2 − 1 Materials and manufacturing methods
The role of printing location on the build platform (swath), the thickness of layers, color, and finish type are studied using a full factorial design of experiments as three control factors connected to the measured color. The Stratasys J55 3D printer was used to prepare the samples. A J55 placement zone consists of three areas of the same width: inner, mid, and outer (Fig. 1). The innermost location of the parts should be utilized first for optimal placement and reduced build time. The finish types between the colored layer and white bottom substrate were selected glossy on glossy (GoG) and glossy on matte (GoM) for studying as-printed samples. The specimen dimensions were 10 × 10 × 3.5 mm3 for color study (Fig. 2) and 60 × 13 × 3.5 mm3 for texture evaluation and trial color evaluation, respectively. The thresholds for each parameter were chosen to eliminate the influence of post-processing, as well as the limitations imposed by processing software and the 3D printer. For instance, the matte surface finish was avoided due to surface alteration during the support removal process. Furthermore, parts were designed with the minimum size required for measurement to counteract the effect of extended radial layers.
The primary specimens were 3 mm thick with 1.5 mm support material at the bottom, 1mm white background, and 1 mm colored material on top. This design method is based on Stratasys best practices for PolyJet and according to Pantone validated color matching system. It states that printed parts should have a wall thickness of at least 1 mm white background for optimal color reproduction. Since the defects and errors in observed CIEL*a*b* values for replicated samples were minimal in the trial experiments, one piece is studied under each experimental condition for the main investigation. In order to investigate the influence of each printing process parameter on the color quality, two sets of experiments have been conducted to reach the optimum condition using the minimum required samples. Levels for each of the experiments are shown in Table 1. The total 48 color samples were subjected to in-depth spectral analysis.
Table 1
Experiments and their levels
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Experiment 1
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Experiment 2
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Color
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Finishing
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Swath
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Thickness [mm]
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Swath
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Thickness [mm]
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Cyan
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GoG and GoMa
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Inn, Mid, and Outb
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1
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Mid
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0.2, 0.5, 1 and 2
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Magenta
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GoG and GoM
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Inn, Mid, and Out
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1
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Mid
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0.2, 0.5, 1 and 2
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Yellow
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GoG and GoM
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Inn, Mid, and Out
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1
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Mid
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0.2, 0.5, 1 and 2
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Black
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GoG and GoM
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Inn, Mid, and Out
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1
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Mid
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0.2, 0.5, 1 and 2
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a GoG: Glossy on Glossy finish, and GoM: Glossy on Matte finish |
b Inn: Inner (r-tray < 120 mm), Mid: Middle (120 mm < r-tray < 180 mm) and O: Outer (180 mm < r-tray < 230 mm) Swath. |
2–2 Measurement protocol
A Konica Minolta CS-2000 tele-spectroradiometer (TSR) was used to determine the spectral radiance at the 3D-printed object surface in the 380–780 nm spectral range (Fig. 3). The physical sampling interval was 10 nm, whereas the optical resolution was 1 nm. Using a 45:0 degrees viewing geometry, the surface of the 3D-printed item was evaluated according to CIE Publication 15.2 [20]. Each series of measurements was calibrated with the white Spectralon patch (Barium sulfate coating). The obtained radiances have been averaged from measurements in the field of view of 0.2 degrees on three-centric regions of the surfaces to overcome edge-loss in measuring reflectance on semi-translucent materials. At least ten horizontally distrusted 3D-printed layers were present at each targeted location on the studied surface. Any site having odd coloration, external particles, or support materials was avoided.
Measurements were taken in a dark room to avoid errors caused by other light sources such as ambient lighting. Radiance spectra have been recorded considering noise reduction due to the possible stray lights in the darkroom of the measurement.
Calculations were performed using the computational color science toolbox in MATLAB 2021 [21]. For this purpose, CIEXYZ tristimulus values were calculated according to the CIE 2° color-matching functions, using the sample reflectance and under the D50 illuminant. CIEL*a*b* coordinates were further calculated according to CIE1976 [20] and using the CIEXYZ tristimulus values in Eq. 1–3.
\({L}^{\text{*}}=116{\left(Y/{Y}_{n}\right)}^{1/3}-16\)
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(1)
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\({a}^{\text{*}}=500\left[{\left(X/{X}_{n}\right)}^{1/3}-{\left(Y/{Y}_{n}\right)}^{1/3}\right]\)
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(2)
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\({b}^{\text{*}}=200\left[{\left(Y/{Y}_{n}\right)}^{1/3}-{\left(Z/{Z}_{n}\right)}^{1/3}\right]\)
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(3)
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where Xn, Yn, and Zn are the tristimulus values of a specified white achromatic stimulus (Spectralon).
CIEDE2000 [22] colorimetric differences as given in Eq. 4 was calculated between the object printed on the 3 swaths. CIEL*a*b* values obtained from the objects with 1mm thickness printed in the middle swath were used as reference measurements when calculating the CIEDE2000 difference.
\(CIEDE2000=\sqrt{{\left(\frac{{\varDelta L}^{*}}{{k}_{L}{S}_{L}}\right)}^{2}+{\left(\frac{{\varDelta C}^{*}}{{k}_{C}{S}_{C}}\right)}^{2}+{\left(\frac{{\varDelta h}^{*}}{{k}_{h}{S}_{h}}\right)}^{2}+ {R}_{T}f\left({\varDelta C}^{*}{\varDelta h}^{*}\right)}\)
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(4)
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In Eq. 4, L*, C*, and h* refer to Lightness, Chroma (the distance out from the neutral axis - saturation), and hue as defined in CIE15.2 [20]. The constant values of kL (lightness), kC (chroma), and kh (hue) in computer graphic arts and 3D models are usually unity [23]. Other parameters refer to the hue rotation term (RT) and the compensation for lightness (SL), chroma (SC), and hue (Sh).
