基于几何特征的加工余量优化及仿真研究
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摘要
随着数控技术的广泛应用,零件的制造工艺得到了很大的提升。但是仍有一些零件的制造工艺还比较落后。这些零件毛坯由铸造或锻造生成,余量较小且不均匀。如果余量分配不均,则会导致其一部分余量过大,而另一部分余量不足,造成零件的报废。而当前的余量分配是采用人工划线、反复测量的方法进行的。
本文针对这一情况,采用余量优化的手段对零件各部分的余量进行优化分配,并采用仿真加工的方法进行优化结果的验证。具体工作如下：
1.基于“一面两孔”特征的初始位置调整。提出利用零件中的几何特征——一个平面和两个圆柱孔(“一面两孔”特征),构建局部坐标系的方法进行测量数据与设计模型的初始位置调整。根据特征圆柱孔轴线和特征平面的关系,讨论了适合于构建局部坐标系的特征组合。并在可以进行坐标系构建的组合中,利用最小二乘法在测量数据中进行特征平面和圆柱面的拟合。从而完成局部坐标系的构建,进行初始位置的调整。
2.精确优化计算。首先对测量数据利用均匀采样法进行数据缩减,以调高计算效率,然后将设计模型离散成点云数据,并利用改进的逐点插入法对其进行DT剖分,来进行最近点计算。在计算最近点时,首先搜索测量点的最近网格顶点,然后将测量点投影到包含该顶点的网格面上,判断投影点是否在包含该顶点的网格面上。若不在,则以最近网格顶点为最近点；若在,则以最近顶点和投影点与测量点的距离为判定,距离小的即为所求的最近点。最后使用遗传算法进行精确优化计算。
3.仿真加工验证。利用仿真加工的方法,对优化的结果进行验证。首先进行仿真机床模型的构建,并对仿真机床进行控制系统的配制；然后利用优化得到的最佳定位姿态和实际定位方法,实现零件在仿真机床上的定位；最后进行加工验证。
With the widely useing of numerical control technology, the manufacturing process is improved a lot. But there are also some parts with backwardly manufacturing process whose allowance are small and uneven distribution. If the distribution of allowance is uneven, the allowance of some surfaces might be too large and the other might be not enough. The insufficient allowance might cause scrapped parts. And the current allowance distribution is accomplished by artificial marking and repeated measurement.
Aiming at this situation, this paper focuses on the method of allowance optimization to distribute the allowance and to use the machining simulation to validate the result of allowance optimization. The main work is as follows:
1. Initial position adjusting based on the feature of one plane and two holes. The method of using the feature of one plane and two holes to build local coordinate system to adjust the initial position of measured data and design model is proposed. Base on the spatial relation of axis of the cylindrical hole and the plane, the features which are suitable for the construction of coordinate system are discussed. The planes and cylindrical holes of these features are fitted by least square method in measured data. Finally the local coordinate system is built by these planes and holes, and the initial position adjusting is done.
2. Precise optimization calculation. The mathematical model of precise optimization calculation is proposed based on the least squares method. To improve computational efficiency the measured data is reduced by uniform sampling method. Then design model is tessellated into point cloud data. And Delaunay triangulation is created with theses points by a modified incremental insertion method to search the closet point for measured point. To the same measured point, the closest point is chosen between the closest vertices on the grid and the projection point. If the projection point is not located on the grid, the closest point is the closest vertice. If it is, to compare the two distances, the samller one is the closest point. One of the distances is calculated between the closest vertice and the measured point, the other is calculated between the projection point and the measured one. The closest vertice of the measured point is searched through the process that design model is tessellated into triangular mesh surfaces by Delaunay triangulation. The projection point of the measured one is calculated on these surfaces which contains the closest vertice. Finally the mathematical model is solved by Genetic Algorithms.
3. Machining simulation. The result of allowance optimization is validated through machining simulation. First, the machine simulation model is built. And the Numerical Control System is compounded for it. Then the stock is assembled on the machine worktable with the location method under the most optimization Attitude. Finally the experiment is done to validate the result.
