mathematics

Article

Surface Roughness Investigation of Poly-Jet3D Printing

Nectarios Vidakis 1, Markos Petousis 1,* , Nikolaos Vaxevanidis 2 and John Kechagias 3

1 Mechanical Engineering Department, Hellenic Mediterranean University, 71410 Heraklion Crete, Greece;vidakis@hmu.gr

2 Department of Mechanical Engineering Educators, School of Pedagogical and Technological Education,14121 Athens, Greece; vaxev@aspete.gr

3 General Department, University of Thessaly, 41500 Larissa, Greece; jkechag@uth.gr* Correspondence: markospetousis@hmu.gr; Tel.: +30-2810-37-9227

Received: 7 August 2020; Accepted: 12 October 2020; Published: 13 October 2020�����������������

Abstract: 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 photopolymerdroplets, 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 asthe 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 depositionangle and blade mechanism motion onto the surface roughness. First, linear regression models wereextracted 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 BackPropagation Neural Network (FFBP-NN) was proposed for increasing the prediction performance ofthe surface roughness parameters Ra and Rt. These two models were compared with the reportedones in the literature; it was revealed that both performed better, leading to more accurate surfaceroughness predictions, whilst the NN model resulted in the best predictions, in particular for theRa parameter.

Keywords: Poly-Jet; 3D printing; surface roughness; regression modelling; neural network

1. Introduction

Poly-Jet 3D printing (PJ-3DP) is an Additive Manufacturing (AM) process capable of buildingaccurate 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 physicalfree form prototypes [1]. In PJ-3D printing, layers of a photopolymer resin are selectively jetted onto abuild-tray via inkjet printing [2]. The printing head, composed of several micro-jetting heads, injects a16 µm thick layer of resin into the built tray, corresponding to the built cross-sectional profile. Thejetted photopolymer droplets are immediately cured with ultraviolet lamps that are mounted onto the3D print carriage. A blade (knife), which is mounted onto the 3D print carriage, is used to remove theexcess material as well as to plate the layers each time. The repeated addition and solidification of theresin layers produces an acrylic 3D model with a dimensional resolution of up to 16 microns.

The PJ-3DP process can simultaneously jet multiple materials with different mechanical andoptical properties. 3D printing process quality is affected by the layer thickness, the depositionmechanism dynamics (mass, blade, velocity, viscosity of resins used), the 3D digital model shape, thepart orientation, which is defined by the deposition angle and the blade direction (X-direction), andthe finishing method [3–14].

Mathematics 2020, 8, 1758; doi:10.3390/math8101758 www.mdpi.com/journal/mathematics

Mathematics 2020, 8, 1758 2 of 14

Due to the fact that the material is built layer by layer, a typical staircase error is caused when theshape does not align with the printing orientation [4] (Figure 1). The staircase error can be reduced byusing thinner slices at the cost of more printing layers and building time [15–17].

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part orientation, which is defined by the deposition angle and the blade direction (X-direction), and the finishing method [3–14].

Due to the fact that the material is built layer by layer, a typical staircase error is caused when the shape does not align with the printing orientation [4] (Figure 1). The staircase error can be reduced by using thinner slices at the cost of more printing layers and building time [15–17].

Figure 1. (a) Platform setup—side view [4]; (b) modified model proposed by Ahn, Kim and Lee [16]; (c) model proposed by Kumar and Kumar [17].

The surface quality of the 3D printed parts has been studied in the literature for Fused Filament Fabrication (FFF) [18–26], Micro-Stereolithography [27], Laminated Object Manufacturing [28] and Selective Laser Sintering (SLS) parts [29–31]. Mathematical [18,21], empirical [22] and learning-based predictive [26] models have been presented, considering the 3D printing parameters [24,28], for the surface roughness of FFF parts, while nondestructive characterization methods are used to determine the surface roughness of SLS parts [31]. Moreover, the effect of surface roughness on the fatigue behavior of SLS parts is also studied and it was determined that a linear elastic model produced adequate results. The model was verified with experimental data [29].

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:

= = (1)

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:

Figure 1. (a) Platform setup—side view [4]; (b) modified model proposed by Ahn, Kim and Lee [16];(c) model proposed by Kumar and Kumar [17].

