数控系统插补算法研究及设计
摘要
本文首先着重研究了插补的算法——逐点比较法直线和圆弧插补,数字积分法直线和圆弧插补算法,实现了四个象限的图形仿真和分析,总结不同象限的插补规律。介绍了数字积分法插补减小误差的四种方法,针对脉冲当量方面进行了图形仿真证实了这种方法的可行性。除此之外,介绍了一种当今非常流行的一种数据采样插补算法-NURBS插补算法,并使用多种方法实现NURBS(non uniform rational B-spline,非均匀有理样条)曲线插补,分别使用了参数均匀变化法,速度恒定法,材料去除率法。在各种算法的分析中进行了仿真程序的设计,图像的分析。从几种特殊方法分析了加减速的变化S型加减速的先进方法。在算法研究的最后对数据采样法进行了误差分析。
本文在算法研究和分析的基础上进行了硬件电路的设计,采用了FPGA(Field Programmable Gate Array,现场可编程逻辑门阵列)来设计插补电路。选用的是ALTREA公司的EP2C35F672C8芯片来实现,结合芯片的特性设计了外围硬件电路和内部插补模块的设计,重点是内部模块的设计,结合逐点比较法,数字积分法的方法特性和数字电路实现了两种经典的插补方法,并对设计进行了图像仿真。另外,进行精插补的设计和图形仿真,同时考虑到速度的变化,将速度的加减速变化加入到硬件的设计中。
This paper first focuses on the interpolation algorithm—Use comparative law point by point and DDA act to achieve straight line and circular interpolation, conduct a four-quadrant graphical simulation and analysis, and summary of the laws of the different quadrants of the interpolation. Introduce four methods to reduce errors when carrying out the interpolation of DDA act, method one---using method of reducing pulse equivalent to achieve graphic simulation, confirm the feasibility of this approach. In addition, the paper introduce a very popular data sampling interpolation algorithm- NURBS interpolation algorithm, and use various methods to achieve NURBS curve interpolation, used the method of uniform changes in the parameters, the constant speed method. The design of the simulation program and image analysis is implemented in the analysis of various algorithms. Several special methods are used to analyze the changes in acceleration and deceleration, the advanced methods of the S-type acceleration and deceleration. Finally, I completed the error analysis of data sampling method at the end of algorithm.
In this paper, the design of hardware circuit based on researching and analyzing algorithm, using FPGA to design interpolation circuit. The experiment choose EP2C35F672C8 chip of ALTREA companies to achieve, combine the characteristics of the chip to achieve the peripheral hardware circuit design and the internal design of interpolation module, focused on the design of the internal modules, combined the case-by-point comparison method, the features of digital integration method and the characteristic of digital circuit, to achieve two classic interpolation method, then complete the image Simulation of this design. In addition, the rate of change should be considered when doing the design of accurate interpolation and graphic simulation, add the acceleration and deceleration speed changes to the hardware design.
本文在算法研究和分析的基础上进行了硬件电路的设计,采用了FPGA(Field Programmable Gate Array,现场可编程逻辑门阵列)来设计插补电路。选用的是ALTREA公司的EP2C35F672C8芯片来实现,结合芯片的特性设计了外围硬件电路和内部插补模块的设计,重点是内部模块的设计,结合逐点比较法,数字积分法的方法特性和数字电路实现了两种经典的插补方法,并对设计进行了图像仿真。另外,进行精插补的设计和图形仿真,同时考虑到速度的变化,将速度的加减速变化加入到硬件的设计中。
This paper first focuses on the interpolation algorithm—Use comparative law point by point and DDA act to achieve straight line and circular interpolation, conduct a four-quadrant graphical simulation and analysis, and summary of the laws of the different quadrants of the interpolation. Introduce four methods to reduce errors when carrying out the interpolation of DDA act, method one---using method of reducing pulse equivalent to achieve graphic simulation, confirm the feasibility of this approach. In addition, the paper introduce a very popular data sampling interpolation algorithm- NURBS interpolation algorithm, and use various methods to achieve NURBS curve interpolation, used the method of uniform changes in the parameters, the constant speed method. The design of the simulation program and image analysis is implemented in the analysis of various algorithms. Several special methods are used to analyze the changes in acceleration and deceleration, the advanced methods of the S-type acceleration and deceleration. Finally, I completed the error analysis of data sampling method at the end of algorithm.
In this paper, the design of hardware circuit based on researching and analyzing algorithm, using FPGA to design interpolation circuit. The experiment choose EP2C35F672C8 chip of ALTREA companies to achieve, combine the characteristics of the chip to achieve the peripheral hardware circuit design and the internal design of interpolation module, focused on the design of the internal modules, combined the case-by-point comparison method, the features of digital integration method and the characteristic of digital circuit, to achieve two classic interpolation method, then complete the image Simulation of this design. In addition, the rate of change should be considered when doing the design of accurate interpolation and graphic simulation, add the acceleration and deceleration speed changes to the hardware design.
