Surface Roughness Investigation of Poly-Jet 3D Printing

: An experimental investigation of the surface quality of the Poly-Jet 3D printing (PJ-3DP) process is presented. PJ-3DP is an additive manufacturing process, which uses jetted photopolymer droplets, which are immediately cured with ultraviolet lamps, to build physical models, layer-by-layer. This method is fast and accurate due to the mechanism it uses for the deposition of layers as well as the 16 microns of layer thickness used. To characterize the surface quality of PJ-3DP printed parts, an experiment was designed and the results were analyzed to identify the impact of the deposition angle and blade mechanism motion onto the surface roughness. First, linear regression models were extracted for the prediction of surface quality parameters, such as the average surface roughness ( Ra ) and the total height of the proﬁle ( Rt ) in the X and Y directions. Then, a Feed Forward Back Propagation Neural Network (FFBP-NN) was proposed for increasing the prediction performance of the surface roughness parameters Ra and Rt. These two models were compared with the reported ones in the literature; it was revealed that both performed better, leading to more accurate surface roughness predictions, whilst the NN model resulted in the best predictions, in particular for the Ra parameter.


Introduction
Poly-Jet 3D printing (PJ-3DP) is an Additive Manufacturing (AM) process capable of building accurate physical prototypes with complex geometry, by a process of adding photopolymer resin layers. This is enabled by a technology utilizing simultaneous jetting of modelling materials to create physical free form prototypes [1]. In PJ-3D printing, layers of a photopolymer resin are selectively jetted onto a build-tray via inkjet printing [2]. The printing head, composed of several micro-jetting heads, injects a 16 µm thick layer of resin into the built tray, corresponding to the built cross-sectional profile. The jetted photopolymer droplets are immediately cured with ultraviolet lamps that are mounted onto the 3D print carriage. A blade (knife), which is mounted onto the 3D print carriage, is used to remove the excess material as well as to plate the layers each time. The repeated addition and solidification of the resin layers produces an acrylic 3D model with a dimensional resolution of up to 16 microns.
Several attempts have been made to model or analyze surface quality of PJ-3D printing parts. Reeves and Cobb [32] were the first to derive an analytical model, which calculates analytically the average surface roughness: where, Lt is the layer thickness-height and θ is the sloped surface angle (deposition angle). This equation is used to calculate the average roughness based on geometry ( Figure 1a). Ahn, Kim and Lee [16] modified Equation (1) [4]; (b) modified model proposed by Ahn, Kim and Lee [16]; (c) model proposed by Kumar and Kumar [17].
Several attempts have been made to model or analyze surface quality of PJ-3D printing parts. Reeves and Cobb [32] were the first to derive an analytical model, which calculates analytically the average surface roughness: where, Lt is the layer thickness-height and θ is the sloped surface angle (deposition angle). This equation is used to calculate the average roughness based on geometry ( Figure 1a). Ahn, Kim and Lee [16] modified Equation (1), incorporating a surface profile angle (Φ) (Figure 1b) as: Kumar and Kumar [17] proposed a modified model ( Figure 1c) as: where ϕ is the profile angle, and they experimentally found it to be 12 degrees. Kechagias et al. [1] investigated the effect of the process parameters on the vertical and the planar surface roughness of parts produced by the PJ-3DP process. Analysis of Means diagrams were used to identify the optimum levels for each parameter and Analysis of Variance was used to identify the effect of each parameter on the surface roughness. The 16 microns layer thickness and the glossy style provided the optimum surface roughness results. The details of the specimen and the directions of the surface roughness measurements (A, B and C) are shown in Figure 2.
Kumar and Kumar [17] proposed a modified model ( Figure 1c) as: where φ is the profile angle, and they experimentally found it to be 12 degrees. Kechagias et al. [1] investigated the effect of the process parameters on the vertical and the planar surface roughness of parts produced by the PJ-3DP process. Analysis of Means diagrams were used to identify the optimum levels for each parameter and Analysis of Variance was used to identify the effect of each parameter on the surface roughness. The 16 microns layer thickness and the glossy style provided the optimum surface roughness results. The details of the specimen and the directions of the surface roughness measurements (A, B and C) are shown in Figure 2.  [1,12]; (b) specimens used for dimensional and surface roughness measurements [1,12].
Kechagias et al. [1,12] also investigated the effect of the process parameters on the dimensional accuracy of the same specimens. It is concluded that the layer thickness is the dominant factor for the linear dimensions of the X and Y directions. The impact on the X direction was found to be 44% while for the Y direction it was 97%. It is also pointed that this difference probably was due to the blade movement in the X direction and affected the surface roughness when the deposition angle changed.