The surface quality of the 3D printed parts has been studied in the literature for Fused FilamentFabrication (FFF) [18–26], Micro-Stereolithography [27], Laminated Object Manufacturing [28] andSelective Laser Sintering (SLS) parts [29–31]. Mathematical [18,21], empirical [22] and learning-basedpredictive [26] models have been presented, considering the 3D printing parameters [24,28], for thesurface roughness of FFF parts, while nondestructive characterization methods are used to determinethe surface roughness of SLS parts [31]. Moreover, the effect of surface roughness on the fatiguebehavior of SLS parts is also studied and it was determined that a linear elastic model producedadequate results. The model was verified with experimental data [29].

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 theaverage surface roughness:

Ra =Ltsin(θ)4tan(θ)

=Ltcos(θ)

4(1)

where, Lt is the layer thickness–height and θ is the sloped surface angle (deposition angle). Thisequation is used to calculate the average roughness based on geometry (Figure 1a). Ahn, Kim andLee [16] modified Equation (1), incorporating a surface profile angle (Φ) (Figure 1b) as:

Ra =Ltsin(θ)4tan(θ)

=Ltcos(θ)

4(2)

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Kumar and Kumar [17] proposed a modified model (Figure 1c) as:

Ra =Ltsin(θ)4tan(θ)

=Ltcos(θ)

4(3)

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 usedto identify the optimum levels for each parameter and Analysis of Variance was used to identify theeffect of each parameter on the surface roughness. The 16 microns layer thickness and the glossy styleprovided the optimum surface roughness results. The details of the specimen and the directions of thesurface roughness measurements (A, B and C) are shown in Figure 2.

Mathematics 2020, 8, x FOR PEER REVIEW 3 of 14

= 4 = 4 (2)

Kumar and Kumar [17] proposed a modified model (Figure 1c) as: = 4 = 4 (3)

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.

Figure 2. (a) Shape and direction of Ra measurements [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

Figure 2. (a) Shape and direction of Ra measurements [1,12]; (b) specimens used for dimensional andsurface roughness measurements [1,12].

Kechagias et al. [1,12] also investigated the effect of the process parameters on the dimensionalaccuracy of the same specimens. It is concluded that the layer thickness is the dominant factor for thelinear dimensions of the X and Y directions. The impact on the X direction was found to be 44% whilefor the Y direction it was 97%. It is also pointed that this difference probably was due to the blademovement 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 surfaceroughness parameters (Ra and Rt). It was found that the results did not follow the analytical modelproposed by Reeves and Cobb [32], and they showed this graphically. Miyanaji, Momenzadeh andYang [33] investigated the effect of the velocity of the droplets impinging the powder bed surface on thedroplet spreading and absorption dynamics for the Binder Jetting Process. The effect of the 3D printingspeed on the dimensional accuracy and the equilibrium saturation level of the 3D printed samples wereinvestigated experimentally and the trends observed were discussed in detail. Khoshkhoo, Carranoand Blersch [34] studied the effect of the surface slope and the build orientation on the surface finishand the dimensional accuracy in the material jetting process. Specimens with flat area and four featuredesigns (i.e., spherical and prismatic hole and protrusions) were 3D printed in two orientations andthe results were analyzed.

The current work extends the existing literature in the field by providing two experimentalpredictive 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 effecton the surface roughness parameters (Ra and Rt) of Poly-Jet 3D printed specimens. Layer thickness waskept 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

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used and gives uniform view of the models [1]. The analysis and modelling of the experimental setupwas done in a previous authors’ work [11]. The two models developed were compared and evaluatedwith other similar models found in the literature [17,32], showing increased accuracy, while extendingthe capabilities of the existing models at the same time (measurements in more than one direction).

Mathematics 2020, 8, x FOR PEER REVIEW 4 of 14

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).

Figure 3. (a) Basic specimen dimensions and shape details for identifying the X, Y, and Z directions, after build. (b) “Striped surface” result, due to knife movement.

2. 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):

• Ra (μm) (Figure 5a): The arithmetic mean surface roughness (mean of the sums of all profile values). Ra is by far the most commonly used parameter in surface finish measurements. Despite its inherent limitations, it is easy to measure and offers a good overall description of the height characteristics of a surface profile.

