Intelligent Modeling and Multiobjective Optimization of Electric Discharge Diamond Grinding

The grinding of metal matrix composites (MMCs) is very difficult by conventional techniques due to its improved mechanical properties. It often results in poor surface quality (surface damage) in the form of surface cracks/residual stresses and requires frequent truing and dressing due to clogging of the grinding wheel. The electric discharge diamond grinding (EDDG), a hybrid process of electric discharge machining and grinding may overcome these problems up to some extent. But low material removal rate (MRR) and high wheel wear rate (WWR) are the main problems in EDDG to achieve economic performance. The present paper investigates the EDDG process performance during grinding of copper-iron-graphite composite by modeling and simultaneous optimization of two important performance characteristics such as MRR and WWR. A hybrid approach of artificial neural network, genetic algorithm, and grey relational analysis has been proposed for multi-objective optimization. The verification results show considerable improvement in the performance of both quality characteristics.

Keywords: Artificial neural network; Electric discharge diamond grinding; Genetic algorithm; Grey relational analysis; Metal matrix composites

There has been growing interests in the use of advanced metal matrix composites (MMCs) in the recent past due to their superior mechanical properties [[1]]. Improved mechanical properties render conventional machining processes uneconomical and sometimes unfeasible to process these materials.

The grinding of MMCs still remains a challenge due to its hard reinforcement and hybrid nature of the constituents. The investigations on the grindability of MMCs are few. Ilio et al. [[2]] developed predictive models of forces, surface roughness (SR), and specific energy during grinding of Al/SiC MMC. Thiagarajan et al. [[3]] suggested grinding input conditions to obtain good surface quality.

In order to overcome the machining challenges, the unconventional machining processes have been found as an alternative for shaping advanced difficult-to-cut materials. Electric discharge machining (EDM) is such an unconventional machining process, which is widely used to create complex shapes and intricate profiles in the electrically conductive materials irrespective of their superior mechanical properties. EDM and its variants are widely used in a variety of industrial applications [[4]]. Material removal rate (MRR), tool wear rate (TWR), and surface integrity, are the important process performance parameters in EDM. Seo et al. [[5]] did electric discharge drilling of functionally graded SiCp/Al MMC under varying input conditions to study the MRR, TWR, and drilled hole quality. They found the optimum combination of process parameters to obtain best machining conditions. Somashekhar et al. [[6]] developed artificial neural network (ANN) model for MRR during micro-electric discharge machining. Furthermore, they did single objective optimization for MRR using genetic algorithm (GA). Abdulkareem et al. [[7]] investigated the effect of electrode cooling during the EDM of titanium alloy by considering TWR as the performance parameter. It was found that there is a 27% reduction in the TWR due to cooling. Kumar et al. did review of research work in the area of additive mixed EDM process [[8]] and usefulness of powder metallurgy processed electrode in imparting desirable surface properties to machined surface [[9]], and they suggested future research directions for both cases.

Low machining rate and high investment costs are some practical problems which restrict the use of unconventional machining processes. But the high demand of advanced materials has motivated the researchers to develop and apply such machining methods which have capabilities to machine advanced difficult-to-cut materials with improved performances. The hybrid machining is such a concept that combines the mechanism of two different machining processes (often one of them is an unconventional machining process) for material removal.

As the grindability of MMCs is poor, EDM also suffers from the drawback of tool wear, low MRR, high specific energy, and formation of recast layer. The machining/grinding performance of MMCs may be enhanced by combining and utilizing the potential of both processes, grinding and EDM, in a better manner. Electric discharge abrasive grinding (EDAG) is such a hybrid machining process in which tool electrode of EDM system is replaced by rotating metal bonded abrasive wheel, similar to grinding wheel. In EDAG sparks created by EDM action soften the work surface as well as helps in truing and dressing while abrasive action removes the material. If diamond is used as an abrasive, then the process is termed as electric discharge diamond grinding (EDDG) [[4]]. The schematic of EDDG used in present study is shown in Fig. 1.

Graph: FIGURE 1 —Schematic diagram of EDDG.

Few researchers have tried to explore the potential of EDDG. Kumar et al. [[10]] performed EDDG experiments on high speed steel, using central rotatable composite design of experiments and developed response surface models and ANN models for the WWR and SR and found that both models suitably predict the EDDG process behavior. Chandrasekhar et al. [[11]] elucidated the effect of important electrical input parameters and wheel speed on the MRR and SR during electric discharge face grinding of high carbon steel and high speed steel workpiece. They found that both performances improved by the use of a rotating wheel as compared to the stationary wheel. Singh et al. [[12]] performed EDDG experiments on tungsten carbide-cobalt composite and predicted optimum process parameters using grey relational analysis (GRA).