Kechagias and Maropoulos [11] designed an experiment ( Figure 3) and measured the surface roughness parameters (Ra and Rt). It was found that the results did not follow the analytical model proposed by Reeves and Cobb [32], and they showed this graphically. Miyanaji, Momenzadeh and Yang [33] investigated the effect of the velocity of the droplets impinging the powder bed surface on the droplet spreading and absorption dynamics for the Binder Jetting Process. The effect of the 3D printing speed on the dimensional accuracy and the equilibrium saturation level of the 3D printed samples were investigated experimentally and the trends observed were discussed in detail. Khoshkhoo, Carrano and Blersch [34] studied the effect of the surface slope and the build orientation on the surface finish and the dimensional accuracy in the material jetting process. Specimens with flat area and four feature designs (i.e., spherical and prismatic hole and protrusions) were 3D printed in two orientations and the results were analyzed.
The current work extends the existing literature in the field by providing two experimental predictive models, a regression model, and a Feed Forward Back Propagation (FFBP) Neural Network (NN) model for the determination of the deposition angle and the blade mechanism movement effect on the surface roughness parameters (Ra and Rt) of Poly-Jet 3D printed specimens. Layer thickness was kept constant at 16 μm, as in this process only two discrete values for the layer Kechagias et al. [1,12] also investigated the effect of the process parameters on the dimensional accuracy of the same specimens. It is concluded that the layer thickness is the dominant factor for the linear dimensions of the X and Y directions. The impact on the X direction was found to be 44% while for the Y direction it was 97%. It is also pointed that this difference probably was due to the blade movement in the X direction and affected the surface roughness when the deposition angle changed.
Kechagias and Maropoulos [11] designed an experiment ( Figure 3) and measured the surface roughness parameters (Ra and Rt). It was found that the results did not follow the analytical model proposed by Reeves and Cobb [32], and they showed this graphically. Miyanaji, Momenzadeh and Yang [33] investigated the effect of the velocity of the droplets impinging the powder bed surface on the droplet spreading and absorption dynamics for the Binder Jetting Process. The effect of the 3D printing speed on the dimensional accuracy and the equilibrium saturation level of the 3D printed samples were investigated experimentally and the trends observed were discussed in detail. Khoshkhoo, Carrano and Blersch [34] studied the effect of the surface slope and the build orientation on the surface finish and the dimensional accuracy in the material jetting process. Specimens with flat area and four feature designs (i.e., spherical and prismatic hole and protrusions) were 3D printed in two orientations and the results were analyzed.
The current work extends the existing literature in the field by providing two experimental predictive models, a regression model, and a Feed Forward Back Propagation (FFBP) Neural Network (NN) model for the determination of the deposition angle and the blade mechanism movement effect on the surface roughness parameters (Ra and Rt) of Poly-Jet 3D printed specimens. Layer thickness was kept constant at 16 µm, as in this process only two discrete values for the layer thickness, 30 µm (quick) and 16 µm (fine) choices, can be used. Mate style was preferred for the experiment as it is the most used and gives uniform view of the models [1]. The analysis and modelling of the experimental setup was done in a previous authors' work [11]. The two models developed were compared and evaluated with other similar models found in the literature [17,32], showing increased accuracy, while extending the capabilities of the existing models at the same time (measurements in more than one direction). thickness, 30 μm (quick) and 16 μm (fine) choices, can be used. Mate style was preferred for the experiment as it is the most used and gives uniform view of the models [1]. The analysis and modelling of the experimental setup was done in a previous authors' work [11]. The two models developed were compared and evaluated with other similar models found in the literature [17,32], showing increased accuracy, while extending the capabilities of the existing models at the same time (measurements in more than one direction).

Experimental Set-up
The specimen for this work was designed with two details on the top surface ( Figure 3) and it is placed seven times, on the same platform, as shown in Figure 4. The sloped surfaces for both X and Y directions are 0, 15, 30, 45, 60, 75 and 90 degrees from the build platform. The selected part geometry was prepared in STL file format. The surface texture parameters measured during this study are the following (Figure 5a The seven prototypes were built on an Objet Eden 250 (Stratasys Ltd., Rehovot, Israel) 3D printing machine, using the Fullcure 720 RGD material ( Figure 5b). FullCure 720 is a translucent amber acrylic-based photopolymer material, with high durability (tensile strength 50-65 MPa according to the American Society for Testing and Materials (ASTM) D638-03 standard) and it is suitable for a wide range of rigid models, particularly where visibility of liquid flow or internal details is needed, making it ideal for moulds. It is used in applications, such as bottles and containers, lenses, packaging, general consumer products and others. Additionally, it is certified for medical use and it is appropriate for creating models for guided surgery [35,36]. For the experimental setup, layer thickness was set at 16 microns due to its great impact on planar and vertical dimensional accuracy [12]. The build style was defined by the control factor "Mate-M" or "Glossy-G", where glossy means that the sides of the part were built without support material. Mate mode was selected for all specimens, as it is more efficient for parts with complicated geometry.