• 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, Rt = Zp + Zv. 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.

Figure 3. (a) Basic specimen dimensions and shape details for identifying the X, Y, and Z directions,after build. (b) “Striped surface” result, due to knife movement.

2. Experimental Set-up

The specimen for this work was designed with two details on the top surface (Figure 3) and it isplaced seven times, on the same platform, as shown in Figure 4. The sloped surfaces for both X and Ydirections are 0, 15, 30, 45, 60, 75 and 90 degrees from the build platform. The selected part geometrywas prepared in STL file format. The surface texture parameters measured during this study are thefollowing (Figure 5a):

• Ra (µm) (Figure 5a): The arithmetic mean surface roughness (mean of the sums of all profilevalues). Ra is by far the most commonly used parameter in surface finish measurements. Despiteits inherent limitations, it is easy to measure and offers a good overall description of the heightcharacteristics of a surface profile.

• Rt or Rmax (µm) (Figure 5a): Total height of the roughness profile, i.e., the vertical distancebetween the highest peak and the lowest valley along the assessment length of the profile. As itcan been seen from Figure 5a, Rt = Zp + Zv. This parameter is extremely sensitive to high peaks ordeep scratches.

The seven prototypes were built on an Objet Eden 250 (Stratasys Ltd., Rehovot, Israel) 3D printingmachine, using the Fullcure 720 RGD material (Figure 5b). FullCure 720 is a translucent amberacrylic-based photopolymer material, with high durability (tensile strength 50–65 MPa according tothe American Society for Testing and Materials (ASTM) D638-03 standard) and it is suitable for a widerange of rigid models, particularly where visibility of liquid flow or internal details is needed, makingit ideal for moulds. It is used in applications, such as bottles and containers, lenses, packaging, generalconsumer products and others. Additionally, it is certified for medical use and it is appropriate forcreating models for guided surgery [35,36]. For the experimental setup, layer thickness was set at 16microns due to its great impact on planar and vertical dimensional accuracy [12]. The build style wasdefined by the control factor “Mate-M” or “Glossy-G”, where glossy means that the sides of the partwere built without support material. Mate mode was selected for all specimens, as it is more efficientfor parts with complicated geometry.

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Figure 4. Specimens manufactured by Kechagias and Maropoulos, 2015: (a) the orientation the specimens were built in the different cases studied in this work, (b) typical samples of the different 3D printed specimens studied in this work.

Figure 5. (a) Surface texture parameters; (b) Eden250™ 3D Printing System.

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.

3. Modelling

3.1. 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): = 0.5205 + 0.1971 ∙ (4) = 1.403 + 1.621 ∙ (5) = 1.621 + 0.1555 ∙ (6)

Figure 4. Specimens manufactured by Kechagias and Maropoulos, 2015: (a) the orientation thespecimens were built in the different cases studied in this work, (b) typical samples of the different 3Dprinted specimens studied in this work.

Mathematics 2020, 8, x FOR PEER REVIEW 5 of 14

Figure 4. Specimens manufactured by Kechagias and Maropoulos, 2015: (a) the orientation the specimens were built in the different cases studied in this work, (b) typical samples of the different 3D printed specimens studied in this work.

Figure 5. (a) Surface texture parameters; (b) Eden250™ 3D Printing System.

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.

3. Modelling

3.1. 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): = 0.5205 + 0.1971 ∙ (4) = 1.403 + 1.621 ∙ (5) = 1.621 + 0.1555 ∙ (6)

Figure 5. (a) Surface texture parameters; (b) Eden250™ 3D Printing System.

Scanning Electron Microscopy (SEM) images were taken on the top and the side surface of thespecimens, in order to visualize the surface pattern in a better way and to be able to further characterizethe 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 onnon-coated samples.

3. Modelling

3.1. Regression Models

The seven parts were oriented and set on a platform, as shown in Figure 4. The layer thicknesswas set at 16 microns and the build style was set in mate mode, as mentioned in Section 2. After themanufacturing of the seven parts, they were cleaned using a waterjet machine and the sloped surfaceswere 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 andY directions.

