五轴加工奇异问题分析与非线性误差控制
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摘要
在计算机辅助制造软件中进行五轴加工编程时,后置处理反求旋转轴角度存在无解,即五轴加工的奇异问题,具体表现为旋转轴运动产生突变、非线性误差增大、加工质量下降。以A-C型五轴机床为例,通过研究刀轴的运动过程,证明C轴的转角是奇异问题产生的原因。基于该结论提出一种新的检测奇异刀位点的刀轴分量k值遍历法和基于刀轴矢量插值与样条曲线拟合的非线性误差控制方案。通过S样件的五轴加工实验表明,相比于线性插值,所提方案在奇异区域内误差显著减小,曲面更加光滑,加工效率有所提高。
Tool orientation is very complicated for the 5-axis machining. At the singularity point of a 5-axis machine, there is no solution to the inverse kinematics when the post-processing is performed by CAM software, which leads to acute change of rotation axis. As a result, the non-linear error increases while the machining quality decreases. By taking a Table(C-axis)-tilting(A-axis) 5-axis machine as an example, the C-axis rotation was proved to be the reason of the singularity problem by studying the tool axis movement. Then a novel k-value method of cutter location data was proposed for detecting whether the tool axis vector is located in singular region. A scheme based on tool axis vector planar interpolation and spline curve fitting to control non-linear error was also proposed. Through the S surface test, the proposed method was demonstrated much better than the linear interpolation. Experiment results showed that the non-linear errors in singularity area declined significantly, the surface was smoother and the machining accuracy and efficiency were also improved.
Tool orientation is very complicated for the 5-axis machining. At the singularity point of a 5-axis machine, there is no solution to the inverse kinematics when the post-processing is performed by CAM software, which leads to acute change of rotation axis. As a result, the non-linear error increases while the machining quality decreases. By taking a Table(C-axis)-tilting(A-axis) 5-axis machine as an example, the C-axis rotation was proved to be the reason of the singularity problem by studying the tool axis movement. Then a novel k-value method of cutter location data was proposed for detecting whether the tool axis vector is located in singular region. A scheme based on tool axis vector planar interpolation and spline curve fitting to control non-linear error was also proposed. Through the S surface test, the proposed method was demonstrated much better than the linear interpolation. Experiment results showed that the non-linear errors in singularity area declined significantly, the surface was smoother and the machining accuracy and efficiency were also improved.
引文
[1] WANG Feng,LIN Hu,ZHENG Liaomo,et al.Detection and treatment of singular area in five-axis machining[J].Computer Integrated Manufacturing Systems,2011,17(7):1435-1440(in Chinese).[王峰,林浒,郑飂默,等.五轴加工奇异区域的检测和处理[J].计算机集成制造系统,2011,17(7):1435-1440.]
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[3] MUNLIN M,MAKHANOV S S,BOHEZ E L J.Optimization of rotations of a five-axis milling machine near stationary points[J].Computer-Aided Design,2004,36(12):1117-1128.
[4] MAKHANOV S S,MUNLIN M.Optimal sequencing of rotation angles for five-axis machining[J].International Journal of Advanced Manufacturing Technology,2007,35(1/2):41-54.
[5] S?RBY K.Inverse kinematics of five-axis machines near singular configurations[J].International Journal of Machine Tools and Manufacture,2007,47(2):299-306.
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[9] WANG Dan,CHEN Zhitong,CHEN Wuyi.Detection and control of non-linear errors in 5-axis machining[J].Journal of Beijing University of Aeronautics and Astronautics,2008,34(9):1003-1006,1091(in Chinese).[王丹,陈志同,陈五一.五轴加工中非线性误差的检测和处理方法[J].北京航空航天大学学报,2008,34(9):1003-1006,1091.]
[10] ZHENG Liaomo,LIN Hu,ZHANG Xiaohui,et al.Control of the non-linear errors in five-axis NC machining based on real time interpolation[J].Journal of Chinese Computer Systems,2010,31(7):1389-1392(in Chinese).[郑飂默,林浒,张晓辉,等.基于实时插补的五轴加工非线性误差控制[J].小型微型计算机系统,2010,31(7):1389-1392.]
