Multi-response optimization of process parameters for powder mixed electro-discharge machin- ing according to the surface roughness and surface micro-hardness using Taguchi-TOPSIS

Article history: Received: June 1, 2018 Received in revised format: June 18, 2018 Accepted: September 14, 2018 Available online: September 14, 2018 In this study, the efficiency of integration between Taguchi and TOPSIS in multi-response optimization of powder mixed electrical discharge machining (PMEDM) process was evaluated. The input parameters, such as workpiece and tool electrode material, polarity, pulse on time (ton), pulse off time (toff), Current (I) and powder concentration have been selected to optimize two responses; namely surface roughness (Ra) and surface hardness (HV). The results show that titanium powder mixed dielectric fluid improves multi-response optimization efficiency in PMEDM. In addition, machining conditions, such as tool electrode material, powder concentration, pulse on time, polarity, current density, A×G and B×G interactions play a very important role on S/N ratio of C* whereby powder concentration has the strongest influence. TOPSIS -Taguchi is a potential method for multi-response optimization in PMEDM. However, the optimal results using ANOVA analysis show that there is a necessity to have more studies in TOPSIS-Taguchi to improve the integration efficiency between two methods for optimizing multiple responses in PMEDM. © 2018 by the authors; licensee Growing Science, Canada.


Introduction
Powder mixed electrical discharge machining (PMEDM) recently has shown its potential for concurrent improving material removal rate and surface quality. However, this method has a large amount of machining parameters and it still remains challenges, such as the uniformity of particles in dielectric fluid, particle trajectory in discharge gap, shape and physical properties of powder material, etc. It leads to many difficulties for optimizing PMEDM process, especially in multi-response optimization.
Taguchi has been widely applied to deal with responses affected by many parameters (Ahmed & Arora, 2017). However, Taguchi can only be an effective approach for optimizing process performance with a single quality response. Nowadays, TOPSIS-Taguchi integration is commonly used to solve multi-re-sponse optimization problems in many technical fields, such as: information technology; electrical, electronic and mechanical engineering, etc. This combination can reduce experimental costs and increase optimization efficiency. TOPSIS is used for multi-response optimization in both traditional machining (milling, turning, drilling, grinding, etc.), non-traditional machining (EDM, water jet machining, etc.) and many other fields (Shukla et al. 2017;Mohapatraa & Sahooa, 2018). TOPSIS's algorithms allow to optimize a large number of responses with high quality of optimal results. In multi-response optimization, TOPSIS is a very simple method and easy to implement (Gadakh et al., 2012). Simultaneously, this method is also allowed to use both quantitative and qualitative input parameters. Therefore, it is a solution that can solve multi-response optimization problems more objectively. Many results of TOPSIS-Taguchi optimization method in EDM were shown. It can be used for optimizing material removal rate, electrode wear and surface roughness responses in PMEDM (Tripathy & Tripathy, 2017). Material removal rate (MRR), surface roughness and fractal dimension are also responses to optimize when machining AISI D2 tool steel (Prabhu & Vinayagam, 2016;Zerti et al., 2018). The results showed that voltage has the strongest effect (42.42 %) and pulse on time has the smallest effect (11.13%). Seven multiple responses in electrical discharge machining have been optimized using TOPSIS-Taguchi with a significant increase in machining efficiency (Manivannan & Kumar, 2017;Khanna et al., 2015;Manivannan & Kumar, 2016). Besides, many other methods have also been used as Artificial neural network, Response surface methodology, and Taguchi's combination with other methods (GRA, MOORA-PCA, VIKOR, multiple response signal-to-noise, weighted signal-to-noise,...) for multi-target optimization in EDM (Tirumala et al., 2018;Munmun & Kalipad, 2017;Bhaumik & Maity, 2017;Nayaka et al., 2017;Munmun & Kalipada, 2017;Dey & Chakraborty, 2015). However, Taguchi-TOPSIS and Taguchi-GRA are the most commonly used (Kumar et al., 2018;Zerti et al., 2018;Mohapatraa et al., 2017). Dastagiri et al. (2016) have shown that TOPSIS-Taguchi is more effective than Taguchi-GRA in multi-response optimization of PMEDM.
In this study, the authors have made the optimization of process parameters in PMEDM using titanium powder for die steels, surface quality after PMEDM has been evaluated by the two indicators SR and HV. In addition, the topography and composition of the chemical elements on the surface of the workpiece at optimum conditions are also analyzed.

