NURBS曲线插补实时前瞻控制方法的研究
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摘要
数控系统被称为机床的“大脑”,是数控装备的核心,它关系到国家经济利益、产业安全和国防安全,在国家工业制造中起着非常重要的作用。运动控制器作为数控系统的核心,其最重要的部分是插补器,插补器所具有的插补功能可以决定数控系统档次的高低。
当前大部分的计算机数控系统只提供小线段和圆弧插补,CAD/CAM系统只得按照要求的精度将参数曲线离散成大量的微小线段后传到CNC中进行零件加工,这种处理方式存在着加工指令多,加工精度低等缺点。高速高精、复杂运动轨迹的运动控制技术是当前运动控制算法研究的热点,NURBS曲线插补技术是其典型代表。NURBS作为描述自由型曲线的标准已被广泛应用于CAD/CAM软件中,它解决了使用小线段进行插补的缺点,具有可靠性高、加工时间短、精度高等优点。
本文对常用的加减速规划方法进行比较,分析了影响机床加工的各种因素,采用现有的S曲线速度规划方法对NURBS插补进行加减速控制,设计了一种基于曲率变化率的段内前瞻预测S曲线减速点的方法,该方法能够动态预测减速点的起始位置,提高了减速点判断的精度,实现了加速度的连续控制。本算法分为预处理和实时插补两部分,预处理中进行一次快速插补过程得到NURBS曲线的相关信息并将加工曲线按曲率的变化率进行分段,实时插补过程中按分段的类型进行插补,并在段内进行动态前瞻。仿真实验结果表明,该插补算法能够在保证加工精度的前提下,实现速度和加速度的平滑过渡。
The CNC(computer numerical control) system is called the "brain" of the machine tool, it is the kernel of the numerical control equipments, it relates to our country economy, industry safety and national security. So it plays a very important role in natioanl industry. Further, in the CNC, the motion controler is very important in which its kernel is interpolation. Interpolation function can determines the grade of CNC.
Present, most CNC provide liner and circle interpolation, so CAD/CAM have to disperse the curve into minuteness liners then pass them to CNC to finish machining. The process will lead too many programes and less accuracy. High speed, high accuray, complex motion trajectory motion control method is the researching hot, NURBS interpolation is typical representative, it resovles the probem which the liner interplotion comes with, and the NURBS interpolation have many advantages, for example, high reliability, short maching time and high accuracy.
This dissertation compares the common accelerate/decelerate methods, analyzes the factors that affect the real machining. Using the present S-shape accelerate/decelerate to combine with the NURBS interplation, design a real-time looking-forward NURBS interpolation algorithm which can forecast the decelerating points based on curvatures changing rate with smooth accelerate, solving the problem of the traditional way which calculates decelerating points accompanied with error. This algorithm has a looking-ahead interpolation and a real-time interpolation. First, the curve is dividing into some segments according to the different curvature changing rate after looking-ahead. Second, the real-time interpolation is working within the segments with a looking-forward process which can forcast the starting point of the third stage to the S-shape A/D. By the results of simulations, it demonstrats that this interpolator can get a smooth feedrate and accelerate profile with high machining accuracy.
当前大部分的计算机数控系统只提供小线段和圆弧插补,CAD/CAM系统只得按照要求的精度将参数曲线离散成大量的微小线段后传到CNC中进行零件加工,这种处理方式存在着加工指令多,加工精度低等缺点。高速高精、复杂运动轨迹的运动控制技术是当前运动控制算法研究的热点,NURBS曲线插补技术是其典型代表。NURBS作为描述自由型曲线的标准已被广泛应用于CAD/CAM软件中,它解决了使用小线段进行插补的缺点,具有可靠性高、加工时间短、精度高等优点。
本文对常用的加减速规划方法进行比较,分析了影响机床加工的各种因素,采用现有的S曲线速度规划方法对NURBS插补进行加减速控制,设计了一种基于曲率变化率的段内前瞻预测S曲线减速点的方法,该方法能够动态预测减速点的起始位置,提高了减速点判断的精度,实现了加速度的连续控制。本算法分为预处理和实时插补两部分,预处理中进行一次快速插补过程得到NURBS曲线的相关信息并将加工曲线按曲率的变化率进行分段,实时插补过程中按分段的类型进行插补,并在段内进行动态前瞻。仿真实验结果表明,该插补算法能够在保证加工精度的前提下,实现速度和加速度的平滑过渡。
The CNC(computer numerical control) system is called the "brain" of the machine tool, it is the kernel of the numerical control equipments, it relates to our country economy, industry safety and national security. So it plays a very important role in natioanl industry. Further, in the CNC, the motion controler is very important in which its kernel is interpolation. Interpolation function can determines the grade of CNC.
Present, most CNC provide liner and circle interpolation, so CAD/CAM have to disperse the curve into minuteness liners then pass them to CNC to finish machining. The process will lead too many programes and less accuracy. High speed, high accuray, complex motion trajectory motion control method is the researching hot, NURBS interpolation is typical representative, it resovles the probem which the liner interplotion comes with, and the NURBS interpolation have many advantages, for example, high reliability, short maching time and high accuracy.
