自由曲线曲面数控加工复合刀具路径生成方法研究
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摘要
对于大多数由软件生成的数控加工程序,常用直线和圆弧两种插补方式。而样条曲线插补以其良好的平稳光顺性,成为直线插补和圆弧插补的补充。将多种插补方式进行组合,对于自由曲线曲面数控加工具有重要意义。
本文提出了基于刀位点的复合刀具路径生成方法。建立了组合直线拟合、圆弧拟合、B样条曲线拟合的数学模型,通过对三种拟合方式的误差分析,实现不同拟合方式的迭代及刀具路径优化分段,并生成复合刀具路径。
首先,运用最小二乘方法进行圆弧和B样条曲线拟合。B样条曲线拟合分两步进行,在对被拟合数据点进行均匀参数化拟合得到初始控制点之后,重新优化参数值得到新的控制顶点。
其次,给出了将直线拟合,圆弧拟合,B样条曲线拟合按照从高到低优先级进行选择的方法,实现了三种拟合方式的组合。对拟合误差的判断决定了三种拟合方式之间的转换。并引入阀值,设定刀位点距大于阀值时直接进入直线拟合方式,减少不必要的拟合运算量。
再次,读取刀位点,计算得到由直线插补、圆弧插补和B样条曲线插补所组成的加工方式,生成复合刀具路径优化平面轮廓加工;得到由直线插补、圆弧插补和B样条曲线插补所组成的复合刀具路径进行曲面加工。优化后的复合加工路径可以提高铣削过程的平稳性,减少机床频繁的加减速从而提高整个加工的切削效率、缩短加工时间,改善曲面的粗糙度并提高曲面的光顺性。
论文将上述理论和算法得到的复合刀具路径和初始刀具路径进行加工,实例分析和比较证明了复合刀具路径方法使加工表面质量得到改善,加工效率提高且易于在数控加工中实现,能够满足自由曲线曲面数控加工的需要。
As to most programs given by CAM software, line interpolation and arc interpolation are the interpolations which are mostly used. Spline interpolation could be the powerful supplement for line and arc interpolation as its brevity and smoothness. Integrating several interpolations are significant to free-form curve and surface NC machining.
A new approach to compound tool path generation based on discrete cutter locations is proposed. The mathematical model integrating line fitting, arc fitting and B-spline fitting is constructed. Through error analysis of three fitting methods, the iteration of different fitting methods and tool path segmenting could be carried out. Compound tool paths are produced.
First, arc fitting and B-spline fitting are carried out based on least square method. The procedure for B-spline is divided into two parts. After the original control points being gotten on the uniform parameterization of data points, the parameter values are optimized to get new control points.
Second, the method for selecting line fitting, arc fitting and B-spline fitting according to precedence level is given, implementing the combination of three fitting methods. The judgement of fitting error decides the iteration of different fitting methods. The line fitting method is definitely used when the points distance is beyond the set valve value in order deduce calculation.
Third, reading cutter location points, the machining method consists of line interpolation, arc interpolation and B-spline interpolation is achieved. The compound tool paths are generated for planer machining. The compound tool paths integrating line and B-spline are used for surface machining. The optimized tool paths could advance stability for milling and shorten the time for continual speeding up and speeding down in order to increase efficiency, shorten machining time and improve the surface roughness.
Comparing the parts using compound tool paths generating method to using original method, the surface quality and efficiency are both improved.
本文提出了基于刀位点的复合刀具路径生成方法。建立了组合直线拟合、圆弧拟合、B样条曲线拟合的数学模型,通过对三种拟合方式的误差分析,实现不同拟合方式的迭代及刀具路径优化分段,并生成复合刀具路径。
首先,运用最小二乘方法进行圆弧和B样条曲线拟合。B样条曲线拟合分两步进行,在对被拟合数据点进行均匀参数化拟合得到初始控制点之后,重新优化参数值得到新的控制顶点。
其次,给出了将直线拟合,圆弧拟合,B样条曲线拟合按照从高到低优先级进行选择的方法,实现了三种拟合方式的组合。对拟合误差的判断决定了三种拟合方式之间的转换。并引入阀值,设定刀位点距大于阀值时直接进入直线拟合方式,减少不必要的拟合运算量。
再次,读取刀位点,计算得到由直线插补、圆弧插补和B样条曲线插补所组成的加工方式,生成复合刀具路径优化平面轮廓加工;得到由直线插补、圆弧插补和B样条曲线插补所组成的复合刀具路径进行曲面加工。优化后的复合加工路径可以提高铣削过程的平稳性,减少机床频繁的加减速从而提高整个加工的切削效率、缩短加工时间,改善曲面的粗糙度并提高曲面的光顺性。
论文将上述理论和算法得到的复合刀具路径和初始刀具路径进行加工,实例分析和比较证明了复合刀具路径方法使加工表面质量得到改善,加工效率提高且易于在数控加工中实现,能够满足自由曲线曲面数控加工的需要。
As to most programs given by CAM software, line interpolation and arc interpolation are the interpolations which are mostly used. Spline interpolation could be the powerful supplement for line and arc interpolation as its brevity and smoothness. Integrating several interpolations are significant to free-form curve and surface NC machining.
