基于相位测量的不规则曲面重建与快速开发
|
摘要
不规则复杂曲面的三维建模和快速开发是产品设计制造的难点,也是近几年研究的热点问题。把逆向工程与正向加工技术相结合,可从根本上改变传统产品的开发设计和制造模式,缩短产品开发周期,解决复杂形体难以建模和难加工的问题。基于此,本文重点研究基于相位测量的点云数据获取与预处理技术,NURBS曲面重构与品质分析,曲面优化算法研究和产品快速开发等内容。
首先,研究三维点云数据获取与预处理技术,分析基于相位测量的光栅投影原理、相位调制、相位解调和相位去包裹等理论。重点介绍3D CaMeGa光学三维扫描仪的校准、零件定位和点云数据获取过程。在此基础上,对点云进行预处理：采用最大允许偏差法进行数据精简,该方法精简率达40%,而且有效保留了零件关键的细节特征,还对点云进行除噪、平滑、分割等处理。
其次,研究NURBS曲面拟合理论,实现整体曲面拟合和曲面拼接,点云-曲面偏差最大误差为0.270mm,符合高精度拟合曲面要求。比较曲面拟合各种算法的优缺点,提出基于正交函数的最小二乘曲面优化算法。该算法仅采用4x4阶共36个控制点拟合,就能达到较好的拟合效果。重构平均偏差仅为0.0461mm,与最小二乘法在曲面重构精度、曲面光顺性方面进行综合比较,验证本文算法的优越性。通过实验分析控制点数、曲面阶次对重构精度的影响,提出根据曲面控制点数合理选择曲面阶次,进行曲面拟合的方法。
最后,设计三维曲面凸模及凹模,并进行数控仿真加工。对数控仿真加工刀路源文件进行后置处理,针对CNC840D控制系统、机床型号为fz37的数控机床生成数控加工车间NC程序,实现不规则曲面零件的二次开发。
The 3D modeling, machining and rapid developing of irregular and complex surface have always been difficult for products design and manufacture, and it has become research emphasis recently. Combining reverse engineering and positive processing technology is a good way to solve these problems. It fundamentally changes the traditional mode for product development and manufacturing. It solves the difficulty in modeling and manufacturing for some complex products. It shortens the time to develop and machine new products. Thus point clouds acquisition and pre-processing, NURBS surface reconstruction and quality analysis, surface optimization algorithm and rapid developing of the products are studied in the paper.
Firstly, acquisition and pre-processing technology for 3D point clouds data are studied. Some theories based on phase measurement, such as fringe projection, phase modulation, phase demodulation and phase unwrapping are analyzed.3D scanner calibration, object positioning and the acquisition process of point cloud data are implemented in the paper. Then the point clouds data is pre-processed. The data is compacted applying the maximum allowable deviation method with the precision of 40%. The important details of the morphology are effectively retained. In addition, noises elimination, data smoothing and segmentation of the point clouds are conducted.
Secondly, NURBS surface fitting theory is studied, and the whole surface fitting and splicing are achieved. The maximum error of point clouds-surface is 0.270mm, which meets the requirement of high precision fitting. The least-square surface optimization algorithm based on orthogonal function is proposed according to the comparison results among several surface fitting methods. With the proposed algorithm, satisfactory fitting result can be achieved only by 36 control points of 4x4 orders, and the average error of reconstruction is only 0.0461mm. Therefore, the superiority of proposed method can be verified through the comprehensive comparison with the least-square method in such aspects as surface reconstruction precision and surface smoothness. The influence of surface order and the number of control points on reconstruction precision are studied through experiments. Moreover, the surface fitting method that reasonably selects the surface order according to the number of control points is proposed.
Finally,3D punch and die for surface are designed, and NC machining is simulated. Through the post processing for source files of cutting track, the NC programs of fz37 CNC machines with CNC840D control system are generated. Therefore, secondary development for irregular surface components is achieved.
