圆锥样条合成矢量插补及C机能刀补
|
摘要
插补精度是数控系统的重要指标之一,插补算法的好坏决定着数控系统的性能优劣。传统的插补算法多以直线、圆弧为主要插补对象,随着椭圆、抛物线等圆锥曲线在数控加工中越来越多的应用,简单的直线或圆弧插补算法已不能满足现代高精度数控加工的要求。圆锥样条由彼此相邻圆锥曲线首尾连接组成,目前已成为CAD系统中对复杂型工件的通用描述形式。采用圆锥样条拟合工件轮廓,可以保证拟合曲线具有更小的拟合误差。本文研究了适合圆锥样条加工的通用合成矢量插补算法,并在此基础上解决了圆锥曲线衔接处的尖角和内角自动过渡问题。圆锥样条合成矢量插补及C机能刀补主要内容包括:
(1)综述了数控插补技术及C机能刀补技术的国内外研究现状,从机床用户的角度分析了圆锥样条合成矢量插补及C机能刀补关键技术研究的必要性。
(2)在数控差分插补算法的基础上,通过构建矢量圆,对圆锥样条的数控加工轨迹进行矢量分析,研究了适合直线(退化的圆锥曲线)、圆弧、椭圆、双曲线、抛物线等圆锥曲线数控加工的通用插补算法,分析了圆锥样条合成矢量插补算法的数控加工余量等问题。
(3)全面分析了圆锥曲线衔接处25种可能出现尖角、内角的情况,在圆锥样条合成矢量插补理论的基础上,提出了圆锥样条数控加工中的尖角、内角自动过渡算法,解决了圆锥样条C机能刀补涉及的问题。
(4)建立反向坐标系,研究了圆锥样条数控加工反向插补算法,解决了加工过程中的过象限问题。通过建立插补数学模型,对圆锥样条差分插补算法、合成矢量插补算法的误差进行了分析。
实验证明,圆锥样条合成矢量插补算法具有较高的插补精度。
Interpolation precision is one of the most important indicators for Numerical Control (NC) system, and the interpolation algorithm determines the performance of a NC system. In traditional interpolation algorithms, line and arc are the main interpolation targets. With the more applications of conic curves (elliptic and parabolic, etc) in NC machining, simple linear or circular interpolation algorithms can not satisfy the requirement of modern high precision NC processing. Cone Spline consists of conic curves which are connected with each other, and it now has become a general description form of complex work pieces in CAD system. By using cone spline to fit the work piece, the fitted curve is assured to have higher fitting precision. A general vector synthesis interpolation algorithm for cone spline is proposed, and on the basis of it, the sharp and internal auto-transition problems are solved. In this thesis, the main contents of vector synthesis interpolation and C function cutter radius compensation are as follows:
(1) In this thesis, both at home and abroad researches of NC interpolation and C function cutter radius compensation are firstly introduced. The necessity of the research above is analyzed from the view of the machine user.
(2) Based on the difference interpolation algorithm, vector analysis of the cutter location point’s track of cone spline is proceeded by creating a normal vector circle. In conic curves machining, a universal interpolation algorithm for line (degradation of conic curve), arc, elliptic, parabolic is researched. In the meantime, some other problems regard to vector synthesis interpolation algorithm, such as machining allowance, are analyzed.
(3) After comprehensive analyzing of the possible 25 cases in the connection of conic curves, sharp and internal corner transition theories for cone spline NC machining are proposed based on the vector synthesis interpolation algorithm. Other problems regard to C function cutter radius compensation for cone spline are solved.
(4) Reverse coordinate system is established and reverse interpolation algorithm is proposed. After that, post-quadrant problem is resolved successfully. An error mathematic model is established, and error analyses are compared between difference interpolation and vector synthesis interpolation by the average error method.
Experiment show that vector synthesis interpolation algorithm for cone spline has high interpolation precision.
