Der Artikel untersucht die Herausforderungen bei der Pulverschmelzung von Metallen mit Laserstrahl (PBF-LB / M), wie Porosität, Risse und Restspannungen. Es wird die Strategie der Random Polygon Partitioning (RPP) eingeführt, die die Vektororientierung innerhalb der Voronoi-Zellen variiert, um interne Spannungen zu minimieren und eine gleichmäßige Wärmeverteilung sicherzustellen. Die RPP-Strategie wird mit traditionellen Streifen- und Schachbrettverteilungsmethoden verglichen und hebt ihre überlegene Leistung in Bezug auf Oberflächenrauheit, relative Dichte und Maßhaltigkeit hervor. Die Studie diskutiert auch die Implementierung benutzerdefinierter Partitionsstrategien unter Verwendung von Open Vector Format (OVF) und EOS CLI-Workflows und zeigt die Durchführbarkeit der Integration fortschrittlicher Scanstrategien in industrielle PBF-LB / M-Prozesse auf. Die Ergebnisse zeigen, dass RPP eine vielversprechende Lösung zur Verbesserung der Qualität und Präzision gefertigter Bauteile bietet und damit einen wertvollen Beitrag im Bereich der additiven Fertigung leistet.
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Abstract
Powder Bed Fusion of Metals with Laser Beam (PBF-LB/M) is an additive manufacturing technology that creates parts layer by layer from metal powder. The scanning strategy, which defines the geometrical arrangement of laser scan vectors, influences the part quality. In this contribution, based on the literature, we identified efficiently assessable geometrical properties of scanning strategies as requirements for a high part quality, i.e. low porosity, high dimensional accuracy and low surface roughness. We used these requirements to assess stripes as a representative state-of-the-art linear strategy and chessboard as a representative state-of-the-art island partitioning strategy. We found that island and chessboard strategies do not fully fulfill the identified requirements. Thus, we introduced a novel strategy for the geometric arrangement of scan vectors, called Random Polygon Partition (RPP), which fulfills the identified requirements better than the strategies discussed in the literature. To test the performance of RPP, we printed test specimens and compared the achieved porosity, dimensional accuracy, and surface roughness with specimens created with stripes and chessboard. The results demonstrate the usability of RPP in creating high-quality test specimens. However, further comparative studies on RPP and state-of-the-art scanning strategies using more challenging geometries and alloys prone to cracking, porosity, and more are needed to assess the full potential of the new scanning strategy.
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1 Introduction
Additive manufacturing technologies have become prominent methods for producing complex metal components, particularly Powder Bed Fusion of Metals with Laser Beam (PBF-LB/M) [1, 2]. These technologies enable the creation of intricate geometries and high material utilization. However, the PBF-LB/M process involves rapid heating and cooling cycles that lead to variable metallurgical conditions during solidification, fostering defects such as porosity [3, 4], cracking [5, 6], loss of alloying elements [7], and residual stresses [7, 8].
Adjusting process parameters to specific materials and geometries is crucial for ensuring the component quality [9‐11]. Scanning strategies significantly influence the heat flow, solidification conditions, and residual stress distribution [12, 13]. Systematic adaptation of these strategies can result in fine-grained microstructures and minimized residual stresses [14], enhancing the mechanical properties and manufacturing efficiency by reducing laser movement [15, 16].
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Partition strategies are a subset of scan strategies that segment each layer into distinct partitions filled with vectors aligned at a specific hatch distance. Commonly used scan strategies include linear approaches like stripes and island approaches like the chessboard pattern [17, 18]. Linear strategies provide a predictable heat distribution along the feed direction, minimizing porosity through fixed vector lengths [19, 20]. Conversely, island strategies reduce component stresses by varying vector directions. Still, they are critical due to increased overlapping regions (OR), which can repeat unfavorably across layers, leading to crack formation or reduced component density [21]. Stripes partitioning utilizes one-dimensional and chessboard partitioning two-dimensional patterns clipped according to part contours.
This contribution presents an alternative scanning strategy that combines the strengths of the stripes and chessboard partition to enhance the quality and productivity of the manufactured components. The proposed “Random Polygon Partition” (RPP) strategy, based on Voronoi cells, aims to address the challenges of traditional methods. The RPP strategy varies vector orientations within Voronoi cells to minimize internal stresses and ensure a uniform heat distribution, offering a promising solution for improving additive manufacturing quality.
