List of Tables
3. Parametric study of lattice structure
3.4 Result and analysis
Statistical analysis was used to determine the interaction between the process parameters of the SLS equipment and the cushioning properties of the lattice structures and was performed using the commercial tool Minitab® (Minitab Inc., State College, PA, USA).
Main effect analysis of Load-deflection behavior
The main effect plots showing the relationship between the three process parameters, laser power (LP), scan speed (SS), hatching distance (HD), and compressive load, are shown in Figure 3.6. The results of 25% compressive load and 65% compressive load showed similar results.
According to the equation of energy density, energy density increases as LP increases, and energy density decreases as SS and HD increase. In many studies studying the process parameters of SLS, both mechanical strength and modulus tend to increase as energy density increases [13-16].
The derived experimental results showed similar tendencies to previous studies in LP and HD.
As the LP increased, the compressive load increased, and as the HD increased, the compressive load decreased. However, the increase in SS did not show an apparent relationship with the compressive load. Analysis of Variance (ANOVA) was conducted for each parameter to verify the statistical significance of the three process parameters.
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Figure 3.6 Main effect plot of 25% compressive load (upper), and 65% compressive load (lower)
The results of ANOVA confirmed the statistical significance of LP and HD, and SS was not statistically significant in both compressive loads. ANOVA of LP and HD showed a p-value of 0.05 or less in both compressive loads. However, the p-values of SS were calculated as 0.862 and 0.939 at 25% and 65% compressive load, respectively. Since SS did not show a clear correlation in compressive load, a single factor analysis was additionally conducted for the two factors, LP and SS, for additional verification.
ANOVA of LP
Figure 3.7 Individual value poly of 25% (left) and 65% (right) compressive load vs. laser power
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Table 3.5 Analysis of Variance (LP - 25% Compressive load)
Source DF Adj SS Adj MS F-Value P-Value
LP 4 460.3 115.08 4.55 0.009
Error 20 505.4 25.27
Total 24
Table 3.6 Analysis of Variance (LP - 65% Compressive load)
Source DF Adj SS Adj MS F-Value P-Value
LP 4 5098 1274.6 3.18 0.036
Error 20 8022 401.1
Total 24 13120
ANOVA of SS
Figure 3.8 Individual value poly of 25% (left) and 65% (right) compressive load vs. scan speed
Table 3.7 Analysis of Variance (SS - 25% Compressive load)
Source DF Adj SS Adj MS F-Value P-Value
SS 4 57.82 14.45 0.32 0.862
Error 20 907.96 45.40
Total 24
Table 3.8 Analysis of Variance (SS - 65% Compressive load)
Source DF Adj SS Adj MS F-Value P-Value
SS 4 489.8 122.4 0.19 0.939
Error 20 12630.0 631.5
Total 24 13119.8
２１ ANOVA of HD
Figure 3.9 Individual value poly of 25% (left) and 65% (right) compressive load vs. hatching distance
Table 3.9 Analysis of Variance (HD - 25% Compressive load)
Source DF Adj SS Adj MS F-Value P-Value
HD 4 396.5 99.13 3.48 0.026
Error 20 569.3 28.46
Total 24
Table 3.10 Analysis of Variance (HD - 65% Compressive load)
Source DF Adj SS Adj MS F-Value P-Value
HD 4 6446 1611.4 4.83 0.007
Error 20 6674 333.7
Total 24 13120
Single factor analysis
To verify the high p-value in SS, specimens of single-factor analysis were additionally produced.
For comparison of the results, LP with demonstrated statistical significance was also output. The level (Table 3.11) of each parameter was set to 7, and the repetition of the specimen was 2.
Table 3.11 Level of SLS process parameter in single factor analysis
Parameter Level 1 Level 2 Level 3 Level 4 Level 5 Level 6 Level 7
LP [W] 84 96 108 120 132 144 156
SS [mm/s] 16000 18000 20000 22000 24000 26000 28000
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The results of the single-factor analysis (Figure 3.10) showed the same results as the orthogonal analysis. The p-value of LP was 0.043, and the correlation with compressive load was verified even in single factor analysis. The p-value of SS was 0.598, which was not statistically significant.
Figure 3.10 Individual value plot of 65% compressive load vs. LP (left) and SS (right) in single factor analysis
Table 3.12 Analysis of Variance (LP - 65% Compressive load) in single factor analysis
Source DF Adj SS Adj MS F-Value P-Value
LP 6 10.622 1.7704 4.13 0.043
Error 7 3.004 0.4292
Total 13 13.627
Table 3.13 Analysis of Variance (SS - 65% Compressive load) in single factor analysis
Source DF Adj SS Adj MS F-Value P-Value
SS 6 0.3161 0.05269 0.80 0.598
Error 7 0.4598 0.06568
Total 13 0.7759
Scanning electron microscope (SEM) images were captured to confirm the sintered shape in the TPU lattice structure according to the process parameters. FE-Cold SU7000 (Hitachi high-tech, Singapore) was used for SEM imaging. Images were taken under LP and SS level 1 and 7 conditions, and the rough surface due to the under-sintering was observed at LP level 1 (84W). On the other hand, level 7 (156W) showed a relatively even surface (Figure 3.11). SS level 1 and level 7 showed no significant difference in terms of sintering morphology (Figure 3.12).
The SLS printer used in this study uses a fiber laser and supports laser power of up to 500W.
However, the SLS printer used in other studies uses a CO2 laser, and the laser power applied for the lattice specimen reaches under the tens of watts [13-18, 21]. However, in order to maintain a
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similar level of energy density, the SS value in this study was much faster than the value used in other studies. Therefore, the effect of LP is expected to be stronger, while the effect of SS is weaker.