(1)综述了数控插补技术及C机能刀补技术的国内外研究现状,从机床用户的角度分析了圆锥样条合成矢量插补及C机能刀补关键技术研究的必要性。
(2)在数控差分插补算法的基础上,通过构建矢量圆,对圆锥样条的数控加工轨迹进行矢量分析,研究了适合直线(退化的圆锥曲线)、圆弧、椭圆、双曲线、抛物线等圆锥曲线数控加工的通用插补算法,分析了圆锥样条合成矢量插补算法的数控加工余量等问题。
(3)全面分析了圆锥曲线衔接处25种可能出现尖角、内角的情况,在圆锥样条合成矢量插补理论的基础上,提出了圆锥样条数控加工中的尖角、内角自动过渡算法,解决了圆锥样条C机能刀补涉及的问题。
(4)建立反向坐标系,研究了圆锥样条数控加工反向插补算法,解决了加工过程中的过象限问题。通过建立插补数学模型,对圆锥样条差分插补算法、合成矢量插补算法的误差进行了分析。
实验证明,圆锥样条合成矢量插补算法具有较高的插补精度。
Interpolation precision is one of the most important indicators for Numerical Control (NC) system, and the interpolation algorithm determines the performance of a NC system. In traditional interpolation algorithms, line and arc are the main interpolation targets. With the more applications of conic curves (elliptic and parabolic, etc) in NC machining, simple linear or circular interpolation algorithms can not satisfy the requirement of modern high precision NC processing. Cone Spline consists of conic curves which are connected with each other, and it now has become a general description form of complex work pieces in CAD system. By using cone spline to fit the work piece, the fitted curve is assured to have higher fitting precision. A general vector synthesis interpolation algorithm for cone spline is proposed, and on the basis of it, the sharp and internal auto-transition problems are solved. In this thesis, the main contents of vector synthesis interpolation and C function cutter radius compensation are as follows:
(1) In this thesis, both at home and abroad researches of NC interpolation and C function cutter radius compensation are firstly introduced. The necessity of the research above is analyzed from the view of the machine user.
(2) Based on the difference interpolation algorithm, vector analysis of the cutter location point’s track of cone spline is proceeded by creating a normal vector circle. In conic curves machining, a universal interpolation algorithm for line (degradation of conic curve), arc, elliptic, parabolic is researched. In the meantime, some other problems regard to vector synthesis interpolation algorithm, such as machining allowance, are analyzed.
(3) After comprehensive analyzing of the possible 25 cases in the connection of conic curves, sharp and internal corner transition theories for cone spline NC machining are proposed based on the vector synthesis interpolation algorithm. Other problems regard to C function cutter radius compensation for cone spline are solved.
(4) Reverse coordinate system is established and reverse interpolation algorithm is proposed. After that, post-quadrant problem is resolved successfully. An error mathematic model is established, and error analyses are compared between difference interpolation and vector synthesis interpolation by the average error method.
Experiment show that vector synthesis interpolation algorithm for cone spline has high interpolation precision.