Linear regression models were adopted in order to fit the results, leading to Equations (4)–(7):

Rax (µm) = 0.5205 + 0.1971·θ (4)

Rtx (µm) = 1.403 + 1.621·θ (5)

Ray (µm) = 1.621 + 0.1555·θ (6)

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Rty (µm) = 14.10 + 1.091·θ (7)

where θ is the angle that was used in Equations (1)–(3). These models are presented graphically inFigure 6. Figure 6a shows the Ra values calculated with the regression model in the X direction for thedifferent deposition angles studied, while Figure 6b shows the Rt values calculated with the regressionmodel in the X direction for the different deposition angles studied. Figure 6c,d show the equivalentsurface roughness values (Ra and Rt, respectively) in the Y direction.

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= 14.10 + 1.091 ∙ (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.

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.

Figure 6. Plot lines for the regression models: (a,b) X direction; (c,d) Y direction.

Table 1. Measurements: Actual and predicted values.

Deposition Angle (Degrees)

0 15 30 45 60 75 90 Actual Ra (X, μm) 0.537 4.188 6.259 8.377 12.425 15.211 18.722 Actual Rt (X, μm) 4.294 29.311 44.345 61.807 102.280 140.930 137.540 Actual Ra (Y, μm) 1.985 3.584 5.367 8.729 12.035 14.142 14.496 Actual Rt (Y, μm) 13.393 25.167 43.641 76.513 80.545 97.445 105.620

Predicted Ra (X, μm) 0.521 3.477 6.434 9.390 12.347 15.303 18.260 Predicted Rt (X, μm) 1.403 25.718 50.033 74.348 98.663 122.978 147.293 Predicted Ra (Y, μm) 1.621 3.954 6.286 8.619 10.951 13.284 15.616 Predicted Rt (Y, μm) 14.100 30.465 46.830 63.195 79.560 95.925 112.290

Error Ra (X, %) −3 −17 3 12 −1 1 −2 Error Rt (X, %) −67 −12 13 20 −4 −13 7 Error Ra (Y, %) −18 10 17 −1 −9 −6 8

Figure 6. Plot lines for the regression models: (a,b) X direction; (c,d) Y direction.

Table 1. Measurements: Actual and predicted values.

Deposition Angle (Degrees)

0 15 30 45 60 75 90

Actual Ra (X, µm) 0.537 4.188 6.259 8.377 12.425 15.211 18.722Actual Rt (X, µm) 4.294 29.311 44.345 61.807 102.280 140.930 137.540Actual Ra (Y, µm) 1.985 3.584 5.367 8.729 12.035 14.142 14.496Actual Rt (Y, µm) 13.393 25.167 43.641 76.513 80.545 97.445 105.620

Predicted Ra (X, µm) 0.521 3.477 6.434 9.390 12.347 15.303 18.260Predicted Rt (X, µm) 1.403 25.718 50.033 74.348 98.663 122.978 147.293Predicted Ra (Y, µm) 1.621 3.954 6.286 8.619 10.951 13.284 15.616Predicted Rt (Y, µm) 14.100 30.465 46.830 63.195 79.560 95.925 112.290

Error Ra (X, %) −3 −17 3 12 −1 1 −2Error Rt (X, %) −67 −12 13 20 −4 −13 7Error Ra (Y, %) −18 10 17 −1 −9 −6 8Error Rt (Y, %) 5 21 7 −17 −1 −2 6

Ra(X)-Ra(Y), Actual −1.448 0.604 0.892 −0.352 0.390 1.069 4.226Rt(X)-Rt(Y), Actual −9.099 4.144 0.704 −14.706 21.735 43.485 31.920

Table 1 gives the prediction values of the proposed models and their errors (percentage, %), whileFigure 7 graphically presents these values. In the literature, the Ra models presented [17] do notdistinguish the calculated Ra values in the X and the Y direction, while the model presented in the

Mathematics 2020, 8, 1758 7 of 14

current work calculates the Ra values separately for each one of the directions X and Y. On the otherhand, Table 1 shows that in some cases the error is unacceptable, especially for the Rt predictions inboth directions. For this reason, it is evident that further improvement is needed for more accuratepredictions in specific cases.

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Error Rt (Y, %) 5 21 7 −17 −1 −2 6 Ra(X)-Ra(Y), Actual −1.448 0.604 0.892 -0.352 0.390 1.069 4.226 Rt(X)-Rt(Y), Actual −9.099 4.144 0.704 −14.706 21.735 43.485 31.920

Figure 7. Bar charts for Ra and Rt values (actual, predicted and errors).

