Evaluation of productivity in laser sintering by measure and assessment of geometrical complexity

AM

= Additive manufacturing;

CAD

= Computer-aided design;

CLI

= Common-layer interface;

DLP

= Digital light processing;

FFF

= Fused filament fabrication;

HSS

= High-speed sintering;

KPI

= Key performance indicator;

LS

= Laser sintering;

MEX-TRB

= Material extrusion – thermal reaction bonding;

MJF

= Multi jet fusion;

PBF-IrL

= Powder bed fusion – infrared light;

PBF-LB

= Powder bed fusion – laser based;

PR

= Packing ratio;

STL

= Standard tessellation language; and

VPP-UVM

= Vat photopolymerization – ultraviolet light, mask.

Compared to traditional manufacturing technologies, one of the main advantages of additive manufacturing (AM) is often described as freedom of design and its associated unrestricted complexity. Manufacturing efforts and costs are often considered mainly independent of part complexity in this regard (Klahn et al., 2014; Adam, 2015; Conner et al., 2014). Thus, the concept of “complexity for free” usually refers to traditional cost drivers, e.g. for tooling and customization (Gibson et al., 2021; Klahn et al., 2014). Theoretically, “complexity for free” leverages economic production, allowing for enhanced resource efficiency throughout the whole product life cycle (e.g. by reducing part volume and energy consumption) (Gibson et al., 2021; Wohlers Associates, 2022). Due to significantly higher costs of AM processes (e.g. expenses for production equipment, materials and quality assurance), the introduction of complexity must be compensated for by the resulting complexity-induced features of the parts. However, in research and practice, “complexity for free” is no longer shared beyond the generation process. Increased efforts may arise in the design and post-processing stage due to dependencies on traditional manufacturing processes, which are used in the post processing of additively manufactured parts (Wohlers Associates, 2022; Gebhardt et al., 2019). In addition, the seven AM process categories according to ASTM52900 (ISO/ASTM International, 2021) and sub-processes differ in performance, cost and resulting part quality (Gibson et al., 2021). Regarding productivity, they vary significantly through the processing method and their sensitivity to complex structures, as explained in the following.

Previous studies have already addressed the evaluation and comparison of complexity, especially when the use of additive versus conventional processes is worthwhile, as described in Conner et al. (2014) and Almaghariz et al. (2016). Furthermore, other studies indicate that complexity has a significant impact on the generation time of point-to-point based processes such as the MEX-TRB/P, i.e. fused filament fabrication (FFF), as shown in Pradel et al. (2017), Ben Amor et al. (2022b), as well as for the PBF-LB/P process, i.e. laser sintering (LS) of polymers, in Ruffo et al. (2006a), Häfele et al. (2023). Because the most widely used processes are affected, monitoring complexity is crucial for economic production and competitiveness in the AM industry. The geometry-related influence is important to improve existing processes without changing the hardware. Especially when competitiveness can only be guaranteed with corresponding productivity and costs. This article therefore presents a method for measuring and assessing the influence of geometric complexity on AM processes using the example of LS.

First, an overview of different AM processes is given to clarify the interactions between geometric complexity and the respective processing tool. In the following, the interactions between LS and part geometry are presented. Complexity is then defined in the context of this study and potential evaluation methods are analyzed to compare their applicability with the previously presented effects.

Although AM processes are all based on a layer-by-layer principle, there are differences concerning feedstock material (e.g. powder, liquid, filament) and processing tools (e.g. laser, jetting head) (Gibson et al., 2021; Wohlers Associates, 2022). Processing is based on defined slice layer data, including machine-specific tool paths and part cross-sections. Part geometry mainly affects time per layer in point-to-point-based processes like FFF or LS (Gebhardt, 2016; Pradel et al., 2017; Häfele et al., 2023). By contrast, layer time is constant for line-based processes, e.g. PBF-IrL (multi-jet fusion (MJF) and high-speed sintering (HSS), as well as mask-based VPP-UVM processes, e.g. digital light processing (DLP), as they are independent of complexity (Gibson et al., 2021; Pradel et al., 2018).

