﻿ 基于约束Delaunay三角剖分的筋特征识别与构建算法
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1. 北京航空航天大学机械工程及自动化学院, 北京 100083;
2. 麦吉尔大学机械工程系, 蒙特利尔 H3A0G4;
3. 沈阳飞机工业(集团)有限公司, 沈阳 110034

Algorithm for recognizing and constructing rib feature based on constrained Delaunay triangulation
ZHOU Min1, ZHENG Guolei1 , LUO Zhibo2, CHEN Shulin3
1. School of Mechanical Engineering and Automation, Beijing University of Aeronautics and Astronautics, Beijing 100083, China;
2. Department of Mechanical Engineering, Mcgill University, Montreal H3A0G4, Canada;
3. Shenyang Aircraft Industry(Group) Corporation Ltd, Shenyang 110034, China
Abstract: In order to recognize the rib feature in aircraft structural parts, a recognition and construction algorithm based on the constrained Delaunay triangulation is presented. First, according to the different machining methods between the real bottom plane and the flat rib as well as the similar geometric characters of these two features, the concept of generalized bottom plane is introduced to represent the real bottom plane and the flat rib. Moreover, a representation model of the rib feature is established for further recognition and construction. Second, the constrained Delaunay triangulation method is adopted to decompose the generalized bottom plane, recognize and distinguish it as the flat rib or bottom plane, and then extract the medial axis of the flat rib. Finally, the flat rib is divided as per the medial axis while the declining rib is recognized and constructed as a sub-feature of the generalized bottom plane. The validity and efficiency of this algorithm have been verified through examples.
Key words: NC programming     feature recognition     aircraft structural part     rib     Delaunay triangulation

1 筋的表示模型 1.1 广义腹板

 图 1 广义腹板与槽的关系 Fig. 1 Relationships between generalized bottom plane and pocket

〈GFB〉::=(〈Layernum〉,〈Fh〉,〈Type〉)
〈Type〉::=(〈Fuban〉〈Rib〉)

1.2 筋的几何属性

 图 2 筋几何属性示意图 Fig. 2 Schematic diagram of geometrical attribute of rib
1.3 筋的参数属性

PA〉::=(〈Width〉,〈Height〉,〈Location〉,〈ToolAxis〉,〈DriveCell〉)

1.4 范式表达及层次模型

〈RF〉::=(〈SubType〉,〈ID〉,〈FG〉,〈PA〉,

[〈RFf〉],{〈RFc〉})

〈SubType〉::=(〈Rf〉〈Rd〉〈Rb〉)

FG〉::=(〈Fm〉,[Fl],〈ft〉,〈fb〉,[Fr],

[Fa],〈Fs〉)

PA〉::=(〈Width〉,〈Height〉,〈Location〉,

〈ToolAxis〉,〈DriveCell〉)

 图 3 广义腹板树状模型 Fig. 3 Tree-model of generalized bottom plane

1.5 面的凹凸性

 图 4 圆柱面的凹凸性 Fig. 4 Cylinder surface being convex or concave
2 筋的识别与构建 2.1 广义腹板面的识别

 图 5 近二次规则面识别方法示意图 Fig. 5 Schematic diagram of recognition of approximate square regular surface

1) cuscumcue均为半径相同的圆弧,圆心两两互不重合,并且cvscvmcve均为相互平行的直线。

2) cvscvmcve均为半径相同的圆弧,圆心两两互不重合,并且cuscumcue均为相互平行的直线。

f为近圆柱面。

2.2 广义腹板面的三角网格划分

2.2.1 边界离散与区域三角剖分

 图 6 广义腹板面边界点的离散点加密 Fig. 6 Making dense discrete points of generalized bottom planes boundary points

2.2.2 平顶筋面和腹板面的区分

 图 7 广义腹板面的约束Delaunay三角剖分 Fig. 7 Constrained Delaunay triangulation of generalized bottom plane
2.2.3 平顶筋面中轴线提取