3.2. 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)–(10); in Matlab code):

D = [14 × 4]; (8)

T = D(:,3:4)’; (9)

I = D(:,1:2)’; (10)

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;

Figure 7. Bar charts for Ra and Rt values (actual, predicted and errors).

3.2. Arithmetic Modelling Using Neural Network (NN)

In order to predict the output values for the Ra and Rt values, according to the orientation ofthe 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 reorganizedand tabulated to Table 2. Data were divided as targets (columns 2 and 3; Table 2) and inputs (columns3 and 4; Table 2). Deposition angle (DA, deg) is the angle formed by the sloped surface and the X–Yplane. Z axis rotation (Zrot, deg) gives the orientation of the sloped surface, according to the blademechanism motion. When Zrot is zero (0) degrees, the sloped surface is in the same direction with theblade motion (Ra, X). Accordingly, ninety (90) degrees of Zrot means that the direction is perpendicularto the blade mechanism motion.

D (data), I (input) and T (target) tables were formed as follows (Equations (8)–(10); in Matlab code):

D = [14 × 4]; (8)

T = D(:,3:4)’; (9)

I = D(:,1:2)’; (10)

Then, the “nntool” module (Matlab software, Mathworks, MA, USA) was used to train, validateand generalize an FFBP-NN model. Feed forward (FF) neural networks (NN), were trained with aclassic BackPropagation (BP) algorithm. BP is a gradient descent (GD) algorithm that takes into accountthe 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, thefollowing settings were used:

Mathematics 2020, 8, 1758 8 of 14

• Network type: Feed-forward backprop;• Input data: I (Equation (6));• Target data: T (Equation (5));• Training function: TRAINLM (Levenberg–Marquardt);• Adaptation learning function: LEARNGDM;• Performance function: MSE (mean squared error);• One hidden layer with 5 neurons using TANSIG as the transfer function;• Transfer function for output: PURELIN.

Table 2. Inputs and targets for the NN modeling.

Inputs Targets

Da (deg) Zrot (deg) Ra (µm) Rt (µm)

Column 1 Column 2 Column 3 Column 4

Row 1 0 0 0.537 4.294

Row 2 15 0 4.188 29.311

Row 3 30 0 6.259 44.345

Row 4 45 0 8.377 61.807

Row 5 60 0 12.425 102.28

Row 6 75 0 15.211 140.93

Row 7 90 0 18.722 137.54

Row 8 0 90 1.985 13.393

Row 9 15 90 3.584 25.167

Row 10 30 90 5.367 43.641

Row 11 45 90 8.729 76.513

Row 12 60 90 12.035 80.545

Row 13 75 90 14.142 97.445

Row 14 90 90 14.496 105.62

TANSIG is a hyperbolic tangent sigmoid transfer function. Transfer functions calculate a layer’soutput from its net input. PURELIN is a linear transfer function. Graphically, these two functions areshown in Figure 8.

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• Input data: I (Equation (6)); • Target data: T (Equation (5)); • Training function: TRAINLM (Levenberg–Marquardt); • Adaptation learning function: LEARNGDM; • Performance function: MSE (mean squared error); • One hidden layer with 5 neurons using TANSIG as the transfer function; • Transfer function for output: PURELIN.

Table 2. Inputs and targets for the NN modeling.

Inputs Targets Da (deg) Zrot (deg) Ra (μm) Rt (μm) Column 1 Column 2 Column 3 Column 4

Row 1 0 0 0.537 4.294 Row 2 15 0 4.188 29.311 Row 3 30 0 6.259 44.345 Row 4 45 0 8.377 61.807 Row 5 60 0 12.425 102.28 Row 6 75 0 15.211 140.93 Row 7 90 0 18.722 137.54 Row 8 0 90 1.985 13.393 Row 9 15 90 3.584 25.167

Row 10 30 90 5.367 43.641 Row 11 45 90 8.729 76.513 Row 12 60 90 12.035 80.545 Row 13 75 90 14.142 97.445 Row 14 90 90 14.496 105.62

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.