This dissertation compares the common accelerate/decelerate methods, analyzes the factors that affect the real machining. Using the present S-shape accelerate/decelerate to combine with the NURBS interplation, design a real-time looking-forward NURBS interpolation algorithm which can forecast the decelerating points based on curvatures changing rate with smooth accelerate, solving the problem of the traditional way which calculates decelerating points accompanied with error. This algorithm has a looking-ahead interpolation and a real-time interpolation. First, the curve is dividing into some segments according to the different curvature changing rate after looking-ahead. Second, the real-time interpolation is working within the segments with a looking-forward process which can forcast the starting point of the third stage to the S-shape A/D. By the results of simulations, it demonstrats that this interpolator can get a smooth feedrate and accelerate profile with high machining accuracy.
引文
[1]邓奕.现代数控机床及应用[M].第1版.国防工业出版社, 2008.10:1-10.
[2]冯勇.现代计算机数控系统[M].第1版.机械工业出版社, 1999.7:100-150.
[3] C H Yang Daniel,Tom Kong. Parametric Interpolator Versus Linear Interpolator for Precision CNC Machining[J].CAD,1994(26).
[4]李思益,罗为. NURBS曲线高速高精插补及加减速控制方法研究[J].计算机集成制造系统, 2008,14(06):3411-3414
[5] Bedi S,Ali I,Quan N. Advanced interpolation techniques for CNC machines .ASME ,Journal of Engineering for Industry[J], 1993,115 (08) :329-336 .
[6] Yeh S-S, Hsu P L. The speed-controllled interpolator for machining parametric curves[J] .Computer-Aided Design, 1999, 31 (05) :349-357 .
[7] Syh-Shiuh Yeh, Pau-Lo Hsu. Adaptive-feedrate interpolation for parametric curves with a confined chord error[J] .Computer-Aided Design, 2002,34 (03) :229-237 .
[8]徐宏,胡自化,张平,杨冬香,杨端光.基于冗余误差控制的非均匀有理B样条曲线插补算法研究[J].计算机集成制造系统, 2007,13(05) :962-966
[9]梁宏斌,王永章,李霞.自动调节进给速度的NURBS插补算法的研究与实现[J].计算机集成制造系统, 2006,12(03):429-432
[10] Sung-Ho Nam, Min-Yang Yang. A study on a generalized parametric interpolator with real-time jerk-limited acceleration[J] .Computer-Aided Design, 2004,36 (01) :27-36.
[11]杜道山,燕存良,李从心.一种实时前瞻的自适应NURBS插补算法[J].上海交通大学学报,2006.5,40(05):844-847
[12]冷洪斌,邬义杰,潘晓弘.三次多项式型微段高速自适应前瞻插补方法[J].机械工程学报,2009,45(06):73-79.
[13]姬晓天,施寅. NURBS的概念与使用.计算机辅助设计与制造[J], 1998 ,12, 25-26.
[14] Pieg1,L.,and Ti11er,W. The NURBS Book[M],berlin, springer,1995 .
[15] Piegl. L. Modifying the shape of rational B-spline[M], Part 1:curves. CAD 1989, 21:509-518.
[16]潘日晶. NURBS曲线曲面的显式矩阵表示及其算法[J].计算机学报, 2001,24(04) :355-366
[17] Choi B K,Yoo W S,L ee C s.Matrix representation for NURBS curves and surfaces[J]. Computer-Aided Design, 1990,22 (04) :235-240.
[18]李曦,唐小琦. NC伺服的加减速控制算法的研究与实现[J].机床与液压, 2000,(3):3-5
[19]胡鸿豪,吴勇翀,肖绚. CNC系统直线加减速优化算法[J].机床与液压, 2008,36(05):287-289
[20]朱晓春,屈波,孙来业,汪木兰. S曲线加减速控制方法研究[J].中国制造业信息化, 2006,35(23):38-43
[21]陈绪兵,熊蔡华,熊有伦. S曲线加减速模式下的加工轨迹效率评价[J].华中科技大学学报(自然科学版), 2008,36(02) :1-4
[22]何均,游有鹏,陈浩,王化明.形加减速的嵌套式前瞻快速算法[J].航空学报, 2010,31(04) :843-844
[23]吴宇燕,彭志牛,王宇晗. NURBS曲线数控插补方法及误差控制[J].机械设计与研究,2006.8, 22(4) :76-80
[24] R.T. Farouli,YF. Tsai,Exact Taylor series coefficient for variable-feedrate CNC curve interpolators[J].Computer-Aided Design, 2001,33(05): 155-165.
[25] Cunliang Yan,Daoshan Du,Congxin Li. Design of a real-time adaptive interpolator with parameter compensation[J] .Inter-national Journal of Machine Tools and Manufacture. 2007, 35 :169-178 .
