五轴NC铣削加工几何仿真中若干关键技术研究
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摘要
随着工业的不断发展，零件的几何形状越来越复杂，加工仿真已成为实际数控加工前NC程序验证和CL数据证实必不可少的一个环节。它也是CAD／CAM、CIMS和虚拟制造的重要内容之一，其中五轴NC加工仿真越来越受到研究者的重视，本文在参阅了大量相关文献的基础上，主要对五轴NC铣削加工几何仿真中的仿真速度、三维图形显示质量、仿真误差三项关键技术进行了研究。
在仿真速度方面：根据包络理论，以通用刀具几何模型为基础推导了刀具扫描体的显式求解方法，相对刀具扫描体的隐式求解方法，较大地提高了扫描体的计算速度；采用快速定位方法和快速求交算法，提高生成刀具扫描体dexel模型的速度；采用dexel模型的一维布尔运算方法，大大提高了“材料”移除过程的计算速度。
在图形显示方面：改进传统的dexel模型显示方法，在OpenGL环境中借助三角面片显示仿真图形，成功地实现了仿真图形的任意视点变换；采用改进WM_PAINT机制的动画方法和实时获取键盘消息的方法，提高了图形的显示质量和人机交互性能。
在仿真误差方面：通过对工件逼近误差、采样点的拾取误差和扫描体逼近误差的分析，给出了误差的计算公式和误差控制方法，提出了dexel优化建模方法，建立了仿真环境中的加工误差模型、刀杆与工件的干涉与碰撞检测模型。
另外，为了使本仿真模块能应用于CL数据驱动的加工仿真，在机床坐标系中建立了CL数据变换为本仿真模块驱动数据的数学模型。
经过加工仿真实验表明：五轴NC加工几何仿真在个人PC机上达到了仿真的实时性要求，有较高的图形显示质量和较好的人机交互性能。
With the development of modern industry, the geometrical shape of a part is becoming more and more complex. Machining simulation has become an indispensable and important processing to verify NC programs and CL data before actually machining. It is also an important field in CAD/CAM, CIMS and virtual manufacturing. Specially, many investigators have attached importance to 5-axis NC machining simulation. In this thesis, three key technologies have been solved partly such as simulation efficiency, high quality three-dimensiona graphics display and simulation errors.
For efficiency of simulation, the explicit solution has been obtained based on the theory of envelope with the geometrical model of general cutter. Calculational efficiency of a sweep volume of cutter has been geatly enhanced by our method comparing with the conventional implicit method. The approachs of finding intersecting points rapidly between triangles and lines which paralleling Z-axis and rapid location are proposed to improve forming dexel model of sweep volume of the cutter. One-dimensional bool subtraction of dexel models can be used to improve the efficiency of the processing for removing material.
As far displaying graphics, the point-view can be changed during machining simulation by displaying the perspective projections of triangles with OpenGL. Those techniques such as prefect WM_PAINT mechanism for animation and real-time capturing keyboard message are adopted to enhance the quality of graphics and the performance of man-machine interaction.
As far as simulation errors are concerned, analyzing approximation and sampling error of work-piece and cutter introduce models and controlling methods of errors. An optimized dexel model is presented as well. Machining error and collision detection are modeled between cutter holder and work-piece in simulation.
Moreover, CL data driving the simulation model conversion model from CL data to inputting data for machining simulation in the machine coordinate frame is represented to drive models of simulation by CL data.
Experiments are conducted to demonstrate the developed methods. The results show that these techniques are very efficient for real-time machining simulation, high quality three-dimensional graphics and performance for man-machine interaction.