Figure 8. (a) PURELIN linear transfer function; (b) TANSIG hyperbolic tangent sigmoidtransfer function.

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The “best validation performance” and the “training” stage are shown in Figure 9. Figure 9ashows 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 calculatedvalues. The number of points considered for the verification of each case (training, validation, test, andall) are shown in the corresponding graphs. In all cases, the R factor is higher than 0.99, showing theaccuracy and the reliability of the model results.

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Figure 8. (a) PURELIN linear transfer function; (b) TANSIG hyperbolic tangent sigmoid transfer function.

Figure 9. Training and performance of the FFBP-NN: (a) Mean square error graphs for the 6 epochs, (b) graphs produced during the model development, showing the reliability of the model.

3.3. 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%.

Figure 9. Training and performance of the FFBP-NN: (a) Mean square error graphs for the 6 epochs, (b)graphs produced during the model development, showing the reliability of the model.

Another indicator used for the performance evaluation for the network efficiency is the regressioncoefficient (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 NNperformance is very accurate.

3.3. Comparison with the Literature

The two proposed models (regression and FFBP-NN) are used in this section for the evaluationof 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 andKumar [17] (see Table 3). The data that were used can be found in Kumar and Kumar [17]. Theevaluation experiments in this work were applied on the proposed models for the average surfaceroughness Ra (µm), as mentioned above, since the literature models only study this surface roughnessparameter. The deposition angle was calculated using an approximation, because it was not specificallymentioned in the study of Kumar and Kumar [17]. Figure 10a shows a comparison for the Ra errorbetween the two prediction models. The results show that both the regression model and the FFBP-NNmodel give more accurate prediction results than the literature ones (Figure 10b). FFBP-NN improvesthe approximations even more and gives errors of less than 9%.

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Table 3. Comparison of Ra predictive models.

Evaluation Experiments 1 2 3 4 5

Deposition Angle (θ, Degrees) 10 25 45 65 90

Average Surface roughness (Ra, µm)

Measured Ra 2.77 5.24 7.91 13.77 17.63Kumar and Kumar model (Equation (3)) 4 5 8 15 20Reeves and Cobb model (Equation (1)) 8 7.51 6.12 4 0.7

Proposed model (Equation (4)) 2.4915 5.448 8.4045 13.332 18.2595NN–X direction (Zrot = 0 deg) 2.5676 4.9179 7.2871 14.9647 18.0279

Error (%)

Kumar and Kumar model (Equation (3)) 44.4% −4.6% 1.1% 8.9% 13.4%Reeves and Cobb model (Equation (1)) 188.8% 43.3% −22.6% −71.0% −96.0%

Regression model (Equation (4)) −10.1% 4.0% 6.3% −3.2% 3.6%FFBP-NN model −7.3% −6.1% −7.9% 8.7% 2.3%

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Table 3. Comparison of Ra predictive models.

Evaluation Experiments 1 2 3 4 5 Deposition Angle (θ, Degrees) 10 25 45 65 90

Average Surface roughness (Ra, μm) Measured Ra 2.77 5.24 7.91 13.77 17.63

Kumar and Kumar model (Equation (3)) 4 5 8 15 20

Reeves and Cobb model (Equation (1)) 8 7.51 6.12 4 0.7 Proposed model (Equation (4)) 2.4915 5.448 8.4045 13.332 18.2595 NN–X direction (Zrot = 0 deg) 2.5676 4.9179 7.2871 14.9647 18.0279

Error (%) Kumar and Kumar model (Equation

(3)) 44.4% −4.6% 1.1% 8.9% 13.4%

Reeves and Cobb model (Equation (1)) 188.8% 43.3% −22.6% −71.0% −96.0% Regression model (Equation (4)) −10.1% 4.0% 6.3% -3.2% 3.6%

FFBP-NN model −7.3% −6.1% −7.9% 8.7% 2.3%

Figure 10. (a) Error of Ra for the prediction models (Table 3); (b) comparison of the Ra error between the prediction models and the literature.

4. 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

Figure 10. (a) Error of Ra for the prediction models (Table 3); (b) comparison of the Ra error betweenthe prediction models and the literature.

