Optimization of Fused Deposition Modeling Parameters for Tensile Performance of Thermoplastic Polyurethane via Taguchi-Analysis of Variance Analysis

Additive manufacturing (AM), commonly referred to as 3D printing, comprises more than 30 related technologies and has experienced rapid expansion across a wide range of application domains, including food processing, healthcare, education, consumer and household products, as well as high-performance sectors such as automotive engineering, aerospace, security, and defense. Among these technologies, fused deposition modeling (FDM) has become one of the most widely adopted methods due to its relatively low cost, ease of implementation, and broad material compatibility. As a result, numerous studies have investigated the application of FDM in diverse fields, including biomedical material development and testing [1-3], medical device manufacturing [4], aerodynamic drag reduction [5], aircraft and unmanned aerial vehicle components [6], gearbox development [7], and construction applications [8, 9].

In many of these applications, mechanical performance-particularly tensile behavior-plays a critical role in determining the functionality, durability, and reliability of printed components. Tensile strength and elongation are especially important for parts subjected to continuous tensile and deformation loads, such as flexible transmission elements and airless tire structures fabricated using elastomeric materials like thermoplastic polyurethane (TPU) [10]. Consequently, understanding and optimizing tensile mechanical properties have become a central topic in FDM research.

Tensile strength in FDM is governed by interlayer bonding quality, material flow behavior, and internal structural continuity, all of which are directly influenced by printing parameters. Consequently, extensive research has been conducted to identify the dominant parameters affecting tensile performance across different thermoplastic materials. Although the specific influence of individual parameters varies with material type, several consistent trends can be identified.

Across rigid thermoplastics such as Acrylonitrile Butadiene Styrene (ABS) and Polyethylene Terephthalate Glycol-modified (PETG), infill density and layer height consistently emerge as the primary determinants of tensile strength. Studies by Gupta et al. [11] demonstrated that increasing layer height reduces tensile strength due to weakened interlayer adhesion, while higher infill densities enhance tensile strength by improving internal load transfer. Notably, printing speed exhibits negligible influence on tensile strength for these materials, suggesting that within typical processing ranges, mechanical performance is more strongly governed by geometric and structural factors than by deposition rate.

For Polylactic Acid (PLA), which has been the most extensively studied FDM material, the dominance of infill density and layer height is even more pronounced. Multiple studies indicate that high infill density maximizes tensile strength by reducing internal voids and enhancing stress distribution. Ekşi and Karakaya [12] confirm that infill density is the most influential parameter, followed by layer height and layer width, while printing speed plays a secondary role. This hierarchy reflects the fact that tensile failure in PLA specimens is largely controlled by interlayer bonding area and internal porosity rather than by extrusion dynamics alone.

However, the influence of thermal parameters and printing speed becomes more significant when infill orientation is considered. Sapkota et al. [13] showed that at higher infill angles (e.g., 90°), extruder temperature dominates tensile behavior by directly affecting polymer chain diffusion and layer fusion. In contrast, at lower infill angles (0°), layer height becomes the most critical parameter, as load is primarily carried along filament deposition paths. These findings indicate that the mechanical response of FDM parts is highly anisotropic and that parameter significance is strongly dependent on filament orientation relative to the loading direction.

Thermal effects are further emphasized in the work of Trinh et al. [14], who reported that increasing extruder temperature generally enhances tensile strength by improving interlayer bonding, particularly at higher printing speeds. Nevertheless, excessive printing speed and increased layer height reduce tensile strength due to insufficient bonding time and reduced contact area between layers. Bed temperature also contributes positively by reducing thermal gradients and residual stresses, although its influence is secondary compared to extruder temperature and layer height. These results highlight the coupled nature of thermal and geometric parameters in determining tensile performance.

The role of internal structure has also been widely investigated. Studies on infill type and infill ratio [14-18] consistently indicate that tensile strength increases with infill ratio, while the influence of infill type becomes negligible at 100% infill. Concentric and hexagonal infill patterns frequently outperform other geometries due to a more uniform stress distribution. Across these studies, layer height remains a dominant factor, with increased layer height leading to a systematic reduction in tensile strength. Printing speed, in contrast, shows inconsistent influence, further supporting the conclusion that its effect is material- and structure-dependent rather than universal.