首先,研究三维点云数据获取与预处理技术,分析基于相位测量的光栅投影原理、相位调制、相位解调和相位去包裹等理论。重点介绍3D CaMeGa光学三维扫描仪的校准、零件定位和点云数据获取过程。在此基础上,对点云进行预处理：采用最大允许偏差法进行数据精简,该方法精简率达40%,而且有效保留了零件关键的细节特征,还对点云进行除噪、平滑、分割等处理。
其次,研究NURBS曲面拟合理论,实现整体曲面拟合和曲面拼接,点云-曲面偏差最大误差为0.270mm,符合高精度拟合曲面要求。比较曲面拟合各种算法的优缺点,提出基于正交函数的最小二乘曲面优化算法。该算法仅采用4x4阶共36个控制点拟合,就能达到较好的拟合效果。重构平均偏差仅为0.0461mm,与最小二乘法在曲面重构精度、曲面光顺性方面进行综合比较,验证本文算法的优越性。通过实验分析控制点数、曲面阶次对重构精度的影响,提出根据曲面控制点数合理选择曲面阶次,进行曲面拟合的方法。
最后,设计三维曲面凸模及凹模,并进行数控仿真加工。对数控仿真加工刀路源文件进行后置处理,针对CNC840D控制系统、机床型号为fz37的数控机床生成数控加工车间NC程序,实现不规则曲面零件的二次开发。
The 3D modeling, machining and rapid developing of irregular and complex surface have always been difficult for products design and manufacture, and it has become research emphasis recently. Combining reverse engineering and positive processing technology is a good way to solve these problems. It fundamentally changes the traditional mode for product development and manufacturing. It solves the difficulty in modeling and manufacturing for some complex products. It shortens the time to develop and machine new products. Thus point clouds acquisition and pre-processing, NURBS surface reconstruction and quality analysis, surface optimization algorithm and rapid developing of the products are studied in the paper.
Firstly, acquisition and pre-processing technology for 3D point clouds data are studied. Some theories based on phase measurement, such as fringe projection, phase modulation, phase demodulation and phase unwrapping are analyzed.3D scanner calibration, object positioning and the acquisition process of point cloud data are implemented in the paper. Then the point clouds data is pre-processed. The data is compacted applying the maximum allowable deviation method with the precision of 40%. The important details of the morphology are effectively retained. In addition, noises elimination, data smoothing and segmentation of the point clouds are conducted.
Secondly, NURBS surface fitting theory is studied, and the whole surface fitting and splicing are achieved. The maximum error of point clouds-surface is 0.270mm, which meets the requirement of high precision fitting. The least-square surface optimization algorithm based on orthogonal function is proposed according to the comparison results among several surface fitting methods. With the proposed algorithm, satisfactory fitting result can be achieved only by 36 control points of 4x4 orders, and the average error of reconstruction is only 0.0461mm. Therefore, the superiority of proposed method can be verified through the comprehensive comparison with the least-square method in such aspects as surface reconstruction precision and surface smoothness. The influence of surface order and the number of control points on reconstruction precision are studied through experiments. Moreover, the surface fitting method that reasonably selects the surface order according to the number of control points is proposed.
Finally,3D punch and die for surface are designed, and NC machining is simulated. Through the post processing for source files of cutting track, the NC programs of fz37 CNC machines with CNC840D control system are generated. Therefore, secondary development for irregular surface components is achieved.
引文
[1]刘伟军,孙玉文.逆向工程原理方法及应用[M].北京：机械工业出版社,2008.
[2]刘涛,陈邦道,苏家强.反求工程技术及应用研究[J].装备制造技术,2006,(4)：45-47.
[3]Martin R R, Varady T, Cox J. Reverse engineering of geometric models-An introduction [J]. Computer Aided Design,1997,29(4):255-268.
[4]Berthold K, Horn P, Brooks M J. The variational approach to shape from point [J]. Computer Vision Graphics and Image Processing,1986,33:174-208.
[5]由志福.曲面形体三维相位法检测技术及CAD/CAM集成的研究[D].清华大学,1998.
[6]张丽娜,计欣华,陈金龙.光弹性八步相移法的研究和应用[J].机械强度,2009,31(3)：378-381.
[7]杨亚良,吴兰,丁志华.基于傅里叶变换的确定性相位去包裹算法的应用研究[J].光学仪器,2005,27(3)：33-36.
[8]官云兰,程效军,施贵刚.一种稳健的点云数据平面拟合方法[J].同济大学学报(自然科学版),2008,36(7)：981-984.
[9]沈海平,达飞鹏,雷家勇.基于最小二乘法的点云数据拼接研究[J].中国图象图形学报,2005,10(9)：1112-1116.
[10]盖绍彦,达飞鹏,雷明涛,郑君立.三维重构中的杂乱点云排序问题研究[J].计算机与现代化,2003,(10)：33-35.
