The material addition rate (MAR) of fused filament fabrication (FFF) is an indicator of process efficiency varied by process parameter settings, which affects energy consumption and part quality in FFF. This study aims to identify the optimal MAR of FFF using carbon-fiber-reinforced polyether-ether-ketone (CFR-PEEK) by considering a trade-off between energy consumption and the dimensional accuracy of FFF outputs. A design of experiments considering two main process parameters is planned to print three sample types through FFF for CFR-PEEK. Then, the MAR (i.e., deposited material volume per build time) of FFF is obtained to derive individual regression models of energy consumption and the dimensional accuracy measured for each sample type. Furthermore, a trade-off between energy consumption and dimensional accuracy on the MAR is formulated to derive an optimal MAR for each sample type. The results show that FFF for CFR-PEEK has a trade-off between energy consumption and dimensional accuracy; there exists a specific MAR that maximizes the overall performance of energy consumption and dimensional accuracy for each sample type. The optimal MAR is the highest for the small volume sample, whereas it becomes the lowest for the vertical build orientation sample. This study suggests that the optimal MAR should be flexibly adjusted based on a fabricated part. The findings from this study also address the fact that decision-making for optimal FFF operations needs a transition from the identification of specific process parameter settings to the management of a proper process efficiency level in FFF.
Keywords: fused filament fabrication; CFR-PEEK; material addition rate; energy consumption; dimensional accuracy
Additive manufacturing (AM) has received increasing attention as an innovative manufacturing technology in that AM provides new manufacturing opportunities with cost-effectiveness and environmental sustainability [[
As the role of AM has been emphasized to realize sustainable manufacturing, recent studies have investigated energy performance in FFF to understand energy behavior and optimal AM operations for energy savings [[
Along with the energy consumption in FFF, the dimensional accuracy of FFF outputs has been considered one of the important aspects of evaluating part quality in AM. For this, existing studies have primarily investigated the effects of FFF process parameters on dimensional accuracy along with other performance measures [[
The MAR of FFF indicates process efficiency in the AM process, which leads to less printing time for a given amount of material deposition at a higher MAR [[
The consideration of both energy consumption and part quality in FFF becomes more critical for a high-end polymer such as carbon-fiber-reinforced PEEK (CFR-PEEK). CFR-PEEK is one of the most popular high-performance polymers for medical and advanced engineering applications as a metal substitute due to its superior mechanical and chemical properties [[
As a response, this study aims to identify an optimal MAR level for the FFF of CFR-PEEK to maximize the overall performance in both energy consumption and dimensional accuracy as a function of the MAR of the FFF. First, a full-factorial experimental design consisting of layer thickness at five levels and printing speed at six levels is planned to fabricate samples in three types, which are used to compare groups for part volume and build orientation. The energy consumption of each experimental sample is collected while the sample is being fabricated, and the overall dimensional error of each fabricated sample from the original dimensions is measured to represent the dimensional accuracy of FFF using CFR-PEEK. The MAR value of each fabricated sample is calculated using the consumed material volume and printing time of each fabrication to build the regression models of energy consumption and dimensional accuracy on the MAR. Then, a performance model that integrates the fitted regression models of energy consumption and dimensional accuracy is derived to identify an optimal MAR level of FFF for CFR-PEEK. The above procedure is performed for three sample types to identify changes in the optimal MAR level and to achieve the overall performance of both energy consumption and dimensional accuracy.
The following subsections illustrate the main steps to derive an optimal MAR that simultaneously considers both energy consumption and the dimensional accuracy of FFF for CFR-PEEK. Section 2.1 presents an experimental design to collect energy consumption and dimensional accuracy data for three sample types through FFF using CFR-PEEK. Section 2.2 performs regression modeling for energy consumption and dimensional accuracy on the MAR of FFF. Section 2.3 proposes a trade-off analysis procedure to derive an optimal MAR that simultaneously improves both performance measures.
