Neural networks for predicting kerf characteristics of CO 2 laser-machined FFF PLA/WF plates

. The current work is a follow-up of previous research published by the authors and investigates the effect of CO 2 laser cutting with variable cutting parameters of thin 3D printed wood flour mixed with poly-lactic-acid (PLA/WF) plates on kerf angle (KA) and mean surface roughness (Ra). The full factorial experiments previously conducted, followed a custom response surface methodology (RSM) to formulate a continuous search domain for statistical analysis. Cutting direction, standoff distance, travel speed and beam power were the independent process parameters with mixed levels, resulting to a set of 24 experiments. The 24 experiments were repeated three times giving a total of 72 experimental tryouts. The results analyzed using analysis of variance (ANOVA) and regression, to study the synergy and effect of the parameters on the responses. Thereby, several neural network topologies were tested to achieve the best results and find a suitable neural network to correlate inputs and outputs, thus; contributing to related academic research and actual industrial applications.

Laser beam machining (LBM) is a non-traditional process that can achieve high dimensional accuracy, surface quality, and process efficiency [1]. A laser beam can apply cutting, milling, turning, drilling, etching, and welding [2,3]. Laser processing is applied in many materials, i.e., in metals [4], thermo-plastics [5], composites [6], and 3D printed materials [7][8][9][10], to name a few. In literature, a continuous-wave, low-power CO 2 laser cutting has been used efficiently on sheet-form thermoplastic materials [11][12][13][14][15]. Driving parameters for the machinability performance of laser cutting process are: (i) the beam parameters including the beam power (BP), the frequency, the TEM mode, and the spot radius; (ii) the focal parameters including the focal distance, the orifice diameter, the stand-off distance, the assist-gas pressure and the spot radius at the upper cut-surface, (iii) the cut material parameters such as surface texture, absorptivity, thickness, thermal and physical properties, and finally, (iv) the machine parameters including the mechanical elements, the type of assist-gas, the orifice type, the laser travel velocity, etc. [11]. Kerf profile (Kerf), cut average surface roughness (Ra), heat-affected zone (HAZ) and material removal rate (MRR) is considered crucial attributes that are investigated the most [16,17]. Fused Filament Fabrication (FFF) is a widely-applied 3D printing method for low-cost production of physical final parts and prototypes [18]. Dimensional accuracy and surface quality are the two main concerns of the FFF process that need improvement [19,20]. This is even more notable by using the low-cost FFF 3D printers where it is complicated to be achieved good shape characteristics such as circle or cuboid edges and small details like pines or pillows [21]. Hybrid methods that combine the 3D printing process shape flexibility and dimensional accuracy of the material removal processes are investigated in literature as an alternative. For this purpose, a laser beam process can be considered a post-processing method for improving the FFF parts quality. Kechagias et al. [9] experimented with the combination of FFF 3D printed plates and laser cutting. They 3D-printed 4mm pure PLA plates and cut them using a continuous-wave CO 2 Laser. It is found that the parallel and vertical cuts had different mean values and spread for both the kerf angle and surface roughness performance characteristics. They used beam power between 82.5 and 97.5 W and laser travel speed between 8 and 18 mm/s. The kerf angles were between 0.884 and 1.612 degrees, and the Ra values were 0.81 to 6.193μm. These values are very close to them, achieved by cutting pure PMMA materials [5] and better than 12.84 -21.77 μm achieved by the FFF-3D printing process [8][9][10]. There are many recent works regarding laser cutting of thin thermoplastic materials, but very few concerning 3D printed materials [7][8][9][10]. However, the 3D printed thin plates of organic, eco-friendly composite materials combined with laser processing could be an alternative for low-cost tailored products and assemblies [22][23][24]. Furthermore, the systematic investigation of the influence of the deposition angle during laser cutting of PLA with wood flour filler (PLA/WF) plates is investigated for the first time. Organic materials such as PLA mixed with wood flour (PLA/WF) are available nowadays in various mixtures of WF and PLA [25]. The PLA/WF composite material has an echo-friendly profile and a wooden appearance [26]. The purpose of this research is to further investigate the machinability of the PLA with wood floor printed plates during the laser cutting of a continuous-wave low-power CO 2 laser. The kerf angle (KA, degrees) and mean surface roughness Ra (μm) were measured under a range of different cutting directions and conditions. Three cutting directions (CD: 0 o , 45 o , 90 o ), two stand-off distances (SoD: 7 and 8 mm), three beam travel speeds (TS: 8, 13, and 18 mm/s), and four laser beam powers (BP: 82.5, 90, 97.5 and 105 W) were examined. Consequently a total of 72 cuts were performed to achieve all the possible parameter's level combinations according to the full factorial design. Following that, a continuous experimental search domain was formulated using a custom response surface design. The results were statistically analyzed whereas several neural network topologies were tested to end up with the best predictive network for practical applications.
Three thin plates (X, Y, Z: 100 X 20 X 4 mm) were manufactured using an FFF 3DP process. The FFF 3D printer was Craftbot® Plus. The PLA/WF material used for this experiment was the NEEMA3D™ WOODPLUS (30% WF; 70% PLA; 1.1-1.2 g/cm 3 ; 140-150 o C melting range; 1.75 mm filament). The printing head nozzle diameter was 0.4 mm, while the printing temperature was set at 200 o C-the bed temperature was set at 60 o C. The three 4 mm plates were printed with 100% infill density (one top layer, one bottom layer, one shell, 0.3 mm layer thickness, 13 layers in total, 40mm/s printing speed, 9.51 gr weight). Finally, the three different raster deposition angles (0 o , 45 o , and 90 o ) were measured from the X-axis (100mm in length). A continuouswave CO 2 laser BCL 1325B with a 10.6 μm wavelength and 2mm tip diameter was used.
RDWorks® v. 8.0 software environment is used for the laser-cut design. The parameters' values are concluded after an extensive literature survey, preliminary experimental work, and previous publications [5,9]. Two levels of stand-off distance (SoD: 7 and 8 mm), three levels of travel speed (TS: 8, 13, and 18 mm/s), and four levels of beam power (BP: 82.5, 90, 97.5, and 105 W) are finally selected. In this experimental space and for the specific material cutting, the airflow pressure kept constant at 1 bar. The manufacturer's focal length is fixed at 46 mm. The laser beam focal spot is about 0.4 mm when the SoD is 8 mm from the upper surface. Changing the SoD, the spot diameter and the airflow distribution at the upper surface also change. All three plates before cutting had the same orientation in the laser bed. Full factorial experimental design methodology is selected. All twenty-four experiments were repeated three times for the three PLA/WF plates (DA: 0 o , 45 o , and 90 o from the X-axis, respectively) resulting to a total of 72 results. Fig.1a shows the laser-cut procedure on the three PLA/WF plates with the total of 72 cuts (Fig.1b). The laser is adjusted to perform all cuts in Yaxis; when DA (deposition angle) is 90 o while laser CD (cutting direction) is zero, therefore parallel with the filament.   Fig.2a). Thereby, kerf angle KA was calculated using Eq.1.
where, d is the thickness for the plates; 4mm.
Surface roughness Ra was measured with the Surftest® SJ-210 profilometer (Fig.2b). To measure Ra, each plate was separated into twenty-four smaller items (Fig.2c).  Table 2 tabulates the experimental results for KA and Ra objectives along with corresponding readings of upper width (W u , mm) and down width (W d , mm) for the cuts performed on the three plates.

