Mechanical Properties of 3D-Printed Components Using Fused Deposition Modeling: Optimization Using the Desirability Approach and Machine Learning Regressor

: The fused deposition modelling (FDM) technique involves the deposition of a fused layer of material according to the geometry designed in the software. Several parameters affect the quality of parts produced by FDM. This paper investigates the effect of FDM printing process parameters on tensile strength, impact strength, and flexural strength. The effects of process parameters such as printing speed, layer thickness, extrusion temperature, and infill percentage are studied. Polyactic acid (PLA) was used as a filament material for printing test specimens. The experimental layout is designed according to response surface methodology (RSM) and responses are collected. Specimens are prepared for testing of these parametersasperASTMstandards. Amathematicalmodelforeachoftheresponsesisdevelopedbasedon the nonlinear regression method. The desirability approach, nonlinear regression, as well as experimental values are in close agreement with each other. The desirability approach predicted the tensile strength, impact strength, and flexural strength with a less percentage error of 3.109, 6.532, and 3.712, respectively. The nonlinear regression approach predicted the tensile strength, impact strength, and flexural strength with a less percentage error of 2.977, 6.532, and 3.474, respectively. The desirability concept and nonlinear regression approach resulted in the best mechanical property of the FDM-printed part.


Introduction
Fused deposition modelling is an additive manufacturing technology in which the mechanical and surface properties obtained should be comparable to those of the conventional injection moulding process [1][2][3][4].Numerous studies have been conducted to study the effect of process parameters on the fused deposition modelling parts' mechanical and surface properties.Kantaros et al. [5] examined the effect of layer thickness and deposition orientation on the magnitude of the solidification-induced residual strains.Further, the specimens were subjected to a thermal cycle.The developed residual strains and coefficient of thermal expansion of the ABS parts were measured using an optical sensor with a short fiber Bragg grating.Sood et al. [6] utilized Taguchi's experimental layout to investigate the effect of layer thickness, part orientation, raster angle, air gap, and raster width on the part dimensional accuracy in terms of the percentage change in length, width, and thickness during 3D printing of ABSP400.Artificial neural network was employed for the prediction of dimensional accuracy.Sood et al. [7] employed a central composite design to investigate the influence of air gap, raster width, raster angle, part orientation, and layer thickness on impact, flexural, and tensile strength.Distortion between or within layers resulted in lower strength of the parts.Es-Said et al. [8] developed the ABS parts using a Stratasys machine for five-layer orientations.The parts' impact resistance, modulus of rupture, and tensile strength were observed, and it was found that, at 0 degrees, orientation layers deposited along the length of samples showed better considered mechanical properties than other orientations.Fragile interlayer bonding and porosity may result in the anisotropic properties.Kantaros et al. [9] discussed the 3D printing challenges faced by the users of a low-cost desktop 3D printer.The illustrated the means of addressing these challenges by tuning selected process parameters to obtain the best print quality.Vasudevarao et al. [10] designed an experimental layout using fractional factorial design with two levels for each factor to estimate the optimal surface finish by obtaining optimal parameter settings of layer thickness, air gap, build orientation, and road width.Kantaros et al. [11] demonstrated the effect of bead orientation and air gap on the developed residual strains in prismatic specimens built using fused deposition modeling.Residual strains are measured using an optical sensor with a short fiber Bragg grating.
The literature suggests that 3D-printed parts have at least 30% worse mechanical behaviour than injection-moulded parts.The process parameters are scattered over a large range, which results in the best mechanical and surface properties.This requires significant experimentation to identify the influencing parameters.Different optimization techniques were employed by researchers, namely, response surface methodology, Taguchi method, full factorial design, fractional factorial design, grey relation analysis, artificial neural network, fuzzy logic, genetic algorithm, and so on, to improve the mechanical properties of parts by optimizing a number of FDM process parameters [12][13][14][15][16][17].Selecting a part for an application requires the forecasting of how the part will perform under different loading conditions.Hence, it is becoming essential to study the effect of FDM process parameters on mechanical properties.The literature depicts that various studies have been carried out using different types of materials and settings of process parameters.Table 1 provides a summary of the literature survey in terms of process parameters, filament material, output parameters, methods adopted for experimentation and optimization, and key findings.Awasthi and Banerjee [44] presented a review on methods to 3D print thermoplastic materials.They depicted the strategies to overcome defects in 3D printing of thermoplastic elastomers, enhancing the mechanical and thermoplastic elastomeric properties of 3Dprinted parts.They identified the scope for future work and motivation to enhance the research in this field.The authors summarized the research carried out to date on thermoplastic elastomeric material, which can act as a guideline to academics and the industry.Cuan-Urquizo et al. [45] presented a review on experimental, computational, and theoretical approaches with regard to fused filament fabrication parts' mechanical properties.The authors depicted the applications and limitations of each of these approaches.At the end, they provided future directions for characterizing printed materials and areas that require further research.Verma et al. [46] studied the influence of styrene/isoprene/styrene, bed temperature, print temperature, layer thickness, print speed, infill density, and the number of shells on the mechanical properties and printability using the Taguchi method.The authors claimed that their study resulted in less voids in the printed parts and improved the adhesion between phases.
The main objective of this study was to achieve the optimal settings of 3D printer process parameters to obtain enhanced tensile, impact, and flexural strength of the printed components using PLA filament material.The scope of this study includes the design of experimentation as per central composite design with 31 runs.The three responses considered as parameters for the study are tensile, impact, and flexural strength.The test specimens for tensile, impact, and flexural strength are prepared as per ASTM D638, ASTM D256, and ASTM D790, respectively.The mathematical model for predicting tensile, impact, and flexural strength was devloped according to a machine learning non-linear regression approach.Optimization of the input parameters was performed using a desirability approach and non-linear regression approach.Further validation experiments were carried out to confirm the optimized values obtained from the nonlinear regression approach and desirability concept.
The paper is organized into Section 2 presenting the materials and methods, Section 3 presenting the results and discussion, and Section 4 presenting the conclusions with future work.