The available literature on EDDG shows that most researchers have focused on parametric study and/or optimization of different characteristics such as MRR, WWR grinding forces, and SR. Also, the studies mainly concentrated on metals and alloys. Very few researchers have studied the EDDG process behavior during grinding of composites. Furthermore, no work has been reported for EDDG of copper-iron-graphite composite, which is being widely used in automobile industries for manufacturing of disc brake, clutch plate, etc. The aim of the present research is to study the process behavior during EDDG of copper-iron-graphite MMC. The experiments have been performed using Taguchi methodology based L27 orthogonal array (OA) matrix [[13]], to observe two important performances: MRR and WWR. The hybrid approach of ANN, GA, and GRA based entropy measurement techniques have been applied for modeling and multi-objective optimization of MRR and WWR. The predicted optimum results have been verified by confirmation tests.

ANN is information processing paradigm in which a large number of highly interconnected processing elements (neurons) are working together [[14]]. In the network, each neuron receives total input from all of the neurons in the preceding layer as

Graph

where netr is the total or net input, and N is the number of inputs to the rth neuron in the forward layer. wqr is the weight of the connection to the qth neuron in the forward layer from the rth neuron in the preceding layer, Xr is the input from the rth neuron in the preceding layer to the forward layer, and bq the bias to qth neuron. A neuron in the network produces its output (outr) by processing the net input through an activation function Ғ, such as log sigmoid function and pure linear function chosen in this study as below:

Graph

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The selection of activation functions is done by trial and error. The different activation functions and their different combinations for hidden and output layer are tried and the combination, which gives the minimum mean square error (MSE) is selected.

For simultaneous optimization of more than one quality characteristic, sometimes it is desirable to normalize the quality characteristics. So the training data set, i.e., the experimental values of quality characteristics, have been normalized using the following formula:

Graph

where xni is the normalized value of the kth response during ith observation, and max yi(K) is the maximum value of yi(K) for the kth response.

The present optimization problem is the nonlinear optimization problem and GA is quite suitable for non-linear optimization problems. GA is based on Darwin's principle of "survival of the fittest." The algorithm starts with the creation of a random population. The individual with the best fitness is selected to form the mating pair, and then the new population is created through the process of cross-over and mutation. The new individuals are again tested for their fitness and this cycle is repeated until some termination criteria are satisfied [[15]]. Since GA works with a population of points instead of a single point, it is very likely that the result predicted by GA may be more accurate and better than many of the traditional optimization methods.

A common difficulty with multiobjective optimization is the appearance of an objective conflict. To get the solution of a multiobjective optimization problem, using a classical method like objective weighting, all the objectives are converted into a single objective function. In objective weighting method, multiobjective functions are combined into one overall objective function by assigning different weights to different objectives [[15]]. The determination of weight is a critical aspect, which sometimes is decided by designer's experience or some mathematical techniques. In this study, the GRA coupled with entropy measurement technique [[16]] has been used to find the weight of each quality characteristic for multiobjective optimization.

The EDDG setup was designed and fabricated. The setup was attached to the die sinking EDM system. The setup consists of a shaft which holds the metal bonded diamond grinding wheel and performs face grinding. The shaft was rotated by a DC motor, through a belt, and pulley arrangement (Fig. 1). The different control factors and their levels are given in Table 1. The wheel speed was kept constant (900 RPM) throughout the experiment. Copper-Iron-Graphite MMC is used as workpiece material. Each experiment was performed for 30 minutes and the quality characteristics, i.e., MRR and WWR in each experimental run are obtained by measuring the mass difference before and after the experiment, using precision electronic digital weight balance with a 0.1 mg resolution.

TABLE 1.—Control factors and their levels

The MRR (g/min) and WWR (g/min) were calculated by the following formula:

Graph

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where miw and mit are the initial mass of workpiece and wheel in gram (before machining), respectively and mfw and mft are final mass of workpiece and wheel in gram (after machining); tp is machining time in minutes. The normalized value of the quality characteristics, corresponding to each experimental run, have been calculated using Eq. (4), and are shown in Fig. 2.

Graph: FIGURE 2 —Normalized values of quality characteristics.

The optimal neural network architecture, used for normalized material removal rate (NMMR) and normalized wheel wear rate (NWWR), is shown in Fig. 3. The network for both NMRR and NWWR consists of one input, one hidden, and one output layer. The input and output layers have four and one neurons, respectively. The neurons in input layer corresponds to peak current, pulse-on time, pulse-off time, and grit number. Output layer corresponds to NMRR and NWWR. The hidden layer has one neuron for the NMRR model, whereas it has five neurons for the NWWR model. The activation functions used for the hidden layer and output layer were log sigmoid and pure linear, respectively.