Experimental Set-up
The specimen for this work was designed with two details on the top surface ( Figure 3) and it is placed seven times, on the same platform, as shown in Figure 4. The sloped surfaces for both X and Y directions are 0, 15, 30, 45, 60, 75 and 90 degrees from the build platform. The selected part geometry was prepared in STL file format. The surface texture parameters measured during this study are the following (Figure 5a Rt or Rmax (µm) ( Figure 5a): Total height of the roughness profile, i.e., the vertical distance between the highest peak and the lowest valley along the assessment length of the profile. As it can been seen from Figure 5a, R t = Z p + Z v . This parameter is extremely sensitive to high peaks or deep scratches.
The seven prototypes were built on an Objet Eden 250 (Stratasys Ltd., Rehovot, Israel) 3D printing machine, using the Fullcure 720 RGD material (Figure 5b). FullCure 720 is a translucent amber acrylic-based photopolymer material, with high durability (tensile strength 50-65 MPa according to the American Society for Testing and Materials (ASTM) D638-03 standard) and it is suitable for a wide range of rigid models, particularly where visibility of liquid flow or internal details is needed, making it ideal for moulds. It is used in applications, such as bottles and containers, lenses, packaging, general consumer products and others. Additionally, it is certified for medical use and it is appropriate for creating models for guided surgery [35,36]. For the experimental setup, layer thickness was set at 16 microns due to its great impact on planar and vertical dimensional accuracy [12]. The build style was defined by the control factor "Mate-M" or "Glossy-G", where glossy means that the sides of the part were built without support material. Mate mode was selected for all specimens, as it is more efficient for parts with complicated geometry.   Scanning Electron Microscopy (SEM) images were taken on the top and the side surface of the specimens, in order to visualize the surface pattern in a better way and to be able to further characterize the surface quality of the 3D printed surfaces. Images were taken with a JEOL model JSM 6390LV (JEOL Ltd., Tokyo, Japan) electron microscope in low vacuum mode at 5kV acceleration voltage on non-coated samples.

Regression Models
The seven parts were oriented and set on a platform, as shown in Figure 4. The layer thickness was set at 16 microns and the build style was set in mate mode, as mentioned in Section 2. After the manufacturing of the seven parts, they were cleaned using a waterjet machine and the sloped surfaces were measured using a Mitutoyo Surftest RJ-210 ® tester (Mitutoyo Corporation, Kanagawa, Japan). The measured values of the surface roughness parameters are presented in Table 1 for both the X and Y directions.
Linear regression models were adopted in order to fit the results, leading to Equations (4)- (7)    Scanning Electron Microscopy (SEM) images were taken on the top and the side surface of the specimens, in order to visualize the surface pattern in a better way and to be able to further characterize the surface quality of the 3D printed surfaces. Images were taken with a JEOL model JSM 6390LV (JEOL Ltd., Tokyo, Japan) electron microscope in low vacuum mode at 5kV acceleration voltage on non-coated samples.

Regression Models
The seven parts were oriented and set on a platform, as shown in Figure 4. The layer thickness was set at 16 microns and the build style was set in mate mode, as mentioned in Section 2. After the manufacturing of the seven parts, they were cleaned using a waterjet machine and the sloped surfaces were measured using a Mitutoyo Surftest RJ-210 ® tester (Mitutoyo Corporation, Kanagawa, Japan). The measured values of the surface roughness parameters are presented in Table 1 for both the X and Y directions.
Linear regression models were adopted in order to fit the results, leading to Equations (4)- (7) Scanning Electron Microscopy (SEM) images were taken on the top and the side surface of the specimens, in order to visualize the surface pattern in a better way and to be able to further characterize the surface quality of the 3D printed surfaces. Images were taken with a JEOL model JSM 6390LV (JEOL Ltd., Tokyo, Japan) electron microscope in low vacuum mode at 5kV acceleration voltage on non-coated samples.