Materials and Methods
The FDM process involves the following steps.A CAD model is generated and then converted into STL files for stereolithography.Three-dimensional surfaces are represented in this file as an assembly of planar triangles.The greater the number of triangles, the better the accuracy.Once the STL file has been converted, the slicing process involves steps including describing the 3D part, dividing the parts into slices, and determining the support material and path as well as the angle of the tool.Various parameters are set in the STL file to specify how the machines will operate in the various layers.The FDM samples are created using a Creality Ender 3 machine with a bed size of 220 × 220 × 250 mm 3 .CATIA software is used to design the parts.It is then converted into an STL file, which is sliced into machinereadable g-code files using the Cura engine of the Repetier software.The dimensions of the tensile specimen are 63.5 × 9.53 × 3.2 mm 3 , which are as per the ASTM D638 requirements.The impact specimen dimensions are 63 × 12.7 × 3.2 mm 3 , follow the ASTM D256 requirements.The dimensions of the flexural specimen are 125 × 12.7 × 3.2 mm 3 , which are as per the ASTM D790 requirements.The dimensions are shown in Figure 1.The material used to create the specimen is polylactic acid (PLA), which is commonly used for FDM-processed parts.The tensile strength of the specimens is determined using the uniaxial tensile tests.
software.The dimensions of the tensile specimen are 63.5 × 9.53 × 3.2 mm 3 , which are as per the ASTM D638 requirements.The impact specimen dimensions are 63 × 12.7 × 3.2 mm 3 , follow the ASTM D256 requirements.The dimensions of the flexural specimen are 125 × 12.7 × 3.2 mm 3 , which are as per the ASTM D790 requirements.The dimensions are shown in Figure 1.The material used to create the specimen is polylactic acid (PLA), which is commonly used for FDM-processed parts.The tensile strength of the specimens is determined using the uniaxial tensile tests.Print Speed-The speed of the nozzle with which the material will be deposited is denoted as the print speed.A very high printing speed will cause the wear and tear of physical parts and lead to improper distribution of materials.Moreover, a low printing speed is not suitable as it will increase the time required to print one specimen.Hence, the values for print speed are set as 20, 35, 50, 65, and 80 mm/s.4.
Extrusion Temperature-The extrusion temperature is the temperature at which the material is extruded from the nozzle.The extruder contains a heater that heats the material up to a semi-liquid state.As the temperature increases, the viscosity of the material increases.As a result, it is necessary to set the extruder temperature within the limits where semi-liquid materials can be kept.The capacity of the heating system decides the temperatures at which materials are extruded.Temperatures are set at 190, 200, 210, 220, and 230 • C.
Table 2 depicts the experimental runs and observed values of responses.Tensile test specimens were prepared as per ASTM D638 standard, flexural test specimens were prepared as per ASTM D790 standard, and impact test specimens were prepared as per ASTM D256.Tensile and flexural test was conducted on UTM of VEEKAY TESTLAB and the impact test was conducted on an impact testing machine of ADVANCE EQUIPMENTS having a least count of 0.0001 J. Figure 2a-c shows the setup of the tensile, flexural, and impact test.Figure 2d-f shows the actual test piece after the performance of tests.