引文
[1]李叶农.数控机床及其应用[M].北京:国防工业出版社,2006.1
[2]刘沂.数控机床控制技术基础[M].机械工业出版社.2006.8
[3]陈蔚芳,王宏涛.机床数控技术及应用[M].北京:科学出版社,2005.1
[4]杨叔子,吴波.先进制造技术及其发展趋势[J].机械工程学报,2003,39(10):73-78
[5]邓朝晖,盛晓敏.先进制造技术[M].北京:机械工业出版社,2000.3
[6]徐树滋.2007年世界机床产销情况和特点简析[J].制造技术与机床,2008(4):10-11
[7]刘祖其.数控系统及发展趋势[J].制造业自动化,2009(12): 4-6
[8]汪俊俊.论数控技术发展趋势—智能化数控系统[J].装备制造,2009(6): 242-243
[9]徐伟,刘朝明.数控系统发展趋势的研究[J].制造业自动化,2009(9): 1-3
[10]廖永忠,廖春成,李学庭.开放式数控系统的研究与开发[J].机械与电子,2009 (1): 10-13
[11]周宏甫.数控技术.广州:华南理工大学出版社, 2003
[12]赵巍,王太勇.最小偏差椭圆插补方法误差分析[J].机床与液压.2005(1):20-22
[13]陈贵银.脉冲间隔法抛物线插补的研究[J].机械工程与自动化,2006,6(3):100-102
[14]赵彤,吕强,张辉等.三次均匀B样条曲线高速实时插补研究.计算机集成制造系统.2008(9):1830-1836
[15]赵万生,史旭明.参数方程曲线的直接插补算法研究[J].哈尔滨工业大学学报,2000(1):133-136
[16]肖本贤.多轴运动下的轮廓跟踪误差控制与补偿方法研究[D].合肥工业大学,2004
[17]马桦.高性能曲线及空间曲线插补方法的探讨[J].机械与电子,1995(6):24-25
[18]游有鹏.改进最小偏差法-一种高精度插补算法[J].机械工业自动化,1995(1):32-34
[19]汪洋.数控机床样条曲线刀具半径补偿算法研究[J].机械设计与制造,2007(6):110-112
[20]谢琼,李适民,周新军等.刀具半径补偿中的矢量法[J].工业控制计算机,1998(4):38-40
[21]周建来,邱白晶,王丽华等.数控车系统刀具补偿的一种改进算法[J].机床与液压,2006(11):21-24
[22]王凌云.数控系统的刀具半径补偿技术研究[J].浙江工业大学学报,2005(2):219-222
[23]周坚.电火花线切割加工中的偏移轨迹算法[J].电加工,1991(5):2-5
[24]黄坚.数控铣床刀具半径补偿中尖角过渡的计算[J].机械工业自动化,1995.9(3):26-28
[25]孟俊焕.基于CNC的零件廓形拐角尖角过渡的实现[J].纺织机械,2007(5):53-56
[26]乐光学.CNC加工中尖角过渡处理和切入切出程序设计.机械工艺师,2000(3):15-17
[27]何伟,张桂花.刀具半径补偿过程中过切现象及解决对策.装备制造技术,2007(2):24-27
[28] Mohri.N,et al.System identification of wire electrical discharge machining.Annals of the CIRP,1998,47 (1)
[29]马方魁.数控机床NURBS曲线插补运动误差分析与仿真[J].中国机械工程,2008(10):2446-2449
[30] A.B.Puri, B.Bhattacharyya.An analysis and optimization of the geometrical inaccuracy due to Wire lag phenomenon in WEDM.Machine Tools&Manufacture, 2003, Volume 43:151-159
[31] A.B.Puri, B.Bhattacharyya.Modeling and analysis of the Wire-tool vibration in Wire-cut EDM.Journal of Materials Processing Technology,2003,Volume 141:295-301
[32]王延忠,周云飞.螺旋锥齿轮空间曲面NC加工插补误差分析[J].华中科技大学学报,2002(2):9-12
[33]董为民.插补算法的误差及实时性研究[J].机械制造与研究,2006,35(6):18-20
[34]李恩林.数控系统插补原理通论.国防工业出版社,2008.7
[35]黄家善.计算机数控技术.北京:机械工业出版社,2004:7-10
[36]张俊,魏红根.数控技术发展趋势-智能化数控系统.制造技术与机床,2000(4):7-9
[37]逄启寿,杨杰,刘本辉等.数控加工中两种插补原理及对应算法[J].机械工程师,2007.2:121-122
[38]曹立凡,史万明.数值分析[M].北京:北京工业学院出版社,1977.6
[39]《简明数学手册》编写组编.简明数学手册[M].上海:上海教育出版社,1986.3
[40]王敏.差分插补方法及其在数控线切割机中的应用(一)[J].电加工,1981(4):16-22