Regression Models
The seven parts were oriented and set on a platform, as shown in Figure 4. The layer thickness was set at 16 microns and the build style was set in mate mode, as mentioned in Section 2. After the manufacturing of the seven parts, they were cleaned using a waterjet machine and the sloped surfaces were measured using a Mitutoyo Surftest RJ-210 ® tester (Mitutoyo Corporation, Kanagawa, Japan). The measured values of the surface roughness parameters are presented in Table 1 for both the X and Y directions.
Linear regression models were adopted in order to fit the results, leading to Equations (4)- (7): Rt x (µm) = 1.403 + 1.621·θ Ra y (µm) = 1.621 + 0.1555·θ Rt y (µm) = 14.10 + 1.091·θ (7) where θ is the angle that was used in Equations (1)-(3). These models are presented graphically in Figure 6. Figure 6a shows the Ra values calculated with the regression model in the X direction for the different deposition angles studied, while Figure 6b shows the Rt values calculated with the regression model in the X direction for the different deposition angles studied. Figure 6c,d show the equivalent surface roughness values (Ra and Rt, respectively) in the Y direction. = 14.10 + 1.091 • where θ is the angle that was used in Equations (1)-(3). These models are presented graphically in Figure 6. Figure 6a shows the Ra values calculated with the regression model in the X direction for the different deposition angles studied, while Figure 6b shows the Rt values calculated with the regression model in the X direction for the different deposition angles studied. Figure 6c,d show the equivalent surface roughness values (Ra and Rt, respectively) in the Y direction. Table 1 gives the prediction values of the proposed models and their errors (percentage, %), while Figure 7 graphically presents these values. In the literature, the Ra models presented [17] do not distinguish the calculated Ra values in the X and the Y direction, while the model presented in the current work calculates the Ra values separately for each one of the directions X and Y. On the other hand, Table 1 shows that in some cases the error is unacceptable, especially for the Rt predictions in both directions. For this reason, it is evident that further improvement is needed for more accurate predictions in specific cases.     Table 1 gives the prediction values of the proposed models and their errors (percentage, %), while Figure 7 graphically presents these values. In the literature, the Ra models presented [17] do not distinguish the calculated Ra values in the X and the Y direction, while the model presented in the  Table 1 shows that in some cases the error is unacceptable, especially for the Rt predictions in both directions. For this reason, it is evident that further improvement is needed for more accurate predictions in specific cases.

Arithmetic Modelling Using Neural Network (NN)
In order to predict the output values for the Ra and Rt values, according to the orientation of the sloped surface, a Feed Forward Back Propagation (FFBP) Neural Network (NN) was developed. Actual values for the Ra and Rt surface parameters were taken from Table 1; they were reorganized  and tabulated to Table 2. Data were divided as targets (columns 2 and 3; Table 2) and inputs (columns 3 and 4; Table 2). Deposition angle (DA, deg) is the angle formed by the sloped surface and the X-Y plane. Z axis rotation (Zrot, deg) gives the orientation of the sloped surface, according to the blade mechanism motion. When Zrot is zero (0) degrees, the sloped surface is in the same direction with the blade motion (Ra, X). Accordingly, ninety (90) degrees of Zrot means that the direction is perpendicular to the blade mechanism motion. D (data), I (input) and T (target) tables were formed as follows (Equations (8) Then, the "nntool" module (Matlab software, Mathworks, MA, USA) was used to train, validate and generalize an FFBP-NN model. Feed forward (FF) neural networks (NN), were trained with a classic BackPropagation (BP) algorithm. BP is a gradient descent (GD) algorithm that takes into account the networks' error function, which is a sum of squares, with the weights as its variables [37,38].
Neural networks consist of processing elements-neurons that are grouped in layers. Generally, each NN consists of the input vector, one or more hidden layers and the output layer. In this case, the following settings were used:

Arithmetic Modelling Using Neural Network (NN)
In order to predict the output values for the Ra and Rt values, according to the orientation of the sloped surface, a Feed Forward Back Propagation (FFBP) Neural Network (NN) was developed. Actual values for the Ra and Rt surface parameters were taken from Table 1; they were reorganized  and tabulated to Table 2. Data were divided as targets (columns 2 and 3; Table 2) and inputs (columns 3 and 4; Table 2). Deposition angle (DA, deg) is the angle formed by the sloped surface and the X-Y plane. Z axis rotation (Zrot, deg) gives the orientation of the sloped surface, according to the blade mechanism motion. When Zrot is zero (0) degrees, the sloped surface is in the same direction with the blade motion (Ra, X). Accordingly, ninety (90) degrees of Zrot means that the direction is perpendicular to the blade mechanism motion. D (data), I (input) and T (target) tables were formed as follows (Equations (8) Then, the "nntool" module (Matlab software, Mathworks, MA, USA) was used to train, validate and generalize an FFBP-NN model. Feed forward (FF) neural networks (NN), were trained with a classic BackPropagation (BP) algorithm. BP is a gradient descent (GD) algorithm that takes into account the networks' error function, which is a sum of squares, with the weights as its variables [37,38].
Neural networks consist of processing elements-neurons that are grouped in layers. Generally, each NN consists of the input vector, one or more hidden layers and the output layer. In this case, the following settings were used:

•
Network type: Feed-forward backprop; • Input data: I (Equation (6)); • Target data: T (Equation (5)  TANSIG is a hyperbolic tangent sigmoid transfer function. Transfer functions calculate a layer's output from its net input. PURELIN is a linear transfer function. Graphically, these two functions are shown in Figure 8.
The "best validation performance" and the "training" stage are shown in Figure 9. Figure 9a shows the mean square error, which is the objective function, and at which value it is optimized (13.3725 at epoch 0). Figure 9b shows the convergence between the experimental and the calculated values. The number of points considered for the verification of each case (training, validation, test, and all) are shown in the corresponding graphs. In all cases, the R factor is higher than 0.99, showing the accuracy and the reliability of the model results.
Another indicator used for the performance evaluation for the network efficiency is the regression coefficient (R). Regression values measure the correlation between the output values and the targets. For training, testing and validation, data were found to be higher than 0.99, which means that the NN performance is very accurate. The "best validation performance" and the "training" stage are shown in Figure 9. Figure 9a shows the mean square error, which is the objective function, and at which value it is optimized (13.3725 at epoch 0). Figure 9b shows the convergence between the experimental and the calculated values. The number of points considered for the verification of each case (training, validation, test, and all) are shown in the corresponding graphs. In all cases, the R factor is higher than 0.99, showing the accuracy and the reliability of the model results.

Comparison with the Literature
The two proposed models (regression and FFBP-NN) are used in this section for the evaluation of the surface roughness Ra parameter with the corresponding models presented in the literature. They are compared with the models found in the studies of Reeves and Cobb [32] and Kumar and Kumar [17] (see Table 3). The data that were used can be found in Kumar and Kumar [17]. The evaluation experiments in this work were applied on the proposed models for the average surface roughness Ra (μm), as mentioned above, since the literature models only study this surface roughness parameter. The deposition angle was calculated using an approximation, because it was not specifically mentioned in the study of Kumar and Kumar [17]. Figure 10a shows a comparison for the Ra error between the two prediction models. The results show that both the regression model and the FFBP-NN model give more accurate prediction results than the literature ones (Figure 10b). FFBP-NN improves the approximations even more and gives errors of less than 9%. Another indicator used for the performance evaluation for the network efficiency is the regression coefficient (R). Regression values measure the correlation between the output values and the targets. For training, testing and validation, data were found to be higher than 0.99, which means that the NN performance is very accurate.

Comparison with the Literature
The two proposed models (regression and FFBP-NN) are used in this section for the evaluation of the surface roughness Ra parameter with the corresponding models presented in the literature. They are compared with the models found in the studies of Reeves and Cobb [32] and Kumar and Kumar [17] (see Table 3). The data that were used can be found in Kumar and Kumar [17]. The evaluation experiments in this work were applied on the proposed models for the average surface roughness Ra (µm), as mentioned above, since the literature models only study this surface roughness parameter. The deposition angle was calculated using an approximation, because it was not specifically mentioned in the study of Kumar and Kumar [17]. Figure 10a shows a comparison for the Ra error between the two prediction models. The results show that both the regression model and the FFBP-NN model give more accurate prediction results than the literature ones (Figure 10b). FFBP-NN improves the approximations even more and gives errors of less than 9%.    (Table 3); (b) comparison of the Ra error between the prediction models and the literature.

