Traditional path planning methods, such as contour and raster methods, suffer from problems like uneven filling, overfilling, and underfilling in the sliced layers, resulting in poor continuity of the lattice melt pool, internal porosity defects, and severe powder adhesion at the contour edges, while research on path planning for three-periodic minimal surfaces lattices is relatively limited. In this study, a scanning path planning method based on lattice equations control is proposed, which differs from traditional contour paths and raster paths. The new paths are controlled by the isosurface parameters of the lattice equation and optimized using the traveling salesman problem, resulting in more uniform scanning paths. The new paths avoid the underfilling issue present in raster path and the sawtooth-shaped borders of raster path. Additionally, they circumvent the nonuniform scanning path problem caused by uneven wall thickness in contour path. Through visualizing the paths and conducting printing experiments on the lattice, it is found that the new path is more uniform compared to contour paths, effectively addressing the issue of overfilling. Compared to raster paths, the new path has smoother boundaries and reduces internal porosity and powder adhesion within the lattice. This research has important value in reducing internal porosity and external powder adhesion issues in three-period minimal surface (TPMS) lattice printing processes, further enhancing the manufacturing quality of TPMS lattices.

Various lattice structures exist in nature at different scales (microscopic, mesoscopic, and macroscopic), such as butterfly wings and beetle exoskeletons.1,2 Lattice structures have been widely explored and applied in various fields, including aerospace components and biomedical implants.3 Among these lattice structures, three-period minimal surfaces (TPMSs) have garnered increasing research attention due to their smooth surfaces, highly interconnected porous structures, and mathematically controllable geometric properties. TPMS, a periodic implicit surface with zero mean curvature, exhibits two significant advantages. First, its entire structure can be precisely represented using mathematical functions, such as pore ratio or volume-to-surface area ratio. Second, its surface is exceptionally smooth, lacking sharp boundaries and nodes typical in other lattice structures, thereby demonstrating excellent mechanical performance. Leveraging these advantages, TPMS showcases promising applications in mechanical, thermal, biological, chemical, acoustic, and optical fields. Laser Powder Bed Fusion (LPBF) exhibits significant potential in manufacturing intricate free-form structures and demonstrates considerable promise in producing lattice structures with fine features at high resolutions. Yan et al.4 discussed the feasibility of manufacturing TPMS using LPBF technology and 316L stainless steel powder. Experimental results demonstrated that LPBF can produce defect-free units of 2–8 mm without the need for additional support structures, but many partially melted metal particles are bonded to strut surfaces. The new path proposed in this paper can reduce powder adhesion as well as the porosity within the lattice.

Currently, the processing of TPMS lattices typically involves contour path and raster path. Contour path generate infill paths by inwardly offsetting the cross-sectional contour at each layer by a certain distance. This method, as the scanning paths are parallel to the contour boundary, achieves higher surface forming accuracy for components with uniform wall thickness. However, for parts with uneven wall thickness or complex cavities, the scanning process may encounter complex situations such as loop self-intersection, islands, and loop intersection, making it challenging to achieve complete and uniform infill in certain regions. Raster path primarily fill polygonal regions with parallel scanning lines aligned with the coordinate axes. The advantage of this method lies in its simplicity, ease of control, and high adaptability. However, due to the singularity of the scanning strategy, it can result in serrated boundaries, leading to powder adhesion issues and lower boundary accuracy. However, current manufacturing of TPMS lattices commonly encounters issues such as powder adherence and dimensional errors. Ma et al.5 compared the CT images of LPBF-manufactured TPMS lattices with the design models and found that the lattice pore sizes were consistently smaller than the design requirements, with more voids and powder adherence observed in regions with long and narrow features. Mahmoud et al.6 employed three different scanning strategies to print TPMS lattices with gradient porosity and observed that the scanning strategy in LPBF significantly influenced the accuracy of the TPMS lattice. The key factors for improving lattice dimensional accuracy included appropriate melt pool size and fill spacing. They also discovered that using contour path during printing led to failures due to path overlap issues. Yavari et al.7 manufactured TPMS implants using titanium powder and optimized the biased laser path to avoid contour overlap. However, further research is still required to enhance TPMS lattice dimensional accuracy and reduce powder adherence on the lattice surface.

