参数曲线曲面的曲率自适应实时插补技术研究
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摘要
参数曲线曲面插补运算和加减速控制模块是高性能CNC系统研究开发的重要内容之一。自由曲线曲面理论在CAD/CAM技术上的应用以及具有自由曲线曲面特征零件的数控加工对CNC系统插补技术提出了更高的要求。研究开发支持曲线曲面实时插补加工功能的CNC系统,对于提高CNC系统整体性能,促进CAD/CAM/CNC技术的集成意义重大。
本文针对自由曲线曲面CNC系统插补技术应用编写了NURBS曲线曲面类,并提出了一种基于三次样条函数的柔性加减速算法,通过设定最大加速度和加加速度条件,获得直至二阶可导的速度曲线,可以实现平滑无突变的速度控制目标。
改进了预估-校正参数计算方法,提出了基于一阶泰勒展开式的预估-迭代修正法,有效地减小截断误差对速度的影响,改善了曲线插补过程中的速度特性。提出了一种曲线曲率自适应参数插补算法,通过引入离线插补预处理过程,检测曲线上速度敏感区域,按照柔性加减速控制规律对该区域进行速度平滑处理,使之在满足弦高差和机床加速能力约束的前提下,速度平稳变化。本文对常用的曲面刀具路径生成方法进行了分析研究,提出了一种在线刀具路径生成的算法,该算法以等参数线法为原型,并根据国内外相关研究前沿对其做了改进,在结合曲率自适应参数插补算法的基础上,能够获得可靠稳定的连续路径生成及实时曲线插补性能。最后,利用VC++和Matlab软件对曲率自适应参数插补和曲面刀具路径生成算法进行了仿真,并根据仿真结果对参数插补的误差和速度控制效果进行了分析验证,对曲面加工刀具路径生成算法的有效性和可靠性进行了分析说明。仿真结果说明了算法的正确性和有效性,对于提高CNC系统的曲面路径处理能力和曲线插补能力具有重要意义。
Parametric curves and surfaces interpolaiton and velocity control are very important in the CNC system modules. More requirements for the CNC interpolation have been brought by application of free-form curves and surfaces theory in CAD/CAM and NC machining of components with characteristics of free-form curves and surfaces.The research on the development of a kind of CNC system which supports real-time interpolation for free-form curves and surfaces is of great significance on the improvement of the overall performance of the CNC system and the integration of the CAD/CAM/CNC technique.
NURBS curve and surface class is developed for the application of the curve and surface interpolation technique of the CNC system. A flexible acceleration and deceleration algorithm based on the cubic spline function is proposed in this dissertation for curve and surface interpolation. By setting the terms of maximum acceleration and jerk, even the second derivative velocity curve can be obtained and the control objective that the velocity is in a smooth profile without jerk limit can be achieved.
The predictor-corrector(预估-校正)parameter calculation method is bettered, and the predictor-iterative correction method is proposed based on the first-order Taylor expansion, which effectively reduces the impact of truncation error on the velocity, and improves the speed characteristics during the process of curve interpolation. A curvature adaptive parametric interpolation algorithm is presented in this thesis. The feed-rate sensitive areas on the curves are detected through offline interpolation preprocessing, where the velocity is planned in accordance with the flexible acceleration and deceleration control method, so that the velocity profile can be smooth as long as it can satisfy the chord error and meet the constraint of machine acceleration.
In this paper, the commonly used tool path generating method for parametric surfaces is analyzed, and then an on-line tool path generation algorithm is presented, which takes iso-parametric as the prototype, and has made further improvements about it according to the current research at home and abroad. Based on its combination with the curvature adaptive parametric interpolation algorithm, reliable and continuous path generation and real-time interpolation properties can be gained.
At last, the curvature adaptive parametric interpolation and tool path generation for NURBS surfaces are simulated using VC++ and Matlab, and then according to the simulation results, the velocity control effect and parametric interpolation error are analyzed and verified, also the validity and reliability of the tool path generation algorithm for surfaces are specified. The simulation results show that the algorithm is correct and valid, and has important significance for improving the parametric surface path processing ability and the curve interpolation ability of CNC system.
