一种自由曲线廓形误差的高效可靠评价方法
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摘要
为实现对自由曲线廓形误差的高效可靠评价,提出了一种结合多项式方程求根与实数编码遗传算法(RCGA)的评价方法。首先,根据最小二乘准则建立了廓形误差评价的优化模型;进而,通过构造多项式方程,并采用Halley迭代对方程求根,实现了点到自由曲线距离的高效计算;然后,采用RCGA完成了优化模型的求解,并与分割逼近法得到的结果进行了对比。结果表明,该方法高效可靠,相同条件下计算时间约为分割逼近法的5%,能够满足自由曲线廓形误差的评价。
To obtain the profile error of the freeform curves, an efficient evaluation method is brought out which is based on root-finding of polynomial equations and real coded genetic algorithm(RCGA). Firstly, the optimization model for the profile error evaluation was established based on the least squares criterion. Then, the polynomial equations were constructed and the point to curve distance can be obtained effectively by solving the polynomial equations via the Halley iteration. After that, the optimization model was solved by the RCGA and the profile error was obtained. The computation results were also compared with the subdivision method. From the evaluation process, it can be seen that the proposed method is efficient and robust. The computing time is about 5% of that the subdivision method needs under the same condition. Thus, it is more suitable for evaluating the profile error of the freeform curves.
To obtain the profile error of the freeform curves, an efficient evaluation method is brought out which is based on root-finding of polynomial equations and real coded genetic algorithm(RCGA). Firstly, the optimization model for the profile error evaluation was established based on the least squares criterion. Then, the polynomial equations were constructed and the point to curve distance can be obtained effectively by solving the polynomial equations via the Halley iteration. After that, the optimization model was solved by the RCGA and the profile error was obtained. The computation results were also compared with the subdivision method. From the evaluation process, it can be seen that the proposed method is efficient and robust. The computing time is about 5% of that the subdivision method needs under the same condition. Thus, it is more suitable for evaluating the profile error of the freeform curves.
引文
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[13]王建录,刘学云,廖平,等.结合分割逼近和粒子群法的燃气轮机叶片轮廓度误差计算[J].西安交通大学学报,2010,44(7):42-45,74.
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[2]高健,陈岳坪,邓海祥,等.复杂曲面零件加工精度的原位检测误差补偿方法[J].机械工程学报,2013,49(19):133-143.
[3]雷贤卿,李济顺,薛玉君,等.基于极坐标测量的圆度误差评定算法[J].工程图学学报,2010,31(2):188-191.
[4]何雪明,叶水平,童洁,等.基于B样条曲线的双螺杆压缩机转子型线设计[J].机械设计与研究,2015,31(5):133-137.
[5]FANG F Z,ZHANG X D,ALBERT W,et al.Manufacturing and measurement of freeform optics[J].CIRP Annals-Manufacturing Technology,2013,62(2):823-846.
[6]刘日良,张承瑞.基于B样条曲线的通风机叶型及特性分析[J].工程图学学报,2003,24(2):98-104.
[7]伍丽峰,陈岳坪,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.
[8]廖平.基于分割逼近法和遗传算法的复杂平面曲线形状误差计算[J].机械科学与技术,2009,28(9):1121-1124.
[9]王宇春,孙和义,唐文彦,等.评定二次曲面轮廓度误差的角度分割逼近法[J].光学精密工程,2014,22(6):1606-1612.
[10]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):835-842.
[11]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):203-205,217.
[12]廖平,喻寿益.基于遗传算法的复杂平面曲线形状误差计算[J].计量学报,2003,24(3):181-184,224.
[13]王建录,刘学云,廖平,等.结合分割逼近和粒子群法的燃气轮机叶片轮廓度误差计算[J].西安交通大学学报,2010,44(7):42-45,74.
[14]朱心雄.自由曲线曲面造型技术[M].北京:科学出版社,2000:66-93.
[15]ZBIGNIEW M.Genetic algorithms+data structures=evolution programs[M].Berlin:Springer,1996:97-118.
[16]KUSUM D,MANOJ T.A new crossover operator for real coded genetic algorithms[J].Applied Mathematics and Computation,2007,188(1):895-911.