．非圆曲线的最少节点拟合法．组合机床与自动化加工技术．1998．NO．7
[29] 余世林、朱国宝．数控加工中列表曲线的数学处理．武汉交通科技大学学报．2003．NO．3
[30] 陈艳红．基于VB的数控编程数值处理．机床与液压．2003．NO．5
[31] 陈明君、赵清亮、董申、李旦．基于双圆弧步长伸缩数控插补非圆曲线算法的研究．机械工程学报．2003．NO．1
[32] 魏绍凯、邝自强、郑叔芳、张乐年．叶型列表曲线自适应算法．燃气轮机技术．2001．
[33] 范云霄、郑轶、于涛、杨俊茹．等误差直线逼近非圆曲线的节点计算及刀
具轨迹模拟．工具技术．2002
[34] 郭培全、藤浩．非圆曲线的最小拟合误差逼近法．机械工艺师．1999．NO．6
[35] 庄严．经济型数控机床加工非圆弧曲线的切线法节点计算．新技术新工艺．2001．NO．8
[36] 焦永和、郝永平、刘鹤杰．计算机图形学．北京理工大学出版社．出版年：1998．
[37] 庞琳、宋利．数控加工非圆曲线轮廓的节点坐标优化算法．焦作工学院学报．2002．NO．5
[38] 全国数控培训网络天津分中心主编．数控编程．北京．机械工业出版社．出版年：1999
[39] 房京．李世杰．NURBS自由曲线、曲面的等距算法及其在数控加工中的应用．河北工业大学学报．2002．NO．5
[40] Albert Herrsecher、Wolf gang Walter. Programming system for workshop and work preparation. Industry And Production Engineering. 1989. Vol.2
[41] Millan K Yeung etc . Curve fitting with arc splines for NC tool path generation. Computer Aided Design. 1994. Vol.26
[42] Loney G C. Ozsoy T M. NC machining of free form surfaces. Computer Aided Design. 1987. Vol.2
[43] Wood C D. Skinning techniques for interactive B-spline surfaces interpolation. Computer Aided Design. 1998. Vol.20
[44] Hwang J S. Interference-free tool-path generation in the NC machining of parametric compound surfaces. Computer Aided Design. 1992. Vol.24
[45] Choi B K, Special Issue. NC machining and cutter path generation. Computer Aided Design. 1994. Vol.26
[46] 姜慧．董黎敏．吴会林．牛占文．徐燕申．回转类零件自由曲线CAD／CAM集成的实现．天津大学学报．1996．NO．4
[47] 庄品．复杂曲面数控加工自动编程及其干涉处理算法研究．南京航空航天大学硕士学位论文．答辩年份：1999．
[48] 孟雅琴．叶正麟．CAD／CAM中常用曲线之间的转换．航空计算技术．1996．NO．2
[49] 赵海信．基于拟实制造技术的数控自动编程系统的研究．武汉理工大学硕士学位论文．答辩年份：2001
[50] 谢叻．曲面造型和多坐标数控编程的研究．上海交通大学博士论文．2001
[2] 《实用数控加工技术》编委会编．实用数控加工技术．北京：兵器工业出版社．出版年：1995
[3] 王爱玲、沈全兴等主编．现代数控编程技术及应用．北京：国防工业出版社．出版年：2002
[4] 刘雄伟等编著．数控加工理论及编程技术．第二版．北京：机械工业出版社．出版年：1994[]
[5] 唐建主编．数控加工及程序编制基础．北京：机械工业出版社．出版年：2000
[6] 《加工中心应用与维修》编委会编．加工中心应用与维修．北京：机械工业出版社．出版年：1992
[7] 曾小慧．吴明华．周济．戴同．数控加工教学仿真系统的设计与开发．组合机床与自动化加工技术．1996．NO．12
[8] 吴祖育．秦鹏飞主编．数控机床．北京：机械工业出版社．出版年：1994．
[9] 温宝俊、唐文献等编著．数控机床加工程序编制及设计制造一体化．中国标准出版社．出版年：1998
[10] 唐浩强编著．C程序设计．清华大学出版社．出版年：1997
[11] Jani Shan. Survey of CAD/feature Based Process and NC Programming Techniques. Computer_Aided Engineering Journal. 1991. No.4
[12] 李浙昆、樊瑜瑾、杨晓京、任伟．NC加工刀具轨迹设计中的几个优化问题．机械设计与制造．1999．NO．4
[13] Kunwoo Li et al. Generation of toolpath with selection of proper tools for rough cutting process. Computer_Aided design. 1994. Vol.26
[14] Suh 、Ys et al. Nc milling tool path generation for arbitrary pockets definded by sculptured surfaces.. Computer_Aided design. 1990. Vol.22
[15] 寇有顺、倪亚萍等编著．数控机床编程．北京理工大学出版社．出版年：1996
[16] 王强如、李兰友编著．C语言绘图与计算机仿真技术．北京航空航天大学
