- Email: [email protected]
Stress-based tool-path planning methodology for fused filament fabrication
Journal Pre-proof Stress-based tool-path planning methodology for fused filament fabrication Lingwei Xia, Sen Lin, Guowei Ma
PII:
S2214-8604(19)31565-9
DOI:
https://doi.org/10.1016/j.addma.2019.101020
Reference:
ADDMA 101020
To appear in:
Additive Manufacturing
Received Date:
11 September 2019
Revised Date:
17 December 2019
Accepted Date:
27 December 2019
Please cite this article as: Lingwei Xia, Sen Lin, Guowei Ma, Stress-based tool-path planning methodology for fused filament fabrication, (2020), doi: https://doi.org/10.1016/j.addma.2019.101020
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Stress-based tool-path planning methodology for fused filament fabrication Lingwei Xiaa , Sen Linb , Guowei Maa,1,∗ a
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School of Civil and Transportation Engineering, Hebei University of Technology, 5340, Xiping Road, Beichen District, Tianjin 300401, China b State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, College of Mechanical and Vehicle Engineering, Hunan University, Changsha City 410082, China
Abstract
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Tool-path planning has a considerable impact on the quality of components printed by fused filament fabrication (FFF). This research proposes a path generation strategy based on the orientations
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of the maximum principal stresses. According to stress calculations from finite element analysis
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(FEA) of the components, tool-paths, which are programmed as parallel to the maximum principal stress directions, are constructed with the depth-first search (DFS) method and a connection criterion. The breakpoints in the tool-paths are then eliminated by connecting adjacent tool-paths.
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The Dijkstra algorithm is engaged to reduce the nozzle jump distance and shorten the production time. Stretching tests of different specimens printed with the developed path generation algorithms
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demonstrate that the model with the stress-based path has better mechanical performance. The
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digital image correlation (DIC) method and scanning electron microscopy (SEM) are employed to observe the fracture processes and fracture surfaces, respectively. Corresponding results of DIC and SEM reveal that different path filling forms exhibit variable failure patterns because of filament anisotropy. The filling fraction is calculated and indicates that the deposition quality of the advanced path is not compromised. This work provides a synthesis methodology for
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improving the mechanical performance of 3D printing products. Keywords: Additive manufacturing; Fused filament fabrication; Path planning; Stress-based path.
1. Introduction Fused filament fabrication (FFF), as a key additive manufacturing (AM) technology, uses a
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movable nozzle to deposit materials that solidify at a predetermined temperature layer by layer [1]. Because of its low cost and short cycles, FFF has been widely applied in mechanical design [2], biomedical engineering [3, 4], prototype fabrication [5] and topology optimization [6], among
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other fields. Due to its widespread application, this technology has a significant impact that will
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only increase in the future [7]. The quality of the model fabricated by FFF is affected by several parameters, such as the layer thickness [8], working temperature [9], building materials [10] and
voids in the 2D layers [12].
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extrusion rate [11]. One of the most crucial parameters is the path planning to fill the inherent
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Several filling patterns, such as spiral curves [13], Hilbert curves [14], and hybrid [15] and maze-like [16] path filling algorithms, have been developed in previous studies. The contour and
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parallel paths are the most prevalent algorithms [17] because of their high precision and simplicity. The methods used to generate tool-paths are intended to offset the original outlines [18, 19] and
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straight lines [20]. However, the above algorithms focus only on the geometric accuracy and printing efficiency without considering the external forces that the members sustain. Undesirable deterioration in mechanical properties due to anisotropy of the tool-paths is incurred when specimens sustain external loads [21]. To clarify this problem, researchers have tested specimens ∗ 1
Corresponding author Email: [email protected]
Preprint submitted to Additive Manufacturing
December 16, 2019
with different path orientations and found that the strength reaches a peak when the orientation is parallel to the force direction [22, 23]. Furthermore, specimens are damaged by shear forces due to the concentration of stress in certain cases. This phenomenon is similar to that of wood, which can bear a large force in alignment with the wood fibers, whereas its capacity to resist shear force
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orientated perpendicular to the fibers is poor. To solve this problem, Ulu et al. [24] introduced an algorithm to optimize the build orientation subjected to specific boundary conditions with the aim of maximizing the safety factor of an input
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object under prescribed loads. Both computational simulation and physical experiments showed that this algorithm considerably improved the capacity of a printing object to resist damage.
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On the other hand, the tool-paths generated by this algorithm do not adapt to changes of stress orientation. Subsequently, Steuben et al. [25] introduced a new implicit slicing algorithm by
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defining heuristics or physics fields on the geometry. In addition, finite element analysis (FEA) results were used to compute the infill tool-paths densely and sparsely in areas with and without
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concentrated stress, respectively. The ultimate stresses of components printed by this algorithm were improved remarkably. However, this path generation method may cause underfilled areas
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and rough surfaces of members, resulting in low printing precision [26].
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Low printing quality will ensue due to frequent nozzle jumps to incur discontinuities in the tool-paths [27]. On another negative note, redundant feeding of material will occur when the nozzle moves up and down due to switching between different tool-paths. Because the materials are suspended in the nozzle for a few seconds during the switching of tool-paths, it is expelled by redundant material feeding before the next tool-path is printed. This material may scatter onto the positions of tool-paths, resulting in printing imprecision. Therefore, it is desirable to shorten the 3
nozzle jump distance to decrease the redundant feeding of material. As amendments, continuous Fermat spirals [28] and smooth spirals [29] were successfully applied to achieve one-stroke printing to ensure continuity of the tool-path. However, these algorithms do not account for the stress conditions of specimens. Moreover, the underfillings as a consequence of unequal distances
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between adjacent tool-paths will incur stress concentration [30], which will compromise the mechanical performance of the printing models.
In this paper, a stress-based path planning algorithm is proposed to construct tool-paths
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that are parallel to the maximum principal stresses to prevent shear failure of printing models, thereby improving mechanical performance. To evaluate the effectiveness of this stress-based
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path planning algorithm, different shapes of samples fabricated by both currently improved and traditional paths are designed to perform mechanical tests. Moreover, the digital image correlation
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(DIC) method is used to monitor the displacements of specimens to observe their failure process from a macroscopic perspective, while scanning electron microscopy (SEM) is performed to
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observe the fracture surfaces to understand the failure mechanism from a microscopic perspective. To further evaluate the deposition quality of the advanced path, the path filling fraction is calculated
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by MATLAB to facilitate comparison with other tool-paths.
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2. Theory
In this section, the stress-based path planning methodology is proposed to generate tool-paths
identical to the maximum principal stress orientations of FEA results. After slicing a 3D model into layers, the hexagonal discretization is employed to avoid overlap of adjacent tool-paths and better control the nozzle movements. Subsequently, a connection criterion is established to construct 4
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Figure 1: Comparison of two types of discretization: (a) square meshes (orange region in blue rectangle indicates repeated area); (b) hexagonal meshes.
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tool-paths based on the maximum principal stress orientations; this process is illustrated in detail in Section 2.3 by being deployed on a sample. However, the tool-paths produce breakpoints that
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reduce printing quality and efficiency. To reduce this effect, the depth-first search (DFS) method
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is introduced to merge adjacent tool-paths and improve printing quality, and the Dijkstra algorithm is introduced to optimize the path-printing sequence and improve printing efficiency.
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2.1. Hexagonal discretization
Generally, two types of meshes are used to discretize 2D layers as shown in Figure 1, i.e.,
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square meshes and hexagonal meshes. The central point N of a square mesh has eight adjacent
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points, enabling more precise calculation compared with the six adjacent points in a hexagonal √ mesh. However, assuming that the nozzle diameter is d, a region with a width of 2 − 2 d will be printed repeatedly if the tool-path orientation is (2k − 1) · π/4 (k = 1, 2, 3, 4), as shown in Fig.
1(a). By contrast, if hexagonal meshes are adopted, this problem will be resolved because the tool-paths in six orientations can be connected without overlap, as shown in Fig. 1(b). In the global coordinate system, the orientation of the maximum principal stress α is calculated 5
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Figure 2: Orientation of hexagonal grids: (a) relation between the global coordinate system and local coordinate system (solid lines represent the global coordinate system, and dotted lines indicate the local coordinate system); (b)
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discretization of hexagonal grids based on β − 30◦ .
