基于DSP的NURBS直接插补技术研究
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摘要
NURBS方法以其在复杂几何造型方面的诸多优势,在CAD/CAM和计算机图形学领域得到越来越广泛的应用。但是,传统的数控机床一般只有直线和圆弧插补功能,必须借助CAM系统将其离散成大量微小直线段再传到CNC系统中加工,难以满足当今高速高精加工的要求。因此,研究NURBS直接插补技术对于开发高速高精CNC系统具有十分重要的意义。
本文结合浙江省重大机电装备专项项目(2006C11067)的科研任务,在深入分析NURBS相关理论知识和数控运动控制技术基础上,提出了新的NURBS直接插补算法。
NURBS直接插补主要分两个步骤完成:轨迹空间到参数空间的映射和参数空间到轨迹空间的映射,综合运用解非线性方程法和de Boor算法实现NURBS直接插补,简化了插补运算,提高了插补效率。同时,本文提出的前瞻自适应算法,使进给速度能根据曲线形状自动进行调整,同时回溯和重插补策略可以保证加工过程中机床运动学参数控制在允许范围内,防止出现大的冲击和振动,提高表面加工质量。为了将危险点的对速度曲线的影响纳入到前期速度规划中,第四章在分段插补思想基础上提出了新的NURBS插补策略。最后,利用NURBS的对称性进行反向插补,实现了对减速点位置的准确预测。
本文算法最终移植到基于DSP TMS320F2812的运动控制卡上,分别从硬件和软件两个方面详细介绍了算法的移植过程。硬件方面着重介绍了DSP上专门用于电机控制的事件管理器的配置情况,包括引脚、定时器、周期寄存器、比较寄存器的配置等;软件方面详细介绍了旋转缓冲区技术、IQmath库引入等。
最后,对NURBS直接插补算法进行仿真分析和实验研究。利用Xk713数控铣床搭建实验平台,并设计了一条既有尖角和又有高曲率点的三次NURBS曲线进行加工实例加工,通过与传统算法比较,借助图形图表等手段分析插补算法在插补效率、精度、运动学参数等方面的性能表现,验证算法的可行性和可靠性。
NURBS is more and more widely applied in the field of CAD/CAM and computer graphics because of its unique advantages in modeling complex parts. However, traditional CNC machine tools only have the direct interpolation function of line and arc, so it's necessary to turn the curves into tiny segments with CAM and then transfer the data to CNC systems. It can't meet the demand of high efficiency and high precision. So the direct interpolation of NURBS is of great significance to the development of CNC machine tools of high efficiency and precision.
This paper proposed a new direct interpolation algorithm of NURBS with the support of the Science and Technology Project of Zhejiang Province (NO. 2006C11067).
There are two steps to realize the direct interpolation of NURBS, first mapping the path into parameters and then mapping the parameters into path. Nonlinear equation method and de Boor algorithm are used to simplify the process and improve the efficiency. In addition, the feed rate optimization is another important task for the direct interpolation of NURBS. Feed rate Adaptation Control Algorithm modifies the feed rate according to the curvature of the curve, meanwhile the look-ahead algorithm with back tracking and re-interpolation strategy keeps the dynamics parameters under control to prevent shocks and vibrations. To take the effect of dangerous points into consider during the planning of feed rate, segment interpolation scheme is proposed in Chapter Four. The symmetry of NURBS is used to predict position of the decelerating point precisely.
The algorithm is transplanted to the motion control card based on TMS320F2812. In term of hardware, the settings of EV are explained in details, including I/O, GP Timer, Period Register, and so forth. Meanwhile, the tech of circular buffer and IQ math library are introduced in term of software.
Finally, analysis of simulations and experiments are conducted to verify the viability and reliability of the algorithm. Xk713 CNC miller and an specific designed NURBS curve are applied in the experiments. The performance of the algorithm in efficiency, precision and axis dynamics is compared with the traditional methods.
本文结合浙江省重大机电装备专项项目(2006C11067)的科研任务,在深入分析NURBS相关理论知识和数控运动控制技术基础上,提出了新的NURBS直接插补算法。
NURBS直接插补主要分两个步骤完成:轨迹空间到参数空间的映射和参数空间到轨迹空间的映射,综合运用解非线性方程法和de Boor算法实现NURBS直接插补,简化了插补运算,提高了插补效率。同时,本文提出的前瞻自适应算法,使进给速度能根据曲线形状自动进行调整,同时回溯和重插补策略可以保证加工过程中机床运动学参数控制在允许范围内,防止出现大的冲击和振动,提高表面加工质量。为了将危险点的对速度曲线的影响纳入到前期速度规划中,第四章在分段插补思想基础上提出了新的NURBS插补策略。最后,利用NURBS的对称性进行反向插补,实现了对减速点位置的准确预测。
本文算法最终移植到基于DSP TMS320F2812的运动控制卡上,分别从硬件和软件两个方面详细介绍了算法的移植过程。硬件方面着重介绍了DSP上专门用于电机控制的事件管理器的配置情况,包括引脚、定时器、周期寄存器、比较寄存器的配置等;软件方面详细介绍了旋转缓冲区技术、IQmath库引入等。
最后,对NURBS直接插补算法进行仿真分析和实验研究。利用Xk713数控铣床搭建实验平台,并设计了一条既有尖角和又有高曲率点的三次NURBS曲线进行加工实例加工,通过与传统算法比较,借助图形图表等手段分析插补算法在插补效率、精度、运动学参数等方面的性能表现,验证算法的可行性和可靠性。
NURBS is more and more widely applied in the field of CAD/CAM and computer graphics because of its unique advantages in modeling complex parts. However, traditional CNC machine tools only have the direct interpolation function of line and arc, so it's necessary to turn the curves into tiny segments with CAM and then transfer the data to CNC systems. It can't meet the demand of high efficiency and high precision. So the direct interpolation of NURBS is of great significance to the development of CNC machine tools of high efficiency and precision.