Statistical analysis.
To enable a suitable experimental region with continuous independent parameters for response prediction, the initial full factorial design was turned to a customized response surface design with the same number of experiments and standard parameters. Thereby, the results referring to KA and Ra were statistically examined through Analysis of Variance (ANOVA), to study the significance of independent parameters. Contour plots (Fig.3) were created to interpret the effects between two pairs of parameters, thus; allowing for more accurate and rigorous representation [27]. Pairs of independent parameters were decided based on their effect hierarchy, i.e.; for kerf angle KA, TS and SoD are the most influential ones, followed by CD and BP. Similarly for Ra, CD and TS are the most influential ones, followed by SoD and BP.  tained to low values when BP is adjusted to a value range between 86-105W. However CD should be adjusted to moderate levels, i.e., 30-70deg. By examining Fig.3c where Ra variation in terms of CD and TS is illustrated, it is shown that Ra is dramatically minimized when setting high travel speed values (14.5-18 mm/s) under low cutting direction degrees (0-15deg). Fig.3d shows that Ra can be maintained at low levels by setting any value for SoD. However a small region for BP between 85-90W should be avoided since this range of setting may increase roughness if SoD is to be set between 7-7.6mm.
A number of different Artificial neural network (ANN) architectures (feed-forward, back propagation) were tested for predicting the responses of kerf angle KA and surface roughness Ra. In the analysis, the four independent variables cutting direction CD, stand-off distance SoD, travel speed TS and beam power BP were considered as the input variables for the ANN. Each of these parameters has been characterized by one neuron, thus, the input layer in the ANN structure had four neurons. The database has been built considering the series of CO 2 laser cutting experiments at the limit ranges of each independent variable. Experimental results for kerf angle and surface roughness were used to train the ANN to investigate the input-output correlations. The database was then divided into two categories, namely the training category which has been exclusively used to adjust the network weights and the test category, which corresponds to the set that validates the results of the training protocol [28,29]. Neural network training involved updating the weights of the connections in such a manner that the error between the network's outputs and the actual output is minimized. To determine the number of neurons in the single hidden layer selected, different network structures with varying number of neurons in the hidden layer were tested [30,31]. After training, the topology 4-12-2 was finally selected as the optimum (Fig.4) Fig. 4. ANN architecture with four inputs, one hidden layer (12 neurons) and two outputs.
The activation level of neurons was determined by tan-sigmoid transfer function except for output layer neurons for which linear output transfer function was used so that output is not limited to small values. The ANN was simulated in MATLAB® 2014b. In order to evaluate the competence of this trained network, the training data set was presented to the trained network. Mean squared error (MSE) in ANNs is the average squared difference between network output values and target values [32]. For the network implemented in the study, best validation performance was equal to 0.25907 at epoch 5 ( Fig. ). Fig. shows
This work examined the effect of four essential parameters, namely cutting direction, standoff distance, travel speed and beam power on the responses, of kerf angle and surface roughness when it comes to CO 2 laser cutting of 3D-printed PLA with wood flour plates with 4 mm thickness. Laser cutting experiments have been established following the full factorial multi-level design concept resulting to 24 experiments per cutting direction. This led to a total of 72 series of experiments that statistically examined after creating a custom response surface design. To investigate non-linearity and parameter effects on the two responses, statistical analysis involved contour plots. Finally the responses were modelled using a back-propagation neural network after testing several architectures with altered topologies in the hidden layer. It was shown that the final ANN architecture adopted, can accurately predict experimental results for laser cutting the PLA with wood flour material, in terms of kerf angle and surface roughness. As a future work authors plan to implement different evolutionary algorithms and optimize the CO 2 laser cutting of PLA/WF material by formulating a multi-objective optimization problem and having either the ANN, or robust full quadratic regression models under the role of objective functions. Moreover, other 3D-printing filament materials of great importance to industrial applications are to be experimentally investigated for characterizing the process and optimizing its control parameters.