4. Conclusions

In this work, two models were developed (a regression model and a NN model) in order to predictthe surface roughness parameters of specimens, 3D printed with the MJ-3DP process. R square valuesfor both models are higher than 96%, showing that the models are reliable. The NN model gives evenbetter R values (more than 99%).

The experimental procedure showed that the surface roughness parameters (Ra and Rt) increasewhen the deposition angle was increased for both the X and Y directions. When the deposition angle iszero (0) degrees, the average surface roughness Ra is better for the X direction (0.537 µm) than for the Ydirection (1.985 µm). The difference (Rax − Ray) is negative, (Rax – Ray) < 0. This is also observed forthe total height Rt (Figure 11). These phenomena are an effect of the blade (knife) motion, moundedon the 3D print carriage, for removing excess material. The wear, as well as the small cured resinimpurities that are deposited on the knife-edge produce the “striped surface” phenomenon along Xdirection (Figure 3b). Therefore, the surface roughness parameters in the Y direction are worse than thesurface roughness parameters in the X direction. More cleaning or replacing of the knife mechanismcan reduce this phenomenon. This was also verified by the SEM images taken on the top and theside surface of the specimens (Figure 12). As it is shown, the top surface has a uniform pattern for

Mathematics 2020, 8, 1758 11 of 14

the surface roughness (Figure 12a,b), indicating a higher reliability on the measurements taken andthe prediction models developed with these measurements, owed to the Poly-Jet 3D printing processcharacteristics, while the side surface images (Figure 12c,d) clearly show the discrete deposited builtlayers, showing the uniform built structure of the specimens. All the SEM images taken during thisstudy can be found in the Supplementary Material of this work.

Mathematics 2020, 8, x FOR PEER REVIEW 11 of 14

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.

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).

Figure 11. (a) Trend lines for (Rax − Ray) − and (Rtx − Rty); (b) Mitutoyo Surftest RJ-210 tester, measuring the surface roughness on a specimen of this work.

Figure 11. (a) Trend lines for (Rax − Ray)(Rax −Ray

)and (Rtx − Rty); (b) Mitutoyo Surftest RJ-210 tester,

measuring the surface roughness on a specimen of this work.

Mathematics 2020, 8, x FOR PEER REVIEW 11 of 14

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.

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).

Figure 11. (a) Trend lines for (Rax − Ray) − and (Rtx − Rty); (b) Mitutoyo Surftest RJ-210 tester, measuring the surface roughness on a specimen of this work.

Figure 12. SEM images taken on the specimen built with X = 0, Y = 0 deposition angle: (a) top surfaceX50 zoom level; (b) top surface X200 zoom level; (c) side surface X50 zoom level; (d) side surface X200zoom level.

When the deposition angle is 45 degrees, the measured surface roughness parameters for theX direction show better performance than for the Y direction: (Rax − Ray) < 0

(Rax −Ray

)< 0. This

happens because of the layer profile geometry. It seems that the effect of the blade motion gives abetter surface for the X direction than the Y direction. For all the other deposition angles, the surfaceroughness 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. Thismodel’s input parameters were the Z-axis rotation angle (Zrot) and the deposition angle (θ). Using this

Mathematics 2020, 8, 1758 12 of 14

NN model, the predictions improved and became less than 9%, as it can been seen in the evaluationexperiments (Table 3).

Supplementary Materials: The following are available online at http://www.mdpi.com/2227-7390/8/10/1758/s1.

Author Contributions: Conceptualization, J.K.; methodology, N.V. (Nikolaos Vaxevanidis); software, M.P.;validation, N.V. (Nectarios Vidakis); formal analysis, M.P.; investigation, J.K. and N.V. (Nikolaos Vaxevanidis);resources, J.K.; data curation, J.K.; writing—original draft preparation, J.K. and N.V. (Nectarios Vidakis);writing—review and editing, M.P.; visualization, N.V. (Nectarios Vidakis); supervision, J.K. and N.V. (NectariosVidakis); project administration, J.K.; funding acquisition, J.K. All authors have read and agreed to the publishedversion of the manuscript.

Funding: This research received no external funding.

Acknowledgments: The authors would like to thank S. Maropoulos (Mechanical Engineering Department,University of Western Macedonia) and candidate K-E Aslani (University of West Attica) for proofreadingthis document.

Conflicts of Interest: The authors declare no conflict of interest.

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