面向STL模型的在机检测系统测点法矢计算
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摘要
为提高在机检测系统的测头半径误差补偿精度,针对测头半径误差补偿的重要参数-测点的法矢方向提出了精确的估算方法。针对测点位于三角网格顶点的情况,提出一种以三角面片的顶角、质心距及周长作为权重因子的顶点法矢的估算方法。采用三种二次曲面的三角网格模型进行实验验证,结果表明,针对测点位于三角网格顶点情况的计算方法可有效地提高法矢计算精度。同时,针对采用截面线法规划测点时,测点普遍位于三角网格内部的情况,提出了计算测点的法矢方向,并通过两种不同网格密度的正弦曲面进行实例验证。结果表明,采用面向STL模型的在机检测系统测点法矢计算方法计算的测点法矢误差的平均值较其他方法分别减少了53.5%、61.7%,使测点法矢的计算精度明显提高,从而有效地提高了半径误差补偿的精度。
To improve the radius error compensation accuracy of an on-machine measurement system,an accurate estimation algorithm is presented for the normal vector of a measurement point,which is an important parameter for radius error compensation. When the measurement point is in the vertices of triangular meshes,a normal vector estimation method is proposed based on the angle,centroids distance and perimeter of a triangle and is validated by the triangular mesh models of three quadric surfaces. The experimental results demonstrate that the improved algorithm can effectively improve the accuracy of normal vector estimation. Meanwhile,under the condition that the measurement points planned by the cross-section curve method are located in the interiors of the triangle,the barycenter coordinate method is proposed to compute the normal vectors of measurement points and verified by the density of two different grids with sine-like surfaces. The experimental results show that the improved algorithm decreases the average normal vector error by 53.5% and 61.7% respectively and obviously enhances the accuracy of normal vector estimation and radius error compensation.
To improve the radius error compensation accuracy of an on-machine measurement system,an accurate estimation algorithm is presented for the normal vector of a measurement point,which is an important parameter for radius error compensation. When the measurement point is in the vertices of triangular meshes,a normal vector estimation method is proposed based on the angle,centroids distance and perimeter of a triangle and is validated by the triangular mesh models of three quadric surfaces. The experimental results demonstrate that the improved algorithm can effectively improve the accuracy of normal vector estimation. Meanwhile,under the condition that the measurement points planned by the cross-section curve method are located in the interiors of the triangle,the barycenter coordinate method is proposed to compute the normal vectors of measurement points and verified by the density of two different grids with sine-like surfaces. The experimental results show that the improved algorithm decreases the average normal vector error by 53.5% and 61.7% respectively and obviously enhances the accuracy of normal vector estimation and radius error compensation.
引文
[1]韩如聪,张建富,冯平法,等.原位检测系统中触发式测头半径误差分析与建模[J].组合机床与自动化加工技术,2014,(12):60-64Han R C,Zhang J F,Feng P F,et al.Analysis and modeling of the radius error of touch trigger probes in onmachine verification system[J].Modular Machine Tool&Automatic Manufacturing Technique,2014,(12):60-64(in Chinese)
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[12]彭育辉,高诚辉.基于形状修正的三角网格模型顶点法矢估算方法[J].中国图象图形学报,2010,15(1):142-148Peng Y H,Gao C H.An improved algorithm for vertex normal computation of triangular meshes based on shape correction[J].Journal of Image and Graphics,2010,15(1):142-148(in Chinese)
[13]杨旭静,赵秋艳,郑娟,等.面向数控加工的三角网格法矢量及曲率估算[J].机械科学与技术,2015,34(3):413-417Yang X J,Zhao Q Y,Zheng J,et al.An improved algorithm for normal vector and curvature estimation based on the triangularly-meshed surface in CNC machining[J].Mechanical Science and Technology for Aerospace Engineering,2015,34(3):413-417(in Chinese)