−2τ xy σ x − σy
α ∈ [0◦ , 180◦ )
(1)
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2α = arctan
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where σ x and σy are the normal stresses along X-axis and Y-axis, respectively, and τ xy denotes
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the shear stress of the discrete unit in the X-Y plane. If σ x ≥ σy , 2α falls in the first or fourth quadrant; if σ x ≤ σy , 2α falls in the second or third quadrant. Assuming that the number of
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hexagonal points is m and that the maximum principal stress in the layers is σmax , the orientation
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of the hexagonal grid is expressed as Pi=m β=
i=1
σi,max /σmax × αi m
(2)
Figure 2(a) shows the relation between the global coordinate system and the local coordinate
system. In the global coordinate system, the x-axis orientation of the local coordinate system is β − 30◦ , and the discretization scheme by hexagonal grids based on the local coordinate system is illustrated in Figure 2(b). Adjacent points of N are numbered from 1 to 6 counterclockwise 6
starting from the x-axis in the local coordinate system. In this case, the orientations of nodes 1 and 4 govern the directions of the tool-paths. In the range of the hexagonal grid and the space Pi − hi (where Pi is the layer height and hi is the layer thickness), assuming that the number of FEA meshes is m and that the maximum principal stress is σmax , the orientation of the maximum 0
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principal stress α in the global coordinate system is calculated as 0
α =
Pi=m0 0 0 0 i=1 σi,max /σmax × αi m0
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In the local coordinate system, α0 is expressed as
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0
0
α ∈ (−180◦ , 180◦ )
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α0 = α − β
(3)
2.2. Connection criterion
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In the proposed stress-based path strategy, establishing an appropriate connection criterion is a prerequisite. The specific connection criterion is shown in Table 1, where s is the total
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number of connectable adjacent points; A denotes the range of α0 ; and n and n0 are the nodes for corresponding adjacencies and the next point to be connected, respectively. If tool-paths are
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constructed directly based on the maximum principal stress orientations, too many sharp corners and short paths will be produced in complicated stress state areas. Given that the angle between
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the maximum principal stress and x-axis of node N is γ (γ [0, π)), then the tool-path of node N can be constructed in two orientations: γ and γ − π. Therefore, the adjacent areas of N are
divided into two parts in the criterion to optimize this situation, i.e., areas Ω1 and Ω2 . Among that, areas Ω1 includes adjacent points 1 through 3 and areas Ω2 includes points 4 through 6. The corresponding figures for Table 1 are shown in Figure. 3. The numbers in red or green 7
Table 1: Connection criterion.
Area
s
A n0 Color disk ◦ 0 ≤ α0 < 60 or 1 (4) Fig. 3(a) orange −180◦ < α0 < −120◦ 60◦ ≤ α0 < 120◦ or 1, 2, 3 2 (5) Fig. 3(a) blue (4, 5, 6) −120◦ ≤ α0 < −60◦ 120◦ ≤ α0 < 180◦ or 3 (6) Fig. 3(a) pink −60◦ ≤ α0 < 0◦ −30◦ ≤ α0 < 60◦ or 150◦ ≤ α0 < 180◦ or 1 (4) Fig. 3(b) orange 1, 2 ◦ ◦ −180 < α0 < −120 (4, 5) 60◦ ≤ α0 < 150◦ or 2 (5) Fig. 3(b) blue −120◦ ≤ α0 < −30◦ 0◦ ≤ α0 < 90◦ or 1 (4) Fig. 3(c) orange −180◦ < α0 < −90◦ 1, 3 90◦ ≤ α0 < 180◦ or (4, 6) 3 (6) Fig. 3(c) pink −90◦ ≤ α0 < 0◦ 30◦ ≤ α0 < 120◦ or 2 (5) Fig. 3(d) blue −150◦ ≤ α0 < −60◦ 2, 3 −60◦ ≤ α0 < 30◦ or (5, 6) 120◦ ≤ α0 < 180◦ or 3 (6) Fig. 3(d) pink −180◦ < α0 < −150◦ Any point Connecting the point Stopping visiting n
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Ω1 (or Ω2 )
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2
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diamonds indicate that the points can be connected, while the numbers in gray circles represent
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the unavailable points, and each color represents a range of orientations in the colored disk.
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Figure 3: Sketches for the connection criterion based on β = 30◦ : (a) criterion for 1-3 and 4-6; (b) criterion for 1-2
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and 4-5; (c) criterion for 1, 3 and 4, 6; (d) criterion for 2, 3 and 5, 6.
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2.3. Preliminary calculation Generate adjacent matrix of hexgon grids
Determine the start point "# among unvisited points
%=1 0
Count connectable adjacent points in area !
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1~3 1~3
Connect the point based on the criterion
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Count connectable adjacent points in ! from "#
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0
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Exist Connectable adjacent points?
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Visited
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?
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Merge two tool-paths
Yes
All points have been visited 漦
Tool-path optimization
Figure 4: Flowchart for stress-based path generation.
The fundamental component of the proposed scheme is the path planning based on the maximum principal stresses. The flowchart for the scheme is presented in Figure 4. The model shown in Figure 5(a) is stretched vertically, where the short lines represent the orientations of 10
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1 6
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Figure 5: Example of a stress-based path before optimization: (a) maximum principal stress orientations; (b) sketch for path calculation based on maximum principal stresses (grid points are marked by hollow dots, and each color line
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represents a different tool-path); (c) calculation result.
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the maximum principal stresses and the different colors indicate different values of the stresses. Figure 5(b) is a sketch of the tool-path generation method for Fig. 5(a). The algorithm starts by
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generating an adjacent matrix based on the central points of hexagons. The point with the largest maximum principal stress (node 1 in Fig. 5(b)) among the unvisited points is selected as the origin.
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The tool-path will be constructed from the origin in Ω1 until no connectable adjacency exits in Ω1 of the current node N. Then, the subsequent points will be connected from the origin in Ω2 .
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For example, nodes 2, 3, 4 in Ω1 and 5, 6, 7 in Ω2 are extracted sequentially after node 1. To improve the printing efficiency and integrity, these two sub-paths are merged into one tool-path, i.e., 4-3-2-1-5-6-7. This calculation is repeated until all points have been visited. Figure 5(c) shows the calculation result when the nozzle diameter is set as 0.8 mm.
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6 7 8
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2
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Figure 6: Sketches for breakpoint elimination: (a) breakpoints in the preliminary calculation (breakpoints are marked by magenta hollow dots, and each color line represents a different tool-path; breakpoint elimination is indicated by
2.4. Tool-path optimization
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2.4.1. Breakpoint elimination
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purple dotted lines); (b) calculation result for Fig. 4(c) after elimination.
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The breakpoint elimination procedure can be divided into three steps as shown in Figure 6(a). The first step is to merge multiple tool-paths and isolate points into one tool-path. For example,
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nodes 1 and 2, which are adjacent endpoints of two paths, are connected directly as nodes 3, 4, and 5. Second, if the endpoint has no adjacency, such as node 7, the tool-path will be extended to intersect with another tool-path with the closest point, such as node 8. The third step is to address the isolated endpoint (node 9) remaining after the first two steps. This node will be connected with another tool-path (node 10) based on the maximum principal stress orientation and the connection 12
criterion. Figure 6(b) shows the calculation result for Fig. 5(c) after eliminating breakpoints. Extract and number the endpoints P
%=1 Determine the start point
!
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Calculate distances from unvisited P to !"#
% =-.1 Retrieve the nearest unvisited point $ to !"#
Store the sequence of endpoints in '! and accumulate (!$ in ) *!
No
Yes
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No
% = 2& ?
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All endpoints have been visited ?
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% =%.1
Yes
Retrieve the +%, ) *! and correspongding '!$
Sort tool-paths based on '!$
Optimization over
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End loop
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Figure 7: Flowchart for tool-path optimization based on the Dijkstra algorithm.
2.4.2. Nozzle jump reduction
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The Dijkstra algorithm, which always yields the local optimal solution when pursuing the
shortest path, is employed here to shorten the nozzle jump distance [31]. The path optimization flowchart based on the Dijkstra algorithm is presented in Figure 7, where Pi and Pi+1 are the endpoints of tool-path i and M denotes the total number of endpoints. Because the printing order of tool-paths is consistent with the previous planning sequence, tool-paths with large stresses 13
will be prioritized for printing. As shown in Figure 8(a), the nozzle will originally move from node 1 to node 2, jump to node 3 to print to node 4, and so forth. After optimization, the printing process starts by extracting an endpoint of the first tool-path, as shown in Figure 8(b). Node 1 is selected as the start point, and the nozzle will then print to node 2. The next step is to retrieve the
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nearest endpoint (node 15) to node 2, and so on. Choosing the optimal start points of the paths to minimize the number of times the nozzles turn on and off is one feasible method [32]. All the endpoints are specified as start points to obtain the closest jump distance. Meanwhile, the nozzle P
Di , and the corresponding sequence of endpoints is stored in
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jump distances are accumulated in
matrix B. Finally, the printing sequence in Bi is retrieved according to the smallest total distance P
Di . The magenta dotted lines in Fig. 8 represent the trajectory of the nozzle jump. In this
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case, after optimization, the jump distance decreases 80.2%. Figure 9 shows the printing models
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5
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4
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5 14 15
15
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6
9
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14
3
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with various tool-paths for Fig. 6(b) when the nozzle diameter is 0.4 mm.
