Abstract
Formation of spikes prevents achievement of the better material removal rate (MRR) and surface finish while using plain NaNO3 aqueous electrolyte in electrochemical machining (ECM) of die tool steel. Hence this research work attempts to minimize the formation of spikes in the selected workpiece of high carbon high chromium die tool steel using copper nanoparticles suspended in NaNO3 aqueous electrolyte, that is, nanofluid. The selected influencing parameters are applied voltage and electrolyte discharge rate with three levels and tool feed rate with four levels. Thirty-six experiments were designed using Design Expert 7.0 software and optimization was done using multiobjective genetic algorithm (MOGA). This tool identified the best possible combination for achieving the better MRR and surface roughness. The results reveal that voltage of 18 V, tool feed rate of 0.54 mm/min, and nanofluid discharge rate of 12 lit/min would be the optimum values in ECM of HCHCr die tool steel. For checking the optimality obtained from the MOGA in MATLAB software, the maximum MRR of 375.78277 mm3/min and respective surface roughness Ra of 2.339779 μm were predicted at applied voltage of 17.688986 V, tool feed rate of 0.5399705 mm/min, and nanofluid discharge rate of 11.998816 lit/min. Confirmatory tests showed that the actual performance at the optimum conditions was 361.214 mm3/min and 2.41 μm; the deviation from the predicted performance is less than 4% which proves the composite desirability of the developed models.
1. Introduction
Advanced high hardness materials have a high importance especially for the applications such as automotive, metal forming, die making, and aerospace industries. ECM is more suitable process to have excellent and precise machining of these hard materials. It is a technical alternate in the field of manufacturing process to machine steels and superalloys due to avoidance of thermal stresses on their microstructures and absence of tool wear during the machining process [1, 2]. It is more appropriate one to machine a nonmachinable hard materials such as HCHCr die tool steel, AISI 202 Austenitic stainless steel, and superalloys [3, 4]. The parameters of the ECM influencing the objectives of MRR and surface roughness are applied voltage, tool feed rate, and electrolyte discharge rate [5–7]. The electrolyte flows through the interelectrode gap (IEG) and the machining reaction is very appreciable when the value of IEG is small [8, 9]. During the electrochemical machining, the formation of spikes, due to presence of passive layer formation, inconsistency of current density, and formation of gas at the IEG, prevent achievement of the better MRR and surface roughness. Hence this attempts to minimize the formation of spikes in the machined component by using copper nanoparticles suspended in NaNO3 aqueous electrolyte solution. In order to find out an optimal condition, multiobjective genetic algorithm (MOGA) has been applied in this research work.
2. Experimental Setup
The experiments were conducted using ECM setup as shown in Figure 1. The selected workpiece material HCHCr die steel with hardness of 67 in HRc scale was one of the poor machinability materials [10]. The complete chemical composition of HCHCr die steel is presented in Table 1. The plain aqueous solution of 15% NaNO3 and 40 g of Cu nanoparticles suspended in plain aqueous solution of 15% NaNO3 were selected as electrolytes in these experiments [11]. The electrolyte solution was completely analyzed using deluxe water and soil analysis kit, Model-191E. A digital flow meter with two-digit accuracy was employed to adjust the flow rate of electrolyte to the IEG. Copper was chosen for fabrication of tool due to high electrical conductivity. In the present work, the IEG is set to be 0.5 mm initially throughout the experimentation [12]. Material removal (MR) is the difference in the weight of the workpiece before and after machining. The accuracy of measurement is ensured using Sartorius electronic weighing machine with three-digit accuracy. Mitutoyo surface tester with a range of 0–150 µm is used to measure surface roughness (Ra) and the average of values observed in three different surfaces on the workpiece is computed in each experiment. The process parameters used in the complete experiment are presented in Table 2.