This study used three hexahedron design cases for experiments (see Figure 1). These sample types were employed as comparison groups for analysis. In Figure 1, Sample A illustrates a cube (i.e., 10 mm × 10 mm × 10 mm) to represent an object with a smaller volume and no build orientation effect (see Figure 1a). Sample B and Sample C represent a larger-volume object group (=2 cm
All experimental samples were fabricated by Apium P220 (Apium Additive Technologies GmbH, Karlsruhe, Germany) [[
Figure 2 illustrates the experimental environment of this study to collect energy data during each experiment. The energy consumption (W·h: watt-hour) of each experiment was recorded by the Wattman HPM-100A (ADpower, Pyeongtaek, Republic of Korea) [[
The dimensions (i.e., width, length, and height) of the fabricated samples were measured by the Mitutoyo NTD13-P15M digital vernier caliper (Mitutoyo, Kawasaki city, Japan) [[
(
where
The total build time during the extrusion stage of each experiment and the total volume of the deposited material for each fabricated sample were also collected by referring to time in measured energy profiles and the Apium P220 data system, respectively. Table 2 summarizes the experimental data collected for this study.
Individual regression models for energy consumption and dimensional accuracy on the MAR of FFF for CFR-PEEK were derived first based on the collected experimental data. The MAR of each experimental sample was calculated by dividing the total deposited volume by the build time (=
(
where
The dimensional accuracy of FFF for CFR-PEEK was expressed as a function of MAR through a linear regression model in Equation (
(
where
The above regression models for energy consumption and dimensional accuracy were fitted using MINITAB 20.3 [[
A trade-off analysis for each sample type was performed to characterize both energy consumption and dimensional accuracy on the MAR of FFF for CFR-PEEK. Since energy consumption and dimensional accuracy have the same objective direction (i.e., to be minimized) with different value scales, a normalization process in Equation (
(
where
Then, the same regression procedure for the original data in Section 2.1 was performed to derive regression models for normalized energy consumption and dimensional accuracy. Then, regression models constructed for normalized energy consumption and dimensional accuracy were added to characterize the overall AM performance. Equation (
(
where P denotes the overall AM performance,
Through the normalization process, both energy consumption and dimensional accuracy are transformed from cost criteria (i.e., the smaller the better) to benefit criteria (i.e., the larger the better). It is assumed that energy consumption and dimensional accuracy are in a trade-off relationship depending on the MAR of FFF; as the MAR increases, the normalized energy consumption performance rapidly increases, whereas the normalized dimensional accuracy performance worsens. Then, the formula for P forms a concave function that reflects the trade-off, where P becomes maximum at a specific MAR. The optimal MAR value that maximizes the overall performance can be obtained by a differential equation of P. That is, the MAR value that satisfies
The regression models for energy consumption and the dimensional accuracy of each sample type are presented in Section 3.1. Section 3.2 shows the results of the trade-off analysis on the MAR.
Table 3 shows the statistical significance of regression models for energy consumption on the MAR of FFF for each sample type. Furthermore, Figure 4 illustrates regression lines of energy consumption on the MAR for each sample type. The regression results of energy consumption for all the sample types reveal that energy consumption is suitably fitted as a linear function of the inverse MAR; the energy consumption of FFF for CFR-PEEK nonlinearly decreases as the MAR increases (see Figure 4b). The inversed MAR is statistically significant in all the derived regression models, regardless of the sample types (see Table 3). Moreover, all the regression models have high explanatory power for a relationship between energy consumption and the inversed MAR.
In Figure 4a, Sample B and Sample C have almost the same energy consumption pattern, and their energy consumption is always higher than the energy consumption of Sample A for every inverse MAR. This result seems to be due to the part volume required for the FFF of Sample B and Sample C; Sample B and C have twice as large a part volume as Sample A. Accordingly, the regression coefficients for the Sample B and C cases are approximately twice as high as the regression coefficient of the energy consumption model for Sample A (see Table 3). This indicates that the energy consumption required for the FFF of Sample B and Sample C more rapidly decreases than for the FFF of Sample A as the MAR increases (see Figure 4b). The regression results indicate that energy consumption is significantly varied depending on the MAR of FFF and the fabricated part volume.
