Table. 4 gives experimental results with control and response parameters.
Table 4
gives experimental results with control and response parameters.
Table 4. Experimental results | | | | |
No. | Control parameters | | Response parameters |
PS (mm/min) | Infill (%) | NT (°C) | | Outer Ovality (mm) | Interior Ovality (mm) | Density (g/cm3) |
1 | 50 | 10 | 195 | | 0.89 | 0.03 | 0.07 |
2 | 100 | 10 | 195 | | 0.9 | 0.06 | 0.1 |
3 | 150 | 10 | 195 | | 0.92 | 0.09 | 0.16 |
4 | 50 | 30 | 195 | | 0.96 | 0.05 | 0.1 |
5 | 100 | 30 | 195 | | 0.95 | 0.06 | 0.1 |
6 | 150 | 30 | 195 | | 0.96 | 0.08 | 0.17 |
7 | 50 | 50 | 195 | | 1 | 0.02 | 0.07 |
8 | 100 | 50 | 195 | | 1.02 | 0.03 | 0.09 |
9 | 150 | 50 | 195 | | 1 | 0.05 | 0.12 |
10 | 50 | 10 | 240 | | 0.9 | 0.04 | 0.09 |
11 | 100 | 10 | 240 | | 0.92 | 0.03 | 0.06 |
12 | 150 | 10 | 240 | | 0.89 | 0.03 | 0.07 |
13 | 50 | 30 | 240 | | 0.93 | 0.06 | 0.11 |
14 | 100 | 30 | 240 | | 0.97 | 0.01 | 0.03 |
15 | 150 | 30 | 240 | | 0.97 | 0.04 | 0.09 |
16 | 50 | 50 | 240 | | 1.02 | 0.06 | 0.13 |
17 | 100 | 50 | 240 | | 1.03 | 0.03 | 0.07 |
18 | 150 | 50 | 240 | | 1.02 | 0.04 | 0.06 |
In the following, each parameter is discussed separately.
Ovality
Ovality parameter is measured in two positions: inner diameter and outer diameter. ANOVA results for inner and outer ovality parameter are listed in Tables. 5 and 6, which shows effects of input variables consisting PS, IP and NT. According to the data in Tables 5 and 6, PS has the most influence on inner and outer ovality individually by contribution of 43.92% and 66.6%, respectively. On the other hand, the simultaneous influence of multiple factors on each response value should be examined in order to understand effects of 3D printing variables together. In this regard, ANOVA results help to study interaction effects of the input variables on the resultant parameter. Interaction of NT and PS has significant influence on inner ovality parameter with p-values < 0.003. This is also the same for outer ovality. Based on Tables 5 and 6, IP and NT has the same influence on outer ovality (14.6%) but in case of inner ovality, IP has more influence (36.3%) compared to NT (11.93%). That is dedicated IP is more influential on inner section of the 3D-printed parts. Hence, for the parts with inner holes, IP parameter will be more significant.
Table 5
Analysis of Variance for inner ovality
Source | Degree of Freedom | Contribution | Sum of squares | Mean | F-Value | P-Value |
Regression | 8 | 99.44% | 0.006913 | 0.000864 | 201.28 | 0.000 |
NT | 1 | 11.93% | 0.000048 | 0.000048 | 11.23 | 0.009 |
IP | 1 | 36.30% | 0.000018 | 0.000018 | 4.11 | 0.073 |
PS | 1 | 43.92% | 0.000014 | 0.000014 | 3.37 | 0.100 |
IP*IP | 1 | 1.94% | 0.000135 | 0.000135 | 31.34 | 0.000 |
PS*PS | 1 | 3.02% | 0.000210 | 0.000210 | 48.98 | 0.000 |
NT*IP | 1 | 0.81% | 0.000056 | 0.000056 | 13.12 | 0.006 |
NT*PS | 1 | 0.98% | 0.000068 | 0.000068 | 15.88 | 0.003 |
IP*PS | 1 | 0.54% | 0.000038 | 0.000038 | 8.82 | 0.016 |
Error | 9 | 0.56% | 0.000039 | 0.000004 | | |
Total | 17 | 100.00% | | | | |
Table 6
Analysis of Variance for outer ovality
Source | Degree of Freedom | Contribution | Sum of squares | Mean | F-Value | P-Value |
Regression | 8 | 98.60% | 0.023720 | 0.002965 | 79.31 | 0.000 |
NT | 1 | 14.63% | 0.000083 | 0.000083 | 2.21 | 0.171 |
IP | 1 | 14.60% | 0.000048 | 0.000048 | 1.30 | 0.284 |
PS | 1 | 66.60% | 0.000694 | 0.000694 | 18.57 | 0.002 |
IP*IP | 1 | 0.17% | 0.000041 | 0.000041 | 1.09 | 0.324 |
PS*PS | 1 | 0.02% | 0.000005 | 0.000005 | 0.14 | 0.713 |
NT*IP | 1 | 0.33% | 0.000078 | 0.000078 | 2.10 | 0.181 |
NT*PS | 1 | 1.49% | 0.000358 | 0.000358 | 9.57 | 0.013 |
IP*PS | 1 | 0.76% | 0.000183 | 0.000183 | 4.90 | 0.054 |
Error | 9 | 1.40% | 0.000336 | 0.000037 | | |
Total | 17 | 100.00% | | | | |
Figure 3 demonstrates main effects values for each factor that influences on inner and outer ovality, respectively. This plot shows influence of NT, infill and PS. Increasing NT causes lower ovality value that means improved dimensional accuracy. That is due to further adhesion of 3D printed layers in case of larger nozzle heat which creates stronger and more stable structure. Moreover, higher NT is required in order to release the material from the extruder without delay.
