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浙江大学学报(工学版)
浙江大学学报(工学版)  2021, Vol. 55 Issue (1): 135-144    DOI: 10.3785/j.issn.1008-973X.2021.01.016
机械工程     
基于三维T样条的异质材料实体建模与切片
李斌(),傅建中*()
浙江大学 机械工程学院，浙江 杭州 310058
Solid modeling and slicing process of heterogeneous materials based on trivariate T-splines
Bin LI(),Jian-zhong FU*()
College of Mechanical Engineering, Zhejiang University, Hangzhou 310058, China
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摘要：

为了实现异质材料实体模型应用于增材制造技术的可能性，开发通用的、可同时用于设计、分析和制造异质材料实体模型的建模与制造工艺. 提出基于三维T样条的异质材料实体重建方法，实施自适应细分得到三维T型控制网格. 通过最小化能量泛函逐步拟合四面体网格模型及异质材料属性，使得几何结构和材料分布均得到较高的拟合精度. 为了提高重建过程的计算效率，只对局部误差较大的区域进行自适应细分，在参数域内插入控制点. 采用自适应细分的三维T样条与均匀细分的三维NURBS，分别实施渐进式重建框架. 结果表明，三维T样条能够在达到相似甚至更优的拟合精度的前提下减少冗余控制点. 针对增材制造中的切片工艺，利用适用于异质材料实体模型的直接切片方法，结合三维T样条和基于八叉树结构的自适应细分过程，得到三角网格分层切片结果. 实验结果表明，该算法对异质材料实体模型的直接切片过程是有效和可靠的.
关键词： 异质材料;  实体模型重建;  三维T样条;  增材制造;  直接切片方法    
Abstract:

A general modeling and manufacturing process that can be used to design, analyze and manufacture heterogeneous material solids was developed in order to apply heterogeneous material solids into additive manufacturing technology. A modeling algorithm for heterogeneous material solids was proposed based on trivariate T-splines. T-mesh was adaptively refined based on the unit cubic. Then the tetrahedral mesh model and its heterogeneous materials were gradually fitted by minimizing the defined energy functional. Adaptive refinement was conducted only in those regions that undergo fine-scale deformation and updated control points were directly inserted in the parametric domain in order to improve computational efficiency. The comparison between trivariate T-splines with adaptive refinement and trivariate NURBS with uniform refinement shows the computational efficiency with much fewer control points. A direct slicing algorithm sliced heterogeneous material solid as the triangular meshes by combining trivariate T-splines and adaptive subdivision process based on the octree structure. The experimental results demonstrated the effectivity and reliability especially for slicing solid heterogeneous objects.
Key words: heterogeneous material    solid modeling    trivariate T-spline    additive manufacturing    direct slicing algorithm
收稿日期: 2020-04-24 出版日期: 2021-01-05
CLC:  TH 164  
基金资助: 国家基金-浙江省两化融合联合基金资助项目（U1609207）
通讯作者: 傅建中     E-mail: lib1992@zju.edu.cn;fjz@zju.edu.cn
作者简介: 李斌（1992—），男，博士生，从事CAD/增材制造的研究. orcid.org/0000-0003-1663-801X. E-mail： lib1992@zju.edu.cn
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李斌
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引用本文:

李斌,傅建中. 基于三维T样条的异质材料实体建模与切片[J]. 浙江大学学报(工学版), 2021, 55(1): 135-144.

Bin LI,Jian-zhong FU. Solid modeling and slicing process of heterogeneous materials based on trivariate T-splines. Journal of ZheJiang University (Engineering Science), 2021, 55(1): 135-144.

链接本文:

http://www.zjujournals.com/eng/CN/10.3785/j.issn.1008-973X.2021.01.016    或    http://www.zjujournals.com/eng/CN/Y2021/V55/I1/135

图 1  异质材料实体的重建框架
图 2  三维T型控制网格的自适应初始化过程
图 3  股骨下端模型的渐进式重建过程
图 4  基于3种不同的细分精度的分层T网格
图 5  基于图4所示的分层T网格的直接切片过程
图 6  股骨上端模型的渐进式重建过程
图 7  橡皮鸭模型的渐进式重建过程
实验模型 三维T样条 nc $ \varepsilon $ ni RS/%
股骨下端 $ G\left({{x}}\right) $ 17 409 0.6 20 86.76
股骨下端 $ M\left({{x}}\right) $ 17 409 0.6 25 90.13
股骨上端 $ G\left({{x}}\right) $ 21 659 0.6 23 85.33
股骨上端 $ M\left({{x}}\right) $ 21 659 0.6 27 88.03
橡皮鸭 $ G\left({{x}}\right) $ 27 455 0.4 23 80.47
橡皮鸭 $ M\left({{x}}\right) $ 27 455 0.4 16 88.66
表 1  基于三维T样条的异质材料实体建模结果
实验模型 三维NURBS nc $ \varepsilon $ ni RS/%
股骨下端 $ G\left({{x}}\right) $ 68 921 0.6 25 84.57
股骨下端 $ M\left({{x}}\right) $ 68 921 0.6 27 82.66
股骨上端 $ G\left({{x}}\right) $ 64 000 0.6 28 84.62
股骨上端 $ M\left({{x}}\right) $ 64 000 0.6 27 85.92
橡皮鸭 $ G\left({{x}}\right) $ 54 872 0.4 31 83.84
橡皮鸭 $ M\left({{x}}\right) $ 54 872 0.4 19 90.27
表 2  基于三维NURBS的异质材料实体建模结果
图 8  股骨下端模型的直接切片结果
图 9  股骨上端模型的直接切片结果
图 10  橡皮鸭模型的直接切片结果
图 11  股骨下端模型的等材料面提取结果
图 12  股骨上端模型的等材料面提取结果
图 13  橡皮鸭模型的等材料面提取结果
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