[14]Chen Y P,Gao J,Wen H,et al.Estimation normal vector of triangular mesh vertex by angle and centroid weights and its application[J].Telkomnika,2013,11(4):1841-1848
[15]赵秋艳.面向数控加工的三角网格法矢量与曲率计算方法研究[D].长沙:湖南大学,2013Zhao Q Y.Research on the normal vector and curvature estimation algorithm for triangular mesh surface in CNC machining[D].Changsha:Hunan University,2013(in Chinese)
[16]黄雪梅,邓春梅,周济,等.基于曲面三角形网格模型的凸、凹模数控编程算法[J].计算机仿真,2000,17(4):52-55,62Huang X M,Deng C M,Zhou J,et al.A NC programming algorithm based on the triangular mesh modeling for manufacturing male and female die of freeform surface[J].Computer Simulation,2000,17(4):52-55,62(in Chinese)
[2]王立成,黄信达,丁汉.原位检测系统中触发式测头的误差分析与补偿[J].中国机械工程,2012,23(15):1774-1778Wang L C,Huang X D,Ding H.Error analysis and compensation for touch trigger probe of on-machine measurement system[J].China Mechanical Engineering,2012,23(15):1774-1778(in Chinese)
[3]王平江,雷宇晴,邹尚波,等.在机测量技术现状与发展趋势[J].组合机床与自动化加工技术,2015,(7):1-4Wang P J,Lei Y Q,Zou S B,et al.Status and development trend of on-machine measurement technology[J].Modular Machine Tool&Automatic Manufacturing Technique,2015,(7):1-4(in Chinese)
[4]诸进才,胡艳娥,张菊红.面向STL格式零件曲面的测点合理规划的研究[J].机械,2014,41(6):29-32Zhu J C,Hu Y E,Zhang J H.Study on measurement points planning regularly for the surfaces of parts in STL format[J].Machinery,2014,41(6):29-32(in Chinese)
[5]Stroud I,Xirouchakis P C.STL and extensions[J].Advances in Engineering Software,2000,31(2):83-95
[6]陈岳坪,靳龙,卢海燕,等.基于三角网格模型的复杂曲面测点规划[J].机床与液压,2015,43(23):42-45Chen Y P,Jin L,Lu H Y,et al.Measured point planning of complex surfaces based on triangular mesh models[J].Machine Tool&Hydraulics,2015,43(23):42-45(in Chinese)
[7]Gouraud H.Continuous shading of curved surfaces[J].IEEE Transactions on Computers,2006,C-20(6):623-629
[8]Taubin G.Estimating the tensor of curvature of a surface from a polyhedral approximation[C]//Proceedings of the 5th International Conference on Computer Vision.Cambridge,MA,USA:IEEE,1995:902-907
[9]Thu··rner G,Wu··thrich C A.Computing vertex normals from polygonal facets[J].Journal of Graphics Tools,1998,3(1):43-46
[10]神会存,周来水.基于离散曲率计算的三角网格模型优化调整[J].航空学报,2006,27(2):318-324Shen H C,Zhou L S.Triangular mesh regularization based on discrete curvature estimation[J].Acta Aeronautica et Astronautica Sinica,2006,27(2):318-324(in Chinese)
[11]Chen S G,Wu J Y.Estimating normal vectors and curvatures by centroid weights[J].Computer Aided Geometric Design,2004,21(5):447-458
[12]彭育辉,高诚辉.基于形状修正的三角网格模型顶点法矢估算方法[J].中国图象图形学报,2010,15(1):142-148Peng Y H,Gao C H.An improved algorithm for vertex normal computation of triangular meshes based on shape correction[J].Journal of Image and Graphics,2010,15(1):142-148(in Chinese)
[13]杨旭静,赵秋艳,郑娟,等.面向数控加工的三角网格法矢量及曲率估算[J].机械科学与技术,2015,34(3):413-417Yang X J,Zhao Q Y,Zheng J,et al.An improved algorithm for normal vector and curvature estimation based on the triangularly-meshed surface in CNC machining[J].Mechanical Science and Technology for Aerospace Engineering,2015,34(3):413-417(in Chinese)
[14]Chen Y P,Gao J,Wen H,et al.Estimation normal vector of triangular mesh vertex by angle and centroid weights and its application[J].Telkomnika,2013,11(4):1841-1848
[15]赵秋艳.面向数控加工的三角网格法矢量与曲率计算方法研究[D].长沙:湖南大学,2013Zhao Q Y.Research on the normal vector and curvature estimation algorithm for triangular mesh surface in CNC machining[D].Changsha:Hunan University,2013(in Chinese)
[16]黄雪梅,邓春梅,周济,等.基于曲面三角形网格模型的凸、凹模数控编程算法[J].计算机仿真,2000,17(4):52-55,62Huang X M,Deng C M,Zhou J,et al.A NC programming algorithm based on the triangular mesh modeling for manufacturing male and female die of freeform surface[J].Computer Simulation,2000,17(4):52-55,62(in Chinese)