Table 4 presents the linear regression results of dimensional accuracy on the MAR of FFF for each sample type. Figure 5 shows the linear regression plots of dimensional accuracy on the MAR. The results show that the overall dimensional error of each fabricated sample statistically increases as the MAR of FFF increases. The t-test for
Sample C, which is a variant of Sample A with an increase in the z-axis dimension from Sample A, has a low dimensional accuracy performance in FFF with process parameters that result in a high MAR. It is noted that the crossing point between the regression lines for Sample A and Sample C in Figure 5 is 1.13 mm
The regression models built for the energy consumption and dimensional accuracy of FFF for CFR-PEEK confirm a trade-off between those performance measures on the MAR. Figure 4b supports that energy consumption is in an inverse relationship with the MAR, whereas Figure 5 shows that dimensional error is in proportion to the MAR. The results show that there can be an optimal MAR at which both performance measures are suitably achieved by avoiding extreme losses in either energy consumption or dimensional accuracy performance.
Table 5 and Figure 6 show an optimal MAR for each sample type when the trade-off between the energy consumption and dimensional accuracy of FFF for CFR-PEEK is considered to maximize the overall performance. The normalized performance plots shown in Figure 6 clearly address the fact that the FFF of CFR-PEEK for all the sample types has a trade-off between energy and quality performance depending on the MAR.
The optimal MAR for the baseline case (i.e., Sample A) to maximize the overall AM performance of energy consumption and dimensional accuracy is 1.40 mm
The optimal MAR for Sample C is lower than that of Sample B, since the dimensional accuracy performance of Sample C decreases faster than that of Sample B (see Figure 6c) without significant variations in energy performance between Sample B and Sample C (see Figure 4b). The findings indicate that the build orientation of a fabricated part can be a critical factor in AM process efficiency. A change to horizontal build orientation to have a wide bottom area can be an effective strategy to pursue higher process efficiency in FFF if mechanical properties (e.g., tensile and compressive strength) affected by the build orientation are not critical for the fabricated part. On the other hand, a part design that has a height size relatively higher than sizes on the x-y plane may require the FFF with a relatively lower MAR to maintain the best energy and quality performance in the FFF if the FFF of the part requires its original build orientation due to mechanical functionality. The above results also suggest that the MAR of FFF for CFR-PEEK should be properly managed to improve the overall AM performance by jointly considering energy consumption and dimensional accuracy, depending on the part designs considered for AM.
Table 6 shows the process parameter combinations of the experiments that lead to the experimental MAR being close to the theoretical optimal value obtained for each sample type. For this, all the MAR values calculated from the experiments were rounded off to the first digit after the decimal point, and then the parameter combinations that result in the MAR value closest to the optimal MAR were identified for each sample type. For Sample A, the process parameter combinations specified in Table 6 are the experimental settings in which all the experimental replicates result in rounded-off MAR values equal to the optimal MAR. It is noted that the energy consumption and dimensional accuracy data specified for Sample A in Table 6 are averaged values for the associated replicates. The results imply that there can be multiple process parameter combinations to satisfy the overall best AM performance of energy consumption and dimensional accuracy. This indicates that the process parameters of FFF for the overall AM performance are not a fixed and single optimal process parameter set but a flexible and selective solution among the alternative parameter combinations leading to the optimal MAR.