本文针对自由曲线曲面CNC系统插补技术应用编写了NURBS曲线曲面类,并提出了一种基于三次样条函数的柔性加减速算法,通过设定最大加速度和加加速度条件,获得直至二阶可导的速度曲线,可以实现平滑无突变的速度控制目标。
改进了预估-校正参数计算方法,提出了基于一阶泰勒展开式的预估-迭代修正法,有效地减小截断误差对速度的影响,改善了曲线插补过程中的速度特性。提出了一种曲线曲率自适应参数插补算法,通过引入离线插补预处理过程,检测曲线上速度敏感区域,按照柔性加减速控制规律对该区域进行速度平滑处理,使之在满足弦高差和机床加速能力约束的前提下,速度平稳变化。本文对常用的曲面刀具路径生成方法进行了分析研究,提出了一种在线刀具路径生成的算法,该算法以等参数线法为原型,并根据国内外相关研究前沿对其做了改进,在结合曲率自适应参数插补算法的基础上,能够获得可靠稳定的连续路径生成及实时曲线插补性能。最后,利用VC++和Matlab软件对曲率自适应参数插补和曲面刀具路径生成算法进行了仿真,并根据仿真结果对参数插补的误差和速度控制效果进行了分析验证,对曲面加工刀具路径生成算法的有效性和可靠性进行了分析说明。仿真结果说明了算法的正确性和有效性,对于提高CNC系统的曲面路径处理能力和曲线插补能力具有重要意义。
Parametric curves and surfaces interpolaiton and velocity control are very important in the CNC system modules. More requirements for the CNC interpolation have been brought by application of free-form curves and surfaces theory in CAD/CAM and NC machining of components with characteristics of free-form curves and surfaces.The research on the development of a kind of CNC system which supports real-time interpolation for free-form curves and surfaces is of great significance on the improvement of the overall performance of the CNC system and the integration of the CAD/CAM/CNC technique.
NURBS curve and surface class is developed for the application of the curve and surface interpolation technique of the CNC system. A flexible acceleration and deceleration algorithm based on the cubic spline function is proposed in this dissertation for curve and surface interpolation. By setting the terms of maximum acceleration and jerk, even the second derivative velocity curve can be obtained and the control objective that the velocity is in a smooth profile without jerk limit can be achieved.
The predictor-corrector(预估-校正)parameter calculation method is bettered, and the predictor-iterative correction method is proposed based on the first-order Taylor expansion, which effectively reduces the impact of truncation error on the velocity, and improves the speed characteristics during the process of curve interpolation. A curvature adaptive parametric interpolation algorithm is presented in this thesis. The feed-rate sensitive areas on the curves are detected through offline interpolation preprocessing, where the velocity is planned in accordance with the flexible acceleration and deceleration control method, so that the velocity profile can be smooth as long as it can satisfy the chord error and meet the constraint of machine acceleration.
In this paper, the commonly used tool path generating method for parametric surfaces is analyzed, and then an on-line tool path generation algorithm is presented, which takes iso-parametric as the prototype, and has made further improvements about it according to the current research at home and abroad. Based on its combination with the curvature adaptive parametric interpolation algorithm, reliable and continuous path generation and real-time interpolation properties can be gained.
At last, the curvature adaptive parametric interpolation and tool path generation for NURBS surfaces are simulated using VC++ and Matlab, and then according to the simulation results, the velocity control effect and parametric interpolation error are analyzed and verified, also the validity and reliability of the tool path generation algorithm for surfaces are specified. The simulation results show that the algorithm is correct and valid, and has important significance for improving the parametric surface path processing ability and the curve interpolation ability of CNC system.
引文
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[3]李诚人等.机床计算机数控[M].西安：西北工业大学出版社,1988.
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[5]徐荣珍.面向高速加工的NURBS曲线插补及直线电机鲁棒控制技术研究[D].上海：上海交通大学塑性成形工程系,2007.
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[8]R. T. Farouki, Y. F. Tsai, Exact Taylor series of coefficient for variable-feedrate CNC curve interpolators[J]. Computer-Aided Design,2001,33:155-165.
[9]Shpitalni M, Koren Y, Lo CC. Real-time parameter curve interpolators [J]. Computer-Aided Design,1994,26(11):832-838.
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[12]Yeh S-S, Hsu P-L.Adaptive-feedrate interpolation for parametric curves with a confined chord error[J]. Computer-Aided Design,2002,34:229-237.