[41]单东日.基于二次代数样条差分插补的平面参数曲线数控加工[J].制造技术与机床,2009(2):95-98
[42]赵庆志.基于可重构理论的慢走丝线切割机床控制系统研究与设计[D].南京:南京航空航天大学,2004
[43]赵庆志.曲线合成插补理论及其在慢走丝切割加工中的应用[J].中国机械工程,2004(4):23-26
[44] L.N.Lopez de Lacalle.Improving the high-speed finishing of forming tools for advanced high-strength steels(AHSS)[J].The International journal of Advanced Manufacturing Technology,2006(5):49-63
[45]朱江新.基于最小偏差法的过象限圆弧插补统一算法[J].西安理工大学学报,2004(1):71-73
[46]阿波罗尼奥斯,朱恩宽.圆锥曲线论[M] :卷I-IV.西安:陕西科学技术出版社,2007.6
[47] Shan dongri, Wang tao.Vector Synthesis Interpolation for Cone Spline[C].2009 International Conference on Mechanical and Electrical Technology.American Society of Mechanical Engineers Press,2009:37-42
[48]冯宪章.先进制造技术基础[M].北京:北京大学出版社,2009.3
[49]王先逵.制造技术的历史回顾与面临的机遇和挑战[J].机械工程学报,2002,38(8):1-8
[50] Y.Altintas, N. Newel I, M.lto.A Hierarichial Open Architecture Multi-Processor CNC System for Motion and Process Control (J) .Manufactural Science and Engineering,ASME,PED,1993, (64) :195-206
[51] P.Orban, I. Yellow, Y. Zhou.Open Architecture Controllers-A Development Platform for Machine Tool Control Applications[C].Proceeding of Mechanismand Controls for Ultra precision Motion,1994
[52]许启发,黄建,江福杰.C机能平面刀补算法研究[J].机电工程技术[J],2004,33(3):56-58
[53]单东日,王涛.圆锥样条合成矢量插补及C机能刀补[J].机械科学与技术,2010(01):68-71
[54]武洪恩,张承瑞,李桂莉等.基于Windows 2000的非圆截面车削数控系统[J].中国机械工程,2006,17(24):2582-2586
[55] T.Arai,Y.Maeda,H.Kikuchi. Automated Calibration of Robot Coordinates forReconfigurable Assembly Systems[J].Annals of the CIRP,2002,Vol51/1:5-8
[56]赵庆志.曲线合成插补理论及其在慢走丝切割外角内角过渡中的应用[J].机械科学与技术,2004,5(23):608-612
[57]盛志冲,张存亮.数控滚齿机紧急回退功能的应用[J].工具技术,2008(11):92-93
[58]杨旭静,谢晖,盛晓敏.提高自由曲面数控加工精度的技术研究[J].湖南大学学报(自然科学版),2002,29(5):80-88
[59]刘敏,潘晓弘,程耀东.圆弧插补中累计误差消除方法探讨[J].机械研究与应用,1998(3):8-10
[60]马玉林.虚拟加工中的加工误差分析与预测[J].机械工程学报,2002(11):65-69
[61] Xincheng Tian,J.P.Huissoon,Qing Xu,et al.Dimensional error analysis and its intelligent pre-compensation in CNC grinding[J].The International Journal of Advanced Manufacturing Technology,2008(2):28-33
[62]赵小松,刘丽冰,章青.四轴联动加工中心误差模型及参数辨识[J].机械工程学报,2000,36(10):76-80
[63] Kun Ren,Jian-zhong Fu,Zi-chen Chen.Research on new software compensation method of static and quasi-static errors for precision motion controller[J].Journal of Zhejiang University-Science A,2007(11):1938-1943