Compared with PLA, PETG has received less attention despite its favorable mechanical and thermal properties. Existing studies [19-21] suggest that tensile strength in PETG is sensitive to infill orientation, layer height, and printing speed, while extruder and bed temperatures exert weaker or non-monotonic effects. Several studies report optimal tensile strength at moderate extrusion temperatures and low printing speeds, indicating a trade-off between improved interlayer diffusion and thermal degradation. As with PLA, increasing the infill ratio consistently enhances tensile performance, reinforcing the importance of internal structural continuity.

In contrast to rigid thermoplastics, TPU exhibits fundamentally different behavior due to its high flexibility and low elastic modulus. TPU printing requires direct-drive extrusion systems to avoid filament buckling and compression, which complicates parameter optimization. Unlike PLA or PETG, TPU must be printed at relatively low speeds and elevated extrusion temperatures to ensure stable material flow and sufficient interlayer bonding. These constraints significantly limit the applicable processing window and increase sensitivity to parameter variations. Despite its growing industrial relevance, systematic studies on TPU tensile optimization-particularly those employing statistically designed experiments-remain limited.

The limited number of existing TPU studies indicates that its tensile behavior is governed by mechanisms distinct from those of rigid polymers. Hohimer et al. [22] reported that TPU tensile strength decreases as the infill angle increases from 0° to 90°, indicating a strong dependence on filament orientation relative to the loading direction. Their results also showed a reduction in tensile strength with increasing extrusion temperature, suggesting that excessive thermal input may degrade interlayer bonding in flexible polymers. Similarly, Le et al. [23] identified infill angle as the most influential parameter affecting TPU tensile strength, followed by extrusion temperature, layer height, and infill ratio. This parameter hierarchy contrasts sharply with findings for PLA and PETG, where infill ratio and layer height typically dominate tensile performance. Such discrepancies highlight the fundamentally different deformation and failure mechanisms of TPU and underscore the need for material-specific optimization strategies.

Moreover, existing TPU studies have largely focused on a limited set of parameters, primarily infill angle and extrusion temperature. The roles of other critical input variables-such as printing speed and infill type-have not been systematically investigated, despite their proven influence on tensile strength, elongation, and secant modulus at 100% strain in rigid thermoplastics. Given the viscoelastic nature of TPU, printing speed may significantly affect filament stretching, bonding time, and interlayer diffusion, while infill type may alter load transfer and deformation modes under tensile loading. The absence of comprehensive studies addressing these parameters represents a clear gap in the current literature.

Therefore, this study aims to systematically evaluate the effects of printing temperature, speed, infill type, and layer height on the tensile properties (strength, elongation, and secant modulus at 100% strain) of TPU. A structured experimental approach based on the Taguchi method with an L9 orthogonal array is employed to identify the optimal parameter combinations, while analysis of variance (ANOVA) is used to quantify the relative significance of each parameter. In addition, scanning electron microscopy (SEM) is utilized to examine microstructural differences resulting from variations in printing temperature and speed, thereby providing a mechanistic interpretation of the observed tensile behavior.

3.1 Results

The printed specimens were subjected to tensile testing using a Tensilon universal testing machine with a 100 kgf load capacity, in accordance with ASTM D412. Dumbbell-shaped specimens were mounted in the machine grips and carefully aligned symmetrically to ensure uniform distribution of tensile stress across the cross-section, thereby minimizing bending effects and ensuring accurate determination of maximum tensile strength.

Unless otherwise specified, the crosshead speed was maintained at 500 ± 50 mm/min (20 ± 2 in./min). The test was initiated, and the distance between the gauge marks was continuously monitored while avoiding parallax errors. The applied force was recorded at the specified elongation and at the point of fracture. Tensile stress, tensile strength, and yield point were determined from the recorded force-elongation data. The specimen was mounted and aligned in the testing grips prior to loading, as shown in Figure 6.

Figure 6. Specimen setup for tensile testing prior to loading

Elongation was measured using an elongation-measuring device or a self-recording mechanism. At the moment of fracture, the elongation was recorded to the nearest 10%, as specified in the standard.

Tensile strain was evaluated by clamping the specimen symmetrically and applying tension smoothly until the specified elongation was reached within 15 seconds. The specimen was held at this elongation for 10 minutes, after which the load was released rapidly without allowing the specimen to retract. The specimen was then allowed to rest for 10 minutes, after which the distance between the reference gauge marks was measured with an accuracy of ± 1% of the original gauge length. A stopwatch was used to ensure precise timing throughout the procedure. The specimen after stretching is shown in Figure 7. As shown in Figure 8, the specimens exhibit distinct fracture patterns following tensile loading.

