【作者】 张志伟；

【导师】 穆国旺；

【作者基本信息】 河北工业大学 ， 应用数学， 2018， 硕士

【摘要】 发动机叶片是飞机重要的组成部分之一,工作环境恶劣,损坏率高,且造价成本大,因此实现叶片的修复再利用可以带来巨大的经济效益。为了在没有叶片原始设计模型也没有叶片标准件的客观条件下进行航空发动机缺损叶片自动焊接修复,需要根据扫描叶片得到的点云数据,通过反求工程重建叶片的完整几何模型。本文采用了基于截面线的修复方法,先通过曲线延伸的方法对缺损截面线进行修复,再通过蒙面的方法完成叶片几何模型的修复。其中截面线延拓修复的好坏从根本上决定了缺损叶片几何修复的效果,因此,本文重点对曲线延拓技术进行了研究,基于此实现了发动机缺损叶片曲面的修复。主要完成的工作如下:1、通过定量地研究两曲线的相似性,提出适合缺损叶片修复的曲线相似性度量方法,在此基础上提出了基于和参考曲线相似性的B样条曲线延拓算法。和已有的曲线延拓方法不同的是,该算法充分利用了缺损截面线与邻近完好截面线的相似性,在满足C~2连续的前提下,使曲线延拓部分的形状更好地反映了原截面线的变化趋势。实验表明,本文算法更能满足发动机叶片修复的应用要求。2、提出了基于对参考曲线做仿射变换的曲线延拓方法,首先通过统一待延拓曲线和参考曲线的节点矢量来确定延拓后曲线的节点矢量,然后利用B样条端点松弛算法得到和待延拓曲线相关的那部分控制顶点,最后,利用优化方法来确定新增加的那些控制顶点。优化的目标函数是经过仿射变换后的参考曲线和延拓后的曲线对应控制顶点之间距离的平方和。实验结果表明,利用本文的延伸算法得到的曲线和参考曲线形状相似,且光顺性较好。更多还原

【Abstract】 Engine blade is one of the most important components of aircrafts.With the bad working environment,the damage rate of engine blade is high,and the cost is large.So the recovery and reuse of blades can be of great economic benefit.In order to carry out automatic welding repair of damaged aero-engine blade under conditions where there is no original design model of blade and there is no standard part of blade,it is required to reconstruct the undamaged geometric model of the blade from point cloud data obtained by scanning the damaged blade through reverse engineering.In this paper,the repair method based on section curves is adopted.Firstly,the damaged section curves are repaired through curve extension,and then surface skinning technology is deployed to complete the recovery of the geometric model of the blade.Among them the repair effect of the geometric modeling of the defective blade heavily depends on the effect of the section curve extension.Therefore,this paper focuses on the algorithms for curve extension,on this basis the repair of the damaged engine blade surface is complemented.The main work is as follows:1.The similarity of two curves is studied quantitatively and a measurement of similarity between two curves suitable for repairing defective blade is proposed,on this basis,an algorithm for B spline curve extension based on the similarity with reference curve is presented.Different from the existing curve extension method,the proposed algorithm takes full advantage of the similarity between the defect section curves and the near intact section curves.Under the constraint of C~2continuity,the algorithm makes the shape of the extended curve reflect the change trend of the original section curve better.Experimental results show that the algorithm can meet the requirements in engine blade repair.2.A method for curve extension based on affine transformation of reference curve is presented.Firstly,the knot vector of the extended curve is determined by unifying the knot vector of the original curve and the reference curve.Then,the B spline unclamping algorithm is used to obtain the control vertices related to the original curve.Finally,optimization method is used to determine the new added control vertices.The objective function is the sum of the squares of distance between the control vertices of the reference curve after affine transformation and the corresponding vertices of the curve after extension.The experimental results show that the curve obtained from this extended algorithm is similar to the reference curve in shape,and has better fairness.更多还原