[26] Ming-Tzong Lin,Tsai Meng-Shiun,Yau Hong- Tzong. Development of a dynamics -based NURBS interpolator with real-time look-ahead algorithm[C]. International Journal of Machine Tools and Manufacture, 2007(06):1-17.
[27]孙玉娥,林浒.基于前瞻算法的高效非均匀有理B样条曲线插补器[J].计算机集成制造系统,2009,15(10):2029-2033
[28]周凯,陆启建.高速高精度采样插补技术[J].中国机械工程, 1998,9(10): 15-18.
[2]冯勇.现代计算机数控系统[M].第1版.机械工业出版社, 1999.7:100-150.
[3] C H Yang Daniel,Tom Kong. Parametric Interpolator Versus Linear Interpolator for Precision CNC Machining[J].CAD,1994(26).
[4]李思益,罗为. NURBS曲线高速高精插补及加减速控制方法研究[J].计算机集成制造系统, 2008,14(06):3411-3414
[5] Bedi S,Ali I,Quan N. Advanced interpolation techniques for CNC machines .ASME ,Journal of Engineering for Industry[J], 1993,115 (08) :329-336 .
[6] Yeh S-S, Hsu P L. The speed-controllled interpolator for machining parametric curves[J] .Computer-Aided Design, 1999, 31 (05) :349-357 .
[7] Syh-Shiuh Yeh, Pau-Lo Hsu. Adaptive-feedrate interpolation for parametric curves with a confined chord error[J] .Computer-Aided Design, 2002,34 (03) :229-237 .
[8]徐宏,胡自化,张平,杨冬香,杨端光.基于冗余误差控制的非均匀有理B样条曲线插补算法研究[J].计算机集成制造系统, 2007,13(05) :962-966
[9]梁宏斌,王永章,李霞.自动调节进给速度的NURBS插补算法的研究与实现[J].计算机集成制造系统, 2006,12(03):429-432
[10] Sung-Ho Nam, Min-Yang Yang. A study on a generalized parametric interpolator with real-time jerk-limited acceleration[J] .Computer-Aided Design, 2004,36 (01) :27-36.
[11]杜道山,燕存良,李从心.一种实时前瞻的自适应NURBS插补算法[J].上海交通大学学报,2006.5,40(05):844-847
[12]冷洪斌,邬义杰,潘晓弘.三次多项式型微段高速自适应前瞻插补方法[J].机械工程学报,2009,45(06):73-79.
[13]姬晓天,施寅. NURBS的概念与使用.计算机辅助设计与制造[J], 1998 ,12, 25-26.
[14] Pieg1,L.,and Ti11er,W. The NURBS Book[M],berlin, springer,1995 .
[15] Piegl. L. Modifying the shape of rational B-spline[M], Part 1:curves. CAD 1989, 21:509-518.
[16]潘日晶. NURBS曲线曲面的显式矩阵表示及其算法[J].计算机学报, 2001,24(04) :355-366
[17] Choi B K,Yoo W S,L ee C s.Matrix representation for NURBS curves and surfaces[J]. Computer-Aided Design, 1990,22 (04) :235-240.
[18]李曦,唐小琦. NC伺服的加减速控制算法的研究与实现[J].机床与液压, 2000,(3):3-5
[19]胡鸿豪,吴勇翀,肖绚. CNC系统直线加减速优化算法[J].机床与液压, 2008,36(05):287-289
[20]朱晓春,屈波,孙来业,汪木兰. S曲线加减速控制方法研究[J].中国制造业信息化, 2006,35(23):38-43
[21]陈绪兵,熊蔡华,熊有伦. S曲线加减速模式下的加工轨迹效率评价[J].华中科技大学学报(自然科学版), 2008,36(02) :1-4
[22]何均,游有鹏,陈浩,王化明.形加减速的嵌套式前瞻快速算法[J].航空学报, 2010,31(04) :843-844
[23]吴宇燕,彭志牛,王宇晗. NURBS曲线数控插补方法及误差控制[J].机械设计与研究,2006.8, 22(4) :76-80
[24] R.T. Farouli,YF. Tsai,Exact Taylor series coefficient for variable-feedrate CNC curve interpolators[J].Computer-Aided Design, 2001,33(05): 155-165.
[25] Cunliang Yan,Daoshan Du,Congxin Li. Design of a real-time adaptive interpolator with parameter compensation[J] .Inter-national Journal of Machine Tools and Manufacture. 2007, 35 :169-178 .
[26] Ming-Tzong Lin,Tsai Meng-Shiun,Yau Hong- Tzong. Development of a dynamics -based NURBS interpolator with real-time look-ahead algorithm[C]. International Journal of Machine Tools and Manufacture, 2007(06):1-17.
[27]孙玉娥,林浒.基于前瞻算法的高效非均匀有理B样条曲线插补器[J].计算机集成制造系统,2009,15(10):2029-2033
[28]周凯,陆启建.高速高精度采样插补技术[J].中国机械工程, 1998,9(10): 15-18.