In the LPBF processing, during the laser scanning of metal powder, there exists a thermal influence zone around the melt pool. This zone causes the metal powder around the melt pool to be incompletely melted or in a sintered state, leading to powder adhesion. Researchers posit that, under stable melt pool conditions, a relatively high laser energy input will result in increased powder adhesion. Wang et al.8 suggest that in the overhanging regions, the energy absorbed when laser irradiates the powder support area is much greater than when it irradiates the solid support area, leading to an enlarged melt pool and increased powder adhesion. Carter et al.9 processing Ti-6Al-4V using powder bed fusion, found that lower energy input reduces surface particle adhesion, thereby lowering overall surface roughness. Therefore, it can be observed that improving the uniformity of scanning paths can, to some extent, ensure a more uniform energy input to the melt pool, avoiding powder adhesion caused by excessively high local energy.

In order to mitigate issues, such as lattice powder adhesion and dimensional errors, and address the uneven infill problem within TPMS lattices, including overfilling and underfilling, this study proposes a scan path generation method based on TPMS implicit functions. The method aims to generate uniform scan paths, particularly addressing the “long and narrow” regions within TPMS. Through experimental validation and microscopic imaging, smoother and more accurate boundaries are achieved compared to raster path and contour path, leading to a reduction in powder adhesion and internal porosity.

This paper is organized as follows: first, in Sec. II, we introduced the novelty of TPMS lattice generation and the new path generation method, the detailed description of the implementation process of the new path is provided in Sec. III. Then, in Sec. IV, a case study of printing experiments using the P lattice is presented and compared it with commonly used contour offset and raster paths to validate the improvement of the new path in filling the internal regions of the lattice. Finally, in Sec. V, concluded the paper by summarizing the findings and discussing future research directions.

Before manufacturing TPMS lattices, it is essential to model the TPMS lattice. TPMS is a type of implicit surface, and the entire geometry can be fully represented by the algebraic equation f (x, y, z) = C, where C is a constant representing an isosurface. Due to the fact that the TPMS can be accurately represented by mathematical functions, its fundamental properties such as porosity, volume-to-surface ratio, and wall thickness can be directly controlled by adjusting functional parameters.10 It should be noted that TPMS is a surface without thickness, and it can be used to construct equidistant porous structures by offsetting the TPMS surface or by enclosing two isosurfaces (named C1 and C2) with different C values to form a porous structure. However, offsetting lattice surfaces can be computationally complex and may result in intersecting or erroneous lattice surfaces. Therefore, using different isosurfaces to enclose the lattice is a more effective approach.

Subsequently, we need to obtain the path files required for printing TPMS lattices. Different isosurface constants C can generate different lattice surfaces, which provide us with inspiration. In this paper, a novel scan path construction design method is proposed to generate scan paths based on the TPMS lattice equation, aiming to achieve uniform filling of TPMS lattices, as shown in Fig. 1. First, based on the TPMS lattice equation, the inner and outer isosurfaces of the lattice (C1 and C2) can be obtained. By inputting the user-provided layer height data and slicing the lattice, contour data for the inner and outer boundaries of each layer of the lattice can be obtained. Detecting the minimum wall thickness of the lattice, combined with user-inputted infill spacing, to determine the offset value C and then obtaining improved paths. At this stage, the paths for each layer, which need further detection and optimization, have been obtained. Next, the paths to be processed are checked, and when the distance between adjacent paths is significantly greater than the set fill spacing, the paths are disconnected, leaving only the paths with distances less than the fill spacing. For the part where the path spacing is significantly greater than the set fill spacing, contour offsetting is performed, and the interior is filled with raster paths. Simultaneously, the interrupted paths are optimized and connected using a traveling salesman problem (TSP) solver, and redundant paths are removed based on the solved connection points. Finally, all the paths are output as executable CLI files, and a common P lattice is printed. Experimental results show that the new scan paths can more uniformly fill the lattice and effectively reduce powder adherence on the lattice surface.

FIG. 1.

The algorithm flowchart for the improved path generation.

