Please wait a minute...
工程设计学报
Chin J Eng Design  2022, Vol. 29 Issue (6): 757-765    DOI: 10.3785/j.issn.1006-754X.2022.00.086
Modeling, Simulation, Analysis and Decision     
Research on spatial mapping modeling of functionally graded material based on coordinate transformation
Xiao-wei HAN(),Guo-lin DUAN(),Shi-jie WANG,Shuo HAN,Shuo MA,Jie YANG
School of Mechanical Engineering, Hebei University of Technology, Tianjin 300401, China
Download: HTML     PDF(4209KB)
Export: BibTeX | EndNote (RIS)      

Abstract  

With the increasing complexity and diversity of 3D printed parts, the single-material parts can no longer meet various special performance requirements. Functionally graded material parts have gradually become a research hotspot in rapid prototyping manufacturing industry. In order to meet the manufacturing requirements of functionally graded material, a spatial mapping modeling method for functionally graded material based on coordinate transformation was proposed. The key of this method was to effectively combine geometry information with material information. Firstly, the material space of functionally graded material model was constructed by using the single gradient source method and multi-gradient source method. When the cross-gradient source model was encountered, the material distribution was calculated by using a specific intersection operator with a certain weight ratio. Then, in the process of combining the geometric space and the material space, the coordinate system of material space and geometric space was cleverly cooverlapped through coordinate transformation to realize the mapping of material space to geometric space, so as to obtain a functionally gradient material model with material information. The required functionally graded material model could be obtained by modifying the gradient source, material distribution function and coordinate transformation method. The results of visual analysis of the instance model through Visual Studio 2019 and OpenGL programming languages showed that the proposed modeling method greatly shortened the modeling time compared with most valuation modeling and non-valuation modeling methods, and fundamentally solved some problems of insufficient storage space and cumbersome modeling process caused by some algorithms. The spatial mapping modeling method for functional gradient material based on coordinate transformation can provide a new modeling method for the additive manufacturing industry and has good application value.

Key words： coordinate transformation      spatial mapping      geometric space      material space      gradient source      visual analysis     
Received: 20 April 2022      Published: 06 January 2023
CLC:  TH 164  
Corresponding Authors: Guo-lin DUAN     E-mail: xiaoweihan1@163.com;glduan@hebut.edu.cn
Service
E-mail this article
Add to my bookshelf
Add to citation manager
E-mail Alert
RSS
Articles by authors
Xiao-wei HAN
Guo-lin DUAN
Shi-jie WANG
Shuo HAN
Shuo MA
Jie YANG
Cite this article:

Xiao-wei HAN,Guo-lin DUAN,Shi-jie WANG,Shuo HAN,Shuo MA,Jie YANG. Research on spatial mapping modeling of functionally graded material based on coordinate transformation. Chin J Eng Design, 2022, 29(6): 757-765.

URL:

https://www.zjujournals.com/gcsjxb/10.3785/j.issn.1006-754X.2022.00.086     OR     https://www.zjujournals.com/gcsjxb/Y2022/V29/I6/757


基于坐标变换的功能梯度材料空间映射建模研究

随着3D打印零件复杂性和多样性的日益增加，单一材质的零件已无法满足各类特殊性能要求，功能梯度材料零件逐渐成为快速成型制造行业的研究热点。为满足功能梯度材料的制造要求，提出了一种基于坐标变换的功能梯度材料空间映射建模方法，该方法的关键是将几何信息与材料信息有效结合。首先，采用单梯度源法、多梯度源法构建功能梯度材料模型的材料空间，在遇到交叉梯度源模型时利用特定的相交算子以一定的权重比进行材料分布计算。然后，在几何空间与材料空间结合的过程中，巧妙地通过坐标变换将材料空间与几何空间的坐标系重合，实现将材料空间映射至几何空间，从而得到带有材料信息的功能梯度材料模型。通过修改梯度源、材料分布函数以及坐标变换方法即可获得所需的功能梯度材料模型。利用Visual Studio 2019软件和OpenGL编程语言对实例模型进行可视化分析的结果表明，所提出的建模方法相比于大部分估值建模、非估值建模方法可大大缩短建模时间，从根本上解决了某些算法所造成的储存空间不足和建模过程繁琐等问题。基于坐标变换的功能梯度材料空间映射建模方法为增材制造行业提供了一种新的建模方法，具有良好的应用价值。


关键词： 坐标变换,  空间映射,  几何空间,  材料空间,  梯度源,  可视化分析 
Fig.1 Mapping relationship between geometric space and material space of a functionally graded material model
Fig.2 Functionally graded material model of material composition changing with single function law
Fig.3 Functional gradient material model of material composition changing with multiple function laws
Fig.4 Mapping schematic of functionally graded material model of material composition changing with multiple function laws
Fig.5 Mapping schematic of functional gradient material modeling
Fig.6 Functionally graded material model based on single point, line and plane gradient source
Fig.7 Material space of different dimensions
Fig.8 Functionally graded material model of non-cross gradient source
Fig.9 Mapping process from material space to geometric space based on coordinate translation transformation
Fig.10 Mapping process from material space to geometric space based on coordinate rotation transformation
Fig.11 Visualization results of cube functionally graded material model with single gradient source
Fig.12 Material space decomposition of bevel gear blank
Fig.13 Mapping process from material space to geometric space of bevel gear blank
Fig.14 Visualization results of functionally gradient material bevel gear blank model with multiple gradient sources
模型