[11]施法中.计算机辅助几何设计与非均匀有理B样条[M].北京：北京航天航空大学出版社,1994.
[12]Ping Xueliang, Zhou Rurong, An Luling. Application of grey system thoery to processing of measuring data in reverse engineering[J]. Transactions of NanJing University of Aeronautics, 2003,1:36-41.
[13]张国雄.三坐标测量机[M].天津：天津大学出版社,1999.
[14]P.F.Wu, F.H.Yu, etc. Analysis technique for the measurement of a three-dimensional object shape. Applied Optics,1993,32(5):737-742.
[15]Huntley J M. Optical shape measurement technology:past, present and future[J]. Proceedings of SPIE,2000,40(6):162-173.
[16]吴禄慎.基于相位法的三维面型测量及曲面重建技术[J].工程图学学报,2004,25(4)：62-68.
[17]金涛,童水光.逆向工程技术[M].北京：机械工业出版社,2003.
[18]赵柳,纪丽婷,王立建.逆向工程中点云数据的曲面重构方法研究[J].电子测试,2010,(2)：19-22.
[19]刘伟军,孙玉文.逆向工程原理、方法及应用[M].北京：机械工业出版社,2008.
[20]Sun Yunwen, Wang Yuechao, Liu Weijun. Free-form surface reconstruction basesd on NURBS to serial Cross- Sections[J]. Chinese Journal of Mechanical Engineering,2003,4: 420-423.
[21]Dyn N, Farkhi E. Spline subdivision schemes for convex compast sets[J]. Comp and App, 2000,119:133-144.
[22]Gabriella T, Marta P. A fast and reliable system for 3D surface acquisition and reconstruction[J]. Image and Vision Computing,2003,21:295-305.
[23]Guo B. Surface reconstruction:from points to splines [J]. Computer Aided Design,1997, 29(4):269-277.
[24]张宏伟,赵小松,张国雄.三维曲面重构技术[J].天津大学学报,2002,(3)：183-186.
[25]Du W H, Schmitt J M. On the G1 continuity of piecewise Bezier surface:a review with new results[J]. Computer Aided Design,1990, (9):556-573.
[26]Deng H, Benzvi A, Wiskela J B. B-spline approximation methods for digital image reconstruction in strain measurement [J]. Journal of Materials Processing Technology,2010, 210(4):593-602.
[27]Che X, Liang X, Li Q. G1 continuity conditions of adjacent NURBS surfaces [J]. Computer Aided Geometric Design,2005,22(4):285-298.
[28]Qin H, Mandal C, Vemuri B C. Dynamic Catmull-Clark subdivision surface[J]. IEEE Transactions on Visualization and Computer Graphics,1998,4(3):215-229.
[29]周密.基于逆向工程的曲面加工及快速制作技术研究[D].西安理工大学,2007.
[30]Meng F W, Wu L SH, Luo Liping.3D point clouds processing and precise surface reconstruction of the face[C]. The 2nd International Conference on Image Analysis and Signal Processing,2010:104-107.
[31]Soille P. Morphological phase unwrapping[J]. Optical Laser Engineering,2000,32(4): 339-352.
[32]Huntley J M, Coggrave C R. Progress in phase unwrapping[J]. SPIE,1998,34(7):86-93.
[33]孟凡文,吴禄慎.基于FTP的二维傅立叶变换的研究[J].激光与红外,2008,38(9)：995-997.
[34]J.M.Huntle, H.Saldner. Temporal phase-unwrapping algorithm for automated interferogram analysi. Appl.Opt,1993,12(17):3047-3052.
[35]孟凡文,吴禄慎,罗丽萍.三维面部数据采集与NURBS曲面重构[J].激光与红外,2010,40(3),335-338.
[36]刘军强,高建民,李言.基于逆向工程的点云数据预处理技术研究[J].仪器仪表与检测,2005,(7)：73-75.
[37]刘立国.点云模型的光顺区噪研究[D].浙江大学,2007.
[38]李道军,刘德平,上官建林.逆向工程中测量数据点的滤波[J].现代制造工程,2006,(3)：92-94.
[39]Chen Y H, Neg C T, Wang Y Z. Data reduction in integrated reverse engineering and rapid prototyping[J]. International Journal of Computer Integrated Manufacturing,1999,12(2): 97-103.