This paper proposed a new direct interpolation algorithm of NURBS with the support of the Science and Technology Project of Zhejiang Province (NO. 2006C11067).
There are two steps to realize the direct interpolation of NURBS, first mapping the path into parameters and then mapping the parameters into path. Nonlinear equation method and de Boor algorithm are used to simplify the process and improve the efficiency. In addition, the feed rate optimization is another important task for the direct interpolation of NURBS. Feed rate Adaptation Control Algorithm modifies the feed rate according to the curvature of the curve, meanwhile the look-ahead algorithm with back tracking and re-interpolation strategy keeps the dynamics parameters under control to prevent shocks and vibrations. To take the effect of dangerous points into consider during the planning of feed rate, segment interpolation scheme is proposed in Chapter Four. The symmetry of NURBS is used to predict position of the decelerating point precisely.
The algorithm is transplanted to the motion control card based on TMS320F2812. In term of hardware, the settings of EV are explained in details, including I/O, GP Timer, Period Register, and so forth. Meanwhile, the tech of circular buffer and IQ math library are introduced in term of software.
Finally, analysis of simulations and experiments are conducted to verify the viability and reliability of the algorithm. Xk713 CNC miller and an specific designed NURBS curve are applied in the experiments. The performance of the algorithm in efficiency, precision and axis dynamics is compared with the traditional methods.
引文
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[6]黄翔,曾荣等.NURBS插补技术在高速加工中的应用研究[J].南京航空航天大学学报,2002,34(1):82-85.
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[9]Forouki RT,Tsai YF.Exact Taylor series coefficients for variable-feed rate CNC curve interpolators[J].Computer-Aided Design,2001,33:155-165.
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[13]C.-W.Cheng,M.-C.Tsai.Real-time variable feed rate NURBS curve interpolator for CNC machining[J].The International Journal of Advanced Manufacturing Technology,2004,(23):865-873.
[14]宋本基.数控技术[M].哈尔滨:哈尔滨工程大学出版社,1999.
[15]陈绍平.三次NURBS曲线的插值与应用[J].机械科学与技术,2001.9,20(5):692-693.
[16]Zhang Deli,Zhou Laishui.Intelligent NURBS Interpolator Based on the Adaptive Feedrate Control[J].Chinese Journal of Aeronautics,2007,(20):469-474.
[17]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.
[18]X.Zhiming,C.Jincheng,F.Zhengjin.Performance Evaluation of a Real-Time Interpolation Algorithm[J].The International Journal of Advanced Manufacturing Technology,2002,20:270-276.
[19]Hong-TzongYau,Ming-TzongLin,Meng-ShiunTsai.Real-time NURBS interpolation using FPGA for high speed motion control[J].Computer-Aided Design,2006,38:1123-1133.
[20]K.K.Krishnan,J.kappen,B.Bahr.Calculation of variable feed rate and spindle speed for NURBS based CNC machining[J].Transactions of NAMRI/SME.2001,(24):429-435.
[21]马朝阳,张承瑞.实时前瞻功能的NURBS动态插补算法[J].组合机床与自动化加工技术,2008(5):7-10.
[22]Nam SH,Yang MY.A study on a generalized parametric interpolator with real-time jerk-limited acceleration[J].Computer-Aided Design,2004,36:27-36.
[23]刘新山.NURBS曲线插补技术研究及其仿真[D].吉林:吉林大学,2007.
[24]边玉超.自由曲线曲面CNC插补技术的研究[D].北京:北京化工大学,2004.
[25]Syh-Shuih Yeh,Pau-Lo hsu.Adaptive-feed rate interpolation for parametric curves with a confined chord error[J].Computer Aided Design,2002,(34):229-237.
[26]Meng-Shiun Tsai,Hao-Wei Nien,Hong-Tzong Yau.Development of an integrated look-ahead dynamics-based NURBS interpolator for high precision machinery[J].Computer-Aided Design.2008,5(40):554-566.
[27]Ming-Tzong Lin,Meng-Shuin Tsai,Hong-Tzong Yau.Development of Real-time Look-Ahead Algorithm for NURBS Interpolator with Consideration of Servo Dynamics[C].IEEE Conference on Decision and Control,2007.12:1862-1867.
[28]彭芳瑜,何莹,罗忠诚等.NURBS曲线机床动力学特性自适应直接插补[J].华中科技大学学报:自然科学版,2005,33(7):80-83.
[29]陈金成,徐志明等.机床沿曲线高速加工时的运动学与运动学特性分析[J].机械工程学报,2002,38(1):31-34.
[30]M.Weck,G.Ye.Sharp corner tracking using the KF control strategy[J].Annals of CIRP,1990,1(39):437-441.
[3 1]彭芳瑜,何莹,李斌.NURBS曲线高速插补中的前瞻控制[J].计算机辅助设计与图形学学报.2006.5,15(5):625-629.
[32]Jinho Park,Sungho Nam,Minyang Yang.Development of a real-time trajectory generator for NURBS interpolation based on the two-stage interpolation method [J].International Journal of Advanced Manufacture Technology,2005,26:359-365.
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