Based on Fig. 3, IP increment produces 3D printed structure with higher dimensional accuracy. This can be interpreted as result of higher 3D printed segment structure at higher IP. In case of low IP, the produced segment will be more porous. Hence, anisotropic shrinkage is happened and dimensional accuracy is reduced.
Figure 3 show that higher PS causes more ovality error amount. That could be due to low cooling time and residual heat from the bottom layer that induces unstable structure in 3D printed segment. On the other hand, Anitha et al.[25] proved that lower PS results in better surface quality. Therefore, lower PS improves both dimensional accuracy and surface quality.
Besides, based on the information obtained from ANOVA, interaction of NT and PS influences on ovality parameter. That is concluded in order to acquire better dimensional accuracy, higher NT and lower PS are more influential to be set together. In higher NT, the material is extruded easily and fills the porosities in the part which induces stronger structure with higher dimensional accuracy. In addition to this, lower PS helps to fill the part further.
As a result, the best dimensional accuracy is achieved in NT of 240°C, IP of 50% and PS of 150 mm/min.
In the following, regression correlations were established in order to estimate inner and outer ovality error (Eq. 1–2). In order to calculate the goodness of fit for Eq. 1–2, R-squared tool can be utilized. Higher R-squared indicates the established regression model strength. The calculated R-squared for Eqs. 1 and 2 is 97.79% and 95.37%, respectively which imply the best fitness of the second order regression correlation.
Inner Ovality = 0.0947–0.000234 NT − 0.000685 IP + 0.000265 PS − 0.000014 IP*IP + 0.000003 PS*PS + 0.000005 NT*IP − 0.000002 NT*PS − 0.000002 IP*PS R2 = 97.79% (1)
Outer Ovality = 0.0973–0.000307 NT − 0.001134 IP + 0.001837 PS − 0.000008 IP*IP + 0.000000 PS*PS + 0.000006 NT*IP − 0.000005 NT*PS − 0.000005 IP*PS R2 = 95.37% (2)
Previously, the regression model should be checked to be adequate. In this regard, normal probability plot of the residuals is used. This plot is a graphical tool in order to compare the response data (dimensional accuracy) with normal distribution. Fig. shows normal probability of residuals for the regression model in Eqs. 1 and 2. That is obvious most of the points are set along a straight line which implies normal distribution of errors of the established model.
Density
ANOVA results for density parameter is presented in Table 7 which shows effects of input parameters consisting PS, IP and NT on final density of the 3D printed part. According to Table 7, IP has the most influence on density individually by contribution of 92.94%. PS and NT are in the next orders but with very low contribution (0.75% and 0.35%, respectively).
On the other hand, ANOVA results help to study interaction effects of the input variables on the resultant parameter. In this regard, interaction of NT and IP have the most significant influence on density (0.52%).
Table 7
Analysis of Variance for density
Source | Degree of Freedom | Contribution | Sum of squares | Mean | F-Value | P-Value |
Regression | 8 | 95.73% | 0.038531 | 0.004816 | 25.21 | 0.000 |
NT | 1 | 0.35% | 0.000021 | 0.000021 | 0.11 | 0.748 |
IP | 1 | 92.94% | 0.000016 | 0.000016 | 0.08 | 0.779 |
PS | 1 | 0.75% | 0.000196 | 0.000196 | 1.02 | 0.338 |
IP*IP | 1 | 0.06% | 0.000025 | 0.000025 | 0.13 | 0.726 |
PS*PS | 1 | 0.99% | 0.000400 | 0.000400 | 2.09 | 0.182 |
NT*IP | 1 | 0.52% | 0.000208 | 0.000208 | 1.09 | 0.324 |
NT*PS | 1 | 0.00% | 0.000000 | 0.000000 | 0.00 | 1.000 |
IP*PS | 1 | 0.12% | 0.000050 | 0.000050 | 0.26 | 0.621 |
Error | 9 | 4.27% | 0.001719 | 0.000191 | | |
Total | 17 | 100.00% | | | | |
As demonstrated in Fig. 5, main effects plot for density is presented. NT and PS are not very influential on final segment density and have a little bit effect which can be neglected. On the other hand, IP increase leads to density increase because of lower part porosity in higher IP.