The literature provides various complexity classifications in AM, such as shape, material, hierarchical and functional complexity. These were systematically described in Gibson et al. (2021) and Kumke (2018). However, the assessment of complexity relies on multiple domains. Those involve geometric features, e.g. part size and quantity (Kushnarenko, 2009; Valentan et al., 2008), processing characteristics like point-to-point-, line- or mask-based tools and material characteristics.

This contribution aims toward shape complexity and its implications on the additive build-up and process productivity. Technological complexity (Kushnarenko, 2009) is included, and machine-specific indications are evaluated based on the definition of Häfele et al. (2023).

Geometric complexity or shape complexity is defined by the number, shape and frequency of necessary elements to describe a component, and that interacts directly with the AM process. The level of influence on the manufacturing process, including productivity and quality, can be determined in the form of process-specific key indicators.

In the category of powder bed fusion (PBF), LS was the first commercialized AM process (Gibson et al., 2021) and is still one of the most widely established (Wohlers Associates, 2022). Due to the powder-based production, parts can be built without support structures throughout the entire build envelope. At the same time, the laser only melts those areas that are specified according to the layer data. After a powder layer has been applied and heated, the laser beam is coupled to the powder surface and is moved by galvanometers to fuse the material according to predefined scan lines (Gibson et al., 2021). The resulting amount of part volume in relation to enclosed material or build envelope is expressed as part packing density or packing ratio. This ratio could be specified in multiple ways because part volume can be related to different build envelope sizes. Depending on the method, part volume may be related to the occupied build chamber (proportional height) or the maximum build envelope (Baumers and Holweg, 2019). To make accurate comparisons, it is essential to specify the reference value. In this contribution, the packing ratio relates to the occupied build chamber and respective part height, as described in the following Figure 1.

Because the packing ratio represents the volume to be melted, it directly influences layer time, which is subject to certain restrictions and resulting cooling times (Ruffo et al., 2006b; Kumke, 2018). These results, e.g. from the narrow sintering window, in crystallization, curling and stresses that occur when a specific time per layer is exceeded (Schmid, 2023). The packing ratio is on average 10% (Baumers and Holweg, 2019; Schmid, 2023), so the rest is unused material that could be partly reused depending on the material and quality demands.

Considering the packing ratio and size of the build envelope, initial information on the productivity of the LS process can be provided. For this purpose, the build-up rate is often used to compare different machines, processes and materials. It represents productivity, e.g. via progress in the z-direction per hour (mm/h), the produced part volume per hour (cm³/h) or the powder volume applied per hour (cm³/h). The latter changes in some cases due to different manufacturers’ reference values. This means the considered build envelope varies, e.g. due to no-build zones and edge distances. For reasons of transparency, a corresponding reference to the assumed size is necessary. When comparing productivity within a plant system, the build-up rate in millimeters per hour (mm/h) is a reliable indicator unaffected by the build-up area. However, for cross-system comparisons, the volume of parts produced per hour (cm³/h) becomes the suitable comparative measure. This assessment is based on the time taken for the entire generation process, including recoating, powder application and melting.

As described for point-to-point-based processes, part geometry must be considered for these characteristic values. In this respect, important geometrical influencing factors are the following:

• Part volume is directly linked to the respective scan cross-section and raw material used (Gibson et al., 2021; Ruffo et al., 2006b).

• Build height, layer height and maximum part dimensions in the z-direction define the number of layers applied.

• Cross-section fragmentation determines the amount and size of melting areas, and as a result, the length and number of scan lines, as well as required position changes (see Figure 2).

Especially for fragmented cross-sections, the necessary movements to guide the laser from one surface to another along travel paths require time to accelerate and decelerate the scan mirrors and to switch the laser on and off (Kaddar, 2010; Ghanekar et al., 2003). If different modes for contour and fill areas are used, the exposure time is influenced even further, as described in Ruffo et al. (2006a). The cross-section distribution is influenced by the geometry of the part and its orientation in the build envelope (Ghanekar et al., 2003).