FIG. 1.

The algorithm flowchart for the improved path generation.

Close modal

Sections III AIII D will provide a detailed introduction to the generation, path detection, and path optimization of TPMS lattice scanning paths, using the P lattice as an example. Subsequently, compare the new path with contour offset and raster path and analyze the differences in the filling effect.

Taking the widely studied P lattice as an example, the initial equation (C = 0) representing its surface porous structure can be expressed as follows:11 
ϕ P ( x , y , z ) = cos 2 π x L 1 + cos 2 π y L 2 + cos 2 π z L 3 = C ,
(1)
where C is the equation value that controls the position of the isosurface and L1, L2, and L3 represent the lengths of individual unit cells in the x, y, and z directions. TPMS lattices are typically defined as the enclosed effective volume between two isosurfaces (C1 and C2, where C1 > C2); therefore, TPMS lattices can be represented as C2 < f (x, y, z) < C1.

To construct the regions of the lattice surface, it can be voxelized or discretized, dividing it into many hexahedral cubes. Extracting arbitrary isosurfaces from defined 3D data fields using the Marching Cubes algorithm is an effective and reliable method.12 For TPMS structures, existing voxelization or discretization methods can be used to divide them into multiple hexahedral cubes. The vertices of each hexahedral cube can reside inside or outside the TPMS surface. By performing interpolation calculations, the isosurfaces of TPMS structures can be obtained and saved as stereo lithography (STL) models, as shown in Fig. 2.

FIG. 2.

TPMS lattice determined by the isosurfaces C1 and C2.

FIG. 2.

TPMS lattice determined by the isosurfaces C1 and C2.

Close modal

Due to the periodic nature of TPMS lattices, the lattice exhibits symmetry. Research has shown that in the Z axis direction of the lattice, the symmetric regions can be roughly divided into three different slicing profiles, as shown in Fig. 3. In the subsequent text, these regions will be collectively referred to as the scanning region.

FIG. 3.

Scanning line design of P lattice at different layer heights: (a) upper layer, (b) transition layer, and (c) middle layer.

FIG. 3.

Scanning line design of P lattice at different layer heights: (a) upper layer, (b) transition layer, and (c) middle layer.

Close modal

Generation of scanning paths is one of the key steps in the process of transforming a CAD model into an AM product. In TPMS lattices, most of the sliced regions exhibit a “long and narrow” morphology. Scanning paths used in commercial software, such as raster path and contour path, may not adequately fill these regions, leading to issues of “underfilling” or “overfilling.”13 

It should be noted that, unlike traditional TPMS lattice printing path settings, the proposed path generation method in this study is based on the constant generation of isosurfaces from the lattice equation. Due to the periodic nature of the lattice equation, the lattice thickness formed by the offset of the isosurfaces is not uniform. Although the lattice equation can control the size of the lattice unit and the trend of wall thickness variation, it is difficult to directly obtain the minimum wall thickness of the lattice in a specific slice layer from the lattice equation. To generate uniform scanning paths, it is necessary to determine the minimum wall thickness of the lattice within the slice layer.

Figure 4 illustrates the steps of implementing this method. First, input the lattice contours and determine their containment relationships. If a containment relationship exists, match them pairwise; if there is no containment relationship, divide them into two groups for matching based on their X coordinates. Then, record the distance between a point on one contour and another point on the other contour and record the minimum distance along with its corresponding point coordinates. Finally, traverse all points on the curve and output the point coordinates with the minimum value of lmin.

FIG. 4.

Algorithm for determining the minimum wall thickness of lattice slices.

FIG. 4.

Algorithm for determining the minimum wall thickness of lattice slices.

Close modal
Once the minimum wall thickness of the slice layer is obtained, the offset value of the lattice isosurface C can be calculated based on the set scanning line distance and the minimum wall thickness. The equation is shown as follows:
C = [ ( C 1 C 2 ) × N ] / l min ,
(2)
C n = C 2 + n C .
(3)

In Eq. (3), C′ represents the offset value of the lattice isosurface during the generation of scanning lines. C1 and C2 are the isosurface parameters that determine the inner and outer contours of the lattice, with C1 > C2. N represents the set scanning line spacing. In Eq. (4), n represents the parameter of the isosurface corresponding to the nth scanning line. By using the above formulas, the lattice scanning lines can be obtained as shown in Fig. 5. By observing the results in the graph, it can be observed that some areas of the scanning paths generated directly from the lattice equation have large scanning gaps, which require further optimization. Therefore, in Secs. III C and III D, we provide detailed instructions on how to detect areas that need to be optimized and the methods for optimizing paths.