[40]周绿,林亨,钟约先.曲面重构中测量点云精简方法的研究[J].中国制造业信息化,2004,33(5)：102-104.
[41]Yang M, Lee E. Segmentation of measured point data using a parametric quadric surface approximation[J]. Computer Aided Design,1999,31:449-457.
[42]Woo H, Kang E, Wang S, et al. A new segmentation method for point cloud data[J]. International Journal of Machine tools & Manufacture,2002,42:167-178.
[43]孙玉文,吴宏基,刘建.基于NURBS的自由曲面精确建模方法研究[J].机械工程学报,2004,(3)：10-14.
[44]Ma W Y, But W CH, He P R. NURBS-based adaptive slicing for efficient rapid prototyping [J]. Computer Aided Design,2004,36(13):1309-1325.
[45]束长林.面向RE/NC的NURBS的集成设计方法研究[D].大连理工大学,2004.
[46]李旭,高峰,王玉林.基于逆向工程的车身测量点云分割方法研究[J].拖拉机与农用运输车,2008,35(5)：6-8.
[47]刘焕章.曲面拼接理论与技术的研究[D].首都师范大学,2007.
[48]Deng H, Benzvi A, Wiskela J B, et al. B-spline approximation methods for digital image reconstruction in strain measurement[J]. Journal of Materials Processing Technology,2010, 210(4):593-602.
[49]李忠学,彭启立,胡彩旗,等.基于光学非接触测量的车身覆盖件曲面品质综合评价[J].汽车技术,2004,25(2)：21-26.
[50]李庆扬,王能超,易大义.数值分析[M].武汉：华中科技大学出版社,2008.
[51]林昌华,赵利华.曲面光顺性检查及改进方法[J].重庆理工大学学报(自然科学),2010,(1)：103-106.
[52]霍晓程,李小平.用最小二乘法拟合曲面方程[J].赤峰学院学报,2009,25(6)：11-13.
[53]袁野,谢韶旺.基于逆向工程的曲面模型重构及误差分[J].应用科技,2008,35(12)：47-50.
[54]王宵,刘会霞,梁佳洪.逆向工程技术及其应用[M].北京：化学工业出版社,2004.
[55]Fan K C, Tsai T H. Optimal shape error analysis of the matching image for a free-form surfaces[J]. Robotics and computer-integrated manufacturing,2001,17:215-222.
[56]单岩,谢斌飞.Imageware逆向造型技术基础[M].北京：清华大学出版社,2006.
[57]徐惠霞.B样条多重乘积理论与有理曲线曲面多项式逼近技术的研究[D].浙江大学,2008.
[58]Vail N K, Willie W, Bieder H, et al. Interfacing reverse engineering data to rapid prototyping[C]. In:Solid Freeform Fabrication Symposium. Texas-USA,2006.
[59]陈厚道.面向快速成形的反求工程关键技术的研究[D].华中科技大学,2003.
[60]张勤,魏保立.应用CATIA的蜗形凸轮三维造型与数控加工[J].工程图学学报,2009,30(1)：193-195.
[61]王亚萍,葛江华,陈文忠.基于CATIA V5的型腔零件三维建模与NC加工[J].机械工程师,2008,(1)：20-22.
[62]严思杰,周云飞,彭芳瑜,等.大型复杂曲面零件加工余量均布优化问题研究[J].华中科技大学学报,2002,(10)：35-37.
[63]刘雄传.数控加工理论与编程技术[M].北京：机械工业出版社,2000.
[64]周济.数控加工技术[M].北京：国防工业出版社,2002.
[65]胡乾坤.基于CATIA平台五轴数控加工编程后置处理技术研究[D].沈阳航空工业学院,2007.
[2]刘涛,陈邦道,苏家强.反求工程技术及应用研究[J].装备制造技术,2006,(4)：45-47.
[3]Martin R R, Varady T, Cox J. Reverse engineering of geometric models-An introduction [J]. Computer Aided Design,1997,29(4):255-268.
[4]Berthold K, Horn P, Brooks M J. The variational approach to shape from point [J]. Computer Vision Graphics and Image Processing,1986,33:174-208.
[5]由志福.曲面形体三维相位法检测技术及CAD/CAM集成的研究[D].清华大学,1998.
[6]张丽娜,计欣华,陈金龙.光弹性八步相移法的研究和应用[J].机械强度,2009,31(3)：378-381.