2 Criteria for Partition Strategies
Based on existing literature, we aim to define the conditions for an effective partitioning strategy and evaluate how well the proposed strategies meet these requirements. For comparison, we use the stripes method as a representative example of linear strategies and chessboard partitioning as an example of island strategies.
Vector Length Consistency:
The vector length determines the laser’s return time, affecting the heat accumulation between melt tracks. Shorter vectors cause a rapid heat buildup, while longer vectors can lead to a significant cooling. The latter can lead to an increased internal stress [22]. A reduced size in island scan strategies can increase the porosity due to overheating or inadequate overlap [23, 24]. Therefore, an adequate and consistent vector length is critical. Stripes are rated high for vector length consistency (at least in rather simple parts, e.g. cubic parts) because short vectors are confined to contour areas. In contrast, the chessboard strategy exhibits a low rating as small vectors also occur within the partitions due to its two-dimensional division and rotation of vectors in consecutive layers.
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Overlapping Region (OR):
The overlap of fusion tracks is critical for the quality and integrity of the final component. A high energy input in ORs increases pore formation [21]. Consequently, a low OR area ratio indicates reduced porosity levels. Both an insufficient and excessive overlap can result in bonding defects or cracking. The stripes strategy receives a low rating for OR due to its one-dimensional partitioning, which minimizes intersections between adjacent partitions. In contrast, the chessboard strategy is rated highly because its two-dimensional partitioning results in higher overlap regions.
Pattern Repetition:
Pattern repetition refers to the frequency with which a specific scanning pattern repeats itself across consecutive layers during the PBF-LB/M process. A high pattern repetition can lead to the alignment of overlapping regions (OR) in successive layers, which may worsen defects such as porosity and cracking due to repeated thermal cycling and localized stress accumulation. Stripes inherently have a low pattern repetition due to their single-directional alignment and incremental rotation between layers, resulting in predictable heat distribution [19, 20]. In contrast, chessboard partitioning exhibits higher pattern repetition because of its fixed two-dimensional grid layout, increasing the risk of defect formation from repetitive heating and cooling cycles [25, 26].
Orientation Diversity:
Orientation diversity is the variation in vector orientations within a layer. A higher orientation diversity reduces residual stress and associated component warping by distributing thermal stresses more evenly [27, 28]. Stripes provide a predictable heat distribution but may lack a sufficient orientation diversity to mitigate internal stresses effectively [19]. In contrast, chessboard partitioning offers a higher orientation diversity due to its two-dimensional grid layout, which helps manage internal stress distributions more effectively [25, 26]. However, increased overlapping regions (OR) can offset these benefits.
Scan Sequence:
The scan sequence, i.e. the order in which the laser traces the geometric pattern, significantly impacts temperature distribution, residual stresses, and distortions in PBF-LB/M [17, 22, 29]. Effective scan sequences include variations to optimize heat management and minimize defects. With stripes, the scan sequence involves tracing lines in a single direction with incremental rotations between layers, providing predictable heat distribution but potentially insufficient stress mitigation for complex geometries [19]. Chessboard partitioning employs more complex sequences where different islands are scanned in varying orders. This variability helps distribute thermal loads evenly, reducing residual stresses and distortions [25, 26]. However, if not managed properly, it can lead to uneven cooling rates and potential defects at overlapping regions (OR).
3 Materials and Methods
3.1 Feedstock Material
The gas-atomized IN718 powder with a grain size fraction of 15–45 µm (Oerlikon Metco Europe GmbH) was utilized. The powder was cold-embedded in epoxy resin, metallographically prepared, and analyzed using a VHX-6000 light optical microscope (LOM, Keyence). Cross-sectional images confirmed almost no detectable pores within the particles, achieving a relative density of 99.92%. The scanning electron micrograph (SEM) indicates that the powder particles have a spherical surface and barely any satellites are present Fig. 1b.
Fig. 1
a Cross-section of IN718 imaged using VHX-6000; b scanning electron micrograph of IN718
PBF-LB/M produced samples using an EOS M290 (EOS GmbH, Krailling, Germany). The system is equipped with an actively cooled OT camera pco.edge 5.5 (Excelitas Technology GmbH, Wiesbaden, Germany) is mounted off-axis outside the process chamber and controlled via an in-house interface.
