Cost-effective printing of 3D objects with skin-frame structures

TLDR: This paper presents an automatic solution to design a skin-frame structure for the purpose of reducing the material cost in printing a given 3D object by solving an l0 sparsity optimization scheme.

Abstract: 3D printers have become popular in recent years and enable fabrication of custom objects for home users. However, the cost of the material used in printing remains high. In this paper, we present an automatic solution to design a skin-frame structure for the purpose of reducing the material cost in printing a given 3D object. The frame structure is designed by an optimization scheme which significantly reduces material volume and is guaranteed to be physically stable, geometrically approximate, and printable. Furthermore, the number of struts is minimized by solving an l0 sparsity optimization. We formulate it as a multi-objective programming problem and an iterative extension of the preemptive algorithm is developed to find a compromise solution. We demonstrate the applicability and practicability of our solution by printing various objects using both powder-type and extrusion-type 3D printers. Our method is shown to be more cost-effective than previous works.

Figures

Figure 2: Common frame structures used in architecture.

Figure 5: Distributions of strut radii and lengths before and after topology optimization and geometry optimization on the HangingBall model shown in Figure 4. Left: the cumulative distributions of strut radii before and after topology optimization. Right: the cumulative distributions of internal strut lengths before and after geometry optimization.

Table 1: The parameters and properties of printing materials for each of the printers. The unit of minimum printable radius η is mm. Units of γ, µ, σ, and τ , are MPa (Mega Pascals). The slenderness ratio α is dimensionless.

Figure 6: For the Buddha Head model (left) with fine geometric details, we over-smooth the mesh and ensure that the smoothed mesh (middle) lies inside the original surface by local modification. Then our algorithm is applied on it to produce a skin-frame (right) for printing. The resulting frame is rendered with a transparent skin as shown on the right.

Figure 7: The Hanging-Ball model in the lower row has a smaller base than the one in the upper row. The struts in (a) are coded with the same color bar in Figure 4. For the model with a smaller base, our algorithm produces thicker struts on the vertical pillar in the right part than the counterparts in the upper row due to the balancing constraint (8). Photos of the printed naked frame and the printed objects using P-1 are shown in (b) and (c), respectively.

Figure 3: Illustration of the skin-frame structure. It consists of a thin skin (shown in orange) bounded by M and its offset M1 with a distance of skin thickness hS and a frame composed of a set of frame nodes (shown in red spheres) and a set of frame struts (shown in blue cylinders).

Frequently asked questions

Q1. What are the contributions mentioned in the paper "Cost-effective printing of 3d objects with skin-frame structures" ?

In this paper, the authors present an automatic solution to design a skin-frame structure for the purpose of reducing the material cost in printing a given 3D object. The authors demonstrate the applicability and practicability of their solution by printing various objects using both powder-type and extrusion-type 3D printers. Furthermore, the number of struts is minimized by solving an ` 0 sparsity optimization. 

Q2. What are the future works in "Cost-effective printing of 3d objects with skin-frame structures" ?

Limitation and future work Their research opens many directions for future studies. Study on how to choose the upright printing direction and how to design frame structures with the least extra supporting structure for practical printability is an intriguing direction for future research. There is much potential in speeding up their algorithm based on advanced optimization techniques. 

Q3. What is the straightforward method of reducing material usage in 3D printing?

Hollowing the objects is the most straightforward scheme to reduce material usage, and has been adopted in commercial printing packages [Shapeways 2012]. 

Q4. What is the purpose of the hollowing method?

The hollowing method is simply to hollow an object and possibly to fill its interior with pre-defined lattices to enhance strength. 

Q5. What is the basic approach used in 3D printing?

The straightforward approach used in commercial printer packages [Shapeways 2012] is to uniformly hollow the 3D object by extruding the outer surface and creating a scaled-down version on its inside. 

Q6. What is the description of the method used for truss structure design?

An optimization method has been presented in [Smith et al. 2002] for designing truss structures of macro-architectures, such as bridges, towers, roof supports and building exoskeletons. 

Q7. How can the authors determine the number of nodes on M1?

Node sampling and their connectivity A stress map can be computed on the solid volume enclosed by M1 based on the finite element method (FEM). 

Q8. What is the basic combinatorial nature of topology design?

The basic combinatorial nature of topology design, i.e., finding the optimal set of frame struts, which remains in structural optimization problems, has been proved to be NP-hard. 

Q9. How many struts are added to the shell and bananaman models?

The volumes of Shell and Bananaman by their approach are 25.977e4 and 23.530e4 mm3, respectively, without adding the volume of external struts. 

Q10. How many nodes can be determined on M1?

Then the number of sampling nodes on M1 can be determined as |Vskin| = 4Area(M1)/( √ 3a2) assuming all triangles are equilateral. 

Q11. What is the algorithm for generating a self-supporting frame?

Algorithm 2 Self-supporting extension for extrusion-type printers Input: a frame T ∗ = (V ∗, E∗) generated by Algorithm 1 Output: a self-supporting frame T (s)1: Let V (s) = V ∗ and E(s) = E∗, and define a base plane B for the input frame. 

Q12. How do the authors determine the mass of the struts?

The authors consider the mass of the skin layer and the struts as the internal load in F by distributing the mass uniformly to their neighborhood nodes. 

Q13. What is the threshold for the topology cleaning?

The first threshold (c) retains 56 internal struts such that the model has no feasible solution in the geometry optimization while the second threshold (d) retains 552 internal struts to reach a solution with the frame volume of 3.389e4 mm3. 

Q14. What is the complexity of exhaustive search?

The complexity of exhaustive search is exponential in the scale of problem and, indeed, it has been proved that the combinatorial search problem is NP-hard. 

Q15. What is the way to print a printer?

For extrusion-type printers, the authors also develop a scheme to add extra struts to support the printed object during the printing process. 

Q16. What is the topology optimization of the Hanging Ball model?

The geometric positions of internal nodes and the radii of struts are refined by the following geometry optimization (GeoOpt in short):min r,Vint Vol(r,V, Ê)s.t. { (1), (11), (5), (10)} (21)where the topological connectivity of the frame structure is fixed as Ê = Eskin ∪ Êint and the reduced set of internal struts Êint is obtained from the topology optimization. 

Q17. Why is the swarm optimization method not applicable to 3D printing?

Due to difference in the types of objectives and constraints, the approach cannot be applied to their optimization problem in 3D printing. 

Q18. What is the way to make a frame?

Assembling parts of various frame structures while maintaining its strength and stiffness appears to be possible but would be challenging.