[11] ZHENG Liaomo,LIN Hu,GAI Rongli,et al.Fast smooth interpolation control strategy of rotary axes for five-axis CNC systems[J].Journal of Mechanical Engineering,2011,47(9):105-111(in Chinese).[郑飂默,林浒,盖荣丽,等.五轴数控系统旋转轴快速平滑插补控制策略[J].机械工程学报,2011,47(9):105-111.]
[12] YANG Xujing,ZHOU Yuansheng,CHEN Zezhong,et al.Analysis andcontrol of tool path interpolation error in rotary axes motions of five-axis CNC milling[J].Journal of Mechanical Engineering,2012,48(3):140-146(in Chinese).[杨旭静,周元生,陈泽忠,等.五轴数控加工中旋转轴运动引起的非线性误差分析及控制[J].机械工程学报,2012,48(3):140-146.]
[13] LI Xianshuang,FAN Liuqun,QI Dangjin.5-axis singular problem and its processing method[J].Modular Machine Tool & Automatic Manufacturing Technique,2013(6):37-39,43(in Chinese).[李显双,樊留群,齐党进.五轴加工奇异问题及其处理方法[J].组合机床与自动化加工技术,2013(6):37-39,43.]
[14] FAN Liuqun,QI Dangjin,SHEN Bin,et al.Plane interpolation of tool orientation algorithm for 5-axis circumference milling[J].Journal of Mechanical Engineering,2011,47(19):158-162(in Chinese).[樊留群,齐党进,沈斌,等.五轴联动刀轴矢量平面插补算法[J].机械工程学报,2011,47(19):158-162.]
[15] LIN Zhiwei,FU Jianzhong,SHEN Hongyao,et al.Non-singular tool path planning by translating tool orientations in C-space[J].International Journal of Advanced Manufacturing Technology,2014,71(9/10/11/12):1835-1848.
[16] ZHANG Jun,ZHANG Liqiang,ZHANG Shoujun,et al.Isometric double-NURBS synchronous interpolation algorithm for five-axis machining[J].Computer Integrated Manufacturing Systems,2015,21(6):1523-1528(in Chinese).[张君,张立强,张守军,等.面向五轴加工的等距双NURBS刀具路径同步插补方法[J].计算机集成制造系统,2015,21(6):1523-1528.]
[17] HU Zeqi,QIN Xunpeng,WU Rui,et al.Teaching-programing technique for spatial curve of five-axis NC machining[J].Computer Integrated Manufacturing Systems,2016,22(12):2836-2844(in Chinese).[胡泽启,秦训鹏,吴锐,等.五轴加工空间曲线示教编程技术[J].计算机集成制造系统,2016,22(12):2836-2844.]
[2] AFFOUARD A,DUC E,LARTIGUE C,et al.Avoiding 5-axis singularities using tool path deformation[J].International Journal of Machine Tools and Manufacture,2004,44(4):415-425.
[3] MUNLIN M,MAKHANOV S S,BOHEZ E L J.Optimization of rotations of a five-axis milling machine near stationary points[J].Computer-Aided Design,2004,36(12):1117-1128.
[4] MAKHANOV S S,MUNLIN M.Optimal sequencing of rotation angles for five-axis machining[J].International Journal of Advanced Manufacturing Technology,2007,35(1/2):41-54.
[5] S?RBY K.Inverse kinematics of five-axis machines near singular configurations[J].International Journal of Machine Tools and Manufacture,2007,47(2):299-306.
[6] WANG Feng,LIN Hu,LIU Feng,et al.Tool path optimization of five-axis machining in singular area[J].Journal of Mechanical Engineering,2011,47(19):174-180(in Chinese).[王峰,林浒,刘峰,等.五轴加工奇异区域内的刀具路径优化[J].机械工程学报,2011,47(19):174-180.]
[7] YU Dan,YAN Guangrong,FAN Qingxiang,et al.Research on optimization of rotation angle and singular area handling in five-axis post-processing[J].Journal of Graphics,2016,37(5):614-619(in Chinese).[余丹,闫光荣,范庆香,等.五轴后置处理转角选解优化及奇异区域处理方法的研究[J].图学学报,2016,37(5):614-619.]