A new approach to compound tool path generation based on discrete cutter locations is proposed. The mathematical model integrating line fitting, arc fitting and B-spline fitting is constructed. Through error analysis of three fitting methods, the iteration of different fitting methods and tool path segmenting could be carried out. Compound tool paths are produced.
First, arc fitting and B-spline fitting are carried out based on least square method. The procedure for B-spline is divided into two parts. After the original control points being gotten on the uniform parameterization of data points, the parameter values are optimized to get new control points.
Second, the method for selecting line fitting, arc fitting and B-spline fitting according to precedence level is given, implementing the combination of three fitting methods. The judgement of fitting error decides the iteration of different fitting methods. The line fitting method is definitely used when the points distance is beyond the set valve value in order deduce calculation.
Third, reading cutter location points, the machining method consists of line interpolation, arc interpolation and B-spline interpolation is achieved. The compound tool paths are generated for planer machining. The compound tool paths integrating line and B-spline are used for surface machining. The optimized tool paths could advance stability for milling and shorten the time for continual speeding up and speeding down in order to increase efficiency, shorten machining time and improve the surface roughness.
Comparing the parts using compound tool paths generating method to using original method, the surface quality and efficiency are both improved.
引文
[1]沈媛媛.矢量汉字数控切削加工的刀具路径规划原理与方法.大连理工大学硕士学位论文. 2007:1-9
[2]姚强.五坐标数控加工空间凸轮CAD/CAM系统.大连理工大学硕士学位论文. 2006.
[3] Bolton K M. Biarc curves. Computer-Aided Design, 1975, 7(2): 89-92
[4] Young Joon Ahn, Hong Oh Kim, Kyoung-Yong Lee. G1 arc spline approximation of quadratic Bezier curves. Computer-Aided Design, 1998, 30(8): 615-620
[5] Parkinson D B, Moreton D N. Optimal biarc-curve fitting. Computer-Aided Design, 1991, 23(6): 411-419
[6] Moreton D N, Parkinson D B. The application of biarc technique in CNC machining. Journal of Computer-Aided Engineering Design, 1991, 8: 54-60
[7] Hoschek J. Circular splines. Computer-Aided Design, 1992, 24(11): 611-618
[8] Meek D S, Walton D J. Approximation of discrete data by GI arc splines. Computer-Aided Design, 1992, 24(6): 301-306
[9] Schonherr, J. Smooth biarc curves. Computer-Aided Design, 1993, 25(6): 365-370
[10] Yong J H, Hu S M, Sun J G. A note on approximation of discrete data by G1 splines. Computer-Aided Design, 1999, 31(14): 911-915
[11] Shen J G. A new algorithm of optimal him fitting. Proceedings of International Conference of Pacific Gmphics’94/CADDM’94, 1994, 150-152
[12]沈纪桂.数控加工圆弧拟合的优化方法.机械工程学报, 1997, 3(6): 64-69
[13] Meek, D S and Walton, D J. Approximating quadratic NURBS curves by arc splines. Computer-Aided Design, 1993, 25(6): 371-377
[14] Walton, D J and Meek, D S. Approximating of quadratic Bezier curves by arc splines. Journal of Computational and Applied Mathematics, 1994, 54(1): 107-120
[15] Ahn Y J, Kim H O, Lee K Y. G1 arc spline approximation of quadratic Bezier curves. Computer-Aided Design. 1998, 30(8): 615-620
[16] Yong J H, Hu S M, Sun J G. Bisection algorithm for approximating quadratic Bezier curves by G1 arc splines. Computer-Aided Design, 2000, 32(4): 253-260
[17] Chuang S H, Kao C Z. One-sided arc approximation of B-spline curves for interference-free offsetting. Computer-Aided Design, 1999, 31(2): 111-118
[18] Ong, C J, Wong. Y S, Loh, H T et al. An optimization approach for biarc curve fitting of B-spline curves. Compute-Aided Design, 1996, 28(12): 951-959
[19] Piegl L, Tiller W. Biarc approximation of NURBS curves. Computer-Aided Design, 2002, 34(11): 807-814
[20] J.-L.Shih, One-sided offset approximation of freeform curves for interference-free NURBS machining. Computer-Aided Design, 2008, 40(9): 931-937
[21] Yang X J, Chen Z C. A new high precision fitting approach for NURBS tool paths generation. Proceeding of ASME 2005, International Design Engineering Technical Conferences & Computers and Information in Engineering Conference. September 24-28, Long Beach, California USA.