The latter affects the mechanical and optical part properties and the heat distribution in the build envelope (Wegner et al., 2015; Blattmeier, 2012). Therefore, optimizing the cross-sectional area regarding the time required for processing always demands particular attention.

After slicing the parts, machine-specific processing paths are defined in accordance with manufacturing parameters (see Figure 2). Here, typical geometry-related interactions with the LS machine are:

• Scan lines as a result of beam diameter, hatch distance, scan count and corresponding compensation factors applied to the geometry. Especially hatch distance and scan count significantly impact the number of hatches and resulting position changes.

• Contour and fill mode are used to meet different requirements according to optical and mechanical part properties, e.g. higher tensile strength and smoother surface (Kaddar, 2010; Wegner, 2015). Exemplarily, contour mode is used with reduced laser power and scan speed, which requires more time to scan depending on contour length and fragmentation (Ruffo et al., 2006a).

As shown in previous studies, the impact of geometry varies, depending on the share of time for scanning compared to recoating for individual machines (Häfele et al., 2023).

Assessment of complexity in AM has been studied extensively in the literature. Applications in this area often involve comparing parts and assessing their suitability for additive and traditional manufacturing processes by defining key performance indicators (KPIs). These are based on, e.g. 3D part information from CAD and STL models as well as 2D slices of parts. Different methods are used to correlate KPIs and manufacturing process data. Few approaches use experimental build times. Instead, various methods are used to estimate or calculate build time and costs. Other methods have no explicit connection to build time because they rely on estimations provided by experts. However, because these methods are often based on models with fixed build-up rates and other constants, they are of limited use in evaluating impacts on productivity. Therefore, real manufacturing process data is used to achieve the best possible results in the following.

A widely adopted method presented in Joshi and Ravi (2010) uses different indicators to measure part complexity for traditional casting parts and respective manufacturing costs. This method has been used and partly modified by a wide range of researchers in AM, especially to compare AM and casting processes (Merkt et al., 2012; Conner et al., 2014; Almaghariz et al., 2016; Gullapalli, 2016; Martof et al., 2018). Specific approaches are used to compare 3D KPIs with manufacturing time (Pradel et al., 2017; George and Chowdary, 2020) or estimated time and cost (Fera et al., 2018; Hartogh and Vietor, 2018). Key attributes include part volume, surface area, bounding box volume and number of facets. For example, a few methods use 3D-based complexity KPIs for the comparison with expert opinions (Valentan et al., 2008; Greco et al., 2023). While 3D part information mainly addresses shape complexity, its validity is limited when considering pre-processing and build-up operations, especially of point-to-point-based AM processes. This is because orienting and nesting parts in the build envelope has no impact on the part volume or surface area information and vice versa. Therefore, there is a need for more appropriate metrics to be used in these cases.

Evaluation methods for 2D slice information use, e.g. the number of perimeters, contour length or cross-section, as described in Martof et al. (2018) for 3D-sand printing and in Garashchenko (2018). 2D slice information suits those needs much better, as it is directly coupled with the build process and respective process parameters, e.g. hatch distance. The resulting area is changed by rotation, translational shift or altered processing strategies and determines contour and hatch length, number of hatches and layer count. Methods using 3D and 2D data are evaluated for FFF correlating complexity to build time in Pradel et al. (2018), and comparing it with estimated costs in Ben Amor et al. (2022a).