Thus, on a broader range, SS experiments must be conducted to confirm the effect of SS.
Figure 3.11 SEM Image of the lattice structure in different laser power levels, 84 W (left), 156 W (right)
Figure 3.12 SEM Image of the lattice structure in different laser power levels, 84 W (left), 156 W (right)
Regression model of compressive load
The objective of the regression curve fitting is to formulate the relationship of the process parameters and the compressive load for presenting the optimal process parameters for realizing the required cushioning properties. In the regression model, SS, a process parameter that is not statistically significant, was removed.
In this study, two regression methods were used, which are the second-order polynomial and exponential models. The results of both regression analyses are described in Table 3.14, and the polynomial model had slightly higher R-sq values than the exponential model. The derived
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regression equations can be selected according to the purpose. A polynomial model is not monotonic because it is a convex or concave function. For example, in Figure 3.6 main effects plot for 65% compressive load, concave curves were observed in both areas of 96 to 120 watts laser powers and hatching distances of 0.20 to 0.24 mm. The cause of the observed concave curve may be the under-sintering of the TPU powder in the low energy density region. In contrast, in the exponential model, the regression curve is simplified because it is a monotonic function. In this study, the response optimization was conducted by adapting a polynomial regression equation due to the higher R-sq value. The result of response optimization was described at the end of the chapter.
Table 3.14 Regression analysis results summary of the compressive load
Second-order polynomial curve fitting
Regression equation R-sq
25%
Compressive load 194.0 - 0.975 LP - 795 HD + 0.00507 LP*LP + 1651 HD*HD 87.58%
65%
Compressive load 869 - 5.80 LP - 3613 HD + 0.02727 LP*LP + 7699 HD*HD 86.98%
Exponential curve fitting
Regression equation R-sq
25%
Compressive load 33.6703 + Exp (3.15348 + 0.00931161 LP - 5.16113 HD) 82.02%
65%
Compressive load 105.898 + Exp (4.31014 + 0.0129111 LP - 9.20218 HD) 77.56%
２５ Regression model of cushion property
The relationship of the process parameter and the two cushion properties can be confirmed in the main effect plot (Figure 3.13). Since the sag factor is the ratio of 65% and 25% compressive load, and the hysteresis loss rate is the ratio of energy absorption in the loading and unloading stages, it does not show a linear relationship.
Figure 3.13 Main effect plot of sag factor(upper), and hysteresis loss rate (lower)
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In the regression model of the cushion property, SS, which does not show a significant difference in the sintering aspect of the lattice structure, was removed, as in the model in the compressive load. Model fitting was performed by stepwise removing the least significant coefficient among all coefficients of the cubic polynomial using the backward elimination of terms among the stepwise methods. The derived regression model is shown in Table 3.15, and the R-sq values of the sag factor and hysteresis loss rate are 78.22% and 45.89%, respectively.
Table 3.15 Regression analysis results summary of the cushion property
Property Regression equation R-sq
Sag factor 4.32 + 0.139 LP - 82.3 HD - 0.001072 LP*LP + 441 HD*HD - 0.301
LP*HD + 0.00651 LP*LP*HD - 3.26 LP*HD*HD 78.22%
Hysteresis loss
rate 0.614 - 0.00366 LP - 3.36 HD + 0.000004 LP*LP + 8.57 HD*HD +
0.0283 LP*HD - 0.0728 LP*HD*HD 45.89%
Response optimization
In practice, there are many applications where multiple competing objective functions need to be satisfied simultaneously. The multi-objective function is affected by more than one objective function that needs to be minimized or maximized. A solution can be derived by scoring two or more responses according to the movement of the independent variables. This means searching for two response surfaces. In addition, another solution can be derived by multiplying each response with a different weight value. In this study, the two types of cushion characteristics were divided into four scenarios, and the optimal process parameters for each scenario were proposed. The results of response optimization are shown in Table 3.16, and the optimal parameters suggested for each type of cushion required can be selected. For example, in the case of car seat cushions, maximum sag factor and minimum hysteresis are needed. At this time, the proposed equipment condition is able to obtain the desired cushion properties by outputting the lattice structure under the maximum condition of both laser power and hatching distance, as in the result of scenario No.
a.
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Table 3.16 Response optimization solution Scenario Sag
factor
Hysteresis loss rate
Laser Power [W]
Hatching Distance
[mm]
Sag factor
Fit
Hysteresis loss rate
Fit
Composite Desirability a Maximum minimum 144.000 0.240000 0.233442 2.74507 0.659186
b minimum Maximum 96.000 0.184682 0.236010 2.71437 0.482292
c Maximum Maximum 144.000 0.185051 0.238257 2.88522 0.721327 d minimum minimum 126.061 0.240000 0.233021 2.53807 0.943264
Figure 3.14 Optimization plot of scenarios a, b, c and d
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After reaction optimization, the recommended process parameters according to the cushion purpose will be especially effective in additive manufacturing processes because the conventional foaming process has a definite limitation that is difficult to control with specific physical properties due to the pseudo-stochastic arrangement inside [41]. In addition, the occurrence of internal void (Figure 3.15) due to random micro-structure further highlights the problems of the conventional process. Whereas, since the additively manufactured lattice structure is composed of an exquisite arrangement of unit cells, it is expected that the reproducibility of compression behavior can be improved. This shows not only the aspect of process automation but also the functional strength of the additive manufacturing process over the conventional foaming process.
Figure 3.15 Internal void of conventional foaming sponge
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