3.1 Influence of the drilling parameters on the delamination factor
Figure 2 illustrates the condition of the holes drilled at the entrance and the exit (#4, #13 and #22) with feed rates of 50, 108 and 190 mm/min and a spindle speed of 355 rpm. Digital images of the machined biosandwich plates were taken with a resolution of 4800 pixels using a professional scanner. Two concentric circles were drawn using image processing software. The damage caused by drilling holes in the manufacture of biosandwiches is part of the delamination factor. This is conditioned by the choice of cutting parameters as well as by the fibre fabric used. Delamination is a fundamental concern for the choice of cutting parameters during the design process. Determination of the delamination factor Fd of biosandwich structures with agglomerated cork-core with epoxy skins reinforced with woven jute (EBJWC) for two drills using HSS-TiN and BSD is related to many factors such as feed rate, cutting speed and tool diameter.
3.2 Response surface methodology and ANOVA for delamination factor
The experimental results were processed using a response surface analysis and to determine the relationship between the delamination and different cutting parameters for HSS-TiN and BSD. Table 3 shows the output parameters represented by the delamination factor for the two drills used in the present study, Fd(HSS-TiN) and Fd(BSD), performed under different machining conditions. These results were obtained according to the optimal design, which consists of analysing the influence of numerical factors on the responses with three levels and three input parameters (f, N et d). Indeed, response surface methodology (RSM) is a mathematical and statistical method that is generally used in applied science and analytical problems such as the mechanics and machining of materials . In addition, this technique represents an empirical modelling approach with the objective of finding the relationship between the input and output parameters, that is, delamination Fd, by changing the different cutting parameters during the drilling of biosandwiches. The mathematical equations of the regression are presented in Table 4 for the different delamination factors obtained by Design-Expert software, which recommended quadratic models. Quadratic regression models are second-order mathematical models based on the RSM. Figures 3a and b highlight the relationship of predicted and experimental results for biosandwich structure delamination of HSS-TiN and BSD drills. Thus, the results obtained show satisfactory agreement of the regression model since the predicted values are statistically identical to the experimental values with a confidence level of 95%. The normal probability curves of the delamination residues Fd are shown in Figures 3c and d; the straight lines reveal a good distribution of errors. The synthesis of the relevance of the results reveal that the quadratic model is statistically significant for the analysis of delamination. Table 4 shows the results of the quadratic ANOVA model. The R2 coefficient and the adjusted R2 coefficient corresponding to the delamination are 87.59% and 81.02% for HSS-TiN and 89.35% and 83.71% for BSD, respectively. It is therefore obvious that this regression model offers a perfect match between the responses and the independent factors. The model is statistically significant because the p value corresponding to the model is less than 0.05. Additionally, factors f and d have significant effects on delamination. Due to the larger Fd value, it appears that the feed rate f and the diameter d are the most significant parameters for the delamination of HSS-TiN and BSD composites compared to N. The rest of the terms in the model are considered insignificant. Therefore, it appears that the feed rate is the main parameter that affects the delamination factor, followed by the diameter and the cutting speed (N). In addition, the contribution of the factor f is the most important (66.04% and 66.03%) for HSS-TiN and BSD. The cutting speed has a less significant influence on delamination than the diameter on delamination.
3.3 3D surface plots for the delamination factor
Figures 4 and 5 describe a mapping in the form of the response surfaces provided for the delamination at the exit of the biosandwiches machined by the HSS-TiN and BSD drills as a function of the feed rate (f) and the cutting speed (N) and of the diameter (d). For the HSS-TiN tool, the delamination does not exceed 1.10 with a feed rate between 50 and 60 mm/min and a diameter of 5 to 7 mm, but further, the delamination exceeds 1.48 when the spindle speed is between 178 and 190 mm/min and a diameter of 9.4 to 10 mm (Fig 4a). For the BSD tool, we also notice that the delamination does not exceed 1.09 for feed rates between 50 and 70 mm/min and a diameter of 5 to 5.5 mm, but it exceeds 1.62 when the cutting speed is between 185 and 190 mm/min and a diameter of 7.8 to 10 mm (Fig 5a). Figures 4b and 5b show how the feed rate and spindle speed significantly affect delamination for the HSS-TiN and BSD drills. It can be seen that the delamination increases significantly with increasing feed rate and very slightly with increasing spindle speed. For HSS-TiN and BSD, the delamination is less than 1.10 when the feed rate is between 50 and 64 mm/min and the cutting speed is between 355 and 1400 rpm and is 1.09 for BSD when the feed rate is between 50 and 75 mm/min and that N is between 562 and 1400 rev/min. The delamination also seems to rise above 1.32 for HSS-TiN when the feed rate is between 182 and 190 mm/min and N is between 510 and 1400 rpm and equals 1.43 for BSD when the feed rate is between 174 and 190 mm/min and the spindle speed is between 355 and 1400 rpm. This corresponds perfectly to the results obtained in the work of Belaadi et al. [22, 32] in the case of epoxy/jute fabric biocomposites for the same cutting conditions. The effect of drill bit diameter and cutting speed (N) on delamination is shown in Figures 4c and 5c. From this figure, it appears that the delamination increases as the diameter increases and increases slightly with the increase of N. The delamination is less than 1.32 and 1.47, when the diameter of the tool (d) and cutting speed are between 5 and 5.8 mm and 355 and 484 rpm for the HSS-TiN tool and 5 and 5.7 mm and 355 and 1400 rpm for the BSD drill, respectively. In addition, it is also observed that Fd seems to exceed 1.52 and 1.62 when d and N are between 9.8-10 mm and 790-1400 rpm for HSS-TiN and 7.8-10 mm and 1295-1400 rpm for BSD, respectively. Figure 6 presents the evolution of the delamination factor as a function of cutting parameters such as the feed rate (f), spindle speed (N) and diameter (d). The delamination factor increases with increasing feed rate and drill diameter, as shown in Figure 6a. The influence of these two cutting conditions (f and d) is also considerable; this is mainly due to the forces produced and the amount of material removed during machining. Figure 6b illustrates the effect of drill diameter and spindle speed on Fd for the two drills comprising HSS-TiN and BSD for a constant feed rate. The diameter of the drill has a great influence on the spindle speed, as clearly shown in Figure 6b for the first drill (HSS-TiN). In the event that the diameter of the drill bit is kept constant (figure 6c), the factor Fd increases with the increasing effect of the feed rate. On the other hand, by increasing the spindle speed, the delamination factor decreases. Generally, it emerges from Figure 6 that the HSS-TiN drill (≈ 1.02 to 1.55) produces lower Fd values than the BSD drill (≈ 1.11 to 1.68).