[13]Yong T, Narayanaswami R. A parametric interpolator with confined chord errors acceleration and deceleration for NC machining[J], Computer-Aided Design,2003, 35:1249-1259.
[14]金建新.机床CNC系统中任意空间曲线的可控步长插补方法[J].机械工程学报,2000,36(4)：95-97.
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[16]游有鹏,王珉,朱剑英.参数曲线的自适应插补算法[J].南京航空航天学报,2000,32(6)：667-671.
[17]周济,周艳红,周云飞.自由曲面的CNC直接插补加工技术[J].高技术通讯,1998,11：30-35.
[18]王水来,周云飞,朱志红.复杂曲面实时插补系统的开发[J].中国机械工程,1998,9(5)：38-41.
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[23]孙家广.计算机图形学[M].北京：清华大学出版社,1998.
[24]DeBoor, C. A Practical Guide of Splines [J]. Approx. Theory.1972,6:50-62.
[25]梁锡坤.B样条类曲线曲面理论研究及其应用研究[D].吉林：合肥工业大学计算机与信息学院,2003.
[26]边玉超.自由曲线曲面CNC插补技术的研究[D].北京：北京化工大学机械设计及理论专业,2004.
[27]刘可照.基于机床动力学特性的NURBS曲线直接插补技术的研究[D].武汉：华中科技大学机械电子工程,2004.
[28]M. C. Tsai, C.W.Cheng. A Real-time Predictor-Corrector interpolation for CNC Machining [J], Journal of Manufacturing Science and Engineering,2003, 125:449-460.
[29]Behnam Bahr, Xiaomao Xiao, Krishnan Krishnan. A real-time scheme of cubic parametric curve interpolations for CNC systems [J]. Computer in Industry,2001, 45:309-317.
[30]S.-S. Yeh, P.-L. Hsu.The Speed-Controlled interpolation for machining parametric curves[J]. Computer-Aided Design,1999,31:349-357.
[31]马朝阳.自由型曲线曲面直接插补技术研究[D].济南：山东大学,2008.
[32]康书杰.NURBS曲线实时插补技术研究[D].南京：南京航空航天大学机电学院,2007.
[33]刘海燕.高精度NURBS插补技术的研究[D].广州：暨南大学,2007.
[34]赵巍.数控系统的插补算法及加减速控制算法研究[D].天津：天津大学,2004.
[35]S. Y. Jeong, Y.J.Choi, PooGyeon Park. Parametric interpolation using sampled data [J]. Computer-Aided Design,2006,38:39-47.
[36]孟书云.高精度开放式数控系统复杂曲线曲面插补关键技术研究[D].南京：南京航空航天大学机电学院,2006.
[37]Xin Wang, Junwei Wang, Zhi Rao. An Adaptive parametric interpolator for trajectory planning[J]. Advances in Engineering Soft,2010,41:180-187.
[38]周凯,陆启建.样条曲线采样插补技术[J].组合机床与自动化制造技术,1998,4：18-21.
[39]黄翔等.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,2002,34：82-85.
[40]李思益,罗为NURBS曲线高速高精度插补及加减速控制方法[J].计算机集成制造系统,2008,14：1142-1147.
[41]赵光.CNC插补过程中加减速控制算法的研究[D].济南：山东科技大学机械电子工程,2007.
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[2]刘新山.NURBS曲线插补技术研究及其仿真[D].吉林：吉林大学机械科学与工程学院,2007.
[3]李诚人等.机床计算机数控[M].西安：西北工业大学出版社,1988.
[4]黄翔,李迎光,陈文亮.数控编程理论、技术与应用[M].北京：清华大学出版社,2006.
[5]徐荣珍.面向高速加工的NURBS曲线插补及直线电机鲁棒控制技术研究[D].上海：上海交通大学塑性成形工程系,2007.
[6]Daniel C. H. Yang, Tom Kong. Parametric interpolator versus linear interpolator for precision CNC machining [J]. Computer-Aided Design,1994,26:225-234.
[7]Rida T. Farouki, Jairam Manjunathaiah, Guo-Feng Yuan. G codes for the Specification of Pythagorean-hodograph tool paths and associated feedrate functions on open-architecture CNC machines [J]. International Journal of Machine tools and Manufacturing,1999,39:123-142.