6
9
2
2
3 1
1
11
11 4
10
10 7
7
12 13
13
8
8
Figure 8: Comparison of nozzle jump trajectory: (a) before optimization; (b) after optimization.
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Figure 9: Models fabricated by (a) parallel path; (b) contour path; (c) stress-based path.
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3. Experimental validation 3.1. Specimen preparation
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To confirm that the load-carrying capacity of components printed by the present stress-based path strategy is higher than that of components printed by traditional algorithms, three types of
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specimens are designed for mechanical tests. The dimensions of these specimens are shown in Figure 10(a-c). Using 1.75 ± 0.02 mm diameter thermoplastic polymer colorFabb PLA filament
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(density: 1.210-1.430 gcm−3 , glass transition temperature: 55 ◦ C), all samples are fabricated with
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a Z-603S 3D desktop printer (Shenzhen JG Aurora Co., Ltd.). The samples are extruded from a 0.4 mm nozzle at a temperature of 205 ◦ C, and the building platform is heated to 55 ◦ C. One-third of the specimens are printed by the stress-based path, and the others are filled with the parallel path (±45◦ ) and the contour path, both generated by commercial slicing software (Cura). The thickness of all specimens is 1 mm, including 0.3 mm for the first layer and 0.1 mm for all other layers. The infill speed is set as 20 mm/s, the travel speed is set as 60 mm/s, and the printing 15
(E)
40mm
2.5mm
20mm
(d) r
10mm R 5mm d
45mm
R 10mm
20mm
(c)
R 15mm
90mm
(a)
!
R 10mm 35mm
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r
Figure 10: Dimensions: (a) specimen 1; (b) specimen 2; (c) specimen 3; (d) simplified model of tool-paths.
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speed of the first layer is reduced to half of these specifications.
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3.2. Tensile tests and fracture analysis
The tensile tests are implemented by stretching with an electromechanical universal machine
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(2 KN capacity, Shenzhen Sans Testing Machine Co., Ltd.). The loading rate is fixed at 0.5 mm/min by displacement control, and all the test results are the average of results from five
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replication experiments.
Meanwhile, DIC, which provides a full-field measurement of the displacement fields at the
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surface with black and white paints [33], is employed to observe the fracture process when
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the specimens are being tested. This technology has been widely adopted in studies of the stress field of components fabricated by AM due to its ability to capture images promptly and accurately [34, 35]. In this research, the failure of specimens is monitored by two CCD cameras, and the commercial VIC-2D system from Correlated Solutions is utilized for DIC. To demonstrate the failure mechanisms and patterns by different tool-paths from a microscopic perspective, SEM is used in this research to observe the fracture surfaces. SEM is a general type 16
of electron microscopy employed to achieve a high spatial resolution by generating a topological image of a sample using a beam of electrons. An FEI Quanta 450 FEG is employed to magnify the fracture surfaces 100 times.
3.3. Filling fraction calculation
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The path filling fraction is an index for printing precision. In this research, the tool-paths are simplified into the model as shown in Figure 10(d), where l0 is the length of the tool-path and d and r are the diameter (0.4 mm) and radius (0.2 mm) of the nozzle, respectively. The filling
S0 × 100% S
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w=
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fraction is expressed by
(5)
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wherein S 0 and S are the areas of the tool-paths and 2D geometries, respectively. The filling
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fraction is calculated by MATLAB.
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4. Results and discussion 4.1. Mechanical properties and fracture process Table 2: Features of specimen 1 fabricated by different tool-paths.
(a)
(E)
(H)
Contour 439.35 1.95 0.74 2071.26
Stress-based 654.61 (+44.65%, +48.86%) 1.96 (0%, +0.51%) 0.74 (0%, 0%) 1938.71 (-7.03%, -6.40%)
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Parallel 452.56 1.96 0.74 2085.20
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Physical quantities Ultimate force (N) Measured mass (g) Filament length (m) Printing time (s)
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Figure 11: Directions of maximum principal stresses and three types of path filling forms (dotted lines represent cracks) and corresponding DIC images for specimen 1: (a) maximum principal stress orientations; path filling forms for (b) parallel path, (c) contour path, (d) stress-based path; displacement fields for (e) parallel path; (f) contour path;
(g) stress-based path.
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The features of specimen 1 shown in Table 2 indicate that the stress-based path demonstrates a much higher load-carrying capacity and less time than the traditional algorithms. Figure 11(a-d) shows the maximum principal stress orientations in the model and the three types of path filling methods used for specimen 1. The displacement fields shown in Fig. 11(e-g) illustrate the different
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performances when the specimens sustain a vertical force. From Fig. 11, the anisotropy of the tool-paths influences the failure patterns. The cracks in Figs. 11(e) and (g) both start from the location of stress concentration. The cracks in the parallel path are not aligned with the maximum
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principal stress orientations because of the stress redistribution by the tool-path anisotropy. In Fig. 11(f), cracks occur in the region away from the location of stress concentration because of
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the air gap between adjacent filaments. For the stress-based path, cracks proceed in 0◦ and 90◦ zigzag patterns that consist of horizontals and verticals, as shown in Fig. 11(g). Consequently, the
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mechanical properties of the specimen printed by the stress-based path planning algorithm are
stress orientations.
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significantly improved because the path orientations are in alignment with the maximum principal
Table 3: Features of specimen 2 fabricated by different tool-paths.
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Physical quantities Parallel Ultimate force (N) 208.88 Measured mass (g) 2.77 Filament length (m) 1.05 Printing time (s) 2607.62
Contour 211.38 2.80 1.06 2608.64
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Stress-based 288.18 (+37.96%, +36.33%) 2.85 (+2.89%, +1.79%) 1.08 (+2.86%, +1.89%) 2869.48 (+10.04%, +9.99%)
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Figure 12: Directions of maximum principal stresses and three types of path filling forms (dotted lines represent
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cracks) and corresponding DIC images for specimen 2: (a) maximum principal stress orientations; path filling forms for (b) parallel path, (c) contour path, (d) stress-based path; displacement fields for (e) parallel path, (f) contour path,
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(g) stress-based path.
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Similarly, the features of specimen 2 shown in Table 3 indicate that the stress-based path
yields a much higher load-carrying capacity but consumes slightly more material and time than the other paths. Figure 12(a-d) shows the maximum principal stress orientations in the model and the three types of path filling methods used for specimen 2. For the specimen in Fig. 12(e), the cracks at the bottom-left and top-right corners of the circle initiate simultaneously because of the 20
stress concentration. The cracks proceed horizontally. For the specimen printed by the contour path, the cracks initiate at the bottom-left corner and proceed transversely. This development is followed by cracks starting at the air gap in the bottom-right corner of the oblique rib, as shown in Fig. 12(f). On the other hand, the crack in the specimen printed by the stress-based path first
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occurs transversely at the bottom-right corner, after which the crack develops at the connection between adjacent tool-paths and proceeds vertically. Finally, the crack advances transversely to the inner circle, as shown in Fig. 12(g). The differences in the behaviors of cracks can be
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attributed to the stress redistribution by inherent anisotropy of the printing techniques. Because the area of damage in Fig. 12(g) is braced by the oblique rib and the tool-paths are parallel to the
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maximum principal stress orientations, the mechanical performance achieved by the proposed path is remarkably superior to those produced by the two traditional paths.
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As shown in Table 4, specimen 3 again indicates that the stress-based path exhibits a much higher load-carrying capacity but consumes slightly more material and time than the other paths.
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Figure 13(a-d) shows the maximum principal stress orientations in the model and the three types of path filling methods used for specimen 3. Specimens with different tool-paths have
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different displacement fields because of the redistribution of stress by anisotropy with regard
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to the tool-paths, as shown in Figure 13(e-g). Although the cracks in both Figs. 13(e) and (g) Table 4: Features of specimen 3 fabricated by different tool-paths.
Physical quantities Parallel Ultimate force (N) 381.86 Measured mass (g) 3.47 Filament length (m) 1.31 Printing time (s) 3279.41
Contour 282.27 3.44 1.30 3235.64
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Stress-based 643.09 (+68.41%, +127.83%) 3.51 (+1.15%, +2.03%) 1.33 (+1.53%, +2.31%) 3326.44 (+1.42%, +2.81%)
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Figure 13: Directions of the maximum principal stresses and three types of path filling forms (dotted lines represent cracks) and corresponding DIC images for specimen 3: (a) maximum principal stress orientations; path filling forms
(g) stress-based path.