Approaches focusing on LS of polymers are exclusively presented in Ruffo et al. (2006a) and Häfele et al. (2023). However, those contributions do not cover the aspect of productivity in LS in its entirety. In Ruffo et al. (2006a), a linear increase of recoating time with increasing height and the effects of part volume on the scanning process are described. However, it is highlighted that both values cannot describe the contour scanning process, which requires more time the longer and more fragmented the contour is. To consider the geometric influence when estimating the scanning time, various correction factors are tested, such as the ratio of the parts volume to its bounding box volume. Another method is given in Häfele et al. (2023), who demonstrated the impact of complexity on build time. Specimens with constant height and volume were used. The scanning area was fragmented to change the perimeter length and increase complexity. For two different LS machines, a strong correlation was found between an increase in contour length and the number of hatches with an increasing generation time. Table 1 provides a concluding summary of the different methods, attributes and ratios for assessing and quantifying complexity. It also shows whether changes to the impact variables (1) result in changes to the attributes (2) and ratios (3).

For example, the rotation of a part around the x- or y-axis does not affect the part volume but does affect the resulting scanning area. In contrast, changing the process parameters (e.g. compensation factors) can change the volume. An evaluation is made in advance to determine which effects can be detected with the respective KPIs.

In addition, three new ratios (4) based on Ruffo et al. (2006a) and Häfele et al. (2023) are introduced to cover as many process changes as possible. For this purpose, the contour length and the number of hatches are related to the respective part volume. Furthermore, the contour length is set in relation to the length of the hatches. This hypothesis is verified for validity in the subsequent experiments.

All test specimens and components are manufactured using the Farsoon HT403P machine. The machine is equipped with a 100 W CO₂ laser and a usable build envelope of 375 × 375 × 450 mm³ (x,y,z), which is used to calculate the packing ratio. The scanning speed for contour and hatch is fixed, while the remaining process parameters can be adjusted as desired (see Table 2).

Therefore, parameters such as laser power, hatch distance, scan count as well as bed and chamber temperatures are tailored to the material in use. For this study, thermoplastic polyurethane powder (BASF Ultrasint® TPU 88A) is used. Build preparation is performed using the manufacturer’s software BuildStar^TM.

The experiment relies on three groups of specimens shown in Figure 3, which are manufactured on the LS machine measuring build time and resulting build-up rate. According to the state of the art, packing ratios are set between 5 and 15% depending on the group of specimens.

The first group (Parts 1–12) includes three sets of simple cubes (40 mm edge length and 28 cm³ volume) manufactured in three different orientations and with a constant packing ratio. Starting from the original orientation (Parts 1–4), one set is rotated by 45° around the z-axis (Parts 5–8). The third set is rotated by 90° around the x-axis (Parts 9–12). Part volume is kept constant while increasing complexity by introducing pockets and thus fragmenting the melting area. Consequently, the hatch length changes according to the individual setup. Those parts serve two different purposes. First, the constant volume ensures a controlled evaluation setting for the build-up rate, which is then only affected by the geometry-induced scanning paths. Second, the reduction of hatch length that occurs due to fragmentation is comparable to real-world settings in which parts are more often thin walled than bulky. In practice, this is more descriptive for geometries that may be relevant for production.

The second group (Parts 13–22) includes two different sizes of the Sierpinski Carpet (SC, 112 mm (Parts 13–17) and 250 mm edge length (Parts 18–22)), each comprising five intricacy levels. This allows the study of miniaturization effects for geometrically similar parts. As a standardized fractal, the SC is suited for this experiment because it enables a decrease in part volume and packing ratio while increasing shape complexity with rising intricacy. Due to process restrictions and expected build errors caused by, e.g. curling or insufficient powder application, the large specimens are only a quarter section, resulting in a 125 mm edge length in the printable configuration. The SC is more of an academic example than an industry-leading use-case. For practical applications, the SC is an adequate representative of fragile lattice structures due to its ever-decreasing feature sizes.

The third group (Parts 23–34) comprises several production parts chosen from industrial applications to validate the approach using Groups 1 and 2. The parts show different sizes, volumes and complexities. The parts are analyzed according to their actual build orientation, which gives a brief insight into how the complexity indicators serve in the assessment of impacts for certain build situations. Parts 26 and 27, e.g. furtherly show the impact of scaling, which might occur in real-world applications due to manufacturing constraints or resizable variants.