[2]刘沂.数控机床控制技术基础[M].机械工业出版社.2006.8
[3]陈蔚芳,王宏涛.机床数控技术及应用[M].北京:科学出版社,2005.1
[4]杨叔子,吴波.先进制造技术及其发展趋势[J].机械工程学报,2003,39(10):73-78
[5]邓朝晖,盛晓敏.先进制造技术[M].北京:机械工业出版社,2000.3
[6]徐树滋.2007年世界机床产销情况和特点简析[J].制造技术与机床,2008(4):10-11
[7]刘祖其.数控系统及发展趋势[J].制造业自动化,2009(12): 4-6
[8]汪俊俊.论数控技术发展趋势—智能化数控系统[J].装备制造,2009(6): 242-243
[9]徐伟,刘朝明.数控系统发展趋势的研究[J].制造业自动化,2009(9): 1-3
[10]廖永忠,廖春成,李学庭.开放式数控系统的研究与开发[J].机械与电子,2009 (1): 10-13
[11]周宏甫.数控技术.广州:华南理工大学出版社, 2003
[12]赵巍,王太勇.最小偏差椭圆插补方法误差分析[J].机床与液压.2005(1):20-22
[13]陈贵银.脉冲间隔法抛物线插补的研究[J].机械工程与自动化,2006,6(3):100-102
[14]赵彤,吕强,张辉等.三次均匀B样条曲线高速实时插补研究.计算机集成制造系统.2008(9):1830-1836
[15]赵万生,史旭明.参数方程曲线的直接插补算法研究[J].哈尔滨工业大学学报,2000(1):133-136
[16]肖本贤.多轴运动下的轮廓跟踪误差控制与补偿方法研究[D].合肥工业大学,2004
[17]马桦.高性能曲线及空间曲线插补方法的探讨[J].机械与电子,1995(6):24-25
[18]游有鹏.改进最小偏差法-一种高精度插补算法[J].机械工业自动化,1995(1):32-34
[19]汪洋.数控机床样条曲线刀具半径补偿算法研究[J].机械设计与制造,2007(6):110-112
[20]谢琼,李适民,周新军等.刀具半径补偿中的矢量法[J].工业控制计算机,1998(4):38-40
[21]周建来,邱白晶,王丽华等.数控车系统刀具补偿的一种改进算法[J].机床与液压,2006(11):21-24
[22]王凌云.数控系统的刀具半径补偿技术研究[J].浙江工业大学学报,2005(2):219-222
[23]周坚.电火花线切割加工中的偏移轨迹算法[J].电加工,1991(5):2-5
[24]黄坚.数控铣床刀具半径补偿中尖角过渡的计算[J].机械工业自动化,1995.9(3):26-28
[25]孟俊焕.基于CNC的零件廓形拐角尖角过渡的实现[J].纺织机械,2007(5):53-56
[26]乐光学.CNC加工中尖角过渡处理和切入切出程序设计.机械工艺师,2000(3):15-17
[27]何伟,张桂花.刀具半径补偿过程中过切现象及解决对策.装备制造技术,2007(2):24-27
[28] Mohri.N,et al.System identification of wire electrical discharge machining.Annals of the CIRP,1998,47 (1)
[29]马方魁.数控机床NURBS曲线插补运动误差分析与仿真[J].中国机械工程,2008(10):2446-2449
[30] A.B.Puri, B.Bhattacharyya.An analysis and optimization of the geometrical inaccuracy due to Wire lag phenomenon in WEDM.Machine Tools&Manufacture, 2003, Volume 43:151-159
[31] A.B.Puri, B.Bhattacharyya.Modeling and analysis of the Wire-tool vibration in Wire-cut EDM.Journal of Materials Processing Technology,2003,Volume 141:295-301
[32]王延忠,周云飞.螺旋锥齿轮空间曲面NC加工插补误差分析[J].华中科技大学学报,2002(2):9-12
[33]董为民.插补算法的误差及实时性研究[J].机械制造与研究,2006,35(6):18-20
[34]李恩林.数控系统插补原理通论.国防工业出版社,2008.7
[35]黄家善.计算机数控技术.北京:机械工业出版社,2004:7-10
[36]张俊,魏红根.数控技术发展趋势-智能化数控系统.制造技术与机床,2000(4):7-9
[37]逄启寿,杨杰,刘本辉等.数控加工中两种插补原理及对应算法[J].机械工程师,2007.2:121-122
[38]曹立凡,史万明.数值分析[M].北京:北京工业学院出版社,1977.6
[39]《简明数学手册》编写组编.简明数学手册[M].上海:上海教育出版社,1986.3
[40]王敏.差分插补方法及其在数控线切割机中的应用(一)[J].电加工,1981(4):16-22