The resultant regression models of energy consumption show that the energy consumption of FFF for CFR-PEEK is expressed as a decreasing non-linear function of the MAR, as addressed in the existing studies. Indeed, process parameter combinations that lead to a short build time in this study show a high MAR and a resultant low energy consumption value in that the energy consumption of FFF for CFR-PEEK is significantly affected by printing time [[
On the other hand, the dimensional accuracy of FFF for CFR-PEEK can be modeled as a linear function of the MAR. A high MAR is achieved when layer thickness and printing speed are set at high levels. However, these process parameter settings can negatively impact printing resolution and thereby may cause an increase in the overall dimensional error of a fabricated part. The negative impact of the MAR on dimensional accuracy is stronger for Sample C than for Samples A and B, which have a similar pattern of overall dimensional error on the MAR. A plausible reason for the worsened dimensional accuracy observed in Sample C compared to Sample B, which has the same design and volume as Sample C, is build orientation that increases the number of deposited layers. Sample C is considered a vertically oriented Sample B on the build platform. FFF has greater residual stress and heat shrinkage in the vertical direction (z-axis) than in the horizontal direction (x-y plane), and therefore this can cause more dimensional deviations in a part fabricated in a vertical orientation [[
The above energy consumption and dimensional accuracy characteristics of FFF for CFR-PEEK clearly show a trade-off on the MAR. The overall AM performance model, through the integration of the normalized energy consumption and dimensional accuracy models, presents that there is an optimal MAR at which FFF for CFR-PEEK is the most effectively operated given the trade-off of energy consumption and dimensional accuracy. Moreover, the fact that the optimal MAR varied by the sample type implies that the FFF for CFR-PEEK should be flexibly operated to achieve an optimal MAR targeted for part volume and orientation; relatively high AM efficiency can be pursued for a small volume part (e.g., Sample A) in the FFF for CFR-PEEK to have the best performance in energy consumption and dimensional accuracy. If the horizontal orientation of a part (e.g., Sample B) is allowed to increase the contract area on the build platform, FFF for CFR-PEEK can be managed to improve process efficiency that is expected to be lower in the original vertical orientation of the part (e.g., Sample C).
This study focused on a trade-off between energy consumption and dimensional accuracy of FFF outputs using CFR-PEEK to identify an optimal MAR to maximize the overall AM performance of both energy consumption and dimensional accuracy. For this, an experimental design considering five levels of layer thickness and six levels of printing speed for FFF using CFR-PEEK was planned to manufacture experimental samples of three types. Energy consumption and dimensional accuracy data measured for each experiment were collected as response data, and the MAR of each experiment was calculated to be used as input data. Herein, the MAR was employed to represent the process efficiency of FFF using CFR-PEEK, which is an operational consequence of selected process parameter settings, to effectively model energy consumption and dimensional accuracy for FFF.
Based on the collected data, individual regression models of energy consumption and dimensional accuracy on the MAR for the considered sample types were derived to confirm the impact of the MAR on the performance measures. Then, the original response data were normalized to derive individual regression models for normalized energy consumption and dimensional accuracy again, and they were integrated to represent the overall AM performance model of FFF for CFR-PEEK for the sample types, respectively. Finally, an optimal MAR to maximize the overall AM performance of each sample type given a trade-off between energy consumption and dimensional accuracy performances was identified to address the role of the MAR in successful FFF operation.
The findings of this study suggest that decision-making in FFF operations should be viewed as maintaining optimal process efficiency instead of selecting optimal parameter settings. Previous attempts to suggest optimal FFF operations in the literature focused on identifying specific process parameter settings that maximize a specific performance measure. This was reasonable when the AM decision-maker was only interested in optimizing a single performance measure. However, it would be difficult to determine specific process parameter settings if multiple performance measures with complex trade-offs should be jointly considered to improve the overall AM performance. In addition, optimal process parameter settings for a specific FFF machine cannot ensure the optimal performance of another FFF machine due to different machine specifications. Thus, FFF operations are required to be considered as a generalized problem of process efficiency rather than specific process parameter selection, and any process parameter combination associated with an optimal MAR can be a solution for the best AM operation based on an AM strategy. For example, if an AM decision-maker wants to significantly save energy consumption to fabricate parts by compromising dimensional accuracy to some degree, process parameter combinations generating a higher MAR in any FFF machine would be preferable.