出版社．出版年：1996
[17] 葛研军、王启义．数控铣床图像编程与仿真系统的研究．制造技术与机床．1998．NO．4
[18] 赵良才、范牧昌等编．数控机床程序编制．镇江航泊学院出版社．出版年：1999
[19] L C.C. A new approach to CNC tool path generation. Computer_Aided design. 1998.30(8)
[20] Lee Y S、Chang T C. Application of computational geometry optimizing 2.5D or 3D NC surface machining. Computers in Industry. 1995.26
[21] Park S.C、Chio B.K. Tool-path planning for direction-parallel area milling. Computer Aided Design. 2000 (32)
[22] Presson H. NC machining of arbitrary shaped pockets. Computer Aided Design. 1978.10(3)
[23] Guyder M.K. Automating the optimization of 2-1/2 axis milling. Computer Aided Design. 1990. Vol.15
[24] Cox J.J. Space-filling curves in tool-path application. Computer Aided Design. 1994. Vol.26
[25] Lambergts C.A.H. An efficient automatic tool-path generator for 2.5D free-form pockets. Computer in Industry. 1998. Vol.29
[26] 于华主编．数控机床的编程及实例．北京．机械工业出版社．出版年：1996
[27] 阮世勋、张建峰、雷运青．基于双圆弧法精确加工母线为非圆曲线工件．机械加工自动化．2003．NO．3
[28] 郭培全．非圆曲线的最少节点拟合法．组合机床与自动化加工技术．1998．NO．7
[29] 余世林、朱国宝．数控加工中列表曲线的数学处理．武汉交通科技大学学报．2003．NO．3
[30] 陈艳红．基于VB的数控编程数值处理．机床与液压．2003．NO．5
[31] 陈明君、赵清亮、董申、李旦．基于双圆弧步长伸缩数控插补非圆曲线算法的研究．机械工程学报．2003．NO．1
[32] 魏绍凯、邝自强、郑叔芳、张乐年．叶型列表曲线自适应算法．燃气轮机技术．2001．
[33] 范云霄、郑轶、于涛、杨俊茹．等误差直线逼近非圆曲线的节点计算及刀
具轨迹模拟．工具技术．2002
[34] 郭培全、藤浩．非圆曲线的最小拟合误差逼近法．机械工艺师．1999．NO．6
[35] 庄严．经济型数控机床加工非圆弧曲线的切线法节点计算．新技术新工艺．2001．NO．8
[36] 焦永和、郝永平、刘鹤杰．计算机图形学．北京理工大学出版社．出版年：1998．
[37] 庞琳、宋利．数控加工非圆曲线轮廓的节点坐标优化算法．焦作工学院学报．2002．NO．5
[38] 全国数控培训网络天津分中心主编．数控编程．北京．机械工业出版社．出版年：1999
[39] 房京．李世杰．NURBS自由曲线、曲面的等距算法及其在数控加工中的应用．河北工业大学学报．2002．NO．5
[40] Albert Herrsecher、Wolf gang Walter. Programming system for workshop and work preparation. Industry And Production Engineering. 1989. Vol.2
[41] Millan K Yeung etc . Curve fitting with arc splines for NC tool path generation. Computer Aided Design. 1994. Vol.26
[42] Loney G C. Ozsoy T M. NC machining of free form surfaces. Computer Aided Design. 1987. Vol.2
[43] Wood C D. Skinning techniques for interactive B-spline surfaces interpolation. Computer Aided Design. 1998. Vol.20
[44] Hwang J S. Interference-free tool-path generation in the NC machining of parametric compound surfaces. Computer Aided Design. 1992. Vol.24
[45] Choi B K, Special Issue. NC machining and cutter path generation. Computer Aided Design. 1994. Vol.26
[46] 姜慧．董黎敏．吴会林．牛占文．徐燕申．回转类零件自由曲线CAD／CAM集成的实现．天津大学学报．1996．NO．4
[47] 庄品．复杂曲面数控加工自动编程及其干涉处理算法研究．南京航空航天大学硕士学位论文．答辩年份：1999．
[48] 孟雅琴．叶正麟．CAD／CAM中常用曲线之间的转换．航空计算技术．1996．NO．2
[49] 赵海信．基于拟实制造技术的数控自动编程系统的研究．武汉理工大学硕士学位论文．答辩年份：2001
[50] 谢叻．曲面造型和多坐标数控编程的研究．上海交通大学博士论文．2001