Graph: FIGURE 3 —Architecture of ANN for NMRR and NWWR.

In this work, a commercially available software package MATLAB 7.4 was used for the network training and optimization. The network training means obtaining the weights so that MSE is minimum. During training, the weights are given quasi-random initial values. They are then iteratively updated until they converge to certain values using the gradient descent method. Gradient descent method updates weights so as to minimize the mean square error between the network output and the training data set.

The values of the weights and biases, after network is fully trained, are shown in Table 2 for both NMRR and NWWR.

TABLE 2.—Final values of weights and biases for NMRR and NWWR

So, in the mathematical form, the ANN model for NMRR and NWWR can be represented as follows:

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where

Graph

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is the weight from hidden layer to output layer, and bias to output layer, respectively.

Also,

Graph

where wq and bo correspond to weight and bias to output layer, and yq is the net input to the output layer from hidden layer and is given by

Graph

The values of wq, bo, wqr, and bq are shown in Table 2.

The results of the ANN model have been compared with the experimental data to check the validity of developed models. The maximum, minimum, and mean square error for the MRR models have been found as 9.23%, 0.22%, and 0.002%, respectively, while these errors for WWR models have been found as 7%, 0.002%, and 0.001%, respectively. The comparison results are also shown in Fig. 4. Hence, it can be concluded that the developed models are suitable for prediction of MRR and WWR.

Graph: FIGURE 4 —Comparison of ANN predicted result with the experimental result for NMRR and NWWR.

Using GRA coupled with entropy measurement, the weight for NMMR and NWWR have been found as 0.46 and 0.54, respectively. Now the multiobjective optimization problem can be transformed into the single objective optimization problem. In the present case, both objective functions are of a conflicting nature because the aim is to maximize the MRR and minimize the WWR.

Thus, the objective function of the optimization problem can be stated as below:

Graph

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where W1 = 0.46 and W1 = 0.54, and NMRR and NWWR correspond to Eqs. (7) and (8), with the following range of process input parameters:

Graph

Graph

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The critical parameters of GA are the size of the population, cross-over rate, mutation rate, and number of generations. After trying different combinations of GA parameters, the population size 20, cross-over rate 0.8, mutation rate 0.01, and number of generation 40, have been taken in the present study. The objective function in Eq. (9) has been solved without any constraint. The generation-fitness graphics have been shown in Fig. 5. The fitness function is optimized when the mean curve converges to the best curve after 7 generations. The corresponding values of control factors peak current, pulse-on time, pulse-off time, and grit number have been found as 5.99 A, 20.22 µs, 15.34 µs, and 240. Hence these are the optimum values of control factors. Using these values, the values of MRR and WWR have been obtained as 0.1068 g/min and 0.024 g/min, respectively.

Graph: FIGURE 5 —Generation-fitness function graphics.

The confirmation experiments have also been performed and shown in Table 3. The experimental results of MRR and WWR shown in this table are the average of three trials at optimum levels. The comparison of optimum results with that of results obtained at initial level of control factors shows considerable improvement in MRR and WWR. The optimal machining parameters are also shown in Fig. 4. It is evident that their combination is best among the group.

TABLE 3.—Optimization and confirmation results

Achieving a good compromise between objective functions in multiobjective optimization problem is a big challenge due to the existence of multiple solutions, known as Pareto-optimal solutions. To overcome it, in the present work, weights for each quality characteristics have been calculated first, to get the optimal solution. Correlation between optimum control factors and quality characteristics can be understood as increase of peak current increases in MRR and/or WWR because peak current increases the input energy that favors the increase of MRR and/or WWR. Moderate level of pulse-on time and low level of pulse-off time reduce overall machining time and thus favor higher MRR. The fine grains result low depth of penetration and hence reduces MRR. Also, there will be a reduced grinding force due to fine or sharp cutting edges and reduction in depth of cut for finer grains that finally reduce the WWR. So, we can conclude that grain fineness favors more towards a low WWR.

The multiobjective optimization of EDDG of copper-iron-graphite MMC, using a hybrid approach of ANN, GA, and GRA with entropy measurement technique has been done. The following conclusions have been drawn on basis of results obtained:

• 1. The developed models for MRR and WWR, with a mean square error of 0.002% and 0.001%, respectively, are well in agreement with the experimental result.
• 2. The optimum levels of control factors are as follows: peak current 5.99 A, pulse-on time 20.22 µs, pulse-off time 15.34 µs, and grit number 240.
• 3. Both performances, MRR and WWR, have simultaneously been improved by 76.80% and 31.85%, respectively.