3.1. Preliminary Test: Measurements of Full-Open Micro-Pores (FOP)
Preliminary tests are performed by 3D printing the designed FOP micro-features without and with the compensation C, defined as equal to the nominal laser beam spot diameter D
LS=85μm. The diameters and depths measurements of micro-pores are reported in
Table 3 with their mean values and standard deviations; the same data are shown in
Figure 5.
The average error on pore diameters spans between -92 and -135 µm, and it is consistent (in value and sign) with the hypothesis of missing compensation of the laser beam spot radius on contours. Further confirmation arises from the measured diameter considering a compensation C= 85µm, increasing the pore dimension accordingly. In this latter case, the reduced error spans between -25 and -75 µm. It is also possible to observe that the error increases when the pore diameter decreases. This behavior can be attributed to the adhesion of the uncured liquid resin on the solid surface due to surface tension, whose effect increases as dimensions decrease and becomes evident for cavities with sub-millimetric diameters. Thus, the IPA washing aimed at removing uncured resin residuals is less effective on pores at the micro-scale, preventing the fabrication of micro-cavities below a threshold size.
The depth of the pores is affected by an average error that spans between -35 and -179µm, which is reduced when the compensation is adopted, varying between 3 and -103µm. The compensation has a beneficial influence on the depth error because it enlarges the cavity, producing two effects: it dampens the cutoff of the geometry slicing and reduces the resin adhesion effect.
3.2. Esteeme of the Compensation Parameter
The preliminary test reveals that the error in diameter is not fully compensated by adopting C equal to the nominal laser spot diameter, also at a millimetric scale.
An assessment of C has been attempted by printing and measuring the part shown in
Figure 6, which presents four repetitions of six squared thin wall features. The wall thicknesses vary in the following sequence: 0.05, 0.1, 0.15, 0.2, 0.25, and 0.17 mm.
Since slicing always has two paths on the edges of each thin wall, a feature with a wall thickness equal to two times the laser beam spot nominal diameter (170μm) was added at the end of the pattern.
Figure 6a shows the drawing of the proposed part for the correction factor estimation. Samples were fabricated according to the described conditions (
Section 2) and parameters (
Table 1). A sample of the part is shown in
Figure 6b,c.
The difference between the nominal and the measured wall thickness returns an estimate of how much the geometrical edge must be moved (offset) to achieve the complete compensation. The measurements are reported in
Table 4 with the estimated value of C.
The C value ranges between 88 and 102 µm, with an average value of 93 µm and a standard deviation of 8 µm. It must be observed that the average value tends to be greater than the nominal diameter of the laser spot (85 µm), with a growing trend when the wall thickness is thinner. This latter effect seems to be related to the step-over of the two on-edge laser paths (squares from 1 to 3), which increases when the wall thickness decreases. The high values of standard deviations are attributed to the different infill of the wall when the thickness increases at higher values (squared walls 4, 5, and 6). In fact, in these cases, when the wall thickness is higher than the laser beam spot diameter, the infill strategy is a rectilinear scan oriented along the machine y-axis. With this evidence (
Figure 7), all walls oriented along the x-axis are filled with a pattern of parallel lines orthogonal to the wall edge. In contrast, all walls oriented along the y-axis are filled with additional lines along the wall edge.
Therefore, this different infill strategy determines different UV-curing for the same walls with related variable thickness, thus higher values of standard deviations in measurements.
Figure 8 reports the graph of measurement of thin wall thicknesses and the estimated compensation parameter C. Nominal values of thin walls are represented by the slanted black dashed line. All deviations from this line are fabrication errors to be quantified. The values of the actual thin wall thicknesses along x- and y-axis are depicted with blue and green solid lines, respectively.
All measured thicknesses are higher than the nominal ones. The average wall thicknesses are depicted with a gray dashed line. As can be seen in the figure, wall thicknesses along the x-direction (blue line) are greater than those along the y-axis (green line), but the difference between them decreases beyond the threshold value of t*=150 μm. The differences between measured and nominal values are reported with an orange line.
As observed before, the estimated C is almost stable to about 100 μm up to the t*, and it decreases to 82-88 μm with thicknesses higher than t*. Indeed, up to t*, the infill is missing along the y-direction, while it is always present along the x-direction. The infill strategy significantly affects wall thickness accuracy, producing a different wall thickness depending on the wall orientation and nominal thickness, as shown in
Figure 8.
The error on the thin wall thickness is 74±4.5 µm and 112±11.9 µm along the y- and x-axis, respectively. The graph in
Figure 8 shows that the error on the wall thickness along the x-axis (blue line) is slightly reduced when its value is greater than 170μm, two times the nominal laser spot diameter. These data suggest that the current infill strategy produces geometrical anisotropy on features. Therefore, the part orientation on the XY plane affects the geometrical accuracy at the micro-scale. A different infill strategy (i.e., offset of the external perimeter) can improve the geometrical accuracy and reduce the anisotropy. More easily, an effective strategy to compensate for this anisotropy is an optimized orientation of the part on the build platform. Since the on-use machine allows only y-axis linear infill, an effective solution is a 45-degree orientation of the part on the XY plane (build platform).
Figure 9 shows the results obtained with the 45-degree orientation. The plot of the thin-wall measurements is depicted in
Figure 9a, while a picture of the confocal acquisition is reported in
Figure 9d. This part orientation (
Figure 9b), generates linear infill patterns (red lines in
Figure 9c) inside the wall thickness, which results in a sharply reduced anisotropy: same thickness (and error) along both the x- and y-axis. In fact, as it can be seen in
Figure 9a, the graph lines (green and blue) of measurements along the two axes are almost superimposed but still exhibit an error due to the missing compensation. Four samples were 3D-printed at different positions on the build platform. The measurements and statistical values are reported in
Table 5.