 图 8 三角元的分类及其中轴线 Fig. 8 Classification of triangular elements and their medial axis
2.2.4 中轴线的合并与修改

 图 9 中轴线的处理 Fig. 9 Processing of medial axis

 图 10 内部三角形与邻接三角形的组合类型 Fig. 10 Composite type of inner triangles and their adjacent triangles

 图 11 中轴线的合并 Fig. 11 Combination of medial axes
2.3 广义腹板面子特征识别与构建

2.3.1 平顶筋面拆分子特征的构建

 图 12 平顶筋拆分子特征流程 Fig. 12 Flowchart of flat rib division into sub-features

Step 1 提取当前平顶筋面的中轴线,构造拆分特征节点,设置其节点类型为平顶筋。

Step 2 提取每条中轴线首末端的Δe

Step 3 提取每个Δe的界边。

Step 4 判断界边的邻接面是否为底圆面类型,若是则设置为当前子特征的底圆面,否则转入Step 6。

Step 5 提取与该子特征底圆面相切的邻接面。

Step 6 设置邻接面为当前子特征的限制元并保存邻接面,以作为子特征关联斜顶筋的搜索面。

2.3.2 平顶筋关联斜顶筋的识别与构建

 图 13 平顶筋关联斜顶筋的识别与构建流程 Fig. 13 Flowchart of recognition and construction for declining rib connected with flat rib

Step 1 获取平顶筋面的斜顶筋搜索面。

Step 2 判断每个搜索面的加工面类型,提取其中的斜向加工面。

Step 3 计算搜索面的主面宽度,若符合设定的筋宽阈值,则继续提取其可能关联的圆柱面作为斜顶筋的过渡面或底圆面,否则返回Step 2。

Step 4 构造斜顶筋节点,并根据主面的几何类型设置当前斜顶筋的类型(斜顶筋或曲顶筋)。

Step 5 根据主面或底圆面,提取其关联的侧壁面作为限制面。

Step 6 设置当前斜顶筋节点为相应平顶筋面拆分特征的子节点,算法结束。

3 实 例

3.1 有效性分析

 图 14 零件模型 Fig. 14 Part model

 特征类型 广义腹板 腹板面 平顶筋面 平顶筋 斜顶筋 正确 197 118 79 146 107 错误 0 0 2 0 16 正确率/% 100 100 97.5 100 87

1) 0° < θ<90°。

2) d∈[dmin,dmax]。

3.2 时效性分析

y=0.002 7x2+0.326 4x+0.571 2

 图 15 时间复杂度测试零件 Fig. 15 Part model for time complexity test

 L Ns Np Nr Nm T/s 1×1 23 2 1 1 1.577 2×2 74 5 5 3 2.798 3×3 159 10 13 5 5.187 4×4 278 17 25 7 9.988 5×5 431 26 41 9 17.463 6×6 618 37 61 11 30.965 7×7 839 50 85 13 47.206 8×8 1 094 65 113 15 69.861 9×9 1 383 82 145 17 110.214 10×10 1 706 101 181 19 146.195
 图 16 时间复杂度 Fig. 16 Time complexity

4 结 论

1) 提出了广义腹板模型并给出筋的表示模型,依据相关规则对广义腹板进行识别。

2) 利用约束Delaunay三角剖分对广义腹板进行三角剖分,以进一步识别平顶筋面并提取平顶筋面的中轴线。

3) 根据中轴线条数对平顶筋面进行拆分并识别关联的斜顶筋,构建平顶筋拆分子特征和斜顶筋特征,实现零件中筋特征的层次模型表达。

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#### 文章信息

ZHOU Min, ZHENG Guolei, LUO Zhibo, CHEN Shulin

Algorithm for recognizing and constructing rib feature based on constrained Delaunay triangulation

Journal of Beijing University of Aeronautics and Astronsutics, 2016, 42(1): 201-210.
http://dx.doi.org/10.13700/j.bh.1001-5965.2015.0049