The camera has a resolution of 5.5 megapixels (2560 px × 2160 px) and records near-infrared signals with wavelengths from 875 to 925 nm.
The parameter study was based on reference parameters from the EOS database. Table 1 shows the most important process parameters. Downskin and upskin parameters were not considered in this study to quantify and qualify the individual influence of the scanning strategy on component quality. Three samples were produced for each parameter set to determine relative density, surface roughness, and dimensional accuracy.
TABLE 1
Process parameters used for the sample production by PBF-LB/M
Laser power (W)
Laser speed (mm/s)
Overlap
(µm)
Vector length (mm)
Contour offset (µm)
Layer thickness (µm)
Angle increment
(°)
Hatch infill
285
960
120
10
–
40
67
Contour
138
390
120
–
12
40
67
Contour
80
800
120
–
0
40
67
3.3 Sample Geometry
A sample part with a ground section measuring 30 × 30 mm was designed to ensure an adequate partitioning with a vector length of 10 mm (Fig. 2a). This area transitions into an overhang at an angle of 35°, allowing us to evaluate the impact of different partitioning strategies on component quality under conditions of impaired heat dissipation.
Fig. 2
a Schematic illustration of the sample part for the quality evaluation, showing the segments 1 and 2 and the cutting planes for evaluation; b the downskin surface area used for the surface roughness measurement; c schematic geometry of the deformation measurement for the dimensional accuracy evaluation
The specimens were metallographically prepared and imaged using the VHX-6000 light microscope. It was divided into two segments for microstructure evaluation in both the xy-plane and xz-plane using a QCUT 250 cutting machine (ATM Qness GmbH, Mammelzen, Germany) (Fig. 2b). The measurements were carried out with three samples for each process parameter set.
3.5 Determination of Surface Roughness
Surface roughness measurements were conducted according to DIN EN ISO 4287 specifications using LOM images presented as a three-dimensional panorama at a magnification of 200x—the examined downskin surface measured 10 mm in width and 20 mm in length. Figure 2b shows that five lines were evenly distributed over the downskin surface. These lines were then converted into a 3D panorama using Keyence software, and a roughness profile was extracted. The average roughness value (Ra) and maximum roughness value (Rz) were calculated from the average of five areas, and they can be adjusted using the cut-off filter to attenuate the short-wave and long-wave profile components. Therefore, the LambdaC value for the long wave profile components was set to 3, while the LambdaS value for the short wave profile component was set to zero. The measurements were carried out with three samples for each process parameter set.
3.6 Dimensional Accuracy
The dimensional accuracy of the components was examined by measuring the superelevation of the tip of the overhang. This deviation from the nominal geometry indicates how much each part has been distorted due to internal stresses during printing. A parallel line was drawn to the part surface for the measurement, and the distance to the highest point in the tip area was measured, as shown in the illustration in Fig. 2c. The measurements were carried out with three samples for each process parameter set.
3.7 Managing Custom Partition Strategies with OVF and EOS CLI Workflow
Custom partition strategies were designed and exported using the Open Vector Format (OVF)1, an open-source format based on Google Protocol Buffers [30, 31]. OVF facilitates the export of vector data, supports custom parameter assignment, and allows for the inclusion of additional metadata.
Due to the lack of a suitable interface on EOS machines, a workaround was implemented using an open-source CLI adapter available on GitHub2 to convert OVF data into a format compatible with CLI. This conversion process required a careful management of several details. Specifically, while EOS represents contour data as polylines, OVF data is initially in a polygon format, necessitating the conversion to polylines. Furthermore, hatch data is stored at a lower resolution (INT16) than contour data (INT32), which can be configured via the CLI adapter by adjusting the BinaryWriteStyle of the hatch data.
Contour and infill data require separate parameter sets and must be packaged into distinct CLI files, since CLI does not support mixed parameter assignments. Three CLI files were generated per part in our setup: two for contour data—each with different parameters—and one for infill data. These CLI files were imported into EOS Studio, and appropriate materials and parameter sets were assigned. Contour data used standard parameter sets, while infill hatch data required support parameters to prevent data loss.