[8]R. T. Farouki, Y. F. Tsai, Exact Taylor series of coefficient for variable-feedrate CNC curve interpolators[J]. Computer-Aided Design,2001,33:155-165.
[9]Shpitalni M, Koren Y, Lo CC. Real-time parameter curve interpolators [J]. Computer-Aided Design,1994,26(11):832-838.
[10]Bedi S, Ali I, Quan N. Advanced interpolation techniques for CNC machines[J]. ASME Journal of Engineering for Industry,1993,115(6):329-336.
[11]Yang DCH, Kong T. Parametric interpolator versus linear interpolator for precision surface machining [J]. Computer-Aided Design,1994,26(3):225-234.
[12]Yeh S-S, Hsu P-L.Adaptive-feedrate interpolation for parametric curves with a confined chord error[J]. Computer-Aided Design,2002,34:229-237.
[13]Yong T, Narayanaswami R. A parametric interpolator with confined chord errors acceleration and deceleration for NC machining[J], Computer-Aided Design,2003, 35:1249-1259.
[14]金建新.机床CNC系统中任意空间曲线的可控步长插补方法[J].机械工程学报,2000,36(4)：95-97.
[15]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.
[16]游有鹏,王珉,朱剑英.参数曲线的自适应插补算法[J].南京航空航天学报,2000,32(6)：667-671.
[17]周济,周艳红,周云飞.自由曲面的CNC直接插补加工技术[J].高技术通讯,1998,11：30-35.
[18]王水来,周云飞,朱志红.复杂曲面实时插补系统的开发[J].中国机械工程,1998,9(5)：38-41.
[19]施法中.计算机辅助几何设计与非均匀有理B样条[M].北京：高等教育出版社,2001.
[20]姬晓天,施寅.NURBS的概念与使用[J].计算机辅助设计与制造,1998,12：42-45.
[21]Kelly Dempski. Focus on Curves and Surfaces [M]. Course Technology Ptr,2002.
[22]朱心雄等.自由曲线曲面造型技术[M].北京：科学出版社,2000.
[23]孙家广.计算机图形学[M].北京：清华大学出版社,1998.
[24]DeBoor, C. A Practical Guide of Splines [J]. Approx. Theory.1972,6:50-62.
[25]梁锡坤.B样条类曲线曲面理论研究及其应用研究[D].吉林：合肥工业大学计算机与信息学院,2003.
[26]边玉超.自由曲线曲面CNC插补技术的研究[D].北京：北京化工大学机械设计及理论专业,2004.
[27]刘可照.基于机床动力学特性的NURBS曲线直接插补技术的研究[D].武汉：华中科技大学机械电子工程,2004.
[28]M. C. Tsai, C.W.Cheng. A Real-time Predictor-Corrector interpolation for CNC Machining [J], Journal of Manufacturing Science and Engineering,2003, 125:449-460.
[29]Behnam Bahr, Xiaomao Xiao, Krishnan Krishnan. A real-time scheme of cubic parametric curve interpolations for CNC systems [J]. Computer in Industry,2001, 45:309-317.
[30]S.-S. Yeh, P.-L. Hsu.The Speed-Controlled interpolation for machining parametric curves[J]. Computer-Aided Design,1999,31:349-357.
[31]马朝阳.自由型曲线曲面直接插补技术研究[D].济南：山东大学,2008.
[32]康书杰.NURBS曲线实时插补技术研究[D].南京：南京航空航天大学机电学院,2007.
[33]刘海燕.高精度NURBS插补技术的研究[D].广州：暨南大学,2007.
[34]赵巍.数控系统的插补算法及加减速控制算法研究[D].天津：天津大学,2004.
[35]S. Y. Jeong, Y.J.Choi, PooGyeon Park. Parametric interpolation using sampled data [J]. Computer-Aided Design,2006,38:39-47.
[36]孟书云.高精度开放式数控系统复杂曲线曲面插补关键技术研究[D].南京：南京航空航天大学机电学院,2006.
[37]Xin Wang, Junwei Wang, Zhi Rao. An Adaptive parametric interpolator for trajectory planning[J]. Advances in Engineering Soft,2010,41:180-187.
[38]周凯,陆启建.样条曲线采样插补技术[J].组合机床与自动化制造技术,1998,4：18-21.
[39]黄翔等.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,2002,34：82-85.
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