引文
1.富大伟,刘瑞素.数控系统[M],化学工业出版社,2005,10-14.
2.郑蓉建.基于复杂曲线插补的数控关键技术的研究与实现[J],2008,9(2):77-79.
3.李莉.三轴联动数控机床控制系统与插补法的研究[J],湖北工业大学2007,5(8):22-23.
4.白刚.基于DSP处理器的数控插补算法实现技术研究[J],湖南师范大学2008,9(8):115-116.
5. Bedis, Alil, Ouan N. Advanced Interpolation Techniques for NC Machines. ASMEJournal of Engineering for Industry,1993,115(3):329.
6. Koren Yoram, Lin R S. Five-axis Surface Interpolators. Annals of CIRP,1995,44(1):379.
7. Syh-Shiuh Yeh, Pau-Lo Hsu. Adative-feedrate Interpolation for Parametric Curves with a Confined Chord Error. Computer Aided Geometric Design,2002,33(34):229-237.
8. Hong-Tzong Yau, Ming-Jen Kuo. NURBS Machining and Feedrate Asjustmentfor High-speed Cutting of Complex Sculptured Surface. International of Journal of Production Research,2001,23(39):21-41.
9. Rida T. Farouki, Yi-Feng Tsai. Exact Taylor Series Coefficients for Variable-feedrate CNC Curve Interpolators. Computer Aided Design,2001,12(33):155-165.
10. Tschaw Yong, Ranga Narayanaswami. A Parametric Interpolator with Confined Chord Errors, Acceleration and Deceleration for NC machining. Computer Aided Design,2003, 89(35):1249-1259.
11. Behnam Bahr, Xiaomao Xiao, Kishnan Krishnan. A Real-time Scheme of Cubic Parametric Curve Interpolations for CNC Systems. Computers Industry.2001.67(45): 309-317.
12. M.-C. Tsai, C.-W.Cheng, M.-Y.Cheng. A Real-time NURBS Surface Interpolator for Precision Three-axis CNCMachining. MachineTools & Manufacting,2003,62(43): 1217-1227.
13.金中波.逐点比较法直线插补原理及改进算法分析[J],机械工程师学报,2008,6(2):15-16.
14.姚道敏.基于嵌入式平台的全软件数控系统研究与开发[J],机械设计与制造,2008,26(3)：30-32.
15.魏胜利.准均匀B样条的插补算法及间过渡研究[J],机械设计与制造,2006,6(43):12-13.
16.杨冬香.基于数据采样的弧面凸轮自适应直接插补算法[J],2006,4(4):8.
17.李建刚,马朝阳.实时前瞻功能的NURBS动态插补算法[J],2007,3(6):4.
18.马朝阳.实时前瞻功能的NURBS动态插补算法[J],机械工程师,2008,12(1):12-13.
19.董伯麟.高速高精度加工中NURBS曲线混合插补算法[J],农业机械学报2004,3(3):40-44.
20.王爱玲,刘永姜.数控原理及数控系统[M],机械工业出版社,2006,40-50.
21.王爱玲.基于FPGA数控精插补芯片的设计[J],农业机械学报,2007,35(3):43-44.
22.逢启寿,杨杰,刘本辉,严少卿.数控加工中两种插补原理及对应算法[J],机械工程师,2007,2(6)：121-122.
23.王建强.DDA插补的高级语言实现[J],机电一体化,2006,3(2):43-46.
24.丁学恭.现代数控系统过的一种计算机数据采样插补算法的实现[J],现代制作工程,2006,2：26-28.
25.赵玉刚.数控技术,机械工业出版社,2004,123-125.
26.周虹.圆弧插补算法的探讨[J],机械制造与研究,2006,35(3):43-44.
27.李恩林.数控系统插补原理通论[M],国防工业出版社,2008,23-25.
28.王爱玲,刘永姜.数控原理及数控系统[M],机械工业出版社,2006,20-40.
29.陈良骥.五轴联动刀具路径生成及插补技术研究[M],知识产权出版社,2008,100-130.
30.游有鹏,王珉,朱剑英NURBS曲线高速高精度加工的插补控制[J],计算机辅助设计与图形学学报,2001,13(10)：943-947.
31.张建生,迟磊.CNC高速插补的探索[J],南通工学院学报2006,17(2)：26-28.
32.张珲,徐宗俊,郭钢.CNC机床中的NURBS插补[J],制造技术与机床,1999,(3)：19-21.