Figure 7. Post-test image of the specimen after uniaxial tensile deformation

Figure 8. Fractured specimens after tensile testing

Figure 9. Representative engineering stress−strain curve for specimen 1 (Printing parameters: 210 ℃, 20 mm/s, 0.12)

From the obtained parameters, the stress-strain curve (Figure 9) is used to determine the fracture point. The tensile properties are calculated according to the ASTM D412 standard. Tensile strength:

$T S=F_{\max } / A$

where, $F_{\max }$ is the maximum force at the fracture point, and A is the original cross-sectional area of the specimen. Elongation at break:

$E=\left(L-L_0 / L_0\right) \times 100$;

where, $L$ is the gauge length at fracture, and $L_0$ is the initial gauge length. Secant modulus at 100% strain (modulus at 100% elongation):

$E_{100}=\sigma_{100} / \varepsilon_{100}$;

where, $\sigma_{100}$ is the engineering stress at 100% strain, and $\varepsilon_{100}=1$ (corresponding to 100% strain).

After recording the results, an overall assessment of samples 1 to 9 showed stable tensile strength from 210 to 350 (12-21 MPa). Samples 1, 2, 5, 6, and 9 achieved elongation at break greater than 300%, elastic modulus greater than 12 MPa, and increased steadily with elongation from 100% to 300%, consistent with elastomer (rubber) in terms of elongation at break. They exhibited higher hardness than conventional rubber while retaining flexibility, with good elasticity and similar properties to TPV.

From Table 7, Sample 2 exhibits the highest tensile strength and secant modulus at 100% strain, reaching 21.1 ± 0.5 MPa and 11.1 ± 0.3 MPa, respectively. These results were obtained with a printing temperature of 210 ℃, a printing speed of 40 mm/s, a layer height of 0.16 mm, and a rectilinear infill pattern. Sample 9 achieved the highest elongation value of 901.1 ± 18.5% using the following parameters: printing temperature of 230 ℃, printing speed of 60 mm/s, layer height of 0.16 mm, and infill type: Grid.

Table 7. Tensile properties of the printed samples under different printing parameter combinations

Note: The symbols x1–x4 represent the coded factors used in the Taguchi experimental design.

Group 8 had the lowest secant modulus at 100% strain value of 8.2 ± 0.2 MPa using the following parameters: printing temperature of 230 ℃, printing speed of 40 mm/s, layer height of 0.1 mm, and infill type: Concentric. Sample 8 has the lowest tensile strength value at 12.5 ± 0.3 MPa, using the following parameters: printing temperature of 230 ℃, printing speed of 20 mm/s, layer height of 0.2 mm, and infill type: Rectilinear.

Sample 3 has the lowest elongation value with an elongation ratio of 230.5 ± 5.5%, using the following parameters: printing temperature of 210 ℃, printing speed of 60 mm/s, layer height of 0.2 mm, and infill type: Concentric. Samples 7 and 8 have similar tensile strength and secant modulus at 100% strain values.

The lowest values for tensile strength and secant modulus at 100% strain are 12.5 ± 0.3 MPa and 8.2 ± 0.2 MPa, respectively. Models 7 and 8 also have elongation values between 250% and 300%. Although the output parameters have nearly identical output values, their input values are only the same at a print head temperature of 230 ℃.

Models 3 and 4 are similar, with output parameters such as elongation of 230.8 ± 5.5% and 248.0 ± 6.0%, the lowest among the elongation values, and tensile strength values of 15.4 ± 0.3 MPa and 15.6 ± 0.3 MPa, respectively, and secant modulus at 100% strain values between 10.2 MPa and 9.9 MPa. Although they have similar output values, only one input value is the Infill Type: Concentric.

Models 7, 8, and 9 have the lowest secant modulus at 100% strain values, with values of 8.3 ± 0.3 MPa, 8.2 ± 0.2 MPa, and 8.3 ± 0.3 MPa, respectively. All three samples were printed at an extrusion temperature of 230 ℃, which is lower than that used for samples exhibiting higher modulus values.

Samples with the lowest elongation ratios, such as samples 3, 4, and 8 (230.8 ± 5.5%, 248.0 ± 6.0%, and 268.3 ± 6.2%), share the same input parameter: Concentric infill type. Samples with high tensile strength values (17.5 MPa to 17.9 MPa), such as samples 1, 5, and 9, share the same input parameter: Grid infill type.