Hatch data was categorized into in-skin, down-skin, and up-skin types. Due to limitations in the CLI representation reducing the effectiveness of these distinctions, down-skin and up-skin strategies were excluded. The CLI processes vectors sequentially; hence, vectors intended for both In-Skin and down-skin are split and stored separately. Consequently, In-Skin hatches are processed before down-skin hatches. All hatches were uniformly treated as In-Skin hatches to mitigate this issue.
3.8 Partition Strategy Implementation
This study investigates three primary partition strategies: Stripes, chessboard, and Random Polygon Partitioning (RPP).
Stripe Partitioning:
This method divides the layer into one-dimensional partitions based on a specified vector length. Each partition was aligned with an alignment vector that rotates by 67° for each subsequent layer, as illustrated by the red line in Fig. 3a. Within each partition, vectors were aligned according to their hatch distance of 110 µm. The overlapping regions (OR) were created by offsetting these partitions by the overlap value of 120 µm and are illustrated by the yellow lines in Fig. 3.
Fig. 3
shows a schematic representation of the partitioning strategies. The contour of the component is outlined in red, while the partitions are outlined in blue. a shows the stripes partitioning, b the chessboard partitioning and c the RPP. The vectors inside the partitions illustrate the hatch orientation
Chessboard partitioning divides the structure into two dimensions, creating overlapping areas in both x and y directions. This method utilizes a specific pattern, such as squares, laid out and clipped according to the part contours (see Fig. 3b). The pattern’s origin remained consistent throughout the entire build height, leading to repetitive ORs at the same positions across layers. The rotation of the single partition was incrementally increased by 67°.
Random Polygon Partitioning (RPP):
Developed as an alternative island partition strategy, RPP creates overlapping areas similar to chessboard partitioning but introduces less repetition along layers due to its random generation approach. The RPP strategy was created by generating random points within a given contour while ensuring a minimum distance between points equal to the vector length (10 mm). To form rounded shapes of a uniform size along the layers, a special form of Voronoi tessellation is used, the centroidal Voronoi tessellation [32]. Centroidal Voronoi are polygons in which the points used for generation are also the corresponding centroids. Figure 3c illustrates this. This results in an island strategy with more variation than chessboard patterns, since randomness ensures no repeated pattern across layers.
4 Results and Discusson
To determine the performance of the newly designed RPP scan strategy compared to established stripes and chessboard strategies, PBF-LB/M sample parts and their surface roughness in the downskin area of the overlap, relative density and dimensional accuracy were determined by optical microscopy. The results are shown in Table 2.
TABLE 2
Results of the evaluation of surface roughness, relative density, and dimensional accuracy were gathered. The values given are the average values of three samples
Stripes partition
Chessboard partition
RPP
Mean
Deviation
Mean
Deviation
Mean
Deviation
Surface roughness—Ra (µm)
67
2
72
1
60
3
Surface roughness—Rz (µm)
337
15
352
7
306
18
Relative density—XY (%)
99.98
0.01
99.82
0.03
99.93
0.03
Relative density—XZ (%)
99.98
0.01
99.88
0.03
99.95
0.01
Dimensional accuracy (µm)
151
3
170
3
145
2
Surface Roughness:
The RPP strategy achieved the smoothest finish, outperforming both stripes and chessboard strategies. This observation is consistent with findings by Yang et al. [33] and Mohanty and Hattel [34], suggesting that smaller subdivisions lead to less local deformation, better densification, and higher surface roughness due to balling effects within individual partitions. Additionally, chessboard strategies may suffer from heat peaks at the corners of partitions due to shorter vectors, leading to an increased roughness along the partition boundaries. Red circles in Fig. 4a indicate these heat peaks. This issue is less pronounced in linear strategies and even less so in RPP, contributing to the improved surface roughness observed with these methods.
Fig. 4
a max-stack image taken with an OT camera during the PBF-LB/M process of a specimen printed in chessboard partition strategy. b light microscopy image of a sample produced with a chessboard scan strategy
The stripes strategy exhibited the highest relative densities in the XY and XZ planes, closely followed by RPP, with chessboard strategies showing lower densities. The microscope images in Fig. 4b reveal increased pores at overlapping regions (ORs) in chessboard partitions, as mentioned by Peng et al. [21]. Some porosities are also found within individual partitions’ inner areas. They are fewer and smaller.