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for (b) parallel path, (c) contour path, (d) stress-based path; displacement fields for (e) parallel path, (f) contour path,
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initiate from the geometrical imperfection to the right edge of the specimens, their shapes are
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different. The crack in Fig. 13(e) develops in a ±45◦ zigzag pattern because not only the external force but also the ±45◦ tool-paths dominate the fracture morphology. Conversely, the crack in Fig. 13(f) is generated at the central region because of the weak connection of the air gap between adjacent filaments, whereas in Fig. 13(g), the crack proceeds along a straight line. In this case, the stress-based path incurs the highest stretching capacity.
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(E)
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(D)
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(G)
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1mm
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(F)
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Figure 14: Sketches for structures and corresponding SEM images of fracture surfaces: (a) parallel path; (b) parallel path; (c) contour path; (d) stress-based path.
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4.2. Fracture surface analysis The fracture surfaces of the specimens observed by SEM during the tensile tests are shown in Figure 14. The surfaces of the fractures in the parallel path exhibit two types of failure modes. If the crack proceeds along a zigzag pattern, the filaments, whose surfaces are perpendicular to
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the path orientations, will fail exactly along the extrusion orientation, as shown in Fig. 14(a). However, in this case, half of the layers will crack at connections of the filaments, which negates the performance of the specimens because of the weak connections between tool-paths. In contrast,
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if the crack proceeds along a straight line, the filaments will generally fail near ±45◦ because of shear stresses and normal stresses, as shown in Fig. 14(b). The angles of the fracture surfaces in
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the contour path, which depend on the angles between the filaments and stresses, are difficult to ascertain, as shown in Fig. 14(c). Generally, a smaller angle creates a rougher fracture surface.
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As a result, the filaments are probably subjected to different shear forces when the stresses are not parallel to the tool-paths. There is only one type of failure in the stress-based path, as shown in
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Fig. 14(d). The fracture surfaces are perpendicular to the maximum principal stresses because the currently developed tool-paths produce a smaller shear force compared with traditional algorithms.
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Therefore, for the situation of large normal stresses, the stress-based path makes full use of the
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material properties to improve the mechanical performance of the models. Consequently, the specimen printed by the currently proposed path has the highest mechanical capacity.
4.3. Filling fraction Sketches for underfilled areas of the three types of path filling methods are given in Figure
15(a-c). From Fig. 15(a), the parallel path offsets the line segments in one direction equidistantly. 24
(a)
(b)
(c)
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(d)
Figure 15: Sketches for underfilled areas of three types of path filling forms (the dark green lines represent the
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trajectory of the tool-paths, the yellow lines represent the areas of the tool-paths, and the green and purple regions indicate underfilled areas) for (a) parallel path; (b) contour path; (c) stress-based path. (d) Histogram of the path
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filling fraction.
Therefore, the tool-paths can closely connect with each other. On the other hand, when the
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offset distance is not an integer multiple of the width of the tool-path, underfillings will be incurred (purple regions). The contour path aims to offset the original outlines to fill 2D layers. Consequently, the underfilled areas of this tool-path can be classified into two types. The first type of underfilled area (green regions in Fig. 15(b)) is produced in regions with sharp corners of two adjacent tool-paths [36]. The second type is similar to the underfilled areas in the parallel 25
path. If the width of the underfilled area is less than the width of the tool-path, the path will not be followed (purple regions in Fig. 15(b)). This type of underfilling usually appears at the offset centers. For the stress-based path, the tool-paths are generated by the connections with the center points of the hexagonal grids. In this case, the underfilled areas (green regions in Fig.
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15(c)) are generated at the joints of adjacent tool-paths because of unequal slopes. In addition, the deficiencies of the center points near the geometry boundary lead to underfillings (purple regions in Fig. 15(c)) near the boundaries. The corresponding histograms of the filling fraction
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with different path filling algorithms are shown in Figure 15(d). Generally, the specimens filled by the parallel path have the highest filling fraction. The specimens filled by the contour path
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have the lowest filling fraction due to the larger curvature of the tool-paths. The filling fraction of
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the stress-based path is between those of the above two path filling techniques.
5. Conclusions
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In this paper, a stress-based path planning algorithm in view of the maximum principal stresses is proposed to improve the mechanical properties of models fabricated by FFF. This algorithm
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generates tool-paths in alignment with the stress orientations by connecting hexagonal points
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based on the connection criterion and depth-first search (DFS) method. After a preliminary calculation, the tool-paths are optimized in two steps, namely, connecting adjacent tool-paths to eliminate breakpoints and introducing the Dijkstra algorithm to improve printing efficiency and quality. The calculation results for the example in Fig. 6(b) and the results of mechanical tests indicate that this algorithm can generate tool-paths to amend the intrinsic deficiencies of the current available printing techniques. 26
To validate the effectiveness of the proposed approach, specimens with three different morphologies of geometries are printed by different tool-paths and mechanically tested. Meanwhile, the DIC method is employed to observe the failure process as the specimens are stretched. The experimental results show that the stress-based path efficiently improves the mechanical perfor-
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mance of the printing specimen. The displacement fields and SEM images demonstrate that the specimens created with different paths generally exhibit different crack patterns because of the redistribution of stress by the inherent anisotropy of the tool-paths. Generally, the cracks of the
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specimens printed by the parallel path proceed along a ±45◦ zigzag pathway or straight lines, and the fracture surfaces indicate that the filaments crack along the extrusion orientations or at
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±45◦ angles. In addition to all the specimens failing at air gaps, the fractures of the specimens printed by the contour path fail at indefinite angles because the filaments in variable orientations
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experience different local shear stresses. For the currently proposed stress-based path, the cracks fail along 0◦ and 90◦ zigzag patterns or along straight lines. The fracture surfaces are generally
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perpendicular to the maximum principal stress orientations. The test results indicate that the stretching capacity is reduced if the filament experiences shear force. The improvement by the
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stress-based path shows that each filament does not sustain a large shear stress. In addition, the
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filling fractions of specimens by different path filling methods are calculated by a simplified model of the tool-path. Calculation results show that the currently proposed path satisfies the required printing precision of specimens. Although implementation of the proposed stress-based path improves the mechanical performance of the printing models, this methodology is still in a preliminary stage and requires further exploration. For instance, sharp corners will reduce the printing quality because the nozzle cannot 27
switch instantly and materials cannot be deposited firmly onto the heating plate. Moreover, this approach eliminates breakpoints. Consequently, a few points are visited repeatedly. Thus, more material than necessary is consumed, and the printing precision is compromised. These challenges will be a focus of future research. The novel methodology in this study improves the mechanical
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performance of the printing models by optimizing path orientations. The current proposed path planning method benefits stressed members for improving mechanical design.
6. Acknowledgments
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The paper is sponsored by National Natural Science Foundation of China (Grant No. 11802082
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and Grant No. 5187083454) and the Hebei Science and Technology Department (Grant No.
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18391203D).
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PII:
S2214-8604(19)31565-9
DOI:
https://doi.org/10.1016/j.addma.2019.101020
Reference:
ADDMA 101020
To appear in:
Additive Manufacturing
Received Date:
11 September 2019
Revised Date:
17 December 2019
Accepted Date:
27 December 2019
Please cite this article as: Lingwei Xia, Sen Lin, Guowei Ma, Stress-based tool-path planning methodology for fused filament fabrication, (2020), doi: https://doi.org/10.1016/j.addma.2019.101020
This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2020 Published by Elsevier.
Stress-based tool-path planning methodology for fused filament fabrication Lingwei Xiaa , Sen Linb , Guowei Maa,1,∗ a
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School of Civil and Transportation Engineering, Hebei University of Technology, 5340, Xiping Road, Beichen District, Tianjin 300401, China b State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, College of Mechanical and Vehicle Engineering, Hunan University, Changsha City 410082, China
Abstract
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Tool-path planning has a considerable impact on the quality of components printed by fused filament fabrication (FFF). This research proposes a path generation strategy based on the orientations
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of the maximum principal stresses. According to stress calculations from finite element analysis
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(FEA) of the components, tool-paths, which are programmed as parallel to the maximum principal stress directions, are constructed with the depth-first search (DFS) method and a connection criterion. The breakpoints in the tool-paths are then eliminated by connecting adjacent tool-paths.
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The Dijkstra algorithm is engaged to reduce the nozzle jump distance and shorten the production time. Stretching tests of different specimens printed with the developed path generation algorithms
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demonstrate that the model with the stress-based path has better mechanical performance. The
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digital image correlation (DIC) method and scanning electron microscopy (SEM) are employed to observe the fracture processes and fracture surfaces, respectively. Corresponding results of DIC and SEM reveal that different path filling forms exhibit variable failure patterns because of filament anisotropy. The filling fraction is calculated and indicates that the deposition quality of the advanced path is not compromised. This work provides a synthesis methodology for
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improving the mechanical performance of 3D printing products. Keywords: Additive manufacturing; Fused filament fabrication; Path planning; Stress-based path.