本文针对这一情况,采用余量优化的手段对零件各部分的余量进行优化分配,并采用仿真加工的方法进行优化结果的验证。具体工作如下：
1.基于“一面两孔”特征的初始位置调整。提出利用零件中的几何特征——一个平面和两个圆柱孔(“一面两孔”特征),构建局部坐标系的方法进行测量数据与设计模型的初始位置调整。根据特征圆柱孔轴线和特征平面的关系,讨论了适合于构建局部坐标系的特征组合。并在可以进行坐标系构建的组合中,利用最小二乘法在测量数据中进行特征平面和圆柱面的拟合。从而完成局部坐标系的构建,进行初始位置的调整。
2.精确优化计算。首先对测量数据利用均匀采样法进行数据缩减,以调高计算效率,然后将设计模型离散成点云数据,并利用改进的逐点插入法对其进行DT剖分,来进行最近点计算。在计算最近点时,首先搜索测量点的最近网格顶点,然后将测量点投影到包含该顶点的网格面上,判断投影点是否在包含该顶点的网格面上。若不在,则以最近网格顶点为最近点；若在,则以最近顶点和投影点与测量点的距离为判定,距离小的即为所求的最近点。最后使用遗传算法进行精确优化计算。
3.仿真加工验证。利用仿真加工的方法,对优化的结果进行验证。首先进行仿真机床模型的构建,并对仿真机床进行控制系统的配制；然后利用优化得到的最佳定位姿态和实际定位方法,实现零件在仿真机床上的定位；最后进行加工验证。
With the widely useing of numerical control technology, the manufacturing process is improved a lot. But there are also some parts with backwardly manufacturing process whose allowance are small and uneven distribution. If the distribution of allowance is uneven, the allowance of some surfaces might be too large and the other might be not enough. The insufficient allowance might cause scrapped parts. And the current allowance distribution is accomplished by artificial marking and repeated measurement.
Aiming at this situation, this paper focuses on the method of allowance optimization to distribute the allowance and to use the machining simulation to validate the result of allowance optimization. The main work is as follows:
1. Initial position adjusting based on the feature of one plane and two holes. The method of using the feature of one plane and two holes to build local coordinate system to adjust the initial position of measured data and design model is proposed. Base on the spatial relation of axis of the cylindrical hole and the plane, the features which are suitable for the construction of coordinate system are discussed. The planes and cylindrical holes of these features are fitted by least square method in measured data. Finally the local coordinate system is built by these planes and holes, and the initial position adjusting is done.
2. Precise optimization calculation. The mathematical model of precise optimization calculation is proposed based on the least squares method. To improve computational efficiency the measured data is reduced by uniform sampling method. Then design model is tessellated into point cloud data. And Delaunay triangulation is created with theses points by a modified incremental insertion method to search the closet point for measured point. To the same measured point, the closest point is chosen between the closest vertices on the grid and the projection point. If the projection point is not located on the grid, the closest point is the closest vertice. If it is, to compare the two distances, the samller one is the closest point. One of the distances is calculated between the closest vertice and the measured point, the other is calculated between the projection point and the measured one. The closest vertice of the measured point is searched through the process that design model is tessellated into triangular mesh surfaces by Delaunay triangulation. The projection point of the measured one is calculated on these surfaces which contains the closest vertice. Finally the mathematical model is solved by Genetic Algorithms.
3. Machining simulation. The result of allowance optimization is validated through machining simulation. First, the machine simulation model is built. And the Numerical Control System is compounded for it. Then the stock is assembled on the machine worktable with the location method under the most optimization Attitude. Finally the experiment is done to validate the result.
引文
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[2]沈兵,帅梅,高军等.大型复杂曲面类毛坯最佳适配算法研究.西安交通大学学报,1999,33(1)：90-94.
[3]Chatelain J F, Fortin C. A balancing technique for optimal blank part machining. Precision engineering,2001,25(1):13-23.
[4]Chatelain J F. A level-based optimization algorithm for complex part localization. Precision engineering,2005,29(2):197-207.
[5]严思杰,周云飞,彭芳瑜等.大型复杂曲面零件加工余量均布优化问题研究.华中科技大学学报,2002,30(10)：35-37.