Samples with the highest secant modulus at 100% strain values, such as samples 1, 2, and 3 (9.5 ± 0.2 MPa, 11.1 ± 0.3 MPa, and 10.2 ± 0.2 MPa, respectively), all have an input temperature of 210 ℃. compared to samples with higher input printing temperature parameters. Samples with a high elastic modulus generally exhibit stiffer properties.

3.2 Taguchi analysis

3.2.1 Taguchi analysis for tensile strength

As shown in Table 8 and Figure 10, we can assess that printing temperature plays the biggest role in tensile strength properties, followed by infill type, layer height, and printing speed. Looking at the S/N ratio chart, we can see that as temperature increases, tensile strength decreases, similar to the study on ABS plastic where increasing temperature leads to decreased tensile strength. Regarding printing speed, when the printing speed increases to a fixed level such as 40 mm/s, the tensile strength begins to decrease gradually. Similarly, with layer height, increasing the layer height to 0.16 mm also causes the tensile strength of the sample to gradually decrease. As for the infill type, it decreases gradually from Grid to Rectilinear and then Concentric. From the S/N ratios of the parameters as analyzed, we can derive the optimal parameters for the tensile strength of the sample: Printing temperature of 210 ℃, Printing speed of 40 mm/s. The layer height is 0.16 mm and the infill type is Grid, with predicted tensile strength and S/N ratio of 21.9234 MPa and 27.097, respectively, as shown in Table 9.

Figure 10. Taguchi S/N ratio analysis for tensile strength optimization

Table 8. S/N ratio response analysis for tensile strength based on printing parameters

Table 9. Optimal printing parameters and predicted tensile strength

3.2.2 Taguchi analysis for elongation

From Table 10 and the S/N ratio chart for elongation in Figure 11, the factor with the greatest influence on elongation is the infill type, followed by printing speed, layer height, and printing temperature. We can assess that as printing temperature increases, elongation increases steadily. Printing speed is similar to printing temperature, increasing gradually with increasing speed. For layer height, when increasing the layer height by 0.16 mm, the elongation increases to that level and then gradually decreases. The influence of infill type on elongation is similar to tensile strength, with elongation decreasing gradually from Grid to Rectilinear and Concentric. The input parameters for elongation in the S/N results achieved the highest value in the parameter set in Sample 9, with an elongation of 901.09% with printing parameters of printing temperature of 230 ℃, printing speed of 60 mm/s, layer height of 0.16 mm, and infill type of Grid, so no further analysis is needed. Provide the optimal set of parameters for elongation.

Table 10. S/N ratio response for elongation under different printing parameters

Figure 11. Main effects of printing parameters on elongation using S/N ratio analysis

3.2.3 Taguchi analysis for secant modulus

Analysis of Table 11 and the S/N ratio plot in Figure 12 indicates that printing temperature has the most significant influence on the secant modulus, followed by layer height, infill type, and printing speed. Similar to the effect on tensile strength, the higher the printing temperature, the lower the secant modulus. Printing speed and layer height increase to a certain level, such as 40 mm/s and 0.16 mm, then decrease gradually. Rectilinear infill achieves the largest Secant modulus, followed by concentric and grid infill. Similar to elongation, the optimal parameters for the secant modulus value are also found in the orthogonal matrix in Sample 2, with a value of 11.099188 MPa, with the parameters being a printing temperature of 210 ℃, a printing speed of 40 mm/s, a layer height of 0.16 mm, and the type of infill. Since the infill is rectilinear, we no longer need an optimization parameter set for this feedback variable.

Figure 12. Main effects of printing parameters on secant modulus using S/N ratio analysis

Table 11. S/N ratio response for secant modulus under different printing parameters

3.3 Analysis of variance analysis

3.3.1 ANOVA analysis for elongation

The goal of ANOVA is to compare the means of multiple groups (populations) based on the means of observed samples from these groups, and through hypothesis testing, to conclude on the equality of these population means. In research, ANOVA is used as a tool to examine the influence of a causal factor (qualitative) on an outcome factor (quantitative). The regression equations for elongation under different infill patterns are presented in Table 12.

Table 12. Regression equations for elongation under different infill patterns

Based on the parameters given in Table 13, all input parameters have values greater than 0.05 and are not statistically significant for elongation. The R² value of 75.89% indicates that the input parameters explain 75.89% of the variation in elongation. Based on the regression model analysis table in Table 14, we observe that the infill type has the greatest impact on elongation, accounting for 38% of the factors, followed by printing speed with an impact of 22.5%, printing temperature with an impact of 14.2%, and the lowest impact is layer height with an impact of 1%. The p-value used as the significance level is 0.05. ANOVA was performed to analyze tensile strength.