坐标变换

算法

体素化

算法

显式函数算法
圆柱体2.574.223.25
正方体3.495.773.95
球体5.9815.128.54
锥齿轮毛坯件4.788.227.41
Table 1 Comparison of modeling time between coordinate transformation algorithm and other algorithms
[1]   夏晓光，段国林.功能梯度材料增材制造技术的研究进展及展望［J］.材料导报，2022，36（10）：134-140. doi：10.11896/cldb.20030137
XIA Xiao-guang， DUAN Guo-lin. Advances and prospects of additive manufacturing technology of functionally graded material［J］. Materials Reports， 2022， 36（10）： 134-140.
doi: 10.11896/cldb.20030137
[2]   高晓菊，王伯芊，贾平斌，等.功能梯度材料的制备技术及其研发现状［J］.材料导报，2014，28（1）：31-36.
GAO Xiao-ju， WANG Bo-qian， JIA Ping-bin， et al. Preparation technology and latest development of functionally gradient materials［J］. Materials Reports， 2014， 28（1）： 31-36.
[3]   李祺祺，温耀杰，张百成，等.梯度功能合金的增材制造技术研究进展［J］.机械工程学报，2021，57（22）：184-200. doi：10.3901/jme.2021.22.184
LI Qi-qi， WEN Yao-jie， ZHANG Bai-cheng， et al. Research progress of functional graded alloy prepared by additive manufacturing technology［J］. Journal of Mechanical Engineering， 2021， 57（22）： 184-200.
doi: 10.3901/jme.2021.22.184
[4]   LI W K， HAN B H. Research and application of functionally gradient materials［J］. IOP Conference Series： Materials Science and Engineering， 2018， 394（2）： 22065.
[5]   刘帅，王阳，刘常升.激光熔化沉积技术在制备梯度功能材料中的应用［J］.航空制造技术，2018，61（17）：47-56.
LIU Shuai， WANG Yang， LIU Chang-sheng. Application of laser melting deposition technique in preparation of functionally gradient materials［J］. Aeronautical Manufacturing Technology， 2018， 61（17）： 47-56.
[6]   TANG Yi， QIU Wen-bin， CHEN Long-qing， et al. Preparation of W‒V functionally gradient material by spark plasma sintering［J］. Nuclear Engineering and Technology， 2020， 52（8）： 1706-1713.
[7]   GUI Cheng-mei， CHEN Zhen-ming， YAO Chen-guang， et al. Preparation of nickel/PA12 composite particles by defect-induced electroless plating for use in SLS processing［J］. Scientific Reports， 2018， 8： 13407.
[8]   OGAWA T， WATANABE Y， SATO H， et al. Theoretical study on fabrication of functionally graded material with density gradient by a centrifugal solid-particle method［J］. Composites Part A： Applied Science and Manufacturing， 2006， 37（12）： 2194-2200.
[9]   吴晓军，刘伟军，王天然.基于八叉树的三维网格模型体素化方法［J］.图学学报，2005，26（4）：1-7. doi：10.3969/j.issn.1003-0158.2005.04.001
WU Xiao-jun， LIU Wei-jun， WANG Tian-ran. Octree structure based voxelization of polygonal meshes［J］. Journal of Graphics， 2005， 26（4）： 1-7.
doi: 10.3969/j.issn.1003-0158.2005.04.001
[10]   BISWAS A， SHAPIRO V， TSUKANOV I. Heterogeneous material modeling with distance fields［J］. Computer Aided Geometric Design， 2004， 21（3）： 215-242.
[11]   JACKSON T R， LIU H， PATRIKALAKIS N M， et al. Modeling and designing functionally graded material components for fabrication with local composition control［J］. Materials & Design， 1999， 20（2/3）： 63-75.
[12]   张贺，敬石开，周竞涛，等.基于从材料空间到几何空间映射思想的功能梯度材料建模方法［J］.计算机集成制造系统，2015，21（8）：2014-2021.
ZHANG He， JING Shi-kai， ZHOU Jing-tao， et al. Functionally graded materials modeling based on thought of mapping from material space to geometrical space［J］. Computer Integrated Manufacturing Systems， 2015， 21（8）： 2014-2021.
[13]   葛正浩，陈浩，雷聪蕊.多材料零件三维打印建模可视化研究［J］.激光与光电子学进展，2020，57（23）：191-199. doi：10.3788/LOP57.231403
GE Zheng-hao， CHEN Hao， LEI Cong-rui. Research on three-dimensional printing modeling visualization of multi-material parts［J］. Laser & Optoelectronics Progress， 2020， 57（23）： 191-199.
doi: 10.3788/LOP57.231403
[14]   YANG Ping-hai， QIAN Xiao-ping. A B-spline-based approach to heterogeneous objects design and analysis［J］. Computer-Aided Design， 2007， 39（2）： 95-111.
[15]   万能，段永吉，杜珂.考虑制备工艺的功能梯度材料零件设计建模［J］.计算机集成制造系统，2018，24（4）：946-955.
WAN Neng， DUAN Yong-ji， DU Ke. Functionally gradient materials component modeling considering manufacture process［J］. Computer Integrated Manufacturing Systems， 2018， 24（4）： 946-955.
No related articles found!