Results and Discussion
In this study, a total of 31 experiments were carried out as per the response surface methodology and a detailed study on all of these results, such as the effect of process parameters on the tensile strength, flexural strength, and impact strength, is discussed below.The graphs for the same are shown below in Figures 3-5, respectively.

Results and Discussion
In this study, a total of 31 experiments were carried out as per the response surface methodology and a detailed study on all of these results, such as the effect of process parameters on the tensile strength, flexural strength, and impact strength, is discussed below.The graphs for the same are shown below in Figures 3-5, respectively. .

Analysis Using Desirability Approach
Using a computerized uniaxial tensile testing machine in accordance with ASTM D638 standards, the mechanical behavior of the parts was investigated.When the specimen breaks under the load, as in tensile testing, the breaking load is noted on the digital screen.From Figure 3, it can be understood that the tensile strength increases with the increase in infill percentage.A greater infill percentage implies a higher density of the part.This will increase the strength required for pulling and breaking the specimen.Hence, the tensile strength will increase.In the extrusion process, the nozzle temperature causes the material to melt into a semi-liquid phase.The material tends to shift slightly towards a liquid state when the extrusion temperature is increased, resulting in reduced viscosity.The less viscous material is now in an oval shape and not circular.The contact area between layers is enlarged as the brittleness of the material is increased with an increase in temperature.Moreover, one can expect that the material becomes more brittle with a larger temperature increase.Thus, larger contact areas tend to increase strength, but the increase is very minimal.As the infill filament has had less time to cool down between each passage, the adhesion between the filaments in a faster-printed object is better.Thus, the filament's maximum strength may be slightly improved.Owing to the unevenness of the material deposit, the overall strength of the fabricated part can be reduced at high speeds.Therefore, the strength increases through adhesion are cancelled out and the tensile strength remains almost constant as the printing speed changes.If the layer height is increased, the tensile strength of the part will decrease.As a result of fewer layers, the printed part has less adhesion and accuracy, which significantly decreases its tensile strength.Flexural strength indicates the amount of bending it can withstand.Flexural strength increases with the increase in infill percentage, layer height, and extrusion temperature, while it decreases slightly with the increase in print speed.Owing to a lower infill percentage, there is less density in the fabricated part.Owing to more hollow space inside the part, there are no proper supports from the inside, hence the part is weaker.For this reason, the part is easily broken upon bending.An increase in infill percentage strengthens the part, thus increasing the flexural strength.However, we have seen that a change in the combination of different parameters actually increases the properties more than just changing one parameter at a time.The above graphs show us that maximum flexural strength can be obtained with a lower value of extrusion temperature, while simultaneously setting a higher value of the infill percentage.
Impact strength is the toughness of the part, which in turn indicates its ability to absorb energy during plastic deformation.Figure 5 shows that the impact strength of the FDM-printed parts is affected by every parameter.Impact strength increases with an increase in infill percentage, layer height, and print speed, while it decreases considerably with an increase in extrusion temperature.Based on our study, there was a significant relationship between the apparent density and the impact absorption capacity, both of which were measured for the components in terms of dissipation of energy.However, the result of layer height was less significant.As discussed earlier, the rise in extrusion temperature reduces the viscosity, which in turn decreases the layer thickness slightly.The dimensional accuracy of the part is affected.There is a decrease in the thickness of the fabricated part and less impact energy is required to cause the failure of the part.Thus, as the extrusion temperature increases, the impact strength decreases.
From Figure 6, the infill percentage, layer height, print speed, and extrusion temperature should be 100%, 0.0962 mm, 20 mm/s, and 230 • C, respectively, to obtain the optimum tensile strength.The optimum impact strength can be obtained if the infill percentage, layer height, print speed, and extrusion temperature are 70%, 0.08 mm, 20 mm/s, and 201 • C, respectively.To obtain optimum the flexural strength, the infill percentage, layer height, print speed, and extrusion temperature should be set at 100%, 0.24 mm, 52 mm/s, and 203 • C, respectively.Similarly, to obtain the optimum surface roughness, the infill percentage, layer height, print speed, and extrusion temperature should be 43%, 0.14 mm, 45 mm/s, and 230 From Figure 6, the infill percentage, layer height, print speed, and extrusion temperature should be 100%, 0.0962 mm, 20 mm/s, and 230 °C, respectively, to obtain the optimum tensile strength.The optimum impact strength can be obtained if the infill percentage, layer height, print speed, and extrusion temperature are 70%, 0.08 mm, 20 mm/s, and 201 °C, respectively.To obtain optimum the flexural strength, the infill percentage, layer height, print speed, and extrusion temperature should be set at 100%, 0.24 mm, 52 mm/s, and 203 °C, respectively.Similarly, to obtain the optimum surface roughness, the infill percentage, layer height, print speed, and extrusion temperature should be 43%, 0.14 mm, 45 mm/s, and 230 °C, respectively.