This study contributes to decision-making for AM as a process efficiency-based AM approach to generally model a trade-off between energy consumption and dimensional accuracy. Nevertheless, this study should be further extended to understand the dynamics of process efficiency not only for various design cases but also for more conflicting AM performance measures in practice. In addition, operation strategies to flexibly handle the MAR of FFF machines in a large-scale AM system can provide a new opportunity to maximize the overall performance of the AM system.
Graph: Figure 1 Three sample types for the experiments.
Graph: Figure 2 Equipment settings for measuring energy consumption in FFF experiments.
Graph: Figure 3 Examples of energy changes during FFF for CFR-PEEK.
Graph: Figure 4 Energy consumption on MAR for each sample type.
Graph: Figure 5 Dimensional accuracy on MAR for each sample type.
Graph: Figure 6 Optimal MAR to maximize overall AM performance.
Table 1 Varied and fixed process parameters for experiments.
Type Process Parameter Value Varied Layer thickness (mm) 0.1 (L1), 0.15 (L2), 0.2 (L3), 0.25 (L4), and 0.3 (L5) Printing speed (mm/min) 1000 (P1), 1100 (P2), 1200 (P3), 1300 (P4), 1400 (P5), and 1500 (P6) Fixed Bed temperature (°C) 120 Nozzle temperature (°C) 510 Nozzle diameter (mm) 0.4 Perimeter shells (# of layers) 3 top layers/bottom layers (# of layers) None Extrusion percentage for the first layer (%) 96 Infill pattern (pattern) Rectilinear Infill density (%) 100
Table 2 Collected data from experiments.
Name Definition Unit Build time ( The total time taken during the material extrusion stage s Deposited material volume ( The total volume of deposited material during the material extrusion stage mm3 Energy consumption ( The total energy consumed during the extrusion stage W·h Dimensional accuracy ( The root mean square error of a final output between original and measured dimensions mm
Table 3 Regression models for energy consumption.
Sample Type Regression Model ( ( Sample A 99.74% Sample B 99.82% Sample C 99.68%
Table 4 Regression models for dimensional accuracy.
Sample Type Regression Model ( ( Sample A 49.94% Sample B 51.00% Sample C 65.02%
Table 5 Derived optimal MAR for overall AM performance.
Sample Type Normalized EC Model Normalized DA Model AM Performance Model Optimal MAR Sample A 1.40 Sample B 1.30 Sample C 1.01
Table 6 Suggested process parameter settings.
Suggested Process Parameters MAR Measured EC Measured DA Sample A 1.40 (optimal) 51.4 (estimated) 0.69 (estimated) L4 and P4 1.38 52.2 0.66 L4 and P5 1.42 50.9 0.64 L5 and P1 1.37 53.5 0.74 Sample B 1.30 (optimal) 96.8 (estimated) 0.61 (estimated) L3 and P4 1.27 98.2 0.63 L3 and P5 1.34 93.8 0.67 L4 and P1 1.28 99.2 0.72 Sample C 1.01 (optimal) 123.6 (estimated) 0.56 (estimated) L2 and P5 0.99 126.3 0.35 L2 and P6 1.04 122.1 0.53 L3 and P1 0.99 129.3 0.65
Conceptualization, K.K., K.P. and H.W.J.; methodology, K.K., K.P. and H.W.J.; analysis, K.K. and K.P.; data collection, K.K.; writing—original draft preparation, K.K. and K.P.; writing—review and editing, K.P. and H.W.J. All authors have read and agreed to the published version of the manuscript.
Not applicable.
The data presented in this study are available on request from the corresponding author. The data is not publicly available due to privacy or ethical restrictions.
The authors have no conflicts of interest to disclose.
By Kyudong Kim; Kijung Park and Hyun Woo Jeon
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