Materials
In this study, a CNC high precision EDM machine (Sodick, Inc. USA) was used to perform the experiments. An external circulation system is shown in Fig. 1. Two stirrers rotate in opposite directions at a speed of 200 rpm to prevent the deposition of titanium powder at the bottom of the tank during the experiment. Dielectric fluid is pumped at a flow of 600 l/h to discharge gap. In order to prevent the debris entering the machining area, magnets are used to attract them.
This study utilised (45 × 27 × 10) mm 3 samples, 23 mm tool electrode diameter with 35 mm length. Dielectric fluid is HD-1 oil which widely used for EDM machine in Vietnam recently. Titanium powder (45 µm size) was mixed with the dielectric fluid in different concentrations. Experimental parameters are given in Table 1.
After machining, the samples were cleaned and later dry. Surface roughness (Ra) was measured using a profilometer (Mitutoyo Surftest SJ-301 -Japan) in a 5 mm measured length. Microhardness tester (model Indenta Met 1106) from Buehler, USA was used to measure microhardness of the surface. A 0.005 HV measuring range for measuring the specimen surface in a perpendicular using 50 g penetration load. SEM images were captured by a scanning electron microscope (model Jeol 6490 Jed 2300, Japan). And chemical composition of EDMed surface was analyzed with the use of an energy-dispersive X-ray spectroscopy (model PDA 7000, Switzerland). The measured repetition on each sampe is three and average results were calculated.

Methods
Experimental design methodology: Taguchi method is used to design the experiments. The advantage of this method is a minimum number of the experiments but a maximum amount of input parameters. In addition, the input parameters are both quantitative and qualitative. Based on orthogonal matrices, an experimental matrix is designed and the identification of the experimental matrix is very simple. A kind of the experimental matrix is selected. It bases on the number of input parameters, pairs of interactions between the parameters and the degree of freedom (DOF) of the parameters. In this study, seven input parameters and three pairs of these interactions are studied (Tab. 1). So, Taguchi matrix L27 is used: values A, B, C, D, E, F and G are assigned to column 1, 2, 9, 10, 12, 13 and 5, respectively. The experimental results of surface roughness Ra and surface hardness HV are shown in Table 2. The Taguchi method uses the signal-to-noise (S/N) ratio to optimize the results, and S/N ratio is determined by the Eq. (1): where:  Multi-response optimization methodology: TOPSIS is a very popular method and provides a more realistic approach used in multi-response optimization. This method can pick out the best response (the most ideally response) from the positive responses and the worst response (the most negative response) from the negative responses. The steps taken in the TOPSIS method are described as follows: Step 1: Arranging the selected responses in matrix form: where: x11, x12, … x1n -Selected responses x11, x21, … xm1 -Values of the first response at different levels n -Amount of the selected responses m -Amount of the values from one response Step 2: Standardizing the matrix, convert the responses to non-dimensional form to make comparisons between response values. The standardized matrix is established through standardized values 0 1 : Step 3: Assigning weights of the selected responses to the standardized matrix defined as follows: Wj-Weight of the responses Y -Standardized matrix of the assigned responses Step 4 where: J is associated with the positive criteria and J′ is associated with the negative criteria. j y  -the best value of xj j y  -the worst value of xj Step 5: The individual distances are calculated using Euclidean distance with n dimensions. Each distance comes from the following ideal problem: Separation from positive ideal solution: Separation from negative ideal solution: Step 6: The nearest distance to the ideal value is calculated. The nearest distance of the alternative value Ai with respect to A + is defined as follows: * * , 1, 2,..., ; 0 1 Step 7: The arrangement is done by values close to C * . The higher C * value provides a better quality of Ai solution.