FIG. 5.

No detection optimization, only scan paths generated by the lattice equation: (a) upper layer, (b) transition layer (there are areas that need to be optimized), and (c) middle layer.

FIG. 5.

No detection optimization, only scan paths generated by the lattice equation: (a) upper layer, (b) transition layer (there are areas that need to be optimized), and (c) middle layer.

Close modal

During the aforementioned generation of TPMS lattice scan lines using the offset paths based on the isosurface, it was observed that there are regions within the slicing plane where the spacing between scan lines undergoes significant variations. This phenomenon is caused by the periodic nature of the TPMS lattice equation, and these regions are typically associated with extreme values of the TPMS lattice equation, often occurring in the regions where lattice cells are connected. These regions usually exhibit complex shapes and are relatively large in size. Therefore, it is necessary to identify and replan the paths for these regions.

To identify all potential areas that require optimization, this paper proposes an algorithm for detecting regions where the distance between adjacent contours exceeds the tolerated filling gap. The algorithm takes two adjacent scan lines as input and calculates the distance between a point on one scan line and the point with the same X-coordinate on the other scan line. This distance is divided by a constant C as a substitute for the shortest distance between the two points on the corresponding scan lines. When the shortest distance exceeds 1.5 times the scan line spacing N, the coordinates of the point and the previous point are recorded as a pair of truncation points. Then, the lattice contour is divided into two regions at the truncation points. Finally, by traversing all adjacent scan lines, the entire slice plane is divided into complete scan line regions and regions to be optimized. The algorithm’s workflow is illustrated in Fig. 6.

FIG. 6.

Algorithm for detecting the areas that require optimization.

FIG. 6.

Algorithm for detecting the areas that require optimization.

Close modal

For the regions to be optimized, their contour lines are often complex and exhibit concave polygon shapes. When using contour path for filling, the accuracy of the contour may decrease due to the offset of concave polygons. In contrast, raster path typically yields better results for filling such areas. Therefore, a raster path is selected for filling these regions. Ultimately, the global path connections on the slicing plane are optimized. The TSP algorithm is employed to establish connections between the truncation points and eliminate the original scan line segments that exist between them. This further enhances the cohesiveness and efficiency of the path. The flowchart of the optimization algorithm is shown in Fig. 7. The scanning and optimization process of the lattice is illustrated in Fig. 8.

FIG. 7.

Optimization algorithm.

FIG. 7.

Optimization algorithm.

Close modal
FIG. 8.

Lattice path detection and scan line optimization. (a) Path directly generated from lattice equations, (b) the paths in the nonconforming areas are removed, (c) the contours in the nonconforming areas are offset, (d) the offset areas are filled using a raster path, (e) the TSP algorithm is used for global optimization of the paths, and (f) local zoom-in of the optimized paths after optimization.

FIG. 8.

Lattice path detection and scan line optimization. (a) Path directly generated from lattice equations, (b) the paths in the nonconforming areas are removed, (c) the contours in the nonconforming areas are offset, (d) the offset areas are filled using a raster path, (e) the TSP algorithm is used for global optimization of the paths, and (f) local zoom-in of the optimized paths after optimization.

Close modal

Due to the symmetry of the P lattice, lattice slice layers typically have three types of contour shape. In order to facilitate the study of the scanning paths of the overall lattice, this study will employ three different scanning strategies corresponding to these three contour shapes for the purpose of comparing and analyzing the paths.

By comparing the three paths, this study observed the following situations. In the contour path, significant uneven offsetting of the fill lines occurs at the axis of the filling area [as shown in Figs. 9(a)11(a)]. This unevenness is particularly pronounced in areas with large contour curvature, mainly due to the differences between the contours on either side of the offset. The presence of these uneven regions results in excessive filling in the interior of the TPMS lattice’s filling area and insufficient filling in adjacent external regions, especially in long and narrow regions of the TPMS lattice.