Dimensional Accuracy:
For the dimensional accuracy, RPP is considered the best, followed closely by stripes and finally by the chessboard. Island strategies like chessboard induce less internal stress due to varied vector orientations [27, 28] and scan sequences [17, 22, 29]. Our measurements show that RPP outperforms chessboard in dimensional accuracy, likely due to its variable cell structures across layers and more stable vector lengths. Short vectors from different patches lying next to each other can create heat peaks in chessboard partitioning, leading to varying internal stresses and diversities in surface roughness [22].
For monitoring, the OVF gathers the average vector length and the OR for each partition for each layer. The results are plotted in a box plot in Fig. 5. RPP achieves a closer approximation to the specified vector length of 10 mm than the stripes or chessboard strategy, with a similar variance to stripes partitioning. In addition, the stripes strategy shows more extreme outliers in vector length. The chessboard strategy performs worst in absolute average vector length and variance.
Fig. 5
Average vector length is shown as a box plot over all layers on the left side (a) and the Overlapping Regions (OR) on the right side (b)
The stripes strategy exhibits the lowest OR values due to its one-dimensional partitioning, which minimizes intersections between adjacent partitions. When comparing the two island strategies, chessboard and RPP, their median OR values are nearly identical. This is because evenly distributing RPP polygons across a layer results in a similar number of partitions as chessboard partitioning, leading to comparable OR ratios. However, RPP demonstrates a significantly lower OR variance than the chessboard strategy through its more circular chase, so the surface area to circumference ratio decreases.
4.1 Requirements
In summary, the following requirements given in Table 3 were met. RPP achieved the same ranking as island strategies like a chessboard but also achieved additional requirements like vector length consistency and overlapping region.
TABLE 3
Qualitative evaluation of partition strategies based on the requirements
Partition Strategies
Description
Defect Case
Stripes
Chessboard
RPP
Vector Length Consistency
Consistency in the length of vectors
Residual Stress,
Pores
High
Low
High
Overlapping Region (OR)
The ratio of overlapping areas to the total layer area
Pores
Low
High
High
Pattern Repetition
Repetition of the pattern along the layers
Pores
Low
High
Low
Orientation Diversity
Greater diversity in vector orientations within a layer
Pores, Residual Stress
Low
High
High
Scan Sequence
The order of scanning
Residual Stress
Low
High
High
5 Conclusion and Outlook
The scan strategy is crucial in determining the quality of the manufactured parts using PBF-LB/M. Traditionally, two main strategies have been prominent: stripes and chessboard. Island strategies like chessboard effectively manage internal stresses, thereby reducing distortion. Conversely, stripes offer a better consistency in vector length and variance in overlapping regions (OR) across layers. Each strategy presents distinct benefits and drawbacks that influence overall part quality.
In this study, we introduced an innovative island strategy called Random Polygon Partitioning (RPP), which integrates the strengths of both the chessboard and stripes strategies. Utilizing the open-source Open Vector Format (OVF) and modifications for CLI export, custom partition strategies were developed and tested on an EOS M290 machine by manufacturing basic sample geometries. This comparison serves as a proof of concept, demonstrating the feasibility of implementing and evaluating these three strategies.
Our evaluation focused on surface roughness, relative density, dimensional accuracy, and adherence to set requirements. The results showed that the RPP strategy outperformed other methods in several key areas. These findings underscore the importance of selecting appropriate partitioning strategies based on specific manufacturing requirements. The RPP strategy shows a considerable promise by combining the advantages from both island and linear approaches to enhance part quality and precision while minimizing defect risks such as porosity and cracking through optimized heat distribution and stress management across layers.
Future research should thoroughly refine these partitioning strategies by investigating their impacts across different materials and geometries. It is essential to examine observed surface roughness, porosity, and dimensional accuracy trends, along with factors contributing to these outcomes. An especially interesting point that will be investigated in further studies is the possible reduction in crack formation with the newly introduced RPP scan strategy by reducing the repetition of overlap regions in consecutive layers.
Acknowledgements
This research is funded by the Digital Photonic Production DPP Research Campus as part of the “Research Campus Public-Private Partnership for Innovation” research funding initiative of the German Federal Ministry of Education and Research (BMBF). As part of the German government’s high-tech strategy, the BMBF is using this initiative to promote strategic and long-term cooperation between science and industry “under one roof”.
Funding
Funding number: 13N15423.
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