基于凸包算法的陶芯弯曲度与扭曲度误差计算
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摘要
陶芯弯扭变形直接关系到空心叶片的壁厚尺寸分布,为克服当前陶芯弯扭变形的计算中测量数据与理论模型三维配准、陶芯截面轮廓线提取或拟合的过程算法复杂、收敛速度慢、效率低等问题,提出了一种通过测量数据点直接计算陶芯弯曲度和扭曲度误差的算法,该算法不需要三维配准和提取陶芯外轮廓线,通过距离权值法计算陶芯弯曲度,凸包算法计算陶芯扭曲度,能大幅提高计算效率。仿真与实验结果表明:该算法弯曲变形计算精度为99.55%,与二维配准算法相差±0.01mm;扭曲变形计算精度为99.98%,与二维配准相差±0.006°。
Bending and torsion deformation of ceramic core have a direct impact on the wall thickness accuracy of hollow turbine blade.To overcome the difficulties for determining deformation by extracting or fitting contour lines based on 3-D registration of measured point sets and CAD model such as the slow convergence and low efficiency,the bending and torsion degree of ceramic core was proposed and a new algorithm for ceramic core bending degree and torsion degree was studied through the geometric characteristics of ceramic core measurement data based on convex-hull algorithm and distance-weighted method.Through corresponding verification experiments the accuracy of proposed method was proved.The results indicated that the accuracy of the calculated torsional and bending deformation was 99.55% and 99.98%,respectively;compared with the two-dimensional registration method,the deviation of the torsional and bending deformation was only ±0.01 mm and ±0.006°,respectively.
Bending and torsion deformation of ceramic core have a direct impact on the wall thickness accuracy of hollow turbine blade.To overcome the difficulties for determining deformation by extracting or fitting contour lines based on 3-D registration of measured point sets and CAD model such as the slow convergence and low efficiency,the bending and torsion degree of ceramic core was proposed and a new algorithm for ceramic core bending degree and torsion degree was studied through the geometric characteristics of ceramic core measurement data based on convex-hull algorithm and distance-weighted method.Through corresponding verification experiments the accuracy of proposed method was proved.The results indicated that the accuracy of the calculated torsional and bending deformation was 99.55% and 99.98%,respectively;compared with the two-dimensional registration method,the deviation of the torsional and bending deformation was only ±0.01 mm and ±0.006°,respectively.
引文
[1]JIANG Ruisong,WANG Wenhu,ZHANG Dinghua.Wall thickness monitoring method for wax pattern of hollow turbine blade[J].International Journal of Advanced Manufacturing Technology,2016,83(5/6/7/8):949-960.
[2]DONG Yiwei,BU Kun,DOU Yangqing.Determination of wax pattern die profile for investment casting of turbine blades[J].Transactions of Nonferrous Metals Society of China,2011,21(2):378-387.
[3]OLEVSKY E A,GERMAN R M.Effect of gravity on dimensional change during sintering:Ⅰshrinkage anisotropy[J].Acta Materialia,2000,48(5):1153-1166.
[4]黄胜利,卜昆,徐岳林,等.基于主动轮廓模型的复杂陶芯弯扭变形分析[J].计算机集成制造系统,2010,16(8):1643-1648.HUANG Shengli,BU Kun,XU Yuelin,et al.Analysis of bending and torsion deformation for complex ceramic core based on active contour model[J].Computer Integrated Manufacturing Systems,2010,16(8):1643-1648.(in Chinese)
[5]DOU Y,YAN F,BU K.Reversing design methodology of ceramic core for hollow turbine blade based on measured data[R].Quebec,Canada:ASME 2014International Mechanical Engineering Congress and Exposition,2014.
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[8]EDDY W.A new convex hull algorithm for planar sets[J].ACM Transactions on Mathematical Software,1977,3(4):398-403.
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[13]彭志光.基于改进凸包算法的叶片型面检测[D].武汉:华中科技大学,2012.PENG Zhiguang.The blade surface inspection based on the improved convex hull algorithm[D].Wuhan:Huazhong University of Science and Technology,2012.(in Chinese)
[14]郝建强.利用正负划分性求平面点集凸包的最优算法[J].中国图像图形学报,2007,12(5):910-916.HAO Jianqiang.Optimum algorithm for constructing convex hull of planar point set utilizing plus or minus characteristic of demarcation[J].Journal of Image and Graphics,2007,12(5):910-916.(in Chinese)
[15]LIU Runzong,FANG Bin,TANG Yuanyan.A fast convex hull algorithm with maximum inscribed circle affine transformation[J].Neurocomputing,2012,77(1):212-221.
[16]WU Xuegang,FANG Bin,TANG Yuanyan.A fast and complete convex-hull algorithm architecture based on ellipse and elastic ellipse methods[J].International Journal of Pattern Recognition and Artificial Intelligence,2013,27(8):316-326.
[17]王结臣,陈焱明.一种栅格辅助的平面点集最小凸包生成算法[J].武汉大学学报(信息科学版),2010,34(4):403-406.WANG Jiechen,CHEN Yanming.A gird-aided slgorithm for fetermining the minimum convex hull of planar points set[J].Geomatics and Information Science of Wuhan University,2010,34(4):403-406.(in Chinese)
[18]陈明,张丰,杜震洪.环状分布平面点集的凸包快速生成算法[J].上海交通大学学报,2014,48(5):658-662.CHEN Ming,ZHNAG Feng,DU Zhenhong.A fast convex-hull algorithm for ring-distributed planar points sets[J].Journal of Shanghai Jiao Tong University,2014,48(5):658-662.(in Chinese)
[19]DATTA A,PARUI S K.A dynamic neural net to compute convex hull[J].Neurocomputing,1996,10(4):375-384.
