2015 International Conference on Virtual Reality and Visualization
Density Aware Internal Supporting Structure Modeling of 3D Printed Objects
Dawei Li, Ning Dai, Xiaotong Jiang, Zhenghong Shen, Xiaosheng Chen College of Mechanical and Electrical Engineering Nanjing University of Aeronautics and Astronautics Nanjing 210016, China E-mail:
[email protected]
Abstract—Physically based modeling is a novel theory for 3D printing; it can use a single material to control the physical properties, such as center of mass, total mass and moment of inertia. In this paper, we present a density variable shape modeling method to meet the required strength of 3D printed objects. We estimate a continuous density distribution that satisfies the detected stress distribution of the 3D objects, which is based on the cross-sectional stress analysis method. We then use a pure mathematical 3D implicit function to create a gradational porous structure to represent this density distribution. With our technique, 3D printed objects that have desired sound structures can be fabricated. Meanwhile the material consumption can be reduced significantly. Keywords-component; Geometric modeling; optimization; Internal support; 3D printing
I.
In this paper, the proposed density aware internal support modeling strategy has three major advantages: First, the stress condition of the loaded object is obtained by cross-sectional structural analysis method, which can provide infilling basis for next steps. Second, the smooth gradational lattice structures can be generated by parametric implicit functions and avoid possible errors brought about by performing a large number of Boolean operations. Last, a triangle mesh surface is extracted from the parametric model to represent the internal structures. II. RELATED WORKS Recently, 3D geometric modeling and printing has begun to study the construction of physical models, and it is a novel concept for 3D print modeling. Obtaining robust structures, using less material and satisfying some mechanical properties are the major research topics. For strength optimization problems, Stava [3] provided an automatically structural detect and fix system which is based on the finite element method (FEM). The systems include internal holes, local thickness and add support for creating a new object meanwhile keeping the external shape as similar as possible and improving its strength. Besides, Zhou [4] proposed a method to find a worst-case load condition but not a specific load, and identify the most fragile areas on the objects, and it also needs FEM solution. However, FEM involves time-consuming volume mesh generation and solutions for large linear systems. Therefore, Umetani and Schmidt [5] proposed a cross-sectional structural analysis method to optimize the strength of the cantilever structures by controlling the print orientation of the objects with Fused Deposition Modeling (FDM) technique; however, it cannot consider every part of the model, and the object is solid. For lightweight modeling problems, current commercial 3D print software is through slicing and path to reduce the use of materials. However, a complex object is difficult to take the strength into consideration. Chen [6] put forward lattice structure generated in the object by choosing one of the units from the library, and then combine offset and Boolean operations, whose method have been widely applied in professional 3D print modeling software such as Magics-RP. Inspired by the construction of truss structures, Wang et al. [7] introduced one of the first cost-effective printing strategies using skin frame structures to support the shape’s interior. Lu et al. [8] introduced a honeycomb-cell
Structure
INTRODUCTION
3D printing technologies are booming in recent years, particularly because they allow anyone to be designers and manufacturers. Software such as Meshmixer [1] and Autodesk 123D [2] provide users with intuitive modeling software for 3D printing. However, because of lacking of design experience and knowledge of mechanics, the result would bring about the strength [3-5], supplies [6-9] and stability [10-11] problems. When creating a 3D object for printing, physical properties, including density, mass, center of mass and moment of inertia, are not considering usually. The physical properties play an important role in many applications, especially for mechanical design, and it is difficult to control objects with these physical properties because they are influenced by an object’s outer geometry. Cantilever structure is a common printed part in numerous 3D models, but it often cannot guarantee enough strength. Therefore, in this study, we are mainly to handle this structure of objects to realize the integral optimization. The internal porous structures widely existing in nature and artificial products is a multiphase structure with large surface area ratio and high strength to weight ratio [12]. So, in lightweight modeling, the internal porous structure can provide support capacity, reduce the weight and material consumption; meanwhile, reasonable internal structural arrangement can form controllable density distribution, to optimize the local area performance of the model. Therefore, we proposed an internal structural optimization method based on physical modeling to reinforce the cantilever structural strength. 978-1-4673-7673-0/15 $31.00 © 2015 IEEE DOI 10.1109/ICVRV.2015.22
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1 0 Stress f1
f2
f3
(a) Input model and offset
(b) Stress distribution
(c) Create internal support
(d) Printed model
Figure 1. Overview of proposed method.
structure by gradually craving out the interior of an object to be printed, but the hollowed cells are enclosed. That makes it difficult to remove the supporting materials. Recently, Zhang et al. [9] proposed an internal supporting structure based on medial axis tree, and the internal results are more complex for 3D printing. Porous structure modeling has been extensively explored in tissue engineering and computer-aided design; they are all called lattice structures. And there are several ways to design lattice structures. Traditionally, lattice structures are created by using commercial CAD packages or reconstruction from images; however, these methods are not convenient for nonprofessional. Another approach to generate the lattice structures is through the implicit functions, and our work is inspired by this technique. Strano et al. [13] used implicit function to generate 3D printing external support with a porous structure. And Pasko [14] and Fryazinov [15] et al. realized gradational modeling of porous structures by this function without any physical principle. Moreover, this porous model is suitable for additive manufacturing [13-15]. In this work, we reformulate the implicit functions combined with local infilling density and create an adaptive internal structure.
(a) Original model
(b) Offset 3mm
(c) Offset 6mm
Figure 2. Model offset.
Let us suppose that a triangle mesh is T=(C, V), where C is the topological relationship between vertices, edges and faces, and V={v1,v2,…,vn} ∈ R3 represents the vertices of the mesh, N={n1,n2,…,nn} ∈ R3 is the corresponding normal vectors. First, if we define an offset distance d, then we need to move every vertex along the normal vectors of a reverse distance d and derive the corresponding vertex set V'={v1',v2',…,vn'} ∈ R3 , vi'=vi-ni*d (0