3.3. Constant Compensation Strategy
Since variability in the esteem of C has been found, the constant model compensations strategy was applied to the micro-pore diameters considering three levels of compensation:
C=+85 μm, is equal to the nominal laser spot diameter;
C=+96 μm, is the value obtained with the calibration tests;
C=+120 μm, value identified as the average error on diameter obtained in the preliminary tests when the compensation of +85μm was applied.
Figure 10 shows the effects of the constant compensation strategy compared with the curve obtained without compensation.
As can be seen from the figure, the constant compensations – the same value of the parameter C for all pores – are not fully effective, especially at the small scale (diameters below 1,2 mm), where the error dramatically increases. The smaller the micro-pore, the higher compensation is required. Furthermore, the value of C=120μm produces an overcompensation (positive errors) for feature diameters higher than 1.0 mm, and similar results are obtained with C=85μm for feature diameters higher than 1.6 mm.
From these results, it can be concluded that inaccuracy related to the laser spot diameter is the most important and can be effectively compensated for pore dimensions down to about 1.2 mm. When the pore diameter gets smaller and smaller, other phenomena become more dominant, and the constant compensation is no longer effective. However, a strategy of variable compensation based on the feature size and the error trend can be investigated in order to empirically compensate all the sources of inaccuracy.
3.4. Variable Compensation Strategy
The results presented in the previous section clearly suggest that a nonlinear compensation law could be more effective than a constant or a linear compensation strategy as the pore dimension decreases to take into account phenomena typically arising at the microscale, such as adhesion and surface tension.
The nonlinear compensation law can be derived by processing the experimental data set. Its identification was performed by following three steps:
Plot of all measurements of features on samples (i.e., FOP pore diameters), with and without compensations;
Identification by polynomial regression of a mathematical relationship between actual and nominal values of the meso- and micro-feature size;
Solving the equation obtained in the previous step, thus the value of the compensation parameter can be derived as a function of the feature size C = f(D) (i.e., pore diameter).
According to this procedure, data of nominal and actual diameters were plotted and analyzed. The polynomial model order for data identification was chosen as a trade-off between the mathematical complexity and the statistical confidence (coefficient of determination R
2) in the model’s data prediction. A second-order polynomial interpolation model (three parameters) was identified by the Microsoft Excel regression algorithm, resulting in a value of R
2=0.9954, which was considered satisfactory for the objective of the work. The model equations (explicit and implicit forms) are given by:
where y is the actual (measured) diameter, x is the related nominal diameter, and (a, b, c) are the parameters of the 2
nd-order polynomial regression model. The values of the model parameters are: a = -0.0001; b = 1.3641; c = -385.77. The equation (1) was solved to obtain the nominal (compensated) values (x) of diameters that give the desired (y) values. Finally, the values of the required compensation parameter C are calculated as the difference between the measured and the compensated values of the pore diameters:
where N is the total number of compensations to be calculated. In this work, eight (N=8) values of FOP diameters were assumed for the final validation of the procedure: 500, 600, 700, 800, 900, 1000, 1500, 2000 μm.
Figure 11 shows the plots of nominal (orange line) and measured (blue line) pore diameters obtained by the SLA fabrications. With the above-described procedure, the eight values of the compensation parameter were calculated and plotted in the same graph (grey line). The 2
nd-order polynomial interpolation curve (blue dashed line) is superimposed to the measured diameter curve, while the explicit form of the equation (1) is reported in the figure inset.
The model prediction of diameters and the related compensations were plotted on an extended and denser range of the nominal diameters (
Figure 12). The curve of the variable compensation parameter (yellow line) reveals that for bigger features (diameters bigger than 1.2 mm), the compensation has values close to the constant nominal compensation and does not vary significantly. For this reason, at the meso scale, a variable compensation is not required, and a constant compensation strategy can be adopted. Therefore, it can be concluded that a discontinuity occurs in the compensation law: variable compensation at the micro-scale, down to D’=1200μm and a constant compensation law beyond this threshold.
Four samples were 3D-printed at different positions on the build platform in order to explore the possible effects of this parameter on data dispersion and part accuracy (
Figure 14). Each sample reports a pattern of three sequences of full-open pores with eight target diameters in the range 500-2000μm. The compensation parameter for diameters higher than 1200μm was set to 96μm, thus the estimated value of the laser spot diameter obtained in
Section 3.3. The drawing of the samples is depicted in
Figure 13, and the nominal value of diameters and compensation parameters are reported in
Table 6.
The error percentages calculated on sample measurements with their dispersions are reported in
Figure 15. The curve of variable compensation (blue line) reveals a sharp improvement in accuracy with errors below 8.2%. The best sample error (yellow curve) is always below 4.4%. A slight overcompensation occurs at the micro-scale (below 900μm). Furthermore, a constant compensation strategy beyond D=1200μm is confirmed to be the best choice.
Table 7 reports mean errors and standard deviations without compensation and with constant and variable compensation.
As can be noticed, the absolute and percentage errors progressively decreased from no compensation to variable compensation. Also data dispersion has been improved. These results demonstrate that a compensation strategy increases the accuracy of technology, especially at the micro level. Furthermore, a variable compensation method based on the feature dimension is successful since it allows further improvement compared to the constant compensation strategy.