[7]杨亚良,吴兰,丁志华.基于傅里叶变换的确定性相位去包裹算法的应用研究[J].光学仪器,2005,27(3)：33-36.
[8]官云兰,程效军,施贵刚.一种稳健的点云数据平面拟合方法[J].同济大学学报(自然科学版),2008,36(7)：981-984.
[9]沈海平,达飞鹏,雷家勇.基于最小二乘法的点云数据拼接研究[J].中国图象图形学报,2005,10(9)：1112-1116.
[10]盖绍彦,达飞鹏,雷明涛,郑君立.三维重构中的杂乱点云排序问题研究[J].计算机与现代化,2003,(10)：33-35.
[11]施法中.计算机辅助几何设计与非均匀有理B样条[M].北京：北京航天航空大学出版社,1994.
[12]Ping Xueliang, Zhou Rurong, An Luling. Application of grey system thoery to processing of measuring data in reverse engineering[J]. Transactions of NanJing University of Aeronautics, 2003,1:36-41.
[13]张国雄.三坐标测量机[M].天津：天津大学出版社,1999.
[14]P.F.Wu, F.H.Yu, etc. Analysis technique for the measurement of a three-dimensional object shape. Applied Optics,1993,32(5):737-742.
[15]Huntley J M. Optical shape measurement technology:past, present and future[J]. Proceedings of SPIE,2000,40(6):162-173.
[16]吴禄慎.基于相位法的三维面型测量及曲面重建技术[J].工程图学学报,2004,25(4)：62-68.
[17]金涛,童水光.逆向工程技术[M].北京：机械工业出版社,2003.
[18]赵柳,纪丽婷,王立建.逆向工程中点云数据的曲面重构方法研究[J].电子测试,2010,(2)：19-22.
[19]刘伟军,孙玉文.逆向工程原理、方法及应用[M].北京：机械工业出版社,2008.
[20]Sun Yunwen, Wang Yuechao, Liu Weijun. Free-form surface reconstruction basesd on NURBS to serial Cross- Sections[J]. Chinese Journal of Mechanical Engineering,2003,4: 420-423.
[21]Dyn N, Farkhi E. Spline subdivision schemes for convex compast sets[J]. Comp and App, 2000,119:133-144.
[22]Gabriella T, Marta P. A fast and reliable system for 3D surface acquisition and reconstruction[J]. Image and Vision Computing,2003,21:295-305.
[23]Guo B. Surface reconstruction:from points to splines [J]. Computer Aided Design,1997, 29(4):269-277.
[24]张宏伟,赵小松,张国雄.三维曲面重构技术[J].天津大学学报,2002,(3)：183-186.
[25]Du W H, Schmitt J M. On the G1 continuity of piecewise Bezier surface:a review with new results[J]. Computer Aided Design,1990, (9):556-573.
[26]Deng H, Benzvi A, Wiskela J B. B-spline approximation methods for digital image reconstruction in strain measurement [J]. Journal of Materials Processing Technology,2010, 210(4):593-602.
[27]Che X, Liang X, Li Q. G1 continuity conditions of adjacent NURBS surfaces [J]. Computer Aided Geometric Design,2005,22(4):285-298.
[28]Qin H, Mandal C, Vemuri B C. Dynamic Catmull-Clark subdivision surface[J]. IEEE Transactions on Visualization and Computer Graphics,1998,4(3):215-229.
[29]周密.基于逆向工程的曲面加工及快速制作技术研究[D].西安理工大学,2007.
[30]Meng F W, Wu L SH, Luo Liping.3D point clouds processing and precise surface reconstruction of the face[C]. The 2nd International Conference on Image Analysis and Signal Processing,2010:104-107.
[31]Soille P. Morphological phase unwrapping[J]. Optical Laser Engineering,2000,32(4): 339-352.
[32]Huntley J M, Coggrave C R. Progress in phase unwrapping[J]. SPIE,1998,34(7):86-93.
[33]孟凡文,吴禄慎.基于FTP的二维傅立叶变换的研究[J].激光与红外,2008,38(9)：995-997.
[34]J.M.Huntle, H.Saldner. Temporal phase-unwrapping algorithm for automated interferogram analysi. Appl.Opt,1993,12(17):3047-3052.