[20]李文龙.一种用于确定叶片加工弯曲度误差的方法:102728658B[P].2014-05-07.
[21]李文龙,尹周平,熊有伦.一种基于弦线的航空薄壁叶片加工扭曲度误差测量方法:102735204B[P].2014-07-23.
[22]DONG Yiwei,ZHANG Dinghua,BU Kun.Geometric parameter-based optimization of the die profile for the investment casting of aerofoil-shaped turbine blades[J].International Journal of Advanced Manufacturing Technology,2011,57(9/10/11/12):1245-1258.
[2]DONG Yiwei,BU Kun,DOU Yangqing.Determination of wax pattern die profile for investment casting of turbine blades[J].Transactions of Nonferrous Metals Society of China,2011,21(2):378-387.
[3]OLEVSKY E A,GERMAN R M.Effect of gravity on dimensional change during sintering:Ⅰshrinkage anisotropy[J].Acta Materialia,2000,48(5):1153-1166.
[4]黄胜利,卜昆,徐岳林,等.基于主动轮廓模型的复杂陶芯弯扭变形分析[J].计算机集成制造系统,2010,16(8):1643-1648.HUANG Shengli,BU Kun,XU Yuelin,et al.Analysis of bending and torsion deformation for complex ceramic core based on active contour model[J].Computer Integrated Manufacturing Systems,2010,16(8):1643-1648.(in Chinese)
[5]DOU Y,YAN F,BU K.Reversing design methodology of ceramic core for hollow turbine blade based on measured data[R].Quebec,Canada:ASME 2014International Mechanical Engineering Congress and Exposition,2014.
[6]GRAHAM R L.An efficient algorith for determining the convex hull of a finite planar set[J].Information Processing Letters,1972,1(4):132-133.
[7]ANDREW A M.Another efficient algorithm for convex hulls in two dimensions[J].Information Processing Letters,1979,9(5):216-219.
[8]EDDY W.A new convex hull algorithm for planar sets[J].ACM Transactions on Mathematical Software,1977,3(4):398-403.
[9]JARVIS A.On the identification of the convex hull of a finite set of points in the plane[J].Information Processing Letters,1973,2(1):18-21.
[10]PREPARATA F P,HONG S J.Convex hulls of finite point sets in two and three dimensions[J].Communications of the ACM,1977,20(1):87-93.
[11]CHADNOV R V,SKVORTSOV A V.Convex hull algorithms review[C]∥Proceedings of the 8th Russian-Korean International Symposium on Science and Technology.Korus:IEEE,2004:112-115.
[12]SHARIF M,NAQVI S Z Z,RAZA M,et al.A new approach to compute convex hull[J].Innovative Systems Design and Engineering,2011,2(3):187-193.
[13]彭志光.基于改进凸包算法的叶片型面检测[D].武汉:华中科技大学,2012.PENG Zhiguang.The blade surface inspection based on the improved convex hull algorithm[D].Wuhan:Huazhong University of Science and Technology,2012.(in Chinese)
[14]郝建强.利用正负划分性求平面点集凸包的最优算法[J].中国图像图形学报,2007,12(5):910-916.HAO Jianqiang.Optimum algorithm for constructing convex hull of planar point set utilizing plus or minus characteristic of demarcation[J].Journal of Image and Graphics,2007,12(5):910-916.(in Chinese)
[15]LIU Runzong,FANG Bin,TANG Yuanyan.A fast convex hull algorithm with maximum inscribed circle affine transformation[J].Neurocomputing,2012,77(1):212-221.
[16]WU Xuegang,FANG Bin,TANG Yuanyan.A fast and complete convex-hull algorithm architecture based on ellipse and elastic ellipse methods[J].International Journal of Pattern Recognition and Artificial Intelligence,2013,27(8):316-326.
[17]王结臣,陈焱明.一种栅格辅助的平面点集最小凸包生成算法[J].武汉大学学报(信息科学版),2010,34(4):403-406.WANG Jiechen,CHEN Yanming.A gird-aided slgorithm for fetermining the minimum convex hull of planar points set[J].Geomatics and Information Science of Wuhan University,2010,34(4):403-406.(in Chinese)
[18]陈明,张丰,杜震洪.环状分布平面点集的凸包快速生成算法[J].上海交通大学学报,2014,48(5):658-662.CHEN Ming,ZHNAG Feng,DU Zhenhong.A fast convex-hull algorithm for ring-distributed planar points sets[J].Journal of Shanghai Jiao Tong University,2014,48(5):658-662.(in Chinese)
[19]DATTA A,PARUI S K.A dynamic neural net to compute convex hull[J].Neurocomputing,1996,10(4):375-384.
[20]李文龙.一种用于确定叶片加工弯曲度误差的方法:102728658B[P].2014-05-07.
[21]李文龙,尹周平,熊有伦.一种基于弦线的航空薄壁叶片加工扭曲度误差测量方法:102735204B[P].2014-07-23.
[22]DONG Yiwei,ZHANG Dinghua,BU Kun.Geometric parameter-based optimization of the die profile for the investment casting of aerofoil-shaped turbine blades[J].International Journal of Advanced Manufacturing Technology,2011,57(9/10/11/12):1245-1258.