一种基于最小条件的线轮廓度误差评定方法
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摘要
提出一种模拟实际量具测量过程的方法来评定线轮廓度误差。该方法遵循国家标准中对形状公差的最小条件要求,通过分析测量点与对应包络边界的位置关系,将测量点集视为刚体,计算边界收缩至最小区域的过程中刚体与边界可能出现的相对运动,最终使所有测点位于最小包容区域内。结果表明:所提方法的评定过程相对于常用优化算法的大范围搜索更有全局性与单一性,可有效避免出现由算法缺陷导致搜索结果陷入局部解的情况。该方法适用于线轮廓度误差的评定。
A measuring method of simulating actual measuring tool processes was proposed to evaluate the line profile errors. The method followed the least condition principle of shape tolerances in the national standard. The position relationship between the measuring points and the corresponding envelope boundary was analyzed,the set of measurement points was regarded as a rigid body. The relative motions were calculated between the rigid body and the boundary which might occur in the processes of the boundary shrinking to the minimum region,and finally all the measured points were located in the minimum containment region. The results show that evaluation processes are more global and directivity than that of the large-scale search of common optimization algorithm,which may effectively avoid the local solutions of the search results caused by the algorithm defects. The proposed method is suitable for the error evaluation of line profiles.
A measuring method of simulating actual measuring tool processes was proposed to evaluate the line profile errors. The method followed the least condition principle of shape tolerances in the national standard. The position relationship between the measuring points and the corresponding envelope boundary was analyzed,the set of measurement points was regarded as a rigid body. The relative motions were calculated between the rigid body and the boundary which might occur in the processes of the boundary shrinking to the minimum region,and finally all the measured points were located in the minimum containment region. The results show that evaluation processes are more global and directivity than that of the large-scale search of common optimization algorithm,which may effectively avoid the local solutions of the search results caused by the algorithm defects. The proposed method is suitable for the error evaluation of line profiles.
引文
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[2]温秀兰,赵艺兵,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):836-842.WEN Xiulan,ZHAO Yibing,WANG Dongxia,et al.Evaluating Freeform Curve Profile Error Based on improved Genetic Algorithm and Quasi Random Sequence[J].Optics and Precision Engineering,2012,20(4):836-842.
[3]廖平.基于遗传算法和分割逼近法精确计算复杂曲面轮廓度误差[J].机械工程学报,2010,46(10):2-7.LIAO Ping.Calculating of Complex Surface Profile Error Based on Subdivision Approach Algorithm and Genetic Algorithm[J].Journal of Mechanical Engineering,2010,46(10):2-7.
[4]王宇春,孙和义,唐文彦,等.最小条件下一般二次曲面轮廓度误差的评定[J].仪器仪表学报,2014,35(8):1804-1809.WANG Yuchun,SUN Heyi,TANG Wenyan,et al.Evaluating General Quadric Profile Error Based on Least Condition Principle[J].Chinese Journal of Scientific Instrument,2014,35(8):1804-1809.
[5]王东霞,温秀兰,赵艺兵.基于CAD模型引导测量的自由曲面定位及轮廓度误差评定[J].光学精密工程,2012,20(12):2721-2727.WANG Dongxia,WEN Xiulan,ZHAO Yibing.Localization and Profile Error Evaluation of Freeform Surface Based on CAD Model-directed Measurment[J].Optics and Precision Engineering,2012,20(12):2721-2727.
[6]郭慧,潘家祯.基于微粒群算法的叶片曲面形状误差评定[J].东华大学学报(自然科学版),2008,34(5):769-772.GUO Hui,PAN Jiazhen.Form Error Evaluation of Cared Blade Surface Based on Particle Swarm Optimization[J].Journal of Donghua University(Natural Science),2008,34(5):769-772.
[7]刘玉君,朱秀莉,纪卓尚,等.船体外板曲面形状误差评定方法分析[J].哈尔滨工程大学学报,2006,27(5):636-638.LIU Yujun,ZHU Xiuli,JI Zhuoshang,et al.Detection of Profile Error of Ship Hull Plate Processing Surface[J].Journal of Harbin Engineering University,2006,27(5):636-638.
[8]BYRD R H,LU P,NOCEDAL J,et al.A Limited Memory Algorithm for Bound Constrained Optimization[J].Siam Journal on Scientific Computing,1995,16(5):1190-1208.
[9]李柱,徐振高,蒋向前.互换性与测量技术--几何产品技术规范与认证GPS[M].北京:高等教育出版社,2015:170-171.LI Zhu,XU Zhengao,JIANG Xiangqian.Geometrical Product Specifications and Verification[M].Beijing:Higher Education Press,2015:170-171.
[10]PIEGL L,TILLER W.非均匀有理B样条[M].2版.赵罡,穆国旺,王拉柱,译.北京:清华大学出版社,2010:46-47.PIEGL L,TILLER W.The NURBS Book[M].2nd ed.ZHAO Gang,MU Guowang,WANG Lazhu,Trans.Beijing:Tsinghua University Press,2010:46-47
[11]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,2001:310-312.SHI Fazhong.CAGD&NURBS[M].Beijing:Higher Education Press,2001:310-312.
[12]茅健,张恒,曹衍龙.基于SDT的平面尺寸公差模型研究及应用[J].工程设计学报,2010,17(5):322-324.MAO Jian,ZHANG Heng,CAO Yanlong.Research and Application on Model of Size Tolerance for Plane Based on SDT[J].Journal of Engineering Design,2010,17(5):322-324.