[35]孟凡文,吴禄慎,罗丽萍.三维面部数据采集与NURBS曲面重构[J].激光与红外,2010,40(3),335-338.
[36]刘军强,高建民,李言.基于逆向工程的点云数据预处理技术研究[J].仪器仪表与检测,2005,(7)：73-75.
[37]刘立国.点云模型的光顺区噪研究[D].浙江大学,2007.
[38]李道军,刘德平,上官建林.逆向工程中测量数据点的滤波[J].现代制造工程,2006,(3)：92-94.
[39]Chen Y H, Neg C T, Wang Y Z. Data reduction in integrated reverse engineering and rapid prototyping[J]. International Journal of Computer Integrated Manufacturing,1999,12(2): 97-103.
[40]周绿,林亨,钟约先.曲面重构中测量点云精简方法的研究[J].中国制造业信息化,2004,33(5)：102-104.
[41]Yang M, Lee E. Segmentation of measured point data using a parametric quadric surface approximation[J]. Computer Aided Design,1999,31:449-457.
[42]Woo H, Kang E, Wang S, et al. A new segmentation method for point cloud data[J]. International Journal of Machine tools & Manufacture,2002,42:167-178.
[43]孙玉文,吴宏基,刘建.基于NURBS的自由曲面精确建模方法研究[J].机械工程学报,2004,(3)：10-14.
[44]Ma W Y, But W CH, He P R. NURBS-based adaptive slicing for efficient rapid prototyping [J]. Computer Aided Design,2004,36(13):1309-1325.
[45]束长林.面向RE/NC的NURBS的集成设计方法研究[D].大连理工大学,2004.
[46]李旭,高峰,王玉林.基于逆向工程的车身测量点云分割方法研究[J].拖拉机与农用运输车,2008,35(5)：6-8.
[47]刘焕章.曲面拼接理论与技术的研究[D].首都师范大学,2007.
[48]Deng H, Benzvi A, Wiskela J B, et al. B-spline approximation methods for digital image reconstruction in strain measurement[J]. Journal of Materials Processing Technology,2010, 210(4):593-602.
[49]李忠学,彭启立,胡彩旗,等.基于光学非接触测量的车身覆盖件曲面品质综合评价[J].汽车技术,2004,25(2)：21-26.
[50]李庆扬,王能超,易大义.数值分析[M].武汉：华中科技大学出版社,2008.
[51]林昌华,赵利华.曲面光顺性检查及改进方法[J].重庆理工大学学报(自然科学),2010,(1)：103-106.
[52]霍晓程,李小平.用最小二乘法拟合曲面方程[J].赤峰学院学报,2009,25(6)：11-13.
[53]袁野,谢韶旺.基于逆向工程的曲面模型重构及误差分[J].应用科技,2008,35(12)：47-50.
[54]王宵,刘会霞,梁佳洪.逆向工程技术及其应用[M].北京：化学工业出版社,2004.
[55]Fan K C, Tsai T H. Optimal shape error analysis of the matching image for a free-form surfaces[J]. Robotics and computer-integrated manufacturing,2001,17:215-222.
[56]单岩,谢斌飞.Imageware逆向造型技术基础[M].北京：清华大学出版社,2006.
[57]徐惠霞.B样条多重乘积理论与有理曲线曲面多项式逼近技术的研究[D].浙江大学,2008.
[58]Vail N K, Willie W, Bieder H, et al. Interfacing reverse engineering data to rapid prototyping[C]. In:Solid Freeform Fabrication Symposium. Texas-USA,2006.
[59]陈厚道.面向快速成形的反求工程关键技术的研究[D].华中科技大学,2003.
[60]张勤,魏保立.应用CATIA的蜗形凸轮三维造型与数控加工[J].工程图学学报,2009,30(1)：193-195.
[61]王亚萍,葛江华,陈文忠.基于CATIA V5的型腔零件三维建模与NC加工[J].机械工程师,2008,(1)：20-22.
[62]严思杰,周云飞,彭芳瑜,等.大型复杂曲面零件加工余量均布优化问题研究[J].华中科技大学学报,2002,(10)：35-37.
[63]刘雄传.数控加工理论与编程技术[M].北京：机械工业出版社,2000.
[64]周济.数控加工技术[M].北京：国防工业出版社,2002.
[65]胡乾坤.基于CATIA平台五轴数控加工编程后置处理技术研究[D].沈阳航空工业学院,2007.