[22] Ferguson J C. Multivariable curve interpolation. Report D2-22504, The Boeing Co. Seattle, Washington, 1963
[23] Ferguson J C. Multivariable curve interpolation. J. ACM, 2, 1964, 221-228
[24] Bezier P E. Numerical control: Mathematics and applications. NewyorkJohn Wiley, 1972
[25] Bezier P E. The mathematical basis of the UNISURF CAD system. London: Butterwort, 1986
[26] Gordon W J, Riesenfeld R F. B-spline curves and surfaces, in Computer-Aided Geometric Design. New York: Acadamic Press, 1974
[27] Versprille K J. Computer-aided design applications of the rational B-spline approximation form. Ph.D. dissertation, Syracuse University, 1975
[28] Piegl L, Tiller W. Curve and surface constructions using rational B-spline. Computer-Aided Design, 1987, 19(9): 485-498
[29] Piegl L. On NURBS: a survey. IEEE Computer Graphic and Application. 1991, 10(1): 55-71
[30] Piegl L, Tiller W. The NURBS Book, 2nd ed. New York: Springer-Verlag, 1997
[31]施法中.计算机辅助几何设计与非均匀有理B样条(CAGC&NURBS).北京航空航天出版社, 1994
[32] Vergeest S M. CAD surface data exchange using STEP. Computer-Aided Design, 1991, 23(l): 268-281
[33]朱永强,鲁聪达.自由曲线曲面造型技术的综述.中国制造业信息化. 2003, 32(5): 110-113
[34]李发致.模具先进制造技术.北京:机械工业出版社, 2004
[35]王润孝.机床数控原理与系统.西安:西北工业大学出版社, 1997, 22-60
[36]龙汉. NURBS曲线实时插补算法及仿真.西南科技大学硕士研究生学位论文, 2007
[37]莫蓉,吴英,常智勇.计算机辅助几何造型技术.北京:科学出版社, 2004, 106
[38]孙家广等.计算机图形学.北京:清华大学出版社, 1998, 308-309
[39]黄翔,曾荣,岳伏军,廖文和. NURBS插补技术在高速加工中的应用研究.南京航空航天大学学报. 2003, 34(1): 82-85
[40]房京.刀具路径自适应规划的研究,河北工业大学硕士学位论文. 2001, 26
[41]毕承恩等.现代数控机床.北京:机械工业出版社, 1993
[42]田春霞.数控铣削刀具路径的规划.工艺与装备, 2008, 11: 72-75
[43]余晓明等.常用数控编程技术.北京:电子工业出版社, 2008
[44]唐志涛,刘战强,周军.虚拟数控加工过程仿真技术.电气技术与自动化, 2005, 34(3): 61-64, 67
[45]乐英,韩庆瑶,王璋奇.数控加工中非圆曲线的最小二乘圆弧逼近.华北电力大学学报, 2006. 33(6): 102-104
[46]施法中.计算机辅助几何设计与非均匀有理B样条.北京:高等教育出版社, 2001, 45-49
[47]康书杰. NURBS曲线实时插补技术研究.南京航空航天大学硕士学位论文. 2007, 23-29
[48]姚英学,蔡颖.计算机辅助设计与制造.北京:高等教育出版社, 2002
[2]姚强.五坐标数控加工空间凸轮CAD/CAM系统.大连理工大学硕士学位论文. 2006.