1. Introduction Fused filament fabrication (FFF), as a key additive manufacturing (AM) technology, uses a
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movable nozzle to deposit materials that solidify at a predetermined temperature layer by layer [1]. Because of its low cost and short cycles, FFF has been widely applied in mechanical design [2], biomedical engineering [3, 4], prototype fabrication [5] and topology optimization [6], among
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other fields. Due to its widespread application, this technology has a significant impact that will
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only increase in the future [7]. The quality of the model fabricated by FFF is affected by several parameters, such as the layer thickness [8], working temperature [9], building materials [10] and
voids in the 2D layers [12].
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extrusion rate [11]. One of the most crucial parameters is the path planning to fill the inherent
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Several filling patterns, such as spiral curves [13], Hilbert curves [14], and hybrid [15] and maze-like [16] path filling algorithms, have been developed in previous studies. The contour and
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parallel paths are the most prevalent algorithms [17] because of their high precision and simplicity. The methods used to generate tool-paths are intended to offset the original outlines [18, 19] and
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straight lines [20]. However, the above algorithms focus only on the geometric accuracy and printing efficiency without considering the external forces that the members sustain. Undesirable deterioration in mechanical properties due to anisotropy of the tool-paths is incurred when specimens sustain external loads [21]. To clarify this problem, researchers have tested specimens ∗ 1
Corresponding author Email: [email protected]
Preprint submitted to Additive Manufacturing
December 16, 2019
with different path orientations and found that the strength reaches a peak when the orientation is parallel to the force direction [22, 23]. Furthermore, specimens are damaged by shear forces due to the concentration of stress in certain cases. This phenomenon is similar to that of wood, which can bear a large force in alignment with the wood fibers, whereas its capacity to resist shear force
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orientated perpendicular to the fibers is poor. To solve this problem, Ulu et al. [24] introduced an algorithm to optimize the build orientation subjected to specific boundary conditions with the aim of maximizing the safety factor of an input
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object under prescribed loads. Both computational simulation and physical experiments showed that this algorithm considerably improved the capacity of a printing object to resist damage.
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On the other hand, the tool-paths generated by this algorithm do not adapt to changes of stress orientation. Subsequently, Steuben et al. [25] introduced a new implicit slicing algorithm by
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defining heuristics or physics fields on the geometry. In addition, finite element analysis (FEA) results were used to compute the infill tool-paths densely and sparsely in areas with and without
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concentrated stress, respectively. The ultimate stresses of components printed by this algorithm were improved remarkably. However, this path generation method may cause underfilled areas
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and rough surfaces of members, resulting in low printing precision [26].
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Low printing quality will ensue due to frequent nozzle jumps to incur discontinuities in the tool-paths [27]. On another negative note, redundant feeding of material will occur when the nozzle moves up and down due to switching between different tool-paths. Because the materials are suspended in the nozzle for a few seconds during the switching of tool-paths, it is expelled by redundant material feeding before the next tool-path is printed. This material may scatter onto the positions of tool-paths, resulting in printing imprecision. Therefore, it is desirable to shorten the 3
nozzle jump distance to decrease the redundant feeding of material. As amendments, continuous Fermat spirals [28] and smooth spirals [29] were successfully applied to achieve one-stroke printing to ensure continuity of the tool-path. However, these algorithms do not account for the stress conditions of specimens. Moreover, the underfillings as a consequence of unequal distances
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between adjacent tool-paths will incur stress concentration [30], which will compromise the mechanical performance of the printing models.
In this paper, a stress-based path planning algorithm is proposed to construct tool-paths
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that are parallel to the maximum principal stresses to prevent shear failure of printing models, thereby improving mechanical performance. To evaluate the effectiveness of this stress-based
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path planning algorithm, different shapes of samples fabricated by both currently improved and traditional paths are designed to perform mechanical tests. Moreover, the digital image correlation
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(DIC) method is used to monitor the displacements of specimens to observe their failure process from a macroscopic perspective, while scanning electron microscopy (SEM) is performed to
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observe the fracture surfaces to understand the failure mechanism from a microscopic perspective. To further evaluate the deposition quality of the advanced path, the path filling fraction is calculated
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by MATLAB to facilitate comparison with other tool-paths.
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2. Theory
In this section, the stress-based path planning methodology is proposed to generate tool-paths
identical to the maximum principal stress orientations of FEA results. After slicing a 3D model into layers, the hexagonal discretization is employed to avoid overlap of adjacent tool-paths and better control the nozzle movements. Subsequently, a connection criterion is established to construct 4
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Figure 1: Comparison of two types of discretization: (a) square meshes (orange region in blue rectangle indicates repeated area); (b) hexagonal meshes.
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tool-paths based on the maximum principal stress orientations; this process is illustrated in detail in Section 2.3 by being deployed on a sample. However, the tool-paths produce breakpoints that
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reduce printing quality and efficiency. To reduce this effect, the depth-first search (DFS) method
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is introduced to merge adjacent tool-paths and improve printing quality, and the Dijkstra algorithm is introduced to optimize the path-printing sequence and improve printing efficiency.
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2.1. Hexagonal discretization
Generally, two types of meshes are used to discretize 2D layers as shown in Figure 1, i.e.,
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square meshes and hexagonal meshes. The central point N of a square mesh has eight adjacent
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points, enabling more precise calculation compared with the six adjacent points in a hexagonal √ mesh. However, assuming that the nozzle diameter is d, a region with a width of 2 − 2 d will be printed repeatedly if the tool-path orientation is (2k − 1) · π/4 (k = 1, 2, 3, 4), as shown in Fig.
1(a). By contrast, if hexagonal meshes are adopted, this problem will be resolved because the tool-paths in six orientations can be connected without overlap, as shown in Fig. 1(b). In the global coordinate system, the orientation of the maximum principal stress α is calculated 5
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Figure 2: Orientation of hexagonal grids: (a) relation between the global coordinate system and local coordinate system (solid lines represent the global coordinate system, and dotted lines indicate the local coordinate system); (b)
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discretization of hexagonal grids based on β − 30◦ .
−2τ xy σ x − σy
α ∈ [0◦ , 180◦ )
(1)
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2α = arctan
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as
where σ x and σy are the normal stresses along X-axis and Y-axis, respectively, and τ xy denotes
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the shear stress of the discrete unit in the X-Y plane. If σ x ≥ σy , 2α falls in the first or fourth quadrant; if σ x ≤ σy , 2α falls in the second or third quadrant. Assuming that the number of
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hexagonal points is m and that the maximum principal stress in the layers is σmax , the orientation
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of the hexagonal grid is expressed as Pi=m β=
i=1
σi,max /σmax × αi m
(2)
Figure 2(a) shows the relation between the global coordinate system and the local coordinate
system. In the global coordinate system, the x-axis orientation of the local coordinate system is β − 30◦ , and the discretization scheme by hexagonal grids based on the local coordinate system is illustrated in Figure 2(b). Adjacent points of N are numbered from 1 to 6 counterclockwise 6
starting from the x-axis in the local coordinate system. In this case, the orientations of nodes 1 and 4 govern the directions of the tool-paths. In the range of the hexagonal grid and the space Pi − hi (where Pi is the layer height and hi is the layer thickness), assuming that the number of FEA meshes is m and that the maximum principal stress is σmax , the orientation of the maximum 0
0
principal stress α in the global coordinate system is calculated as 0
α =
Pi=m0 0 0 0 i=1 σi,max /σmax × αi m0
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In the local coordinate system, α0 is expressed as
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0
0
α ∈ (−180◦ , 180◦ )
(4)
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α0 = α − β
(3)
2.2. Connection criterion
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In the proposed stress-based path strategy, establishing an appropriate connection criterion is a prerequisite. The specific connection criterion is shown in Table 1, where s is the total
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number of connectable adjacent points; A denotes the range of α0 ; and n and n0 are the nodes for corresponding adjacencies and the next point to be connected, respectively. If tool-paths are
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constructed directly based on the maximum principal stress orientations, too many sharp corners and short paths will be produced in complicated stress state areas. Given that the angle between
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the maximum principal stress and x-axis of node N is γ (γ [0, π)), then the tool-path of node N can be constructed in two orientations: γ and γ − π. Therefore, the adjacent areas of N are
divided into two parts in the criterion to optimize this situation, i.e., areas Ω1 and Ω2 . Among that, areas Ω1 includes adjacent points 1 through 3 and areas Ω2 includes points 4 through 6. The corresponding figures for Table 1 are shown in Figure. 3. The numbers in red or green 7
Table 1: Connection criterion.