3. Mathematical Modeling of Machining Parameters
Design Expert 7.0 software is used to determine the relationship among the selected influencing parameters. Three levels have been selected for influencing parameters of the applied voltage, electrolyte discharge rate, and four levels selected for tool feed rate. It is possible to assess the main and interaction effects of different machining parameters in L36 array with most reasonable accuracy. A first-order experiment was performed to determine the magnitudes of the relative changes to the process parameters that would result in optimum MRR and surface roughness. It is obtained from the first-order experiments; copper nanoparticles suspended in aqueous NaNO3 electrolyte significantly improve the MRR and surface roughness compared to plain aqueous NaNO3 electrolyte. Subsequently, a second-order central composite design was selected to identify the optimum conditions which turn into the higher MRR and finest surface roughness. The general form of second-order polynomial mathematical model applied to investigate the parametric effects of ECM iswhere is the response and terms , , and so forth are the second-order regression coefficients. Various sets of parametric combinations results are obtained by conducting a series of experiments. The respective mathematical models representing MRR in view of plain aqueous NaNO3 and Cu nanoparticles suspended in plain aqueous NaNO3 electrolyte are computed as where , , , , and represent MRR of plain aqueous NaNO3, Cu nanoparticles suspended in plain aqueous NaNO3, applied voltage, tool feed rate, and electrolyte discharge rate, respectively. The developed mathematical model will enable improvement of the performance of ECM while machining HCHCr die steel. The degree of fitness of the developed mathematical model is confirmed through ANOVA test. The coefficient of determination for MRR in terms of aqueous NaNO3 and Cu nanoparticles suspended in aqueous NaNO3 solutions were 90.97% and 93.45%, respectively, which confirms the accuracy of fitness of the mathematical model.
The respective mathematical models representing surface roughness in view of plain aqueous NaNO3 and Cu nanoparticles suspended in plain aqueous NaNO3 electrolytes are computed aswhere , , , , and represent surface roughness of aqueous NaNO3, Cu nanoparticles suspended in aqueous NaNO3 electrolyte, applied voltage, tool feed rate, and electrolyte discharge rate, respectively. The coefficient of determination obtained from ANNOVA for surface roughness in terms of aqueous NaNO3 and Cu nanoparticles suspended in aqueous NaNO3 electrolytes were 92.55% and 96.98%, respectively, which confirms the fitness of the mathematical model.
4. Optimization Using Multiobjective Genetic Algorithm in MATLAB
Evolutionary algorithms seem mainly suitable to solve multiobjective optimization problems, because they deal simultaneously with a set of possible solutions (population). The traditional mathematical programming techniques need a series of separate runs to find the optimum solution for multiobjective problems. Contrarily, this method allows finding several members of the optimal set in a single run of the algorithm. In this research work multiobjective genetic algorithm toolbox from the MATLAB software is chosen for optimizing the selected objectives, maximizing the MRR and minimizing the surface roughness. The ability of GA to simultaneously search different regions of a solution space makes it possible to find a diverse set of solutions for difficult problems with nonconvex, discontinuous, and multimodal solutions spaces [13–15].
5. Analysis of the Influence of Parametric on the MRR and Surface Roughness for Aqueous NaNO3 Electrolyte
The mathematical models developed using RSM and presented in (2) and (4) were used in GA toolbox as fitness functions. The limitation for the optimization is given as follows:
The GA generally includes three fundamental genetic operations of selection, namely, population, crossover, and mutation. These operations are used to modify the chosen solutions and select the most appropriate offspring to pass on to succeeding generations. The following parameters were considered during optimization using GA multiobjective tool. Population size = 225, crossover fraction = 0.8, mutation function = constraint dependent, crossover function = scattered, and number of iterations = 188.
Upon applying objective functions in GA tool, the results were obtained as tabulated in Table 3 and Figure 2.
