NURBS曲线插补速度控制改进研究
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摘要
泰勒一阶或二阶级数展开是NURBS曲线迭代插补的常用方法,该方法会导致弦长误差进而产生速度波动。NURBS曲线插补速度控制的难点在于曲线与参数u无精确的解析关系,为完成速度规划,需要以准确的速度控制为基础。提出在二阶泰勒展开法的基础上通过界定搜索领域并采用最小偏差法来精确求取插补点参数的改进方法,实现精确的速度控制,为加减速控制提供速度控制基础。实验结果表明:改进后的速度误差的均方差减小一半,速度控制精度提升一个数量级。
Taylor one or two class number expansion is a common method for NURBS curve interpolation iteration, this method will cause the chord error and speed fluctuation. The difficulty of speed control in NURBS curve interpolation is due to the no exact analytical relationship between the curve and the parameter u. In order to complete the speed planning, it needs to be based on the speed control. Based on the two order Taylor expansion method, an improved method was proposed to obtain accurately interpolate point parameters by defining the search area and using the minimum deviation method based on the second order expansion method, so as to achieve precise speed control and provide speed control basis for acceleration and deceleration control. The experimental results show that the mean square error of the improved speed error is reduced by half, and the error precision of speed control is improved by an order of magnitude.
Taylor one or two class number expansion is a common method for NURBS curve interpolation iteration, this method will cause the chord error and speed fluctuation. The difficulty of speed control in NURBS curve interpolation is due to the no exact analytical relationship between the curve and the parameter u. In order to complete the speed planning, it needs to be based on the speed control. Based on the two order Taylor expansion method, an improved method was proposed to obtain accurately interpolate point parameters by defining the search area and using the minimum deviation method based on the second order expansion method, so as to achieve precise speed control and provide speed control basis for acceleration and deceleration control. The experimental results show that the mean square error of the improved speed error is reduced by half, and the error precision of speed control is improved by an order of magnitude.
引文
[1]韩江,江本赤,夏链,等.基于递归特征分析的NURBS曲线插补算法[J].中国机械工程,2015,26(1):107-111.HAN J,JIANG B C,XIA L,et al.NURBS Curve Interpolation Algorithm Based on Recursive Feature Analysis[J].China Mechanical Engineering,2015,26(1):107-111.
[2]YANG D C H,KONG T.Parametric Interpolator Versus Linear Interpolator for Precision CNC Machining[J].Computer-Aided Design,1994,26(3):225-234.
[3]刘强,刘焕,周胜凯,等.无速度波动的NURBS曲线二次插补算法原理及其实现[J].计算机集成制造系统,2015,21(10):2659-2667.LIU Q,LIU H,ZHOU S K,et al.Principle and Development of NURBS Interpolation Algorithm with Zero-feedrate Fluctuation[J].Computer Integrated Manufacturing Systems,2015,21(10):2659-2667.
[4]张晓辉,于东,洪海涛,等.数控加工中的平滑压缩插补算法研究[J].机械工程学报,2011,47(5):156-162.ZHANG X H,YU D,HONG H T,et al.Research on Smooth Compression Interpolation Algorithm in CNC Machining[J].Journal of Mechanical Engineering,2011,47(5):156-162.
[5]江本赤.B样条曲线曲率简易求解算法[J].制造技术与机床,2014(10):78-80.JIANG B C.A Simple Solution Algorithm for the Curvature of B-spline Curve[J].Manufacturing Technology & Machine Tool,2014(10):78-80.
[6]王国勋,王宛山,王军,等.实时快速NURBS直接插补技术[J].中国机械工程,2013,24(5):617-622.WANG G X,WANG W S,WANG J,et al.Development of Fast Real-time NURBS Direct Interpolation Algorithm[J].China Mechanical Engineering,2013,24(5):617-622.
[7]柳宁,王高.改正的预估校正NURBS实时插补算法[J].华南理工大学学报(自然科学版),2010,38(1):119-123.LIU N,WANG G.Improved Predictor-Corrector Real-Time NURBS Interpolation Algorithm[J].Journal of South China University of Technology(Natural Science Edition),2010,38(1):119-123.
[8]任杰青,刘凯,赵东标.基于预估误差补偿的NURBS曲线插补算法[J].机械科学与技术,2015,34(8):1201-1205.REN J Q,LIU K,ZHAO D B.An Interpolation Algorithm for NURBS Based on Predicted Error Compensation[J].Mechanical Science and Technology for Aerospace Engineering,2015,34(8):1201-1205.
[9]董伯麟,岳云平.基于FIR滤波器的NURBS插补算法研究[J].现代机械,2015(5):1-4.DONG B L,YUE Y P.Study on NURBS Interpolation Algorithm Based on FIR Filter[J].Modern Machinery,2015(5):1-4.
[10]刘献礼,周肖阳,李茂月,等.NURBS曲线S形加减速寻回实时插补算法[J].机械工程学报,2015,53(3):183-192.LIU X L,ZHOU X Y,LI M Y,et al.The Real-time Algorithm of NURBS Curve Retriever Interpolation with S-type Acceleration and Deceleration Control[J].Journal of Mechanical Engineering,2015,53(3):183-192.
[11]岳磊,赵国勇,刘晨希,等.基于S曲线加减速的NURBS插补控制方法研究[J].组合机床与自动化加工技术,2015(5):43-46.YUE L,ZHAO G Y,LIU C X,et al.Research on NURBS Curve Interpolation Method Based on S Curve Acceleration and Deceleration[J].Modular Machine Tool & Automatic Manufacturing Technique,2015(5):43-46.