FIG. 9.

Scanning path diagrams for the 104th layer. (a) Contour path (scan lines close), (b) raster path (scan lines missing), and (c) improved path (more uniform).

FIG. 9.

Scanning path diagrams for the 104th layer. (a) Contour path (scan lines close), (b) raster path (scan lines missing), and (c) improved path (more uniform).

Close modal
FIG. 10.

Scanning path diagrams for the 79th layer. (a) Contour path (scan lines too close), raster path (scan lines missing), and (c) improved path (more uniform).

FIG. 10.

Scanning path diagrams for the 79th layer. (a) Contour path (scan lines too close), raster path (scan lines missing), and (c) improved path (more uniform).

Close modal
FIG. 11.

Scanning path diagrams for the 72nd layer. (a) Contour path (scan lines too close), raster path (scan lines missing), and (c) improved path (more uniform).

FIG. 11.

Scanning path diagrams for the 72nd layer. (a) Contour path (scan lines too close), raster path (scan lines missing), and (c) improved path (more uniform).

Close modal

As for the raster path, the angle variation of the fill lines has a significant impact on the filling effect. From Figs. 9(b)11(b), it can be observed that when the angle between the fill lines and the contour edge is small, underfilling occurs, and in severe cases, the fill lines may be missing, resulting in print model failure.

In contrast, the improved path, by utilizing numerically offset inner and outer contour scanning lines, achieves a uniform distribution of fill lines in long and narrow regions [as shown in Figs. 9(c)11(c)]. This eliminates the uneven regions seen in the contour path and the issue of missing fill lines in the raster path, thereby improving the print quality of TPMS lattices.

This section presents a case study of TPMS lattice design and manufacturing. It demonstrates the improvement in print quality of TPMS lattice structures by comparing the newly proposed digital paths with traditional contour path and raster paths.

The parameters of the lattice in this study are set as L1, L2, and L3 equal to π, C1 equals 0.18, and C2 equals −0.18. Therefore, the designed lattice size is 3.144 mm. The generated lattice model is shown in Fig. 12.

FIG. 12.

Designed lattice parameters.

FIG. 12.

Designed lattice parameters.

Close modal

The experiment was conducted using 316L gas atomized powder with a particle size range of 10–40 μm. The improved Han’s Laser M100 machine equipped with a 500 W IPG fiber laser and a beam diameter of 25 μm was used to print the designed structures. Based on the experience of printing with 316L, the printing parameters were set as shown in Table I.

TABLE I.

Print parameter settings.

Laser powerScanning speedHatch spacingLayer thickness
75 W 600 mm/s 60 μ30 μ
Laser powerScanning speedHatch spacingLayer thickness
75 W 600 mm/s 60 μ30 μ

For the designed lattice structure, three different scanning paths were employed: raster path, contour path, and improved path. Schematic diagrams of each scanning path are presented as shown in Fig. 13. In the raster path, the first layer utilized a scanning line angle of 67°, and the second layer was rotated by 67° relative to the first layer. This helps reduce residual stress in the part under high thermal stress, ensuring that the part can expand or contract freely.14 In the contour path, the inner and outer contours of the lattice are offset along the normal direction until the entire area is fully covered. In this scanning path, the laser moves from the inner contour to the outer contour, and there is no rotation between consecutive layers. As for the improved path, the raster path used for the optimization region also employed a layer rotation method of 67°.

FIG. 13.

The three types of scanning path diagrams: (a) contour path, (b) raster path, and (c) improved path.

FIG. 13.

The three types of scanning path diagrams: (a) contour path, (b) raster path, and (c) improved path.

Close modal

To evaluate the effectiveness of the improved path compared to the grid and contour paths in actual printing, the lattice was printed at three different layers using these three paths. The analysis focused on the improvement of the print quality of the lattice by comparing the print quality in the “long and narrow” region.