在仿真速度方面：根据包络理论，以通用刀具几何模型为基础推导了刀具扫描体的显式求解方法，相对刀具扫描体的隐式求解方法，较大地提高了扫描体的计算速度；采用快速定位方法和快速求交算法，提高生成刀具扫描体dexel模型的速度；采用dexel模型的一维布尔运算方法，大大提高了“材料”移除过程的计算速度。
在图形显示方面：改进传统的dexel模型显示方法，在OpenGL环境中借助三角面片显示仿真图形，成功地实现了仿真图形的任意视点变换；采用改进WM_PAINT机制的动画方法和实时获取键盘消息的方法，提高了图形的显示质量和人机交互性能。
在仿真误差方面：通过对工件逼近误差、采样点的拾取误差和扫描体逼近误差的分析，给出了误差的计算公式和误差控制方法，提出了dexel优化建模方法，建立了仿真环境中的加工误差模型、刀杆与工件的干涉与碰撞检测模型。
另外，为了使本仿真模块能应用于CL数据驱动的加工仿真，在机床坐标系中建立了CL数据变换为本仿真模块驱动数据的数学模型。
经过加工仿真实验表明：五轴NC加工几何仿真在个人PC机上达到了仿真的实时性要求，有较高的图形显示质量和较好的人机交互性能。
With the development of modern industry, the geometrical shape of a part is becoming more and more complex. Machining simulation has become an indispensable and important processing to verify NC programs and CL data before actually machining. It is also an important field in CAD/CAM, CIMS and virtual manufacturing. Specially, many investigators have attached importance to 5-axis NC machining simulation. In this thesis, three key technologies have been solved partly such as simulation efficiency, high quality three-dimensiona graphics display and simulation errors.
For efficiency of simulation, the explicit solution has been obtained based on the theory of envelope with the geometrical model of general cutter. Calculational efficiency of a sweep volume of cutter has been geatly enhanced by our method comparing with the conventional implicit method. The approachs of finding intersecting points rapidly between triangles and lines which paralleling Z-axis and rapid location are proposed to improve forming dexel model of sweep volume of the cutter. One-dimensional bool subtraction of dexel models can be used to improve the efficiency of the processing for removing material.
As far displaying graphics, the point-view can be changed during machining simulation by displaying the perspective projections of triangles with OpenGL. Those techniques such as prefect WM_PAINT mechanism for animation and real-time capturing keyboard message are adopted to enhance the quality of graphics and the performance of man-machine interaction.
As far as simulation errors are concerned, analyzing approximation and sampling error of work-piece and cutter introduce models and controlling methods of errors. An optimized dexel model is presented as well. Machining error and collision detection are modeled between cutter holder and work-piece in simulation.
Moreover, CL data driving the simulation model conversion model from CL data to inputting data for machining simulation in the machine coordinate frame is represented to drive models of simulation by CL data.
Experiments are conducted to demonstrate the developed methods. The results show that these techniques are very efficient for real-time machining simulation, high quality three-dimensional graphics and performance for man-machine interaction.
引文
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[7] http://www. e-works.net.cn//ewkarticles/skjs.htm,五轴数控技术专题．
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Inj. of MACHINE TOOLS& MANUFACTURE 2002 42 1497-1507.
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[30] 范良志，张建钢，杨光友，钟飞，五轴数控铣削加工图形仿真技术，机电一体化，2000，1，45-48．
[31] 方强，张建钢，周国柱，吴斌方，数控加工仿真中换视向问题的研究，CAM与数控加工，2001，8．36-37
[32] 梁小军，韩向利，肖田元，阮建兴，材料切除过程三维动画仿真软件GNCV，系统仿真学报，1998，10，8-13．
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[36] 牛文博，刘进，朱松，一种数控铣床的仿真算法，计算机辅助设计与图形学学报，2002，14(5)，464-467．
[37] 罗，在微机上实现数控铣床加工仿真，计算机辅助设计与图形学学报，2000，12(3)，203-206．
[38] Chung YC, Park JW, Shin H, Choi BK. Modeling the surfaces swept by a generalized cutter for NC verification. Computer Aided Design, 1998, 30(8), 587-94.
[39] Seung Ryol Maeng,Nakhoon Baek,Sung Yong Shin,Byoung kyu Choi, A z-map update method for linearly moving tools, Computer Aided Design, 2002, 34, 1-15.
[40] 韩向利，袁哲俊，肖田元，温秀梅，直线与刀具扫描体求交算法及其应用研究，计算机辅助设计与图形学学报，1997，9(2)，123-129．
[41] D. Blackmore, M.C. Leu, A differential equation approach to swept volumes, 1990, IEEE, 143-149.
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[43] Liping Wang Ming C.Leu, Generating swept solids for NC verification using the SEDE method ACM 1097 364-375.
[44] Blackmore, D., Leu, M.C. and Wang, K.K. (1992a), Application of flows and envelopes to NC machining, Annals of the CIRP 41 (1), 493-496.
[45] Stephane Boussac etc. Swept Volumes Generated from Deformable objects application to NC verification, Proceedings of the 1996 IEEE International conference on robotics and automation minneapoies. 1813-1818.