To give at least a brief overview, a schematic illustration of different parts, their respective orientation and quantity in the build envelope is shown at the bottom in Figure 3. Further, in Table 3, the number of units printed and resulting packing ratios are listed.

Data acquisition relies on three domains: 3D part data from STL files, 2D slice information according to common-layer interface (CLI) files, and manufacturing times per layer obtained from video monitoring. To realize the latter, the build process is recorded at 60 frames per second. The time per parts of a whole part layer is then determined as the timespan between the first and the last layer of each part. 3D part information, such as part volume and surface area, is obtained from STL files. 2D part information like contours and hatches are derived from CLI files. Those are machine-readable, allowing for direct and proxy calculations. A Python^TM script is used to extract the bounding box volume, number and lengths of contours and hatches. The packing ratio is the total part volume over the occupied build chamber volume. The packing ratio of each part is displayed in Table 3. Further, the build-up rate is calculated as the quotient of the latter and the corresponding build time.

The various complexity ratios are first compared to make them easier to understand. A detailed analysis of the individual parts and groups is provided, using the normalized hatches vs volume ratio as an example.

Table 4 lists different complexity ratios for their respective coefficient of determination (R²) in relation to the build-up rate. LS-specific ratios are displayed in Figure 4. Here, enormous differences arise, particularly noticeable between the established KPIs and those proposed in this study.

The literature on LS presents part volume and respective scanning areas as significant drivers of build time. Contrary to these assumptions, the experiment shows no significance when different levels of complexity are applied to the machine-parameter combination. Experiments with a constant volume (as indicated by the red markings in Figures 4–1) show high dependencies on build-up rate and slice area fragmentation rather than on the parts’ cross-section area or volume. As a result, ratios like part volume over bounding box show that their ability to describe the process is severely limited, as they do not capture process-specific details (Figures 4–1). Further, methods that estimate costs and build time based on a constant build-up rate are unsuitable for the LS process. In contrast, a strong correlation between complexity and the resulting build-up rate is evident for all newly defined ratios (Figures 4–2 to 4–4). A significantly differing value distribution on the x-axis can be observed.

Considering solely 3D information does not provide sufficient information about the productivity of the LS generation process, as effects on 2D slice processing are not recognized. Only by considering the layer data, it is possible to make a significant assessment of the interactions between part geometry and LS process. The length and number of contours already serve as indicators for the fragmentation of the layer data and the resulting exposure effort.

In contrast to previous work, the experiments systematically changed part complexity, and the resulting production time was measured. The number and variation of parts contribute to a differentiated view and statistical validation.

As shown in Figure 5, the build-up rate decreases with increasing complexity, especially for a constant packing ratio, but also significantly for reduced packing ratios. For the cubes with a constant packing ratio of 12.40%, the build-up rate for the highest complexity decreases by up to 74.37%. The duration per layer increases from 17.86 s to 70.4 s.

For the Sierpinski Carpet (large, Parts 18–22), the build-up rate for Level 4 (Part 21) was reduced by 43% compared to level one despite a volume reduction of approximately 37%. The small version achieves a 63% reduction in build-up rate despite the lower volume (−44.5%). The inclusion of different sizes is reasonable to cover the whole spectrum of complexity. Compared to the previously defined complexity metrics, the SC provides a good representation of the interactions between complexity and build-up rates. However, more than the resulting sampling points are needed to predict the expected build-up rates. Further attempts are required to provide additional support points for a more uniform distribution along the complexity scale and to improve prediction quality.

As indicated by the application examples, the complexity at any packing ratio (even below 10% based on part nesting) may lead to enormous productivity losses, as shown in Figure 5. Considering the packing ratio used, this circumstance becomes even more significant because the average values of 10% should be achieved and increased in terms of economy. Furthermore, no double exposure was used for the selected parameter combination, which would cause even stronger decreases in the build-up rate.