[3] Bolton K M. Biarc curves. Computer-Aided Design, 1975, 7(2): 89-92
[4] Young Joon Ahn, Hong Oh Kim, Kyoung-Yong Lee. G1 arc spline approximation of quadratic Bezier curves. Computer-Aided Design, 1998, 30(8): 615-620
[5] Parkinson D B, Moreton D N. Optimal biarc-curve fitting. Computer-Aided Design, 1991, 23(6): 411-419
[6] Moreton D N, Parkinson D B. The application of biarc technique in CNC machining. Journal of Computer-Aided Engineering Design, 1991, 8: 54-60
[7] Hoschek J. Circular splines. Computer-Aided Design, 1992, 24(11): 611-618
[8] Meek D S, Walton D J. Approximation of discrete data by GI arc splines. Computer-Aided Design, 1992, 24(6): 301-306
[9] Schonherr, J. Smooth biarc curves. Computer-Aided Design, 1993, 25(6): 365-370
[10] Yong J H, Hu S M, Sun J G. A note on approximation of discrete data by G1 splines. Computer-Aided Design, 1999, 31(14): 911-915
[11] Shen J G. A new algorithm of optimal him fitting. Proceedings of International Conference of Pacific Gmphics’94/CADDM’94, 1994, 150-152
[12]沈纪桂.数控加工圆弧拟合的优化方法.机械工程学报, 1997, 3(6): 64-69
[13] Meek, D S and Walton, D J. Approximating quadratic NURBS curves by arc splines. Computer-Aided Design, 1993, 25(6): 371-377
[14] Walton, D J and Meek, D S. Approximating of quadratic Bezier curves by arc splines. Journal of Computational and Applied Mathematics, 1994, 54(1): 107-120
[15] Ahn Y J, Kim H O, Lee K Y. G1 arc spline approximation of quadratic Bezier curves. Computer-Aided Design. 1998, 30(8): 615-620
[16] Yong J H, Hu S M, Sun J G. Bisection algorithm for approximating quadratic Bezier curves by G1 arc splines. Computer-Aided Design, 2000, 32(4): 253-260
[17] Chuang S H, Kao C Z. One-sided arc approximation of B-spline curves for interference-free offsetting. Computer-Aided Design, 1999, 31(2): 111-118
[18] Ong, C J, Wong. Y S, Loh, H T et al. An optimization approach for biarc curve fitting of B-spline curves. Compute-Aided Design, 1996, 28(12): 951-959
[19] Piegl L, Tiller W. Biarc approximation of NURBS curves. Computer-Aided Design, 2002, 34(11): 807-814
[20] J.-L.Shih, One-sided offset approximation of freeform curves for interference-free NURBS machining. Computer-Aided Design, 2008, 40(9): 931-937
[21] Yang X J, Chen Z C. A new high precision fitting approach for NURBS tool paths generation. Proceeding of ASME 2005, International Design Engineering Technical Conferences & Computers and Information in Engineering Conference. September 24-28, Long Beach, California USA.
[22] Ferguson J C. Multivariable curve interpolation. Report D2-22504, The Boeing Co. Seattle, Washington, 1963
[23] Ferguson J C. Multivariable curve interpolation. J. ACM, 2, 1964, 221-228
[24] Bezier P E. Numerical control: Mathematics and applications. NewyorkJohn Wiley, 1972
[25] Bezier P E. The mathematical basis of the UNISURF CAD system. London: Butterwort, 1986
[26] Gordon W J, Riesenfeld R F. B-spline curves and surfaces, in Computer-Aided Geometric Design. New York: Acadamic Press, 1974
[27] Versprille K J. Computer-aided design applications of the rational B-spline approximation form. Ph.D. dissertation, Syracuse University, 1975
[28] Piegl L, Tiller W. Curve and surface constructions using rational B-spline. Computer-Aided Design, 1987, 19(9): 485-498
[29] Piegl L. On NURBS: a survey. IEEE Computer Graphic and Application. 1991, 10(1): 55-71
[30] Piegl L, Tiller W. The NURBS Book, 2nd ed. New York: Springer-Verlag, 1997
[31]施法中.计算机辅助几何设计与非均匀有理B样条(CAGC&NURBS).北京航空航天出版社, 1994
[32] Vergeest S M. CAD surface data exchange using STEP. Computer-Aided Design, 1991, 23(l): 268-281
[33]朱永强,鲁聪达.自由曲线曲面造型技术的综述.中国制造业信息化. 2003, 32(5): 110-113
[34]李发致.模具先进制造技术.北京:机械工业出版社, 2004
[35]王润孝.机床数控原理与系统.西安:西北工业大学出版社, 1997, 22-60
[36]龙汉. NURBS曲线实时插补算法及仿真.西南科技大学硕士研究生学位论文, 2007
[37]莫蓉,吴英,常智勇.计算机辅助几何造型技术.北京:科学出版社, 2004, 106
[38]孙家广等.计算机图形学.北京:清华大学出版社, 1998, 308-309
[39]黄翔,曾荣,岳伏军,廖文和. NURBS插补技术在高速加工中的应用研究.南京航空航天大学学报. 2003, 34(1): 82-85
[40]房京.刀具路径自适应规划的研究,河北工业大学硕士学位论文. 2001, 26
[41]毕承恩等.现代数控机床.北京:机械工业出版社, 1993
[42]田春霞.数控铣削刀具路径的规划.工艺与装备, 2008, 11: 72-75
[43]余晓明等.常用数控编程技术.北京:电子工业出版社, 2008
[44]唐志涛,刘战强,周军.虚拟数控加工过程仿真技术.电气技术与自动化, 2005, 34(3): 61-64, 67
[45]乐英,韩庆瑶,王璋奇.数控加工中非圆曲线的最小二乘圆弧逼近.华北电力大学学报, 2006. 33(6): 102-104
[46]施法中.计算机辅助几何设计与非均匀有理B样条.北京:高等教育出版社, 2001, 45-49
[47]康书杰. NURBS曲线实时插补技术研究.南京航空航天大学硕士学位论文. 2007, 23-29
[48]姚英学,蔡颖.计算机辅助设计与制造.北京:高等教育出版社, 2002