3.4 Prediction of delamination factor by ANN model
The data were integrated into the network model by the input layer and the response by the output layer. A multilayer perceptron consisting of an input layer, a hidden layer and an output layer was used for the prediction of the delamination factor. The architecture design of the ANN network was designed using the MATLAB Neural Network Toolbox. Modelling by neural networks constitutes a powerful approach, making it possible to reproduce the behaviour of any non-linear process of any kind . For HSS-TiN and BSD drills, three neurons in the input layer, the hidden layers contain ten and twelve neurons, respectively, and one neuron for the output layer (Figure 7). Determining the number of neurons in the hidden layers relies on reducing the error as the number of hidden nodes increases . Table 6 shows the tested ANN architectures and MSE and R values for training, validation and testing of Fd data for the HSS-TiN and BSD drill tools. These neurons are linked together by means of weight weights. In Figures 8 a-c and 8 d-f, neural network prediction of Fd delamination and experimental test results for HSS-TiN and BSD tools, respectively, are compared for the training, testing and validation data sets. It emerges from Figures 8 and 9 that the ANN prediction corresponds perfectly to the experimental results. The ANN models thus developed for HSS-TiN and BSD (Table 7) have the ability to interpret the data well and can serve as an efficient prediction tool for the delamination factor. In addition, the results show that the model is an efficient and applicable way to measure the delamination factor of biosandwiches made from jute fabric.
3.5 Comparison of RSM and ANN models
A comparison of the results predicted by the ANN and RSM models with those obtained experimentally are presented in Figure 10. It was found that the two models satisfactorily describe the results obtained experimentally. The maximum absolute percentage error in the prediction of the delamination factors of the HSS-TiN and BSD tools by the ANN model is 4.16% and 6.28%, respectively, while in the RSM model, this percentage is 6.93% and 7.78% (Figure 9). Thus, the ANN model provides a more accurate prediction than the RSM model. To the extent that these error rates are low, we can say that the optimization process is appropriate and that the model provides response prediction with high accuracy.
3.6 Optimisation of Responses
Figures 12 and 13 illustrate the distribution of the ramp function and the mapping of the desirability contour for the two types of drill material as well as their combination in Figure 12c. The main objective of the optimization is to determine the cutting parameters as well as the minimization of the delamination factors. The cutting parameters used in the optimization process are shown in Table 8, and the optimized values of the factors and responses are shown in Table 9. The ten runs are chosen due to the desirability factor near the unit. The first ten tests show that a high cutting speed and feed rate and a small tool diameter are suitable for reducing the delamination factor with desirability rates of 0.98 and 1.00 for HSS-TiN and BSD, respectively (Figures 12a and b). Indeed, according to the highest desirability value equal to 0.97, the optimal drilling machining conditions according to Table 9 (f = 50 mm/min, N = 1399.99 rev/min and d = 5.61 mm) lead to minimal delamination (Fd) for HSS-TiN and BSD, whose values were 1.09 and 1.10, respectively.
The models obtained by the ANN method were retained for the resolution of the optimization problem using the genetic algorithm (GA) and for the search for the minimal multi-variable nonlinear constraint function (fmincon) using MATLAB software. Table 10 shows the results obtained from the optimization of the input parameters and Fd for the two drill geometries (HSS-TiN and BSD). The results indeed reveal that the response of the GA and fmincon parameters provide approximately similar values. The results for comparison between the response parameters (Fd) obtained for the HSS-TiN and BSD tools with RSM and those predicted by the GA and fmincon algorithm are 1.08 and 1.03 obtained by RSM, 1.04 and 1.05 in the case of GA and 1.04 and 1.09 for the function fmincon, respectively, confirming the relevance of the models and the adequacy of the results with those obtained by .