33.孔亚洲,肖跃加,韩明等.非均匀B样条曲线的插补算法[J],华中科技大学学报,2001,29(4)：69-71.
34.叶伯生,杨叔子.CNC系统中三次B样条曲线的高速插补方法研究[J],中国机械工程,1998,9(3)：42-43.
35.刘可照.基于机床动力学特性的NURBS曲线直接插补的研究[J],机械工业出版社,2008,11(3)：4-5.
36.田兆青.数控系统运动规划及NURBS插补的研究[J],济南,山东大学,2008,6(29)：44-45.
37.王峰,王爱玲.B样条曲线的插补算法实现[J],华北工学院学报,2002,6(29)：449-451.
38.范守文,徐礼钜,李辉.面向新型并联机床的NURBS曲面直线插补算法研究[J],现代制造工程,2006,35(9)：43-46.
39.尔桂花.运动控制系统[M],清华大学出版社,2002,123-125.
40.王爱玲,沈兴全等.现代数控编程技术及应用[M],国防工业出版社,2004,20-21.
41.陈淋艳,崔桂梅,任彦.基于CPLD的曲线插补算法模型及实现[J],微特电机2,2007,2(5)：24-26.
42.崔桂梅,任彦,赵彤.基于CPLD实现的硬件直线插补器在数控车床中的应用[J],制造技术与机床,2005,7(2)：56-59.
43.罗朝霞,高书莉CPLD/FPGA设计及应用[M],人民邮电出版社,2007,80-88.
44.何雪明,吴小光.数控技术[M],华中科技大学出版社,2006,58-60.
45.刘宝廷.步进电机及其驱动控制系统[M],哈尔滨工业大学出版社,1997,120-122.
46.张静亚,周平ALTERAFPGA器件的配置模式及其实现方法[J],常州理工学院学报,2007,2(21)：72-75.
47.宋万杰.CPLD技术及其应用[M],西安电子科技大学出版社,1999,101-110.
48.王芳,王琨琦.基于CPLD的步进伺服系统中插补运算的研究与实现[J],西安工业大学学报,2008,6(5)：121-123
49.王开军.面向CPLD/VHDL的VHDL的设计[M],机械工业出版社,2004,70-75.
50.侯伯亨,顾新.VHDL硬件描述语言与数字电路设计[M],电子科技大学出版社,1999,43-45.
51.李宏胜,李少卿.采用CPLD技术实现数控系统精插补算法的研究[J],组合机床与自动化加工技术,2003,12(2)：21-23.
2.郑蓉建.基于复杂曲线插补的数控关键技术的研究与实现[J],2008,9(2):77-79.
3.李莉.三轴联动数控机床控制系统与插补法的研究[J],湖北工业大学2007,5(8):22-23.
4.白刚.基于DSP处理器的数控插补算法实现技术研究[J],湖南师范大学2008,9(8):115-116.
5. Bedis, Alil, Ouan N. Advanced Interpolation Techniques for NC Machines. ASMEJournal of Engineering for Industry,1993,115(3):329.
6. Koren Yoram, Lin R S. Five-axis Surface Interpolators. Annals of CIRP,1995,44(1):379.
7. Syh-Shiuh Yeh, Pau-Lo Hsu. Adative-feedrate Interpolation for Parametric Curves with a Confined Chord Error. Computer Aided Geometric Design,2002,33(34):229-237.
8. Hong-Tzong Yau, Ming-Jen Kuo. NURBS Machining and Feedrate Asjustmentfor High-speed Cutting of Complex Sculptured Surface. International of Journal of Production Research,2001,23(39):21-41.
9. Rida T. Farouki, Yi-Feng Tsai. Exact Taylor Series Coefficients for Variable-feedrate CNC Curve Interpolators. Computer Aided Design,2001,12(33):155-165.
10. Tschaw Yong, Ranga Narayanaswami. A Parametric Interpolator with Confined Chord Errors, Acceleration and Deceleration for NC machining. Computer Aided Design,2003, 89(35):1249-1259.
11. Behnam Bahr, Xiaomao Xiao, Kishnan Krishnan. A Real-time Scheme of Cubic Parametric Curve Interpolations for CNC Systems. Computers Industry.2001.67(45): 309-317.
12. M.-C. Tsai, C.-W.Cheng, M.-Y.Cheng. A Real-time NURBS Surface Interpolator for Precision Three-axis CNCMachining. MachineTools & Manufacting,2003,62(43): 1217-1227.
13.金中波.逐点比较法直线插补原理及改进算法分析[J],机械工程师学报,2008,6(2):15-16.