[6]严思杰,周云飞,彭芳瑜等.大型复杂曲面加工工件定位问题研究.中国机械工程,2003,14(9)：737-740.
[7]陈满意,李斌,段正澄.叶片零件毛坯余量分布优化问题研究.机械科学与技术,2006,25(2)：246-248.
[8]曾艳,李斌,彭芳瑜等.面向数控加工的大型螺旋桨桨叶的余量估算问题研究.中国机械工程,2006,17(6)：566-569.
[9]杨欣,许述财,王家忠.机械CAD/CAM[M].北京：中国质检出版社,2011.
[10]潘如刚.基于断层轮廓数据的三维形体网格构造方法研究[D].杭州：浙江大学,2004.
[11]钱锦锋.逆向工程中的点云处理[D].杭州：浙江大学,2005.
[12]杜长江.复杂曲面截面特征点云数据处理技术[D].大连：大连理工大学,2012.
[13]王英惠.面向创新设计的逆向工程系统的研究[D].西安：西安交通大学,2003.
[14]Guo B, Surface reconstruction:from points to spline [J], Computer Aided Design, 1997,29(4):269-277.
[15]Chen X. Surface modeling of range data by constrained triangulation[J], Computer Aided Design, 1994,26(3):632-645.
[16]姜寿山,Peter Eberhard多边形和多面体顶点法矢的数值估[J].计算机辅助设计与图形学学报,2002,14(8)：763-767.
[17]Gouraud H. Continuous shading of curved surfaces [J]. IEEE Transactions on Computers,1971, 20(6):623-629.
[18]ThiirmerG, WuthrichA. Computing vertex normals from polygonal facets[J]. Journal of Graphics Tools,1998,3(1):43-46.
[19]Taubin G. Estimating the tensor of curvature of a surface from a polyhedral approximation [C] Grimson E. Proceedings of the 5th International Conference on Computer Vision. Washington, DC, USA:IEEE ComputerSociety,1995:902-907.
[20]神会存,周来水,安鲁陵等.曲面三角网格模型顶点法矢计算与交互式分割[J].计算机辅助设计与图形学学报,2005,17(5)：1030-1033.
[21]MaxN. Weights for computing vertex normals from facet normals [J]. Journal of Graphics Tools, 1999,4(2):1-6.
[22]周儒荣,张丽艳,苏旭等.海量散乱点的曲面重建算法研究[J].软件学报,2001,12(2)：249-255.
[23]黄雪梅,王平江,陈吉红.三维散乱数据三角形网格逼近的一种算法[J].计算机工程与设计,1998,19(2)：9-15.
[24]苏旭.逆向工程中基于散乱数据点的曲面重构方法研究[D],南京：南京航空航天大学,2000.
[25]易传云,王涛.数字化曲面的法矢求解[J],华中科技大学学报,2002,30(8)：49-51.
[26]刘雪梅,冯跃志.空间离散点曲面法矢估算的一种新方法[J],华北水利水电学院学报,1994,20(4)：64-66.
[27]ALingus. Greedy and Delaunay triangulations are not bad in the average case [J].Information Processing Letters,1986,22(1),25-31.
[28]Brassel K E and Reif D1 Procedure to generate thissen polygons [J].Geographical Analysis,1979,11:289-303.
[29]Mc Cullagh MJ and Ross C G T. Delaunay triangulation of random data set for is arithmic mapping [J].The Cartographic Journal,1980,17:93-991.
[30]YI Xia,HONG Yan. Text region extraction in a document image besed on the Delaunay tessellation [J].Pattren Recgonition,2003,361.
[31]LewiS B A,Robinson J S. Triangulation of planar regions with applications [J].The Computer Journal,1978,21 (2):324-332.
[32]Lee D T,Sehaehter B J. Two algorithms for construction a Delaunay Triangulation [J]. Int'I. Journal Computter&Information Seiences,1980,9(3):219-243.
[33]Bowyer A. Computing Dirichlet Tessellations. CooputerJournal,1981(24):162-166.
[34]Watson D F. Computing the n-dimensional Delaunay tessellation with application to Voronoi polytopes [J] The Computer Journal,1981,24(2):167-172.
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