Comparing the printed paths at different layers, it can be observed that for the contour path, there is a noticeable “overfilling” phenomenon in the “long and narrow” region. When the distance between two scan lines is too close, there is a discontinuity in the molten pool in the overlapping area. This may be caused by local high temperatures leading to unstable molten pools. This phenomenon exists in all three scan regions of the lattice [as shown in Figs. 14(a)16(a)]. At the same time, excessively high local temperatures can also lead to a decrease in surface quality in the overhanging regions.15 In summary, this is detrimental to the contour accuracy of the lattice.

FIG. 14.

Top appearance of three scanning paths for the upper layer (104th layer) contour. (a) Contour path, (b) raster path, and (c) improved path.

FIG. 14.

Top appearance of three scanning paths for the upper layer (104th layer) contour. (a) Contour path, (b) raster path, and (c) improved path.

Close modal
FIG. 15.

Top appearance of three scanning paths for transition layer (79th layer) contour. (a) Contour path, (b) raster path, and (c) improved path.

FIG. 15.

Top appearance of three scanning paths for transition layer (79th layer) contour. (a) Contour path, (b) raster path, and (c) improved path.

Close modal
FIG. 16.

Top appearance of three scanning paths for the middle layer (72nd layer) contour. (a) Contour path, (b) raster path, and (c) improved path.

FIG. 16.

Top appearance of three scanning paths for the middle layer (72nd layer) contour. (a) Contour path, (b) raster path, and (c) improved path.

Close modal

For the raster path, the variation in the angle of the infill lines has a significant impact on the infilling effect. As shown in the figure, when the angle between the infill line and the contour edge is small, “underfilling” occurs [as shown in Figs. 14(b)16(b)]. Due to the absence of infill lines, it often leads to the discontinuity of the molten pool and, in severe cases, even results in failed printing of the model. Additionally, due to the width of the infill lines, the contour accuracy of the grid infill path is usually poor, and there may be instances of powder entrapment and surface adhesion between adjacent contours.16 

In contrast, the improved path is obtained by offsetting the contours inside and outside the “long and narrow” region using scan lines, and the infill lines are still evenly distributed. In comparison to the raster path, the improved paths exhibit no missing fill lines, resulting in a more continuous melt pool. The improved path contours are continuous, avoiding the serrated boundaries observed in raster path. This enhances the contour accuracy of the improved paths relative to raster path. Compared to contour path, the improved paths address the issue of uneven scan paths caused by nonuniform wall thickness. With uniform energy input along the entire path during laser energy deposition, the improved paths achieve greater melt pool continuity, as illustrated in Figs. 14(c)16(c). This enhances both the contour accuracy and melt pool continuity of TPMS lattices. This avoids the occurrence of nonuniform regions at the axis of the inner and outer contours in the contour path and avoids the issue of missing infill lines in the raster path [as shown in Figs. 14(c)16(c)], thereby improving the contour accuracy and molten pool continuity of the TPMS lattice.

This study employed three different paths (contour path, raster path, and improved path) to print TPMS lattices and conducted microscopic cross-sectional observations of the “long and narrow” regions in different layers of the lattice (top layer, transition layer, and middle layer), as shown in Fig. 17.

FIG. 17.

Close-up microstructure diagrams of the three scanning paths at different slicing layers. (a) Contour path (upper layer), (b) raster path (upper layer), and (c) improved path (upper layer). (d) Contour path (transition layer), (e) raster path (transition layer), and (f) improved path (transition layer). (g) Contour path (middle layer), (h) raster path (middle layer), and (i) improved path (middle layer).

FIG. 17.

Close-up microstructure diagrams of the three scanning paths at different slicing layers. (a) Contour path (upper layer), (b) raster path (upper layer), and (c) improved path (upper layer). (d) Contour path (transition layer), (e) raster path (transition layer), and (f) improved path (transition layer). (g) Contour path (middle layer), (h) raster path (middle layer), and (i) improved path (middle layer).

