Abstract
This research is done to determine the optimum parameters to drill polytetrafluoroethylene (PTFE) and to investigate the effect of two-tier modeling for enhanced response in optimization. RSM model was done with L27 experimental design, considering speed (N), feed (f), and tool point angle (Ɵ). RSM data were further trained and tested using the Adaptive Neuro-Fuzzy Inference System (ANFIS), and β coefficient values were restructured to form revised RSM model. Both nonrevised RSM model and revised RSM model were used in Genetic Algorithm to locate the minimum surface roughness. ANFIS revised RSM model deviates from the experimental results by 2.6% and 2.86% for dry and wet condition; meanwhile, nonrevised RSM model deviates by 4.76% and 4.94%, respectively. The research concludes that two-tier modeling using RSM and ANFIS is better. Spindle speed of 1656 rpm, feed rate of 0.05 mm/min, and point angle of 100° are the optimum conditions to drill PTFE material where the best surface quality of 0.68 μm at wet drilling can be achieved.
1. Introduction
Optimization of drilling parameters has been attempted to achieve the best surface finish or to increase the material removal rate or to increase the tool life. The problem is considered as a multiobjective optimization when more than one response is used in the optimization. In the past, optimization of drilling parameters was done using response surface model (RSM), grey rational analysis (GRA), and metaheuristic algorithms. Kumar and Hynes [1] predicted the optimized parameters for the surface roughness in thermal drilling by an integrated adaptive network-based fuzzy inference system (ANFIS) and Genetic Algorithm (GA) technique. El-Bahloul et al. [2] applied the Taguchi method and fuzzy logic strategy for the thermal drilling of AISI 304 stainless steel. Latha and Senthilkumar [3] performed the modeling and analysis of parameters in drilling of GFRP composites using fuzzy logic. They analyzed the experimental result with Pareto-ANOVA and ANOVA. Palanikumar [4] employed the fuzzy logic approach for the modeling of parameters in machining glass fibre reinforced plastics using a polycrystalline diamond tool. Krishnamoorthy et al. [5] performed a grey fuzzy logic approach for the optimization of drilling parameters for CFRP composites with multiple performance characteristics. Venkataramaiah et al. [6] targeted on the development of a neural network model to estimate the multiresponses of drilling parameters. Anand et al. [7] inspected the drilling parameters on hybrid polymer composites using grey relational analysis, regression, fuzzy logic, and ANN models. Azarrang and Baseri [8] worked on dry drilling of copper for minimal burr size, desired overcut, and MRR. Natarajan et al. [9] proposed nondominated sorting modified teaching-learning-based optimization for multiobjective machining of polytetrafluoroethylene (PTFE). Kaviarasan et al. [10] conducted the drilling experiment on Delrin polymer using HSS and solid carbide tool and applied desirability approach with the ANN model to achieve minimum surface roughness of drilled holes. Valarmathi et al. [11] investigated the effect of process parameters on surface roughness in drilling of particleboard composite panels using the Adaptive Neuro-Fuzzy Inference System. Hossain and Ahmad [12] predicted an Adaptive Neuro-Fuzzy Inference System (ANFIS)-based surface roughness model for ball end milling operation. Vinod Kumar and Venkateswarlu [13] optimized the process parameters in drilling of GFRP composite using the Taguchi method. Ogawa et al. [14] investigated the cutting mechanism of small diameter drilling on GFRP. Tosun [15] determined the optimum parameters for multiperformance characteristics in drilling by using grey relational analysis. Vimalsamsingh et al. [16] analyzed the thrust force and torque in drilling GFRP composites by multifacet drill using fuzzy logic approach. Abhishek et al. [17] compared the predictability of genetic programming and ANFIS on drilling performance modeling for GFRP composites. Kirsanov and Babae [18] studied the accuracy and surface roughness of holes in comparative testing of small diameters gun drills. Rajmohan et al. [19] examined the surface roughness in drilling of fly ash filled carbon fibre reinforced composites. Davim et al. [20] studied the drilling of glass fibre reinforced plastics (GFRP). The recent research studies [21–28] also built RSM models for optimization. The use of uncoded coefficient that is obtained from experimental data may not be accurate in modeling. In other words, the effect of work piece positional error, instrument condition, and machining environment may also affect the result of the experiments. A small deviation of any parameter is likely to affect the modeling and prediction of responses.
Polytetrafluoroethylene (PTFE) is a synthetic polymer carbon and fluorine molecules. The main constituent is tetrafluoroethylene (TFE), which is a member of the fluorocarbon family. This material is widely used in industries and home appliances. Researchers use this material for preparing ASTM standard moulds for testing and characterisation. Drilling this material is very common process the engineers do. In this research, a new hybrid approach was attempted for modeling of PTFE drill hole quality. Experiments were conducted to form RSM models. The regression coefficients α and β in the RSM model were then updated using Adaptive Neuro-Fuzzy Inference System (ANFIS) to enhance the response of the model. Both RSM model and enhanced RSM model were used in metaheuristic algorithm-based optimization. The results of both models were validated experimentally. At this end, the paper is organised to describe the research with two-tier hybrid approach of modeling and to discuss the optimization of drilling parameters to get the best drill hole quality.