The response plot shows the effects of applied voltage, tool feed rate, and electrolyte discharge rate on MRR and surface roughness of HCHCr die tool steel. MRR increases at higher voltage with the increase of tool feed rate and higher flow of electrolyte discharge rate at a mean time surface roughness slightly increased. A maximum MRR 306.69449 mm3/min was achieved under tool feed rate of 0.5399502 mm/min, 11.97976 lit/min of electrolyte discharge rate, and applied voltage of 17.995820 V. A minimum SR value of 1.513575 µm was observed at 12 V, 0.1100281 mm/min of tool feed rate, and 8.134412 lit/min of electrolyte discharge rate.
6. Analysis of the Influence of Parametric on the MRR and Surface Roughness for Cu Nanoparticles Suspended in Aqueous NaNO3 Electrolyte
Table 4 and Figure 3 present the results from GA for Cu nanoparticles suspended in aqueous NaNO3 electrolyte. MRR increases at higher values of electrolyte discharge rate and tool feed rate. The surface roughness decreases when the electrolyte discharge rate and tool feed rate are decreased. A maximum value of MRR 375.78277 mm3/min was obtained under 17.688986 V, 0.5399705 mm/min tool feed rate, and 11.998816 lit/min electrolyte discharge rate conditions. The minimum surface finish of 1.4973965 µm was observed at 17.999473 V, 0.2344207 mm/min tool feed rate, and 11.997052 lit/min electrolyte discharge rate condition.
It is obvious that the optimum search can be obtained based on the developed second-order response, surface equations for correlating the various process variable effects with the MRR and surface roughness. The optimal combination of various process variables thus obtained for achieving controlled electrochemical machining of the workpieces is found to be within the bounds of the mathematical model.
7. Confirmation Test
The confirmatory experiments were further conducted for the optimal parameters obtained from the MATLAB multiobjective GA tool. The error between optimum values from GA and the confirmation test was derived by considering the serial number 24 and serial number 1 from Tables 3 and 4, respectively, at the condition of maximum MRR and is shown in Table 5.
8. Conclusions
This work employs a multiobjective genetic algorithm (GA) tool to optimize influencing parameters of ECM to maximize the MRR and minimize surface roughness of HCHCr die steel. Based on the experimental results, the following conclusions are drawn.(1)Material removal rate increases linearly with applied voltage and nonlinearly increases with tool feed rate. Surface roughness decreases with increase in the applied voltage and all tool feed rates. Mathematical models for MRR and surface roughness have been developed by Design Expert 7.0 software. It is useful for analyzing the influence of the various process parameters for achieving better MRR and surface roughness of HCHCr die tool steel.(2)Genetic algorithm (GA) tool optimizes the range of influencing parameters in order to obtain a maximum MRR and minimum surface roughness. The experimental results reveal that applied voltage of 18 V, tool feed rate of 0.54 mm/min, and electrolyte discharge rate of 12 lit/min would be the optimum values in ECM of HCHCr die tool steel under copper nanoparticles suspended in aqueous NaNO3 electrolyte solution machining condition.(3)For checking the optimality obtained from the multiobjective GA in MATLAB, MRR of 375.78277 mm3/min and surface roughness Ra of 2.339779 μm were predicted at applied voltage of 18 V, tool feed rate of 0.54 mm/min, and electrolyte discharge rate of 11.99 lit/min.(4)Confirmatory tests showed that the actual performance at the optimum conditions was 361.214 mm3/min and 2.41 μm; a deviation from the predicted performance is less than 4% at maximum material removal rate condition which has proven the composite desirability of the developed models for MRR and surface roughness under copper nanoparticles suspended in aqueous NaNO3 electrolyte solution machining condition. Aqueous NaNO3 electrolyte solutions performance is poor comparing to copper nanoparticles suspended in aqueous NaNO3 electrolyte solution.(5)Comparing the predicted performance of aqueous NaNO3 and copper nanoparticles suspended in aqueous NaNO3 electrolyte solutions on experimentally and mathematically, copper nanoparticles suspended in aqueous NaNO3 electrolyte solution performs better for MRR and surface roughness on HCHCr die tool steel.
Conflict of Interests
The authors declare that there is no conflict of interests regarding the publication of this paper.