Table 13. Statistical summary of the regression model for elongation

Note: S denotes the standard error of the regression model. R-sq (coefficient of determination) represents the percentage of response variation explained by the model. R-sq (Adj) is the adjusted coefficient of determination that accounts for the number of predictors in the model. R-sq (Pred) indicates the predictive capability of the model for new observations.

Table 14. Analysis of variance (ANOVA) for the regression model of elongation

Note: DF = Degrees of freedom; Adj SS = Adjusted sum of squares; Adj MS = Adjusted mean square; F-Value = Ratio of factor mean square to error mean square used to assess statistical significance

The regression equations for tensile strength under different infill patterns are presented in Table 15. The R² value of 69.43%, as shown in Table 16, indicates that the input parameters explain 69.43% of the variation in elongation, which is lower than the elongation itself. Based on the parameters, the input parameters all have values greater than 0.05 and are not statistically significant for tensile strength. Although input parameters such as printing temperature and infill type are not statistically significant, they still play an important role in improving tensile strength.

Table 15. Regression equations for tensile strength under different infill patterns

Table 16. Statistical summary of the regression model for tensile strength

Based on the regression model analysis table in Table 17, we find that printing temperature is the factor with the greatest impact on tensile strength, accounting for 38.2% of the factors. Second is the infill type with 26.65%, followed by printing speed with 4.33%, and the lowest is layer height with 0.24%.

Table 17. Analysis of variance (ANOVA) for the regression model of tensile strength

Note: DF = Degrees of freedom; Adj SS = Adjusted sum of squares; Adj MS = Adjusted mean square; F-Value = Ratio of factor mean square to error mean square used to assess statistical significance

3.3.2 ANOVA analysis for secant modulus

The regression equations for secant modulus under different infill patterns are presented in Table 18. The R² value of 86.93% shown in Table 19 indicates that the input parameters in the regression explain 86.93% of the variation in secant modulus, making this the model with the highest reliability among the models developed.

Table 18. Regression equations for secant modulus under different infill patterns

Table 19. Statistical summary of the regression model for secant modulus

Based on the regression model analysis table in Table 20, we find that printing temperature is the factor with the greatest impact on tensile strength, accounting for 76.5% of the input factors. The infill type is second with an impact of 9.96%, followed by printing speed with an impact of 2.58%, and the lowest impact is layer height with approximately 0%. Based on the parameters, the p-value for printing temperature is 0.025 and statistically significant for the secant modulus at 100% strain. Therefore, to improve the secant modulus at 100% strain, we only need to adjust the printing temperature.

Table 20. Analysis of variance (ANOVA) for the regression model of secant modulus

Note: DF = Degrees of freedom; Adj SS = Adjusted sum of squares; Adj MS = Adjusted mean square; F-Value = Ratio of factor mean square to error mean square used to assess statistical significance

It should be noted that the Taguchi ranking and ANOVA results are based on different evaluation criteria. The Taguchi method identifies influential factors through the range of S/N responses, whereas ANOVA assesses statistical significance based on variance relative to experimental error. Consequently, a factor such as printing temperature may exhibit the strongest influence in S/N analysis but remain statistically insignificant (p > 0.05) due to limited sample size and experimental variability.

This study systematically investigated the effects of key FDM processing parameters on the tensile behavior of TPU by integrating Taguchi design, ANOVA, mechanical testing, and SEM analysis.

• Printing temperature is the primary governing factor across all responses, especially stiffness, highlighting the critical role of interlayer diffusion and bonding in determining mechanical integrity.
• Infill type strongly influences elongation and energy absorption, indicating that mechanical response in TPU is highly sensitive to mesoscale structural design.
• The combined statistical and microstructural analyses demonstrate that optimized processing conditions enhance filament fusion and fracture morphology, leading to improved stress transfer and ductility.

The findings are based on a limited Taguchi design and a single TPU material system, which may constrain generalizability. Future studies should extend validation across broader processing windows, different TPU grades, and more complex geometries, as well as incorporate fully quantitative microstructural characterization to strengthen process-structure-property relationships.

The present study should be regarded as a screening-level investigation aimed at identifying relative parameter effects rather than providing statistically rigorous property evaluation. The observed trends are consistent with findings reported in the literature, which supports the qualitative validity of the identified parameter influences. The findings of this study provide preliminary insights into the influence of FDM process parameters.

Future work will focus on improving the statistical robustness of the findings by incorporating multiple replicates for each parameter combination.