2. Experimental Method
The drilling was performed on Polytetrafluoroethylene (PTFE) polymer material using Fanuc control model CNC turning centre with axial drilling tool setup. Table 1 portrays the mechanical properties of PTFE. It is a biomaterial preferred in health care, food materials, and aerospace applications. Solid TiN-coated Carbide drill bit (code DIN6537) of 10 mm diameter with the point angle of 100°, 118°, and 135° was used for the drilling of PTFE.
Table 2 exhibits the experimental design summary with 3 ranges of process parameters. According to the drill tool manufacturer index chart, the spindle speed (N) is changed from 800 to 2400 rpm, and feed rate (f) is changed from 0.05 to 0.15 mm/minute. In this investigation, the PTFE polymer rod in φ20 mm was chosen as material and the Taguchi L27 orthogonal array was applied. The drilling was done under two conditions, namely, dry condition and wet condition for the same parameter setting. In coolant case (abbreviated as WC), PTFE samples were drilled axially to 20 mm depth using servo supercut coolant 32. In no coolant case (abbreviated as NC), the samples were drilled to 20 mm depth at dry condition. In all 54 experiments, surface roughness of the drill hole was measured at 5 different locations using Mitutoyo Surftest. Table 3 shows the drill conditions and the respective experimental results ( and ). Figure 1 shows drilled samples.
3. Two-Tier Approach of Modeling
3.1. Response Surface Methodology
The regression response models pertaining to correlation between control variables and responses were developed using the experimental data. Using the experimental data from drilling of PTFE at dry condition and wet condition, the following regression models were obtained. These regression models represented in (1) and (2) are the second-order full quadratic regression models formed by Box Benkhan’s uncoded units.
The above models were used to predict the surface roughness of the drilling. The deviation found in RSM predicted results is the prime research problem considered in the current research. It is sure that these deviations will affect the further optimization or prediction models. Hence, the Adaptive Neuro-Fuzzy Inference System was used as discussed in the following section to settle this issue. The deviation of surface roughness values from experimental and calculated results is as shown in Figure 2.
3.2. Adaptive Neuro-Fuzzy Inference System (ANFIS)
Adaptive Neuro-Fuzzy Inference System (ANFIS) is an interesting and effective soft computing technique which combines a couple of well-established machine learning approaches such as an artificial neural network (ANN) and fuzzy logic theory. The ANFIS technique learns the input datasets like ANN does and then maps the solutions using the fuzzy inference system (FIS). As a result, the hidden layers are established precisely by a FIS within the network of an ANFIS. This particular uniqueness eradicates the well-known difficulty in the ANN model of figuring out the hidden layer. And moreover, it enhances its functionality of prediction. It has the credibility of simple, faster, and accurate adaptive technique in building the prediction model.
In ANFIS, the FIS model was built after neural network training from the given data set is done. The outcomes were then mapped through the variables within the setup of Sugeno type IF-THEN rules which are known as membership function (MF). The FIS model was improved and optimized by a trial-and-error method. The different MF was applied for training and testing of data set. Root Mean Squared Error (RMSE) was calculated to verify the performance of the prediction model. Triangular-shaped membership function (trimf), trapezoidal-shaped membership function (trapmf), generalized bell-shaped membership function (gbellmf), Gaussian curve membership function (gaussmf), Gaussian combination membership function (gauss2mf), P-shaped membership function (pimf), difference between two sigmoidal membership functions (dsigmf), and product of two sigmoid membership functions (psigmf) were attempted, and the best MF was finally fixed based on minimum RMSE for both training and testing data. Figure 3 shows the ANFIS network model of the current problem. From the RSM predicted results, 18 datasets (66.7% of total datasets) were randomly chosen and used for training and the remaining 9 datasets (33.3%) was used for testing. Table 4 shows the datasets used for training and testing. The generalized bell-shaped membership function (gbellmf) was selected for training and testing of the current problem as it has resulted with very small RMSE. The minimum RMSE values for Gbell membership function are as follows: for constant output, the training RMSE is 1.41E-06 and testing RMSE is 0.9723. Similarly for linear output, the training RMSE is 0.00046086 and testing RMSE is 0.8101.
After testing the ANFIS model, a new set of predicted results was generated from the trained model. With these new predicted results, RSM models were updated as follows:
These two equations (3) and (4) are new models representing the drill surface quality at dry drilling and wet drilling of PTFE material, respectively.