[46] Wang Guoping, The sweep-envelope differential equation algorithm for general deformed swept volumes, Computer Aided Geometric Design, 2000, 17, 399-418.
[47] W.P. Wang and K.K. Wang. Geometric modeling for swept volume of moving solids. IEEE Computer Graphics and Applications, 1986, 6(12), 8-17.
[48] D.Roth, S.Bedi, F.Ismail,S.Mann, Surface swept by a toroidal cutter during 5-axis machining, Computer Aided Design, 2001 57-63.
[49] Khalid Sheltami, Sanjeev Bedi, Swept volumes of toroidal cutters using generating curves, Int. J.of machine tools & Manufacture 1998 vol.38 855-870.
[50] William J. Schroeder, William E. Lorensen, Implicit Modeling of Swept Surfaces and Volumes,
IEEE,1994, 40-45.
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[62] Andrew Warkentin etc. Comparison between multi-point and other 5-axis tool positioning strategies, International Journal of Machine Tools & Manufacture, 2000, 40, 185-208.
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[2] Albert. M. Five-axis machining proves its worth. Modern Machine Shop, 1986, 59(5), 54-62.
[3] Kim BH, Chu CN. Effect of cutter mark on surface roughness and scallop height in sculptured surface machining, Computer-Aided Design, 1994, 26(3), 179-188.
[4] Vickers GW, Quan KW. Ball-mills versus end-mills for curved surface machining. ASME Journal of Engineering for Industry, 1989, 111, 22-26.
[5] G. Elber, Freeform surface region optimization for 3-axis and 5-axis milling, Computer-Aided Design, 1995, 27(6), 465-469.
[6] Chih-Ching Lo,Real-time generation and control of cutter path for 5-axis CNC machining, International Journal of Machine Tools & Manufacture, 1999, 39, 471-488.
[7] http://www. e-works.net.cn//ewkarticles/skjs.htm,五轴数控技术专题．
[8] Khalid Sheltami, Sanjeev Bedi, Fathy Ismail, Swept volumes of toroidal cutters using generating curves, International Journal of Machine Tools & Manufacture, 1998, 38, 855-870.
[9] G. Elber, E. Cohen A unified approach to verification in 5-axis freeform milling environments, Computer-Aided Design, 1999, 31,795-804.
[10] Admissible tool orientation control of gouging avoidance for 5-axis complex surface machining, Computer-Aided Design, 1997, 29(7), 507-521.
[11] 李光耀，一种适用于微机的三轴加工仿真算法，计算机辅助工程，1998，1，18-22．
[12] 李吉平，张文铭，黄田，NC图形验证与仿真技术的研究概况，计算机仿真，2001，18(5)，52-55．
[13] Jerard RB, Drysdale RL, Hauck K, Schaudt B, Magewick J. Methods for detecting errors in numerically controlled machining of sculptured surfaces. IEEE Computer Graphics & Applications, 1989, 9(1), 26-39.
[14] L.J. Bohez etc. The stencil buffer sweep plane algorithm for 5-axis CNC tool path verification, Computer-Aided Design, 2003, 1-14.
[15] Chappel LT, The use of vector to simulate material removed by numerically controlled milling, Computer-Aided Design, 1983, 15(3), 156-158.
[16] Oliver JH, Goodman ED. Color graphic verification of N/C milling programs for sculptured surface parts. First symposium on integrated intelligent manufacturing, New York: ASME; 1986.
[17] Robert L. (Scot) Drysdale , Robert B. Jerard, Barry Schaudt, and Ken Hauck, Discrete Simulation of NC Machining, Algorithmica, 1989, 4, 33-60.
[18] Yang M, Lee E. NC verification for wire-EDM using an r-map, Computer-Aided Design, 2002, 25(4), 207-216.
[19] Wang WP, Wang KK, Geometric modeling for swept volume of moving solids. IEEE Computer Graphics & Applications, 1986, 6(12), 8-17.
[20] Van Hook T. Real-time shaded NC milling display. SIGGRAPH'86 Proc, 1986, 20(4),15-20.
[21] Huang Y, Oliver JH. Integrated simulation, error assessment, and tool path correction for five-axis NC machining. J Manufact Syst 1995, 14(5), 331-334,
[22] Andreas Holger Konig and Eduard Groller , Real Time Simulation and Visualization of NC Milling Processes for Inhomogeneous Materials on Low-End Graphics Hardware , http://www.cg.tuwien.ac.at/home.