[12]罗福源,游有鹏,尹涓.NURBS曲线泰勒展开插补法的平稳性与改进研究[J].中国机械工程,2012,23(4):383-388.LUO F Y,YOU Y P,YIN J.Researchon Stability and Improvement of Taylor-Expansion-Based Approach for NURBS Curve Interpolation[J].China Mechanical Engineering,2012,23(4):383-388.
[13]BEDI S,ALII,QUAN N.Advanced Techniques for CNC Machines[J].Journal of Engineering for Industry,1993,115(3):329-336.
[14]SHPITALNI M,KOREN Y,LO C C.Real-time Curve Interpolators[J].Computer-Aided Design,1994,26(11):832-838.
[15]刘宇,戴丽,刘杰,等.泰勒展开NURBS曲线插补算法[J].东北大学学报(自然科学版),2009,30(1):117-120.LIU Y,DAI L,LIU J,et al.Study on NURBS Interpolator with Taylor Expansion[J].Journal of Northeastern University(Natural Science),2009,30(1):117-120.
[2]YANG D C H,KONG T.Parametric Interpolator Versus Linear Interpolator for Precision CNC Machining[J].Computer-Aided Design,1994,26(3):225-234.
[3]刘强,刘焕,周胜凯,等.无速度波动的NURBS曲线二次插补算法原理及其实现[J].计算机集成制造系统,2015,21(10):2659-2667.LIU Q,LIU H,ZHOU S K,et al.Principle and Development of NURBS Interpolation Algorithm with Zero-feedrate Fluctuation[J].Computer Integrated Manufacturing Systems,2015,21(10):2659-2667.
[4]张晓辉,于东,洪海涛,等.数控加工中的平滑压缩插补算法研究[J].机械工程学报,2011,47(5):156-162.ZHANG X H,YU D,HONG H T,et al.Research on Smooth Compression Interpolation Algorithm in CNC Machining[J].Journal of Mechanical Engineering,2011,47(5):156-162.
[5]江本赤.B样条曲线曲率简易求解算法[J].制造技术与机床,2014(10):78-80.JIANG B C.A Simple Solution Algorithm for the Curvature of B-spline Curve[J].Manufacturing Technology & Machine Tool,2014(10):78-80.
[6]王国勋,王宛山,王军,等.实时快速NURBS直接插补技术[J].中国机械工程,2013,24(5):617-622.WANG G X,WANG W S,WANG J,et al.Development of Fast Real-time NURBS Direct Interpolation Algorithm[J].China Mechanical Engineering,2013,24(5):617-622.
[7]柳宁,王高.改正的预估校正NURBS实时插补算法[J].华南理工大学学报(自然科学版),2010,38(1):119-123.LIU N,WANG G.Improved Predictor-Corrector Real-Time NURBS Interpolation Algorithm[J].Journal of South China University of Technology(Natural Science Edition),2010,38(1):119-123.
[8]任杰青,刘凯,赵东标.基于预估误差补偿的NURBS曲线插补算法[J].机械科学与技术,2015,34(8):1201-1205.REN J Q,LIU K,ZHAO D B.An Interpolation Algorithm for NURBS Based on Predicted Error Compensation[J].Mechanical Science and Technology for Aerospace Engineering,2015,34(8):1201-1205.
[9]董伯麟,岳云平.基于FIR滤波器的NURBS插补算法研究[J].现代机械,2015(5):1-4.DONG B L,YUE Y P.Study on NURBS Interpolation Algorithm Based on FIR Filter[J].Modern Machinery,2015(5):1-4.
[10]刘献礼,周肖阳,李茂月,等.NURBS曲线S形加减速寻回实时插补算法[J].机械工程学报,2015,53(3):183-192.LIU X L,ZHOU X Y,LI M Y,et al.The Real-time Algorithm of NURBS Curve Retriever Interpolation with S-type Acceleration and Deceleration Control[J].Journal of Mechanical Engineering,2015,53(3):183-192.
[11]岳磊,赵国勇,刘晨希,等.基于S曲线加减速的NURBS插补控制方法研究[J].组合机床与自动化加工技术,2015(5):43-46.YUE L,ZHAO G Y,LIU C X,et al.Research on NURBS Curve Interpolation Method Based on S Curve Acceleration and Deceleration[J].Modular Machine Tool & Automatic Manufacturing Technique,2015(5):43-46.
[12]罗福源,游有鹏,尹涓.NURBS曲线泰勒展开插补法的平稳性与改进研究[J].中国机械工程,2012,23(4):383-388.LUO F Y,YOU Y P,YIN J.Researchon Stability and Improvement of Taylor-Expansion-Based Approach for NURBS Curve Interpolation[J].China Mechanical Engineering,2012,23(4):383-388.
[13]BEDI S,ALII,QUAN N.Advanced Techniques for CNC Machines[J].Journal of Engineering for Industry,1993,115(3):329-336.
[14]SHPITALNI M,KOREN Y,LO C C.Real-time Curve Interpolators[J].Computer-Aided Design,1994,26(11):832-838.
[15]刘宇,戴丽,刘杰,等.泰勒展开NURBS曲线插补算法[J].东北大学学报(自然科学版),2009,30(1):117-120.LIU Y,DAI L,LIU J,et al.Study on NURBS Interpolator with Taylor Expansion[J].Journal of Northeastern University(Natural Science),2009,30(1):117-120.