Analysis by Machine Learning Using a Nonlinear Regressor
A mathematical model for predicting flexural strength, tensile strength, and impact strength was developed using nonlinear regression in MATLAB R2020a.In the equations, , , , and denote the infill percentage, layer height, print speed, and extrusion temperature, respectively, where, , , and denote the corresponding tensile strength, impact strength, and flexural strength, respectively.

by Machine Learning Using a Nonlinear Regressor
A mathematical model for predicting flexural strength, tensile strength, and impact strength was developed using nonlinear regression in MATLAB R2020a.In the equations, x 1 , x 2 , x 3 , and x 4 denote the infill percentage, layer height, print speed, and extrusion temperature, respectively, where, y 1 , y 2 , and y 3 denote the corresponding tensile strength, impact strength, and flexural strength, respectively.
Tensile strength Flexural strength The plots of experimental versus predicted values are shown below in Figure 7.The graphs show that the tensile strength and flexural strength model achieve a minimum error.The optimum values were obtained using MATLAB R2020a on Windows Platform with Intel Core i7 with 8GB RAM.The optimum values were obtained for all of the outputs.The infill percentage, layer height, print speed, and extrusion temperature should be 100%, 0.0962 mm, 20 mm/s, and 230 • C, respectively, to obtain the optimum tensile strength.The optimum impact strength can be obtained if the infill percentage, layer height, print speed, and extrusion temperature are 70%, 0.08 mm, 20 mm/s, and 201 • C, respectively.To obtain the optimum flexural strength, the infill percentage, layer height, print speed, and extrusion temperature should be set at 100%, 0.24 mm, 52 mm/s, and 203 • C, respectively.graphs show that the tensile strength and flexural strength model achieve a minimum error.The optimum values were obtained using MATLAB R2020a on Windows Platform with Intel Core i7 with 8GB RAM.The optimum values were obtained for all of the outputs.The infill percentage, layer height, print speed, and extrusion temperature should be 100%, 0.0962 mm, 20 mm/s, and 230 °C, respectively, to obtain the optimum tensile strength.The optimum impact strength can be obtained if the infill percentage, layer height, print speed, and extrusion temperature are 70%, 0.08 mm, 20 mm/s, and 201 °C, respectively.To obtain the optimum flexural strength, the infill percentage, layer height, print speed, and extrusion temperature should be set at 100%, 0.24 mm, 52 mm/s, and 203 °C, respectively.