14.姚道敏.基于嵌入式平台的全软件数控系统研究与开发[J],机械设计与制造,2008,26(3)：30-32.
15.魏胜利.准均匀B样条的插补算法及间过渡研究[J],机械设计与制造,2006,6(43):12-13.
16.杨冬香.基于数据采样的弧面凸轮自适应直接插补算法[J],2006,4(4):8.
17.李建刚,马朝阳.实时前瞻功能的NURBS动态插补算法[J],2007,3(6):4.
18.马朝阳.实时前瞻功能的NURBS动态插补算法[J],机械工程师,2008,12(1):12-13.
19.董伯麟.高速高精度加工中NURBS曲线混合插补算法[J],农业机械学报2004,3(3):40-44.
20.王爱玲,刘永姜.数控原理及数控系统[M],机械工业出版社,2006,40-50.
21.王爱玲.基于FPGA数控精插补芯片的设计[J],农业机械学报,2007,35(3):43-44.
22.逢启寿,杨杰,刘本辉,严少卿.数控加工中两种插补原理及对应算法[J],机械工程师,2007,2(6)：121-122.
23.王建强.DDA插补的高级语言实现[J],机电一体化,2006,3(2):43-46.
24.丁学恭.现代数控系统过的一种计算机数据采样插补算法的实现[J],现代制作工程,2006,2：26-28.
25.赵玉刚.数控技术,机械工业出版社,2004,123-125.
26.周虹.圆弧插补算法的探讨[J],机械制造与研究,2006,35(3):43-44.
27.李恩林.数控系统插补原理通论[M],国防工业出版社,2008,23-25.
28.王爱玲,刘永姜.数控原理及数控系统[M],机械工业出版社,2006,20-40.
29.陈良骥.五轴联动刀具路径生成及插补技术研究[M],知识产权出版社,2008,100-130.
30.游有鹏,王珉,朱剑英NURBS曲线高速高精度加工的插补控制[J],计算机辅助设计与图形学学报,2001,13(10)：943-947.
31.张建生,迟磊.CNC高速插补的探索[J],南通工学院学报2006,17(2)：26-28.
32.张珲,徐宗俊,郭钢.CNC机床中的NURBS插补[J],制造技术与机床,1999,(3)：19-21.
33.孔亚洲,肖跃加,韩明等.非均匀B样条曲线的插补算法[J],华中科技大学学报,2001,29(4)：69-71.
34.叶伯生,杨叔子.CNC系统中三次B样条曲线的高速插补方法研究[J],中国机械工程,1998,9(3)：42-43.
35.刘可照.基于机床动力学特性的NURBS曲线直接插补的研究[J],机械工业出版社,2008,11(3)：4-5.
36.田兆青.数控系统运动规划及NURBS插补的研究[J],济南,山东大学,2008,6(29)：44-45.
37.王峰,王爱玲.B样条曲线的插补算法实现[J],华北工学院学报,2002,6(29)：449-451.
38.范守文,徐礼钜,李辉.面向新型并联机床的NURBS曲面直线插补算法研究[J],现代制造工程,2006,35(9)：43-46.
39.尔桂花.运动控制系统[M],清华大学出版社,2002,123-125.
40.王爱玲,沈兴全等.现代数控编程技术及应用[M],国防工业出版社,2004,20-21.
41.陈淋艳,崔桂梅,任彦.基于CPLD的曲线插补算法模型及实现[J],微特电机2,2007,2(5)：24-26.
42.崔桂梅,任彦,赵彤.基于CPLD实现的硬件直线插补器在数控车床中的应用[J],制造技术与机床,2005,7(2)：56-59.
43.罗朝霞,高书莉CPLD/FPGA设计及应用[M],人民邮电出版社,2007,80-88.
44.何雪明,吴小光.数控技术[M],华中科技大学出版社,2006,58-60.
45.刘宝廷.步进电机及其驱动控制系统[M],哈尔滨工业大学出版社,1997,120-122.
46.张静亚,周平ALTERAFPGA器件的配置模式及其实现方法[J],常州理工学院学报,2007,2(21)：72-75.
47.宋万杰.CPLD技术及其应用[M],西安电子科技大学出版社,1999,101-110.
48.王芳,王琨琦.基于CPLD的步进伺服系统中插补运算的研究与实现[J],西安工业大学学报,2008,6(5)：121-123
49.王开军.面向CPLD/VHDL的VHDL的设计[M],机械工业出版社,2004,70-75.
50.侯伯亨,顾新.VHDL硬件描述语言与数字电路设计[M],电子科技大学出版社,1999,43-45.
51.李宏胜,李少卿.采用CPLD技术实现数控系统精插补算法的研究[J],组合机床与自动化加工技术,2003,12(2)：21-23.