[23] C.-J. Chiou, Y.-S. Lee A shape-generating approach for multi-axis machining G-buffer models, Computer-Aided Design, 1999, 31, 761-776.
[24] C.-J. Chiou, Y.-S. Lee Swept surface determination for five-axis numerical control machining
Inj. of MACHINE TOOLS& MANUFACTURE 2002 42 1497-1507.
[25] C.-J Chou. Robust Computational Analysis Methods for Multiple-Axis Machining in CAD/CAM/CNC Systems, UMI 2000 doctor.
[26] Kawashima Y, Itoh K, Ishida T, Nonaka S., and Ejiri K. A flexible quantitative method for NC machining verification using a space-division based solid model. Visual Computer, 1991, 7, 149-157.
[27] 朝向利，肖田元等，虚拟加工环境的开发与研究，计算机应用，2000，20，234-237．
[28] 赵继政，魏生民，杨彭基，基于图像空间的数控加工图形仿真，中国机械工程，1998，9(5)，28-31．
[29] 汤幼宁，魏生民，杨海成，基于dexel模型的NC加工仿真和验证研究．西北工业大学学报，1997，15(4)，629-633．
[30] 范良志，张建钢，杨光友，钟飞，五轴数控铣削加工图形仿真技术，机电一体化，2000，1，45-48．
[31] 方强，张建钢，周国柱，吴斌方，数控加工仿真中换视向问题的研究，CAM与数控加工，2001，8．36-37
[32] 梁小军，韩向利，肖田元，阮建兴，材料切除过程三维动画仿真软件GNCV，系统仿真学报，1998，10，8-13．
[33] 王庆霞等，集成环境下NC加工的图形仿真技术研究与实现，CAM与数控加工，57-58．
[34] 张胜等，数控加工过程可视化的实现方法，计算机应用研究，2000，9，78-80．
[35] 李光耀．叶佩青，王清辉，周来水，周儒荣，雕塑曲面数控加工的动态仿真及误差检测，南京航空航天大学学报，1997，29，408-412．
[36] 牛文博，刘进，朱松，一种数控铣床的仿真算法，计算机辅助设计与图形学学报，2002，14(5)，464-467．
[37] 罗，在微机上实现数控铣床加工仿真，计算机辅助设计与图形学学报，2000，12(3)，203-206．
[38] Chung YC, Park JW, Shin H, Choi BK. Modeling the surfaces swept by a generalized cutter for NC verification. Computer Aided Design, 1998, 30(8), 587-94.
[39] Seung Ryol Maeng,Nakhoon Baek,Sung Yong Shin,Byoung kyu Choi, A z-map update method for linearly moving tools, Computer Aided Design, 2002, 34, 1-15.
[40] 韩向利，袁哲俊，肖田元，温秀梅，直线与刀具扫描体求交算法及其应用研究，计算机辅助设计与图形学学报，1997，9(2)，123-129．
[41] D. Blackmore, M.C. Leu, A differential equation approach to swept volumes, 1990, IEEE, 143-149.
[42] D. Blackmore, M.C. Leu, and L.P. Wang. The sweep-envelope differential equation algorithm and its application to NC machining verification. Computer Aided Design, 1997, 29(9), 629-637.
[43] Liping Wang Ming C.Leu, Generating swept solids for NC verification using the SEDE method ACM 1097 364-375.
[44] Blackmore, D., Leu, M.C. and Wang, K.K. (1992a), Application of flows and envelopes to NC machining, Annals of the CIRP 41 (1), 493-496.
[45] Stephane Boussac etc. Swept Volumes Generated from Deformable objects application to NC verification, Proceedings of the 1996 IEEE International conference on robotics and automation minneapoies. 1813-1818.
[46] Wang Guoping, The sweep-envelope differential equation algorithm for general deformed swept volumes, Computer Aided Geometric Design, 2000, 17, 399-418.
[47] W.P. Wang and K.K. Wang. Geometric modeling for swept volume of moving solids. IEEE Computer Graphics and Applications, 1986, 6(12), 8-17.
[48] D.Roth, S.Bedi, F.Ismail,S.Mann, Surface swept by a toroidal cutter during 5-axis machining, Computer Aided Design, 2001 57-63.
[49] Khalid Sheltami, Sanjeev Bedi, Swept volumes of toroidal cutters using generating curves, Int. J.of machine tools & Manufacture 1998 vol.38 855-870.
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