Area
s
A n0 Color disk ◦ 0 ≤ α0 < 60 or 1 (4) Fig. 3(a) orange −180◦ < α0 < −120◦ 60◦ ≤ α0 < 120◦ or 1, 2, 3 2 (5) Fig. 3(a) blue (4, 5, 6) −120◦ ≤ α0 < −60◦ 120◦ ≤ α0 < 180◦ or 3 (6) Fig. 3(a) pink −60◦ ≤ α0 < 0◦ −30◦ ≤ α0 < 60◦ or 150◦ ≤ α0 < 180◦ or 1 (4) Fig. 3(b) orange 1, 2 ◦ ◦ −180 < α0 < −120 (4, 5) 60◦ ≤ α0 < 150◦ or 2 (5) Fig. 3(b) blue −120◦ ≤ α0 < −30◦ 0◦ ≤ α0 < 90◦ or 1 (4) Fig. 3(c) orange −180◦ < α0 < −90◦ 1, 3 90◦ ≤ α0 < 180◦ or (4, 6) 3 (6) Fig. 3(c) pink −90◦ ≤ α0 < 0◦ 30◦ ≤ α0 < 120◦ or 2 (5) Fig. 3(d) blue −150◦ ≤ α0 < −60◦ 2, 3 −60◦ ≤ α0 < 30◦ or (5, 6) 120◦ ≤ α0 < 180◦ or 3 (6) Fig. 3(d) pink −180◦ < α0 < −150◦ Any point Connecting the point Stopping visiting n
3
Ω1 (or Ω2 )
1 0
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2
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◦
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diamonds indicate that the points can be connected, while the numbers in gray circles represent
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the unavailable points, and each color represents a range of orientations in the colored disk.
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Figure 3: Sketches for the connection criterion based on β = 30◦ : (a) criterion for 1-3 and 4-6; (b) criterion for 1-2
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and 4-5; (c) criterion for 1, 3 and 4, 6; (d) criterion for 2, 3 and 5, 6.
9
2.3. Preliminary calculation Generate adjacent matrix of hexgon grids
Determine the start point "# among unvisited points
%=1 0
Count connectable adjacent points in area !
%=2
1~3 1~3
Connect the point based on the criterion
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Count connectable adjacent points in ! from "#
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0
Yes
No
Exist Connectable adjacent points?
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%=2
No
No
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Visited
$
?
Yes
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Merge two tool-paths
Yes
All points have been visited 漦
Tool-path optimization
Figure 4: Flowchart for stress-based path generation.
The fundamental component of the proposed scheme is the path planning based on the maximum principal stresses. The flowchart for the scheme is presented in Figure 4. The model shown in Figure 5(a) is stretched vertically, where the short lines represent the orientations of 10
(a)
(E)
(F)
3
4
1 6
7
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5
1cm
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Figure 5: Example of a stress-based path before optimization: (a) maximum principal stress orientations; (b) sketch for path calculation based on maximum principal stresses (grid points are marked by hollow dots, and each color line
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represents a different tool-path); (c) calculation result.
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the maximum principal stresses and the different colors indicate different values of the stresses. Figure 5(b) is a sketch of the tool-path generation method for Fig. 5(a). The algorithm starts by
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generating an adjacent matrix based on the central points of hexagons. The point with the largest maximum principal stress (node 1 in Fig. 5(b)) among the unvisited points is selected as the origin.
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The tool-path will be constructed from the origin in Ω1 until no connectable adjacency exits in Ω1 of the current node N. Then, the subsequent points will be connected from the origin in Ω2 .
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For example, nodes 2, 3, 4 in Ω1 and 5, 6, 7 in Ω2 are extracted sequentially after node 1. To improve the printing efficiency and integrity, these two sub-paths are merged into one tool-path, i.e., 4-3-2-1-5-6-7. This calculation is repeated until all points have been visited. Figure 5(c) shows the calculation result when the nozzle diameter is set as 0.8 mm.
11
(D)
(E)
5
4
6 7 8
3
9 10
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1
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2
1cm
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Figure 6: Sketches for breakpoint elimination: (a) breakpoints in the preliminary calculation (breakpoints are marked by magenta hollow dots, and each color line represents a different tool-path; breakpoint elimination is indicated by
2.4. Tool-path optimization
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2.4.1. Breakpoint elimination
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purple dotted lines); (b) calculation result for Fig. 4(c) after elimination.
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The breakpoint elimination procedure can be divided into three steps as shown in Figure 6(a). The first step is to merge multiple tool-paths and isolate points into one tool-path. For example,
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nodes 1 and 2, which are adjacent endpoints of two paths, are connected directly as nodes 3, 4, and 5. Second, if the endpoint has no adjacency, such as node 7, the tool-path will be extended to intersect with another tool-path with the closest point, such as node 8. The third step is to address the isolated endpoint (node 9) remaining after the first two steps. This node will be connected with another tool-path (node 10) based on the maximum principal stress orientation and the connection 12
criterion. Figure 6(b) shows the calculation result for Fig. 5(c) after eliminating breakpoints. Extract and number the endpoints P
%=1 Determine the start point
!
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Calculate distances from unvisited P to !"#
% =-.1 Retrieve the nearest unvisited point $ to !"#
Store the sequence of endpoints in '! and accumulate (!$ in ) *!
No
Yes
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No
% = 2& ?
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All endpoints have been visited ?
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% =%.1
Yes
Retrieve the +%, ) *! and correspongding '!$
Sort tool-paths based on '!$
Optimization over
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End loop
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Figure 7: Flowchart for tool-path optimization based on the Dijkstra algorithm.
2.4.2. Nozzle jump reduction
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The Dijkstra algorithm, which always yields the local optimal solution when pursuing the
shortest path, is employed here to shorten the nozzle jump distance [31]. The path optimization flowchart based on the Dijkstra algorithm is presented in Figure 7, where Pi and Pi+1 are the endpoints of tool-path i and M denotes the total number of endpoints. Because the printing order of tool-paths is consistent with the previous planning sequence, tool-paths with large stresses 13
will be prioritized for printing. As shown in Figure 8(a), the nozzle will originally move from node 1 to node 2, jump to node 3 to print to node 4, and so forth. After optimization, the printing process starts by extracting an endpoint of the first tool-path, as shown in Figure 8(b). Node 1 is selected as the start point, and the nozzle will then print to node 2. The next step is to retrieve the
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nearest endpoint (node 15) to node 2, and so on. Choosing the optimal start points of the paths to minimize the number of times the nozzles turn on and off is one feasible method [32]. All the endpoints are specified as start points to obtain the closest jump distance. Meanwhile, the nozzle P
Di , and the corresponding sequence of endpoints is stored in
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jump distances are accumulated in
matrix B. Finally, the printing sequence in Bi is retrieved according to the smallest total distance P
Di . The magenta dotted lines in Fig. 8 represent the trajectory of the nozzle jump. In this
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min
case, after optimization, the jump distance decreases 80.2%. Figure 9 shows the printing models
(D)
5
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4
12
5 14 15
15
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6
9
(E)
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14
3
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with various tool-paths for Fig. 6(b) when the nozzle diameter is 0.4 mm.
6
9
2
2
3 1
1
11
11 4
10
10 7
7
12 13
13
8
8
Figure 8: Comparison of nozzle jump trajectory: (a) before optimization; (b) after optimization.
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(E)
(F)
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(D)
1cm
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Figure 9: Models fabricated by (a) parallel path; (b) contour path; (c) stress-based path.
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3. Experimental validation 3.1. Specimen preparation
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To confirm that the load-carrying capacity of components printed by the present stress-based path strategy is higher than that of components printed by traditional algorithms, three types of
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specimens are designed for mechanical tests. The dimensions of these specimens are shown in Figure 10(a-c). Using 1.75 ± 0.02 mm diameter thermoplastic polymer colorFabb PLA filament
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(density: 1.210-1.430 gcm−3 , glass transition temperature: 55 ◦ C), all samples are fabricated with
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a Z-603S 3D desktop printer (Shenzhen JG Aurora Co., Ltd.). The samples are extruded from a 0.4 mm nozzle at a temperature of 205 ◦ C, and the building platform is heated to 55 ◦ C. One-third of the specimens are printed by the stress-based path, and the others are filled with the parallel path (±45◦ ) and the contour path, both generated by commercial slicing software (Cura). The thickness of all specimens is 1 mm, including 0.3 mm for the first layer and 0.1 mm for all other layers. The infill speed is set as 20 mm/s, the travel speed is set as 60 mm/s, and the printing 15
(E)
40mm
2.5mm
20mm
(d) r
10mm R 5mm d
45mm
R 10mm
20mm
(c)
R 15mm
90mm
(a)
!
R 10mm 35mm
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r
Figure 10: Dimensions: (a) specimen 1; (b) specimen 2; (c) specimen 3; (d) simplified model of tool-paths.
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speed of the first layer is reduced to half of these specifications.