[8] WU Dazhong,WANG Yuhan,FENG Jingchun,et al.Analysis and control of the non-linear errors in five-axis NC machining[J].Journal of Shanghai Jiaotong University,2007,41(10):1608-1612(in Chinese).[吴大中,王宇晗,冯景春,等.五坐标数控加工的非线性运动误差分析与控制[J].上海交通大学学报,2007,41(10):1608-1612.]
[9] WANG Dan,CHEN Zhitong,CHEN Wuyi.Detection and control of non-linear errors in 5-axis machining[J].Journal of Beijing University of Aeronautics and Astronautics,2008,34(9):1003-1006,1091(in Chinese).[王丹,陈志同,陈五一.五轴加工中非线性误差的检测和处理方法[J].北京航空航天大学学报,2008,34(9):1003-1006,1091.]
[10] ZHENG Liaomo,LIN Hu,ZHANG Xiaohui,et al.Control of the non-linear errors in five-axis NC machining based on real time interpolation[J].Journal of Chinese Computer Systems,2010,31(7):1389-1392(in Chinese).[郑飂默,林浒,张晓辉,等.基于实时插补的五轴加工非线性误差控制[J].小型微型计算机系统,2010,31(7):1389-1392.]
[11] ZHENG Liaomo,LIN Hu,GAI Rongli,et al.Fast smooth interpolation control strategy of rotary axes for five-axis CNC systems[J].Journal of Mechanical Engineering,2011,47(9):105-111(in Chinese).[郑飂默,林浒,盖荣丽,等.五轴数控系统旋转轴快速平滑插补控制策略[J].机械工程学报,2011,47(9):105-111.]
[12] YANG Xujing,ZHOU Yuansheng,CHEN Zezhong,et al.Analysis andcontrol of tool path interpolation error in rotary axes motions of five-axis CNC milling[J].Journal of Mechanical Engineering,2012,48(3):140-146(in Chinese).[杨旭静,周元生,陈泽忠,等.五轴数控加工中旋转轴运动引起的非线性误差分析及控制[J].机械工程学报,2012,48(3):140-146.]
[13] LI Xianshuang,FAN Liuqun,QI Dangjin.5-axis singular problem and its processing method[J].Modular Machine Tool & Automatic Manufacturing Technique,2013(6):37-39,43(in Chinese).[李显双,樊留群,齐党进.五轴加工奇异问题及其处理方法[J].组合机床与自动化加工技术,2013(6):37-39,43.]
[14] FAN Liuqun,QI Dangjin,SHEN Bin,et al.Plane interpolation of tool orientation algorithm for 5-axis circumference milling[J].Journal of Mechanical Engineering,2011,47(19):158-162(in Chinese).[樊留群,齐党进,沈斌,等.五轴联动刀轴矢量平面插补算法[J].机械工程学报,2011,47(19):158-162.]
[15] LIN Zhiwei,FU Jianzhong,SHEN Hongyao,et al.Non-singular tool path planning by translating tool orientations in C-space[J].International Journal of Advanced Manufacturing Technology,2014,71(9/10/11/12):1835-1848.
[16] ZHANG Jun,ZHANG Liqiang,ZHANG Shoujun,et al.Isometric double-NURBS synchronous interpolation algorithm for five-axis machining[J].Computer Integrated Manufacturing Systems,2015,21(6):1523-1528(in Chinese).[张君,张立强,张守军,等.面向五轴加工的等距双NURBS刀具路径同步插补方法[J].计算机集成制造系统,2015,21(6):1523-1528.]
[17] HU Zeqi,QIN Xunpeng,WU Rui,et al.Teaching-programing technique for spatial curve of five-axis NC machining[J].Computer Integrated Manufacturing Systems,2016,22(12):2836-2844(in Chinese).[胡泽启,秦训鹏,吴锐,等.五轴加工空间曲线示教编程技术[J].计算机集成制造系统,2016,22(12):2836-2844.]