2–3 Texture evaluation
A total of nine printer objects, including three pieces printed on each swath, have been scanned vertically and horizontally using a coordinate measuring machine (CMM) model ZEISS DuraMax. Step width was set at 10 microns, a probe radius of 1.5 mm was chosen, and the machine was accurate to 2.4 microns. A desktop 3D scanner (AUTOSCAN INSPEC, SHINING 3D) was utilized in dark conditions. An 8-times rotation was made with the specimens mounted on a turntable every 45 degrees until a 360° view was achieved. An object was scanned with an accuracy of ≤ 10 µm under a blue-light projector emitting structured-light patterns. The distorted dimensions are measured using two 5.0MP CCD cameras on the scanner. The registered point cloud is collected from multiple scans at various object orientations. All digitization was merged using UltraScan 2022 software, and a raw texture-based model in STL (stereolithography) format was created in MeshLab (v2022.02). The 3D coordinates of the object were compared with the CMM results. Following the CMM acquisition, the raw data was processed in Gwyddion (v2.59) to determine layer thickness and heights as well as the topography.
Holmberg et al. [24] examined the surface microstructure changes during machining processes based on the full width at half maximum (FWHM) analysis and optical microscopy study. We utilized the FWHM values to analyze the height distribution. Texture evaluation allows reconstructing the profile of additive manufacturing and realizing data registration and appearance evaluation.
The FFT (Fast Fourier Transform) method removes all high-frequency noise, revealing the actual signal [25]. Several authors have demonstrated that the power spectral density (PSD) of a contact area determines the morphology of its surface [26–28]. Accordingly, we developed an algorithm for evaluating the 3-D geometry of additive manufacturing surfaces. Our method transforms 3D texture into a 2D coarseness profile using 1D Gaussian filtering and FFT filter smoothing. The asymmetric profiles associated with shape have been subtracted from the repeated texture profiles using polynomial fitting tools in OriginPro v9.5 to remove the effects of the form on the texture results.
According to ISO 16610-31, the robust regression Gaussian filter calculates weights individually for a primary profile and a waviness profile using iterative algorithms. Using this filter, the mean line is strongly associated with the general trend of the surface profile with spike discontinuities such as deep valleys and high peaks and is unaffected by outliers. FFT algorithm was implemented to remove high-frequency noises and reduce the waveforms to the absolute magnitude and phase data in a frequency domain. The power output versus frequency spectrum of the surface profiles examined by FFT spectra of signals, where power is normalized as the space (time in standard notations)-integral squared amplitude (TISA) using the following equations
\({P}_{xx}\left({e}^{j\omega }\right)={\sum }_{m=-{\infty }}^{{\infty }} {r}_{xx}\left(m\right){e}^{-j\omega m}\)
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(5)
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\(TISA \left(Power\right)=\frac{{\Delta }t\left({{R}_{e}}^{2}+{{I}_{m}}^{2}\right)}{n}\)
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(6)
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where \({P}_{xx}\left({e}^{j\omega }\right)\) is the power density or spectrum (PSD), \({r}_{xx}\left(m\right)\) is the auto-correlation function of the input signal, \({\Delta }t\) is the sampling interval, \({R}_{e}\) and \({I}_{m}\) are the real and imaginary parts of the transform data, and n is the length of the input sequence. In order to mitigate leakage, the single rectangle window function is applied as follows
\(N/{\sum }_{n=0}^{N-1} w(n{)}^{2}\)
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(7)
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where \(w\left(n\right)=1\) for \(0\le n\le N-1\), and zero otherwise.
2–4 Statistical analysis
The procedures were based on ISO/TS 23031:2020 (E). Accordingly, it is possible to evaluate the color difference between reference and test spectra and the root-mean-square error between them using the root-mean-square error (RMSE) and the mean color difference from the mean (MCDM) [29]. The following are the definitions
\(RMSE=\sqrt{\frac{1}{N}\sum _{i=1}^{N}{({\text{r}}_{r,i}-{\text{r}}_{t,i})}^{2}}\)
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(8)
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\(MCDM=\frac{1}{N}\sum _{i=1}^{N}\varDelta E({C}_{i},{C}_{m})\)
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(9)
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where rr and rt are the references and test spectrum, N is the number of reflectance readings, and Ci and Cm are the coordinate colors of the ith measurements and the average reflectance of all measurements, respectively. The RMSE of each quantitative variable is obtained to perform the spectral analysis, comparing the spectra of the target surfaces.
Multivariate analysis of the studied parameters and the response variables were run using principal component analysis (PCA) and the listwise Spearman rank correlation coefficient (Spearman rho, also signified by rs) due to small sample sizes [30]. PCA is a robust way of reducing the dimensionality of data. The raw data is linearly transformed into a set of principal components, which show the most significant variations in the raw sensor data. The PCA method of estimating correlations is a multivariate extension of linear regression to matrices containing independent and dependent variables [31, 32]. Two sets of variables can be viewed as asymmetrical, as one batch is considered an independent variable such as printing parameters and the other as a dependent variable. In this work, the matrix of appearance variables included measurements of color attributes including dL, dC, and dh.
Furthermore, Spearman rho was utilized to measure the relationship between the frequency of print variables and color attributes. It is a non-parametric measure for categorical data, which evaluates monotonic relationships of data that is not normally distributed regardless of linearity. Spearman rho of + 1 or -1 refers to the case where each variable is a mathematically ideal monotone function of the other [30]. Statistical analyses were carried out using OriginPro v9.5.