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3.2. Tensile tests and fracture analysis
The tensile tests are implemented by stretching with an electromechanical universal machine
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(2 KN capacity, Shenzhen Sans Testing Machine Co., Ltd.). The loading rate is fixed at 0.5 mm/min by displacement control, and all the test results are the average of results from five
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replication experiments.
Meanwhile, DIC, which provides a full-field measurement of the displacement fields at the
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surface with black and white paints [33], is employed to observe the fracture process when
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the specimens are being tested. This technology has been widely adopted in studies of the stress field of components fabricated by AM due to its ability to capture images promptly and accurately [34, 35]. In this research, the failure of specimens is monitored by two CCD cameras, and the commercial VIC-2D system from Correlated Solutions is utilized for DIC. To demonstrate the failure mechanisms and patterns by different tool-paths from a microscopic perspective, SEM is used in this research to observe the fracture surfaces. SEM is a general type 16
of electron microscopy employed to achieve a high spatial resolution by generating a topological image of a sample using a beam of electrons. An FEI Quanta 450 FEG is employed to magnify the fracture surfaces 100 times.
3.3. Filling fraction calculation
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The path filling fraction is an index for printing precision. In this research, the tool-paths are simplified into the model as shown in Figure 10(d), where l0 is the length of the tool-path and d and r are the diameter (0.4 mm) and radius (0.2 mm) of the nozzle, respectively. The filling
S0 × 100% S
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w=
-p
fraction is expressed by
(5)
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wherein S 0 and S are the areas of the tool-paths and 2D geometries, respectively. The filling
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fraction is calculated by MATLAB.
17
4. Results and discussion 4.1. Mechanical properties and fracture process Table 2: Features of specimen 1 fabricated by different tool-paths.
(a)
(E)
(H)
Contour 439.35 1.95 0.74 2071.26
Stress-based 654.61 (+44.65%, +48.86%) 1.96 (0%, +0.51%) 0.74 (0%, 0%) 1938.71 (-7.03%, -6.40%)
(G)
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Parallel 452.56 1.96 0.74 2085.20
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Physical quantities Ultimate force (N) Measured mass (g) Filament length (m) Printing time (s)
(J)
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(I)
Figure 11: Directions of maximum principal stresses and three types of path filling forms (dotted lines represent cracks) and corresponding DIC images for specimen 1: (a) maximum principal stress orientations; path filling forms for (b) parallel path, (c) contour path, (d) stress-based path; displacement fields for (e) parallel path; (f) contour path;
(g) stress-based path.
18
The features of specimen 1 shown in Table 2 indicate that the stress-based path demonstrates a much higher load-carrying capacity and less time than the traditional algorithms. Figure 11(a-d) shows the maximum principal stress orientations in the model and the three types of path filling methods used for specimen 1. The displacement fields shown in Fig. 11(e-g) illustrate the different
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performances when the specimens sustain a vertical force. From Fig. 11, the anisotropy of the tool-paths influences the failure patterns. The cracks in Figs. 11(e) and (g) both start from the location of stress concentration. The cracks in the parallel path are not aligned with the maximum
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principal stress orientations because of the stress redistribution by the tool-path anisotropy. In Fig. 11(f), cracks occur in the region away from the location of stress concentration because of
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the air gap between adjacent filaments. For the stress-based path, cracks proceed in 0◦ and 90◦ zigzag patterns that consist of horizontals and verticals, as shown in Fig. 11(g). Consequently, the
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mechanical properties of the specimen printed by the stress-based path planning algorithm are
stress orientations.
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significantly improved because the path orientations are in alignment with the maximum principal
Table 3: Features of specimen 2 fabricated by different tool-paths.
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Physical quantities Parallel Ultimate force (N) 208.88 Measured mass (g) 2.77 Filament length (m) 1.05 Printing time (s) 2607.62
Contour 211.38 2.80 1.06 2608.64
19
Stress-based 288.18 (+37.96%, +36.33%) 2.85 (+2.89%, +1.79%) 1.08 (+2.86%, +1.89%) 2869.48 (+10.04%, +9.99%)
(a)
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(I)
(J)
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-p
(H)
(G)
(F)
(E)
Figure 12: Directions of maximum principal stresses and three types of path filling forms (dotted lines represent
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cracks) and corresponding DIC images for specimen 2: (a) maximum principal stress orientations; path filling forms for (b) parallel path, (c) contour path, (d) stress-based path; displacement fields for (e) parallel path, (f) contour path,
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(g) stress-based path.
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Similarly, the features of specimen 2 shown in Table 3 indicate that the stress-based path
yields a much higher load-carrying capacity but consumes slightly more material and time than the other paths. Figure 12(a-d) shows the maximum principal stress orientations in the model and the three types of path filling methods used for specimen 2. For the specimen in Fig. 12(e), the cracks at the bottom-left and top-right corners of the circle initiate simultaneously because of the 20
stress concentration. The cracks proceed horizontally. For the specimen printed by the contour path, the cracks initiate at the bottom-left corner and proceed transversely. This development is followed by cracks starting at the air gap in the bottom-right corner of the oblique rib, as shown in Fig. 12(f). On the other hand, the crack in the specimen printed by the stress-based path first
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occurs transversely at the bottom-right corner, after which the crack develops at the connection between adjacent tool-paths and proceeds vertically. Finally, the crack advances transversely to the inner circle, as shown in Fig. 12(g). The differences in the behaviors of cracks can be
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attributed to the stress redistribution by inherent anisotropy of the printing techniques. Because the area of damage in Fig. 12(g) is braced by the oblique rib and the tool-paths are parallel to the
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maximum principal stress orientations, the mechanical performance achieved by the proposed path is remarkably superior to those produced by the two traditional paths.
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As shown in Table 4, specimen 3 again indicates that the stress-based path exhibits a much higher load-carrying capacity but consumes slightly more material and time than the other paths.
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Figure 13(a-d) shows the maximum principal stress orientations in the model and the three types of path filling methods used for specimen 3. Specimens with different tool-paths have
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different displacement fields because of the redistribution of stress by anisotropy with regard
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to the tool-paths, as shown in Figure 13(e-g). Although the cracks in both Figs. 13(e) and (g) Table 4: Features of specimen 3 fabricated by different tool-paths.
Physical quantities Parallel Ultimate force (N) 381.86 Measured mass (g) 3.47 Filament length (m) 1.31 Printing time (s) 3279.41
Contour 282.27 3.44 1.30 3235.64
21
Stress-based 643.09 (+68.41%, +127.83%) 3.51 (+1.15%, +2.03%) 1.33 (+1.53%, +2.31%) 3326.44 (+1.42%, +2.81%)
(a)
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(I)
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(H)
(G)
(F)
(b)
Figure 13: Directions of the maximum principal stresses and three types of path filling forms (dotted lines represent cracks) and corresponding DIC images for specimen 3: (a) maximum principal stress orientations; path filling forms
(g) stress-based path.
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for (b) parallel path, (c) contour path, (d) stress-based path; displacement fields for (e) parallel path, (f) contour path,
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initiate from the geometrical imperfection to the right edge of the specimens, their shapes are
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different. The crack in Fig. 13(e) develops in a ±45◦ zigzag pattern because not only the external force but also the ±45◦ tool-paths dominate the fracture morphology. Conversely, the crack in Fig. 13(f) is generated at the central region because of the weak connection of the air gap between adjacent filaments, whereas in Fig. 13(g), the crack proceeds along a straight line. In this case, the stress-based path incurs the highest stretching capacity.
22
(E)
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(D)
1mm
(G)
1mm
1mm
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(F)
-p
1mm
Figure 14: Sketches for structures and corresponding SEM images of fracture surfaces: (a) parallel path; (b) parallel path; (c) contour path; (d) stress-based path.
23
4.2. Fracture surface analysis The fracture surfaces of the specimens observed by SEM during the tensile tests are shown in Figure 14. The surfaces of the fractures in the parallel path exhibit two types of failure modes. If the crack proceeds along a zigzag pattern, the filaments, whose surfaces are perpendicular to
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the path orientations, will fail exactly along the extrusion orientation, as shown in Fig. 14(a). However, in this case, half of the layers will crack at connections of the filaments, which negates the performance of the specimens because of the weak connections between tool-paths. In contrast,
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if the crack proceeds along a straight line, the filaments will generally fail near ±45◦ because of shear stresses and normal stresses, as shown in Fig. 14(b). The angles of the fracture surfaces in
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the contour path, which depend on the angles between the filaments and stresses, are difficult to ascertain, as shown in Fig. 14(c). Generally, a smaller angle creates a rougher fracture surface.
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As a result, the filaments are probably subjected to different shear forces when the stresses are not parallel to the tool-paths. There is only one type of failure in the stress-based path, as shown in
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Fig. 14(d). The fracture surfaces are perpendicular to the maximum principal stresses because the currently developed tool-paths produce a smaller shear force compared with traditional algorithms.