3.3. Optimization of Drilling Parameters Using Metaheuristic Algorithm
Numerous optimization algorithms and solution techniques are available to solve the constrained and unconstrained maximization and minimization problems in Engineering. Genetic Algorithm (GA) has been successfully used in a wide variety of problem domains because of their simplicity, ease of operations, and minimum requirements. Optimization functions of the current problem aresubject to
Equations (5) and (6) are objective functions of RMS model data, while equations (7) and (8) are objective functions of ANFIS updated predicted model data. These objective functions and their respective constraints were used in GA. The set bounds/values used in the GA simulations are as follows: number of variables = 3, population size = 100, fitness scaling function = Rank, selection function = stochastic uniform, reproduction elite count = 2, crossover probability = 0.8, crossover function = scattered, mutation probability = 0.05, initial penalty = 10, and number of generations = 300.
4. Results and Discussion
Deviation or error is quite common in the modeling of experimental data using RSM. The deviation may be minimized by considering higher order of terms. To minimize the error in RSM models as shown in Figure 2, two-tier pipelined approach was applied. New pipelined approach of updating weights of RSM model coefficients with the help of ANFIS was to achieve the error-free RSM models. ANOVA analysis of new RSM models and (dry condition and wet condition, respectively) is shown in Tables 5 and 6. Measure of significance is seen excellent (R2 > 95%) and acceptable in both conditions. Feed rate is seen the most dominant parameter in both wet condition and dry condition. Comparison of training data and test data with FIS output is shown in Figures 4 and 5.
4.1. Investigation of Machining Parameters
It is important to investigate the effect of the drilling parameter on the surface roughness of the drilled hole. To investigate the influence of drilling parameters on surface roughness, the surface plot is drawn. Figure 6 shows the effect of speed (N), feed (f), and point angle on surface roughness (Ra).
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From Figure 6, it is observed that the feed rate causes the sudden increase in Ra and dominates the response parameter strongly. On the other hand, the influence of speed on Ra is slick up in Figure 6(a) and precipitous increase in Figure 6(b). The lowest surface roughness is seen at 0.05 mm/min and 800 rpm. In the same manner, the lowest surface roughness is seen at lowest point angle of 100°. The increase in speed or feed or point angle is not appreciated, as it ends up with the highest surface roughness. At the same time, the machining cannot be done with only lowest parameter settings. For instance, if lowest speed is used every time, it will affect the production (number of quantities per unit time) and productivity. Compromised in other words, optimum parameters are to be used in the drilling for achieving the high productivity.
4.2. Prediction from GA and Validation of Predicted Results
As experimentation is costlier and time consuming, DOE was done and only 27 experiments were conducted in dry condition and wet condition each. RSM models and were established from these experimental datasets. In the use of the metaheuristic algorithm for optimization, more datasets are better to use for ease and accurate convergence of solution. Having this in mind, ANFIS was employed and more accurate RSM models and (dry condition and wet condition respectively) were established. GA was applied into all these four models, and optimum machining condition for minimum surface roughness was predicted. Validation experiments were further conducted for each predicted result. Table 7 shows the predicted results from each model and the validation results.
For model (dry drilling condition) at N = 1138 rpm, f = 0.05 mm/min, and Ɵ = 100°, GA predicted surface roughness is 0.8 μm, while the experimental result is 0.84 μm. For (wet drilling condition) at N = 1204 rpm, f = 0.05 mm/min, and Ɵ = 100°, GA predicted surface roughness is 0.77 μm, while it is 0.81 μm. The errors between predicted results and validation results are 4.76% and 4.94%, respectively.
For the ANFIS updated RSM model (, dry drilling condition) at N = 1533 rpm, f = 0.05 mm/min, and Ɵ = 100°, GA predicated surface finish is 0.75 µm, while it is 0.77 μm from validation experiment. Meanwhile, for the ANFIS updated RSM model at wet condition (), the surface finish predicted by GA is 0.68 μm, while it is 0.70 μm from the validation experiment. The errors between predicted values and validation results are 2.6% and 2.86%, respectively. Figure 7 shows the number of generations used by RSM models and ANFIS updated RSM models.
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5. Conclusions
The main objective of this work was to improve the performance of the RSM model through ANFIS. To investigate and demonstrate the hypothesis, PTFE material was drilled with the dry and wet conditions using a carbide drill tool. Surface roughness was measured with the set parameters such as spindle speed, feed, and point angle. RSM models for both dry and wet conditions were formulated. Later, ANFIS was used to update the RSM model terms, and new ANFIS updated RSM models were formulated. These four models were used for optimization using Genetic Algorithm. The numerical results from GA were validated experimentally to evaluate the effect of using ANFIS. The following points are arrived from the investigations and analysis of the data:(i)The ANOVA result for the dry and wet drilling shows that the models are significant and adequate. The feed rate is the most dominating factor in both dry and wet conditions. The contribution of feed rate in drilling process with dry and wet conditions is 71.5% and 71.0%, respectively, whereas speed and point angle contribute only less than 10% in both the conditions.(ii)Comparing GA predicted results with validation results, ANFIS updated RSM models ( and ) are more accurate than RSM models ( and ). The error percentage when using ANFIS updated RSM models for the dry and wet conditions was only 2.60% and 2.86%, respectively.
Data Availability
The data used to support this study are available upon request.
Conflicts of Interest
The authors declare that there are no conflicts of interest related to this work.