Comparison of Results
Validation experiments were carried out to verify the predicted output parameters as FDM-processed parts are again fabricated using these parameter settings, and all tenimpact, and flexural test were carried out to validate the obtained results, as depicted in Table 3.The desirability approach, nonlinear regression, as well as experimental values are

Comparison of Results
Validation experiments were carried out to verify the predicted output parameters as FDM-processed parts are again fabricated using these parameter settings, and all tensile, impact, and flexural test were carried out to validate the obtained results, as depicted in Table 3.The desirability approach, nonlinear regression, as well as experimental values are much closer to each other, which validates the desirability approach, and the process parameter settings obtained with nonlinear regression will achieve the optimum values of flexural strength, tensile strength, and impact strength.

Conclusions
In this study, two approaches are implemented to understand the effect of process parameters on mechanical properties.The first one is based on design of experiments, i.e., the central composite design of response surface methodology.A total of 31 runs were carried out.The desirability concept was used to optimize the tensile strength, impact strength, and flexural strength by obtaining the optimal settings of input process parameters, namely, infill percentage, layer height, print speed, and extrusion temperature.Secondly, the non-linear regression method was employed to predict the tensile strength, impact strength, and flexural strength.Further, the optimal input parameter settings were also obtained based on non-linear regression.The key finds are as follows: 1.
It was found that the infill percentage has a maximum effect on tensile strength and flexural strength, while extrusion temperature has a maximum effect on impact strength.

2.
Mathematical models for tensile strength, impact strength, and flexural strength were developed using nonlinear regression.

3.
Eventually, optimum values of tensile strength, impact strength, and flexural strength were found using the desirability approach and nonlinear regression and were validated experimentally.4.
The desirability approach predicts the tensile strength, impact strength, and flexural strength with a percentage error of less than 3.109, 6.532, and 3.712, respectively.5.
The nonlinear regression approach predicts the tensile strength, impact strength, and flexural strength with a percentage error of less than 2.977, 6.532, and 3.474, respectively.
The future scope of this study is to work upon improvements in shear strength, fatigue strength, surface properties, and dimensional accuracy of the parts printed using PLA and, furthermore, to use a machine learning regressor and classifier for the prediction of mechanical properties, surface properties, and dimensional accuracy.

Figure 1 .Figure 1 .
Figure 1.Dimensions of the (a) tensile specimen, (b) impact specimen, and (c) flexural specimen.The three main aspects of DOE are factors, levels, and response.The term level indicates the number of different values a variable can assume according to its discretization.Design matrices are used, which have tables that have all of the combinations of levels between the different factors.The DOE factors considered in these experiments are as follows: 1. Infill Percentage-The infill percentage measures the amount of material inside the fabricated part.It represents the density of the part.The infill percentage is set according to the part's requirement.The values for the infill percentage are chosen as 10, 33, 55, 78, and 100%.2. Layer Thickness-In FDM, the thickness of a single layer deposited by the nozzle is the layer thickness.The type of nozzle used decides the paper thickness.The nozzle

Figure 2 .
Figure 2. (a) Tensile test setup, (b) flexural test setup, (c) impact test setup, (d) tensile test piece after test, (e) impact test piece after test, (f) flexural test piece after test.

Figure 3 .
Figure 3.Effect of process parameters on the tensile strength.Figure 3. Effect of process parameters on the tensile strength.

Figure 3 .
Figure 3.Effect of process parameters on the tensile strength.Figure 3. Effect of process parameters on the tensile strength.

Figure 4 .
Figure 4. Effect of process parameters on the flexural strength.

Figure 4 .
Figure 4. Effect of process parameters on the flexural strength.

19 Figure 5 .
Figure 5.Effect of process parameters on the impact strength.

Figure 5 .
Figure 5.Effect of process parameters on the impact strength.

Figure 7 .
Figure 7. (a) Tensile strength between nonlinear regression and experimental, (b) flexural strength between nonlinear regression and experimental, (c) impact strength between nonlinear regression and experimental.

Figure 7 .
Figure 7. (a) Tensile strength between nonlinear regression and experimental, (b) flexural strength between nonlinear regression and experimental, (c) impact strength between nonlinear regression and experimental.

Table 1 .
Summary of the literature review.

Table 2 .
Input and output parameters.