Close modal

From the microscopic cross-sectional observations, it can be observed that the lattice contours printed using the contour path exhibit relatively poor smoothness. There are significant metal adhesions at certain edges of the lattice, and there are large voids within the lattice. In some areas, there are noticeable variations in the wall thickness, as shown in Figs. 17(a), 17(d), and 17(g). This is somewhat related to the defects observed in single-layer printing using the contour path in Sec. V A. This may be attributed to the instability of the molten pool caused by variations in the path spacing in the contour path.

The raster path shows a higher quantity of small voids, and there is some adhesion of metal powder at the lattice edges. Compared to the contour path, the lattice contours printed using the raster path exhibit relatively better smoothness. However, there are still noticeable uneven wall thicknesses in the cross-sectional area, as shown in Figs. 17(b), 17(e), and 17(h). The slightly improved results of the raster path can be attributed to the utilization of layer rotation and alternating paths that better fill the printing area. The occurrence of defects may be due to partial path absence in this area,17 which is somewhat related to the printing defects of the raster path discussed in Sec. V A.

On the other hand, although there are also a small number of voids in the improved path, their quantity and size are relatively low. The improved path demonstrates better smoothness of the lattice edge contours, indicating improved uniformity. This is consistent with the results shown in Sec. V A depicting single-layer displays. Additionally, as observed in Figs. 17(c), 17(f), and 17(i), there is a relative reduction in powder adhesion along the lattice contours. This is primarily attributed to the improved paths avoiding the serrated boundaries present in raster path, thereby mitigating powder entrapment issues caused by serrated boundaries. Moreover, compared to contour path, the improved paths exhibit a more uniform scanning trajectory, resulting in a more consistent energy input. Consequently, under stable melt pool conditions, this reduces powder adhesion and pore formation.

To address the issue of uneven filling in TPMS lattices, including overfilling and underfilling, as well as poor molten pool continuity, internal voids, and significant powder adhesion at contour edges, this study proposes a scan path generation method based on TPMS implicit equations to generate uniform scan paths, particularly for the long and narrow regions in TPMS.

Taking the commonly used P lattice as an example, this study prints three representative slices of the P lattice: the top layer, the transition layer, and the middle layer. The effects of the contour path, raster path, and the proposed improved path on molten pool continuity and existing defects were compared. The results indicate that the contour path exhibits overfilling in the long and narrow regions, and when the scan paths are too close, it can lead to discontinuities in the molten pool and the occurrence of defects. On the other hand, the raster path exhibits underfilling in the long and narrow regions, and the absence of scan lines can also lead to discontinuities in the molten pool and defects. In comparison, the improved path achieves more uniform filling and maintains the continuity of the molten pool.

Furthermore, microscopic observations of the lattice morphology in the three layers were conducted. The observations reveal that the contour path exhibits poor smoothness at the contour edges, significant metal adhesion, uneven wall thickness, and large voids within the lattice. These issues are mainly caused by the uneven filling resulting from the contour path. The raster path improves contour edge smoothness and has fewer voids, primarily due to layer rotation. However, the raster path still exhibits uneven wall thickness and metal powder adhesion, which are mainly related to underfilling caused by the absence of some paths in the raster path. In contrast, the improved path exhibits fewer voids, smoother edges, and relatively uniform wall thickness. This demonstrates that the improved path has a positive effect on enhancing the printing quality of TPMS lattices.

The proposed improved path in this paper has certain reference value in enhancing the printing quality of TPMS lattices, which is of great significance for improving the application of powder bed printing for TPMS lattices.

This work was supported by the Key R&D Program of Guangxi Province (Grant No. GKAB23026101), the National Key R&D Program of China (Grant No. 2021YFE0203500), and the Special Fund for Local Scientific and Technological Development guided by the Central Government (Grant No. GKZY21195029)

The authors have no conflicts to disclose.

Huiliang Tang: Conceptualization; Methodology; Software; Writing–original draft & experiment. Jiangzhao Zhang: Writing – review & editing. Chu Wang: Writing – review & editing. Yu Long: Supervision; Funding acquisition.

Huiliang Tang: Conceptualization (lead); Methodology (lead); Software (lead); Writing – original draft (lead). Jiangzhao Zhang: Writing – review & editing (equal). Chu Wang: Writing – review & editing (equal). Yu Long: Funding acquisition (lead); Supervision (lead).

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