On the other hand, as obtained from ANOVA, NT and IP influence together on density. That was understood in order to obtain higher density, both higher temperature and IP are required. That seems in higher temperatures, the material releases quickly from the extruder and fills more porosities in the produced part.
In the following, regression correlation is established in order to estimate density of the part (Eq. 3). As described previously, in order to calculate the Eq. 2 goodness of fit, R-squared tool can be utilized. The calculated R-squared for Eq. 1 is 95.73% which implies the best fitness of the second order regression correlation.
Density = 0.861–0.000154 NT + 0.00065 IP + 0.000975 PS + 0.000006 IP*IP − 0.000004 PS*PS
+ 0.000009 NT*IP + 0.000000 NT*PS − 0.000003 IP*PS R2 = 81.95% (3)
In the following, adequacy of the established regression model (Eq. 3) is examined by normal probability plot of the residuals. This graphical tool helps to compare the density data with normal distribution. Figure 6 shows normal probability of residuals for the regression model in Eq. 3. That is observed most of the density points are set along a straight line which implies normal distribution of errors of the established model.
Optimization
Multi objective optimization is required to assess the best process condition aimed at the least dimensional error and the largest density. In this regard, desirability method will be applied. The relationships to obtain desirability value is as the following:
While di is the desirability value for each process response; Y is response value; Low and High are the minimum and maximum amount of the resultant response; r is number of the experimental tests; and w is the weight factor.
Optimized process condition is illustrated in Fig. 7. Red lines in Fig. 7 show optimum values for each effective parameter on Density, inner and outer ovality and finally in total process (named by composite desirability). Since composite desirability (D) value is 0.9606 and near to 1, that means the acquired condition is precise. That is shown composite desirability will be occurred in IP of 50%, PS of 50 mm/min and NT of 240° C.
On the other hand, confirmation evaluation should be conducted to verify the optimization procedure. According to Table 8, the verification test carried out and the error values between experimental and predicted results are 2.9%, 6.6% and 7.5% for density, inner and outer ovality, respectively. The error values are in acceptable range which indicate the optimization method is suitable for FDM process control.
Confidential interval demonstrates the probability that a certain parameter value will be in the defined range. The interval is calculated at the designated confidential level that is 95% in this investigation. Wider confidence range shows less confidential level of predicting the process responses. Both the predicted and experimental values are in confidential interval. Prediction interval is an estimation of interval that future results will occur. Prediction interval is always larger than confirmation interval. As shown in Table 8, the experimental results are in the range of prediction interval that shows the model prediction strength.
Table 8
Confirmation test results for optimum condition (NT = 240, IP = 50, PS = 54).
Parameter | Predicted result | Experimental result | Error amount (%) | Confidence interval (%) | Prediction interval (%) |
Density | 1.01 | 0.98 | 2.97 | (0.994,1.041) | ( 0.9788,1.0569) |
Inner ovality | 0.015 | 0.014 | 6.6 | (0.0116,0.0187) | (0.0093,0.0215) |
Outer ovality | 0.040 | 0.037 | 7.5 | (0.0296,0.0503) | (0.0227,0.0572) |
Part geometry effect
Because of axes moving and their interference in FDM process, the product shape influences on the process performance. In this regard, four geometrical shapes are selected for 3D printing: cube, cone, cylinder and pyramid. Influential parameters in determining 3D printing performance are surface quality and dimensional accuracy[26] which selected to examine the part geometrical effect. The produced parts are shown in Fig. 8.
In order to calculate dimensional and geometrical accuracy of the part, all dimensional errors are measured by CMM and the maximum error is reported. As demonstrated in Fig. 9, the cubic part has the best dimensional accuracy comparing to others. In cubic part, the X and Y axes move independently from each other. The error in the movements can be due to friction between the components. That is shown cylindrical part produces more dimensional error compared to cubic one. That could be due to axes movement simultaneously which produces further movement error. Also the parts that the lateral faces are perpendicular to XY plane (cube and cylinder), the dimensional error is lower comparing to conical and pyramidal shapes (lateral faces have lower than 90° angle with XY plane).
Moreover, Fig. 10 shows part geometry effect on surface roughness. The cone and pyramid shaped parts have the worst surface quality. That could be due to slicing procedure. Based on Fig. 11, because of larger dimensional error in nozzle movement, the gap will be produced in different heights which destroys the surface quality. This phenomenon is lower in cube and cylinder parts. Also the parts with circular cross-section (cone and cylinder) have higher surface roughness compared to rectangular cross-section ones (pyramid and cube) which is due to nozzle circular motion that induces further dimensional error and lower slices arrangement.