This study successfully demonstrated a method to describe, measure and evaluate the complexity for LS processes. In contrast to previous methods, production time was determined experimentally, so only measurement data and no assumptions about influencing factors were included in the evaluation. Considering key indicators adapted to the point-by-point-based processing of LS, strong correlations to the resulting build-time could be identified. The presented key indicators for the length and number of contours and hatches achieve high descriptive quality. The parts presented for evaluation have shown that they can represent the complexity over a broad range.

Compared to the specimens with constant part volume, the increase in complexity has a strong negative effect on the build-up rate. It was also shown that part size plays a significant role, but further investigations must be made on their relationship with the hatch length. A manufacturer-specific quantification of the build-up rate concerning the packing ratio, thus, gives significantly better results if a geometry relationship is established. In other words, neglecting the geometry can result in enormous deviations that negatively impact competitiveness.

The Sierpinski Carpet in various stages and sizes has already shown that it can fundamentally map the course of the build-up rate as a function of packing ratio and complexity. An overview of the geometry sensitivity can be generated for the selected material and the corresponding processing parameters. In the sense of a standardized metric, further developments must be made based on the findings to address a more homogeneous complexity distribution. In this context, it is necessary to check at which layer duration the process stability decreases depending on the material used, thus limiting the packing ratio for a certain complexity. Additionally, these metrics should be tested for suitability for other point-based processes, such as FFF.

Regarding productivity, the following potential applications are identified:

First, a comparison of different material-parameter combinations can be carried out by evaluating the individual build-up rates. Depending on the material in use, processing parameters must be adjusted to optimize dimensional accuracy, mechanical and optical properties as well as build time. The results presented in this contribution need to be regained for different materials to include, e.g. different hatch distances and scan counts.

Second, integrating the methodology into the design process in terms of design for productivity is strongly advised. As a result, design choices could be made much earlier, reducing necessary iterations between pre-processing and geometry modeling. Thus, informing designers and process planners early on could save human and financial resources throughout the development stages.

If the complexity of parts is known in advance, this method can be used to assess the suitability of different AM processes and select the most suitable one. For LS, the KPIs could already be used to evaluate productivity due to part orientation. In accordance with the part properties to be accomplished, orientation could be changed to increase build-up rate and therefore reduce overall process duration as well as costs for machine and energy. This method could also be used to achieve a homogeneous distribution of layer time over build height. With regard to part design, there is initially no implementation in CAD. Therefore, an estimate of the effects can only be made by being aware of influencing parameters such as the number of scan lines. For example, when generating a structure, it is possible to estimate the effects of a solid design compared to a lattice design. Current research thus aims to provide tools that enable designers and production planners to find solutions for multi-dimensional optimization problems regarding not only productivity but also strength and durability of parts.

However, further research is required to validate its transferability across different AM processes to make this approach more practical. Besides validating applicability for different AM processes, further steps are the transfer of the presented methods from multivariate analysis to artificial intelligence (AI). This will be used to trace the resulting efforts back to corresponding geometric characteristics and processing parameters. So far, the results are limited to the generation process and should incorporate the aspects of data preparation and post-processing for a holistic evaluation. Furthermore, it must be considered that these productivity aspects, in addition to time and costs, always interact with the resulting part properties and process stability. Therefore, more than a one-sided evaluation is needed. To solve this challenge, further action is required for the analysis of interactions between geometric complexity and resulting mechanical properties. This can be done, e.g. by analyzing the dependence of density on the hatch length. Investigations must be carried out on whether processing parameters, as the introduced energy density, can be adapted for small structures (e.g. by lower laser power or greater hatch distance) to increase the build-up rate while maintaining the same layer properties.

Influences of complexity should also be examined with regard to effects on data acquisition, pre-processing and post-processing. Further, it should be considered in economic costing, e.g. for quotation submission and energy consumption.

The authors would like to thank the Federal Ministry for Economic Affairs and Climate Action (BMWK) for funding this research within their INNO-KOM programme (Grant No. 49VF220001, INNO-KOM).