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Therefore, for the situation of large normal stresses, the stress-based path makes full use of the
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material properties to improve the mechanical performance of the models. Consequently, the specimen printed by the currently proposed path has the highest mechanical capacity.
4.3. Filling fraction Sketches for underfilled areas of the three types of path filling methods are given in Figure
15(a-c). From Fig. 15(a), the parallel path offsets the line segments in one direction equidistantly. 24
(a)
(b)
(c)
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(d)
Figure 15: Sketches for underfilled areas of three types of path filling forms (the dark green lines represent the
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trajectory of the tool-paths, the yellow lines represent the areas of the tool-paths, and the green and purple regions indicate underfilled areas) for (a) parallel path; (b) contour path; (c) stress-based path. (d) Histogram of the path
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filling fraction.
Therefore, the tool-paths can closely connect with each other. On the other hand, when the
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offset distance is not an integer multiple of the width of the tool-path, underfillings will be incurred (purple regions). The contour path aims to offset the original outlines to fill 2D layers. Consequently, the underfilled areas of this tool-path can be classified into two types. The first type of underfilled area (green regions in Fig. 15(b)) is produced in regions with sharp corners of two adjacent tool-paths [36]. The second type is similar to the underfilled areas in the parallel 25
path. If the width of the underfilled area is less than the width of the tool-path, the path will not be followed (purple regions in Fig. 15(b)). This type of underfilling usually appears at the offset centers. For the stress-based path, the tool-paths are generated by the connections with the center points of the hexagonal grids. In this case, the underfilled areas (green regions in Fig.
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15(c)) are generated at the joints of adjacent tool-paths because of unequal slopes. In addition, the deficiencies of the center points near the geometry boundary lead to underfillings (purple regions in Fig. 15(c)) near the boundaries. The corresponding histograms of the filling fraction
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with different path filling algorithms are shown in Figure 15(d). Generally, the specimens filled by the parallel path have the highest filling fraction. The specimens filled by the contour path
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have the lowest filling fraction due to the larger curvature of the tool-paths. The filling fraction of
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the stress-based path is between those of the above two path filling techniques.
5. Conclusions
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In this paper, a stress-based path planning algorithm in view of the maximum principal stresses is proposed to improve the mechanical properties of models fabricated by FFF. This algorithm
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generates tool-paths in alignment with the stress orientations by connecting hexagonal points
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based on the connection criterion and depth-first search (DFS) method. After a preliminary calculation, the tool-paths are optimized in two steps, namely, connecting adjacent tool-paths to eliminate breakpoints and introducing the Dijkstra algorithm to improve printing efficiency and quality. The calculation results for the example in Fig. 6(b) and the results of mechanical tests indicate that this algorithm can generate tool-paths to amend the intrinsic deficiencies of the current available printing techniques. 26
To validate the effectiveness of the proposed approach, specimens with three different morphologies of geometries are printed by different tool-paths and mechanically tested. Meanwhile, the DIC method is employed to observe the failure process as the specimens are stretched. The experimental results show that the stress-based path efficiently improves the mechanical perfor-
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mance of the printing specimen. The displacement fields and SEM images demonstrate that the specimens created with different paths generally exhibit different crack patterns because of the redistribution of stress by the inherent anisotropy of the tool-paths. Generally, the cracks of the
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specimens printed by the parallel path proceed along a ±45◦ zigzag pathway or straight lines, and the fracture surfaces indicate that the filaments crack along the extrusion orientations or at
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±45◦ angles. In addition to all the specimens failing at air gaps, the fractures of the specimens printed by the contour path fail at indefinite angles because the filaments in variable orientations
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experience different local shear stresses. For the currently proposed stress-based path, the cracks fail along 0◦ and 90◦ zigzag patterns or along straight lines. The fracture surfaces are generally
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perpendicular to the maximum principal stress orientations. The test results indicate that the stretching capacity is reduced if the filament experiences shear force. The improvement by the
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stress-based path shows that each filament does not sustain a large shear stress. In addition, the
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filling fractions of specimens by different path filling methods are calculated by a simplified model of the tool-path. Calculation results show that the currently proposed path satisfies the required printing precision of specimens. Although implementation of the proposed stress-based path improves the mechanical performance of the printing models, this methodology is still in a preliminary stage and requires further exploration. For instance, sharp corners will reduce the printing quality because the nozzle cannot 27
switch instantly and materials cannot be deposited firmly onto the heating plate. Moreover, this approach eliminates breakpoints. Consequently, a few points are visited repeatedly. Thus, more material than necessary is consumed, and the printing precision is compromised. These challenges will be a focus of future research. The novel methodology in this study improves the mechanical
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performance of the printing models by optimizing path orientations. The current proposed path planning method benefits stressed members for improving mechanical design.
6. Acknowledgments
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The paper is sponsored by National Natural Science Foundation of China (Grant No. 11802082
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and Grant No. 5187083454) and the Hebei Science and Technology Department (Grant No.
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18391203D).
7. References
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[1] M. Vishwas, C. Basavaraj, Studies on optimizing process parameters of fused deposition modelling technology for abs, Materials Today: Proceedings 4 (10) (2017) 10994–11003. https://doi.org/10.1016/j.matpr.2017.08.057.
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[2] D. M. Yu, C. J. Zhu, J. Su, D. Wang, Process analysis and application for rapid prototyping based on fused deposition modeling, in: G. Zhu (Ed.), Advanced Materials Research, Trans Tech Publ., Switzerland, 2011, pp.
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875–880. https://doi.org/10.4028/www.scientific.net/AMR.179-180.875. [3] Y. L. Hao, S. J. Li, R. Yang, Biomedical titanium alloys and their additive manufacturing, Rare Metals 35 (9) (2016) 661–671. https://doi.org/10.1007/s12598-016-0793-5.
[4] S. Lin, Y. M. Xie, Q. Li, X. Huang, Z. Zhang, G. Ma, S. Zhou, Shell buckling: from morphogenesis of soft matter to prospective applications, Bioinspiration & biomimetics 13 (5) (2018) 051001. https://doi.org/10.1088/17483190/aacdd1.
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[5] T. Rayna, L. Striukova, From rapid prototyping to home fabrication: How 3d printing is changing business model innovation, Technological Forecasting and Social Change 102 (2016) 214–224. https://doi.org/10.1016/j.techfore.2015.07.023. [6] S. Lin, Y. M. Xie, Q. Li, X. Huang, S. Zhou, On the shape transformation of cone scales, Soft Matter 12 (48) (2016) 9797–9802. https://doi.org/10.1039/C6SM01805J.
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[7] S. H. Huang, P. Liu, A. Mokasdar, L. Hou, Additive manufacturing and its societal impact: a literature review, The International Journal of Advanced Manufacturing Technology 67 (5-8) (2013) 1191–1203. https://doi.org/10.1007/s00170-012-4558-5.
[8] M. Vaezi, C. K. Chua, Effects of layer thickness and binder saturation level parameters on 3d print-
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ing process, The International Journal of Advanced Manufacturing Technology 53 (1-4) (2011) 275–284. https://doi.org/10.1007/s00170-010-2821-1.
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[9] J. Zhang, X. Z. Wang, W. W. Yu, Y. H. Deng, Numerical investigation of the influence of process conditions on the temperature variation in fused deposition modeling, Materials & Design 130 (2017) 59–68.
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https://doi.org/10.1016/j.matdes.2017.05.040.
[10] B. Tymrak, M. Kreiger, J. M. Pearce, Mechanical properties of components fabricated with open-
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source 3-d printers under realistic environmental conditions, Materials & Design 58 (2014) 242–246. https://doi.org/10.1016/j.matdes.2014.02.038. [11] J. Go, A. J. Hart, Fast desktop-scale extrusion additive manufacturing, Additive Manufacturing 18 (2017)
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276–284. https://doi.org/10.1016/j.addma.2017.10.016. [12] N. S. A. Bakar, M. R. Alkahari, H. Boejang, Analysis on fused deposition modelling performance, Journal of
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Zhejiang University-Science A 11 (12) (2010) 972–977. https://doi.org/10.1631/jzus.A1001365.
[13] F. Ren, Y. Sun, D. Guo, Combined reparameterization-based spiral toolpath generation for five-axis sculptured surface machining, The International Journal of Advanced Manufacturing Technology 40 (7-8) (2009) 760–768. https://doi.org/10.1007/s00170-008-1385-9.
[14] S. Shaikh, N. Kumar, P. K. Jain, P. Tandon, Hilbert curve based toolpath for fdm process, in: D. K. Mandal, C. S. Syan (Eds.), CAD/CAM, Robotics and Factories of the Future, Springer, New Delhi, 2016, pp. 751–759.
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