基于最小单向Hausdorff距离的线轮廓度误差评定

曹利新; 秦令剑

doi:10.13433/j.cnki.1003-8728.2015.1014

基于最小单向Hausdorff距离的线轮廓度误差评定

doi: 10.13433/j.cnki.1003-8728.2015.1014

1.
大连理工大学机械工程学院, 大连 116024

基金项目:

国家自然科学基金项目(51175065)资助

详细信息

作者简介:
曹利新(1966-),教授,博士生导师,研究方向为机械设计与制造中的几何学方法、曲面多轴数控加工理论,caosm@dlut.edu.cn

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出版历程
- 收稿日期: 2014-01-03
- 刊出日期: 2015-10-05

Evaluation Method of Line Profile Error Based on Minimum Directed Hausdorff Distance

1.
School of Mechanical Engineering, Dalian University of Technology, Dalian 116024, China

摘要

摘要: 为了高效率、高精度的评定平面线轮廓度误差,提出了一种基于平面曲线间最小单向Hausdorff距离的线轮廓度误差评定方法,给出了求解最小单向Hausdorff距离的数学规划模型及其线性化解算方法。该方法可以保证计算结果符合国家标准关于线轮廓度误差定义的最小条件。模型中涉及到的点到曲线最小距离,采用全局算法中的投影多面体方法计算。通过与已有文献中的算例结果进行对比,验证了所提方法的正确性和有效性。数值计算表明,所提方法符合线轮廓度误差评定的最小条件,且具有较高的评定精度。
- 线轮廓度 /
- 最小单向Hausdorff距离 /
- 投影多面体算法
Abstract: In order to improve the evaluation efficiency and accuracy of the line profile error, an evaluation method of the line profile error based on the minimum directed Hausdorff distance between the plane curves is proposed. The mathematical programming model and its linearization method for the minimum directed Hausdorff distance are presented. The results of the present method meet the minimum zone condition of the line profile error issued with national standard. The Projected-Polyhedron algorithm is applied to calculate the minimum distance between a point and a curve in the present method. Comparing with the results of two existed literatures, we verify the correctness and effectiveness of the present method. The numerical examples show that the results of the present method accords with the requirements of the minimum zone condition and the evaluation accuracy is very high.
- algorithms /
- calculations /
- computational efficiency

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参考文献(16)

[1]	GB/T 1182-2008,产品几何技术规范(GPS)几何公差形状、方向、位置和跳动公差标注[S]. 北京:中国标准出版社,2008 Geometrical Product Specifications(GPS):Geometrical tolerancing-Tolerances of form, orientation, location and run-out[S]. Beijing:China Metrology Publishing House, 2008(in Chinese)
[2]	熊有伦.精密测量的数学方法[M]. 北京:中国计量出版社,1989 Xiong Y L. Mathematical method of precision measurement[M]. Beijing:China Metrology Publishing House, 1989(in Chinese)
[3]	刘温,马兰,边景宏.圆锥盘素线线轮廓度误差测量方法[J]. 东北大学学报,2000,21(4):397-400 Liu W, Ma L, Bian J H. Measuring method of the profile errors of generatrix on the cone disc[J]. Journal of Northeastern University, 2000,21(4):397-400(in Chinese)
[4]	张琳,郭俊杰,姜瑞,等.自由曲线轮廓度误差评定中的坐标系自适应调整[J]. 仪器仪表学报,2002,23(2):203-205 Zhang L, Guo J J, Jiang R, et al. Self-adapt adjustment of coordinate system in evaluation of freeform curve profile[J]. Chinese Journal of Scientific Instrument, 2002,23(2):203-205(in Chinese)
[5]	刘文文,聂恒敬.一种自适应的平面线轮廓度误差评定方法[J]. 计量学报,1999,20(1):27-31 Liu W W, Nie H J. An auto-spotting evaluation method of plane profile of any line[J]. Acta Metrologica Sinica, 1999,20(1):27-31(in Chinese)
[6]	张进,王仲,李超,等.离散点的线轮廓度评价算法[J]. 光学精密工程,2008,16(11):2281-2285 Zhang J, Wang Z, Li C, et al. Evaluation algorithm of curve profile based on discrete points[J]. Optics and Precision Engineering, 2008,16(11):2281-2285(in Chinese)
[7]	王伯平.基于遗传算法和自适应的平面线轮廓度误差评定方法[J]. 工程设计学报,2004,11(2):68-72 Wang B P. Evaluation method of plane line profile error based on genetic algorithm and auto-spotting[J]. Journal of Engineering Design, 2004,11(2):68-72(in Chinese)
[8]	于源,邱子魁.平面曲线轮廓度误差评定的算法分析[J]. 北京化工大学学报,2006,33(4):41-43 Yu Y, Qiu Z K. Algorithmic analysis of error evaluation for a planar free-form curve profile[J]. Journal of Beijing University of Chemical Technology, 2006,33(4):41-43(in Chinese)
[9]	温秀兰,赵艺义,王东霞,等.改进遗传算法与拟随机序列结合评定自由曲线轮廓度误差[J]. 光学精密工程,2012,20(4):835-842 Wen X L, Zhao Y B, Wang D X, et al. Evaluating freeform curve profile error based on improved genetic algorithm and quasi random sequence[J]. Optics and Precision Engineering, 2012,20(4):835-842(in Chinese)
[10]	钱春.基于区间牛顿法的点到参数曲线最小距离的计算方法[J]. 机电工程, 2010,27(1):82-84 Qian C. Computing method for the minimum distance from a point to a parametric curve based on the interval Newton method[J]. Mechanical & Electrical Engineering Magazine, 2010,27(1):82-84(in Chinese)
[11]	伍丽峰,陈乐坪,谌炎辉,等.求点到空间参数曲线最小距离的几种算法[J]. 机械设计与制造,2011,(9):15-17 Wu L F, Chen Y P, Chen Y H, et al. Algorithms on calculating minimum distance between point and spatial parametric curves[J]. Machinery Design & Manufacture, 2011,(9):15-17(in Chinese)
[12]	Patrikalakis N M, Maekawa T. Shape interrogation for computer aided design and manufacturing[M]. New York:Springer,2002
[13]	Yau H T, Menq C H. A unified least-squares approach to the evaluation of geometric errors using discrete measurement data[J]. International Journal of Machine Tools and Manufacture, 1996,36(11):1269-1290
[14]	刘健,王晓明.鞍点规划与形位误差评定[M]. 大连:大连理工大学出版社,1996 Liu J, Wang X M. Saddle point programming and geometric error evaluation[M]. Dalian:Dalian University of Technology Press, 1996(in Chinese)
[15]	侯宇,张竞,崔晨阳.复杂线轮廓度误差坐标测量的数据处理方法[J]. 计量学报, 2002,23(1):13-16 Hou Y, Zhang J, Cui C Y. Data processing method of coordinate measurement for complicated curve profile error[J]. Acta Metrologica Sinica, 2002,23(1):13-16(in Chinese)
[16]	Piegle L, Tiller W. The NURBS book[M]. 2nd ed. Berlin:Springer, 1997