Conclusions
In this work, two models were developed (a regression model and a NN model) in order to predict the surface roughness parameters of specimens, 3D printed with the MJ-3DP process. R square values for both models are higher than 96%, showing that the models are reliable. The NN model gives even better R values (more than 99%).
The experimental procedure showed that the surface roughness parameters (Ra and Rt) increase when the deposition angle was increased for both the X and Y directions. When the deposition angle is zero (0) degrees, the average surface roughness Ra is better for the X direction (0.537 μm) than for the Y direction (1.985 μm). The difference (Rax − Ray) is negative, (Rax -Ray) < 0. This is also observed for the total height Rt (Figure 11). These phenomena are an effect of the blade (knife) motion, mounded on the 3D print carriage, for removing excess material. The wear, as well as the small cured resin impurities that are deposited on the knife-edge produce the "striped surface" phenomenon along X direction (Figure 3b). Therefore, the surface roughness parameters in the Y direction are worse than the surface roughness parameters in the X direction. More cleaning or replacing of the knife mechanism can reduce this phenomenon. This was also verified by the SEM images taken on  (Table 3); (b) comparison of the Ra error between the prediction models and the literature.

Conclusions
In this work, two models were developed (a regression model and a NN model) in order to predict the surface roughness parameters of specimens, 3D printed with the MJ-3DP process. R square values for both models are higher than 96%, showing that the models are reliable. The NN model gives even better R values (more than 99%).
The experimental procedure showed that the surface roughness parameters (Ra and Rt) increase when the deposition angle was increased for both the X and Y directions. When the deposition angle is zero (0) degrees, the average surface roughness Ra is better for the X direction (0.537 µm) than for the Y direction (1.985 µm). The difference (Ra x − Ra y ) is negative, (Ra x -Ra y ) < 0. This is also observed for the total height Rt (Figure 11). These phenomena are an effect of the blade (knife) motion, mounded on the 3D print carriage, for removing excess material. The wear, as well as the small cured resin impurities that are deposited on the knife-edge produce the "striped surface" phenomenon along X direction (Figure 3b). Therefore, the surface roughness parameters in the Y direction are worse than the surface roughness parameters in the X direction. More cleaning or replacing of the knife mechanism can reduce this phenomenon. This was also verified by the SEM images taken on the top and the side surface of the specimens ( Figure 12). As it is shown, the top surface has a uniform pattern for the surface roughness (Figure 12a,b), indicating a higher reliability on the measurements taken and the prediction models developed with these measurements, owed to the Poly-Jet 3D printing process characteristics, while the side surface images (Figure 12c,d) clearly show the discrete deposited built layers, showing the uniform built structure of the specimens. All the SEM images taken during this study can be found in the Supplementary Material of this work. deposited built layers, showing the uniform built structure of the specimens. All the SEM images taken during this study can be found in the supplementary material of this work.
When the deposition angle is 45 degrees, the measured surface roughness parameters for the X direction show better performance than for the Y direction: (Rax − Ray) < 0 − < 0. This happens because of the layer profile geometry. It seems that the effect of the blade motion gives a better surface for the X direction than the Y direction. For all the other deposition angles, the surface roughness parameters are better in the Y direction than in the X direction. In order to incorporate the effect of the blade mechanism, an FFBP-NN was developed. This model's input parameters were the Z-axis rotation angle (Zrot) and the deposition angle (θ). Using this NN model, the predictions improved and became less than 9%, as it can been seen in the evaluation experiments (Table 3).  deposited built layers, showing the uniform built structure of the specimens. All the SEM images taken during this study can be found in the supplementary material of this work.
When the deposition angle is 45 degrees, the measured surface roughness parameters for the X direction show better performance than for the Y direction: (Rax − Ray) < 0 − < 0. This happens because of the layer profile geometry. It seems that the effect of the blade motion gives a better surface for the X direction than the Y direction. For all the other deposition angles, the surface roughness parameters are better in the Y direction than in the X direction. In order to incorporate the effect of the blade mechanism, an FFBP-NN was developed. This model's input parameters were the Z-axis rotation angle (Zrot) and the deposition angle (θ). Using this NN model, the predictions improved and became less than 9%, as it can been seen in the evaluation experiments (Table 3).  When the deposition angle is 45 degrees, the measured surface roughness parameters for the X direction show better performance than for the Y direction: (Ra x − Ra y ) < 0 Ra x − Ra y < 0. This happens because of the layer profile geometry. It seems that the effect of the blade motion gives a better surface for the X direction than the Y direction. For all the other deposition angles, the surface roughness parameters are better in the Y direction than in the X direction.
In order to incorporate the effect of the blade mechanism, an FFBP-NN was developed. This model's input parameters were the Z-axis rotation angle (Zrot) and the deposition angle (θ). Using this NN model, the predictions improved and became less than 9%, as it can been seen in the evaluation experiments (Table 3).