[41]单东日.基于二次代数样条差分插补的平面参数曲线数控加工[J].制造技术与机床,2009(2):95-98
[42]赵庆志.基于可重构理论的慢走丝线切割机床控制系统研究与设计[D].南京:南京航空航天大学,2004
[43]赵庆志.曲线合成插补理论及其在慢走丝切割加工中的应用[J].中国机械工程,2004(4):23-26
[44] L.N.Lopez de Lacalle.Improving the high-speed finishing of forming tools for advanced high-strength steels(AHSS)[J].The International journal of Advanced Manufacturing Technology,2006(5):49-63
[45]朱江新.基于最小偏差法的过象限圆弧插补统一算法[J].西安理工大学学报,2004(1):71-73
[46]阿波罗尼奥斯,朱恩宽.圆锥曲线论[M] :卷I-IV.西安:陕西科学技术出版社,2007.6
[47] Shan dongri, Wang tao.Vector Synthesis Interpolation for Cone Spline[C].2009 International Conference on Mechanical and Electrical Technology.American Society of Mechanical Engineers Press,2009:37-42
[48]冯宪章.先进制造技术基础[M].北京:北京大学出版社,2009.3
[49]王先逵.制造技术的历史回顾与面临的机遇和挑战[J].机械工程学报,2002,38(8):1-8
[50] Y.Altintas, N. Newel I, M.lto.A Hierarichial Open Architecture Multi-Processor CNC System for Motion and Process Control (J) .Manufactural Science and Engineering,ASME,PED,1993, (64) :195-206
[51] P.Orban, I. Yellow, Y. Zhou.Open Architecture Controllers-A Development Platform for Machine Tool Control Applications[C].Proceeding of Mechanismand Controls for Ultra precision Motion,1994
[52]许启发,黄建,江福杰.C机能平面刀补算法研究[J].机电工程技术[J],2004,33(3):56-58
[53]单东日,王涛.圆锥样条合成矢量插补及C机能刀补[J].机械科学与技术,2010(01):68-71
[54]武洪恩,张承瑞,李桂莉等.基于Windows 2000的非圆截面车削数控系统[J].中国机械工程,2006,17(24):2582-2586
[55] T.Arai,Y.Maeda,H.Kikuchi. Automated Calibration of Robot Coordinates forReconfigurable Assembly Systems[J].Annals of the CIRP,2002,Vol51/1:5-8
[56]赵庆志.曲线合成插补理论及其在慢走丝切割外角内角过渡中的应用[J].机械科学与技术,2004,5(23):608-612
[57]盛志冲,张存亮.数控滚齿机紧急回退功能的应用[J].工具技术,2008(11):92-93
[58]杨旭静,谢晖,盛晓敏.提高自由曲面数控加工精度的技术研究[J].湖南大学学报(自然科学版),2002,29(5):80-88
[59]刘敏,潘晓弘,程耀东.圆弧插补中累计误差消除方法探讨[J].机械研究与应用,1998(3):8-10
[60]马玉林.虚拟加工中的加工误差分析与预测[J].机械工程学报,2002(11):65-69
[61] Xincheng Tian,J.P.Huissoon,Qing Xu,et al.Dimensional error analysis and its intelligent pre-compensation in CNC grinding[J].The International Journal of Advanced Manufacturing Technology,2008(2):28-33
[62]赵小松,刘丽冰,章青.四轴联动加工中心误差模型及参数辨识[J].机械工程学报,2000,36(10):76-80
[63] Kun Ren,Jian-zhong Fu,Zi-chen Chen.Research on new software compensation method of static and quasi-static errors for precision motion controller[J].Journal of Zhejiang University-Science A,2007(11):1938-1943