Optimization results using TOPSIS-Taguchi:
Step 1: Arranging the selected responses in matrix form by Eq. (10).
Step 2: Standardizing the matrix. The conversion values are determined by Eq. (3). The result is shown in Table 3.
Step 3: Determining the values of y11 and y12. Based on experiences, the weight of the Ra and HV responses is chosen: WRa = 0.4 and WHV = 0.6 and response values are given in Table 5 by Eq. (4).
Step 4: Determining the best solution and the worst solution: From Eq. (5) and Eq. (6), the best solution and the worst solution are determined. HV is described: the higher the better, while Ra is described: the smaller the better. So, the smallest value is the best solution and the biggest value is the worst solution.
The results are shown in Table 4.
Step 5: Determining the values of i S  and i S  [ Table 5] based on Eq. (7) and Eq. (8).
Step 7: Arranging the C * value in the order shown in Table 5. The results shown that: Experiment 6 provides the best surface quality.  Optimal results based on S/N ratio: The study utilized a Taguchi's experimental matrix to investigate seven parameters at a third level. There must be 3 7 experiments to determine exactly the optimal conditions under the traditional method. However, in the Taguchi's experimental matrix, there are only 27 experiments. It is possible to get an optimal value in the rest of the experiments. Therefore, it need to base on the S/N ratio in Taguchi's analysis to find the optimal combination. A higher S/N ratio of C * leads to have a better result. The S/N value of C * is calculated by Eq.
(2) and shown in Table 2. The results showed that: electrode material (F = 28.8), pulse on time (F = 13.58), powder concentration (F = 22.47), A×G (F = 7.58) and B×G (F = 5.14) strongly influence on the S/N ratio of C * (Table 4). Parameters, such as: workpiece material, polarity, pulse off time, current density and A×B, are negligible effect on the S/N ratio of C * . Powder concentration has the strongest influence and workpiece material has the weakest influence. Fig. 2 and Fig. 3 show the influence of machining conditions and some pairs of interactions between them on the S/N ratio of C * . The optimal value can be achieved when using: SKT4 workpiece material, copper electrode, negative electrode, I = 4 A, ton = 5 s, tof = 57 s, and 10 g/l powder concentration. The optimal values of the responses are determined by Eq. (11).

Data Means
Signal-to-noise: Larger is better

Data Means
Signal-to-noise: Larger is better Fig. 3. Influence of interactive pairs on the S/N ratio of C *

Discussion
The optimal results of TOPSIS-Taguchi and ANOVA analysis in Table 5 show that optimal values (Ra = 1.45 m and HV = 649,5 HV) can be achieved for SKD61 when using negative polarity of tool electrode, ton = 5 s, I = 4 A, toff = 57 s at 20 g/l powder concentration. The result shows that: compared to surface hardness of SKD61 steel ( 506.5 HV), the hardness of EDMed surface at the optimal parameter is significantly increased ( 28.2 %) due to the presence of titanium on the workpiece surface (Fig. 4). Simultaneously, topography of EDMed surface at the optimal condition is characterized by small and uniform craters (Fig. 5) which facilitate for storing lubricant on the surface. Both surface hardness and topography enhance the working ability of the mold surface. The optimal results using TOPSIS-Taguchi have been greatly improved (Ra decreases 5.29 % and surface hardness increases 34.6 %) than the optimal results based on the S/N ratio. However, the set of machining parameters and the optimum values of these two methods are different, especially the difference in the level of optimal powder concentration which is the most important parameter of PMEDM. It has caused many difficulties in determining optimal conditions.

Conclusions
The study has evaluated the suitability of Topsis-Taguchi for multi-response optimization in machining mold materials (SKD61, SKD 11 and SKT4) using titanium powder mixed electrical discharge machining. It can be revealed that the machining parameters such as powder concentration, tool electrode material, pulse on time, A×G and B×G interactions play an important role to the S/N ratio of C * , whereby the powder concentration has the strongest influence. Surface roughness Ra = 1.45 m and microhardness 629.84 HV are optimal results using Topsis-Taguchi with parameters to be as follows: SKD61 workpiece material, copper electrode, negative polarity, ton = 5 s, I = 4 A, toff = 57 s and 20 g/l powder concentration. However, other optimal results (2.34 µm Ra and 904,96 HV microhardness) are predicted by ANOVA analysis using other parameters, including: SKT4 workpiece material, copper electrode, negative polarity, ton = 5 s, I = 4 A, toff = 57 s and 10 g/l powder concentration. TOPSIS, with a simple calculating method integrated with Taguchi, can be used to optimize a large number of the responses thereby minimizing the number of the experiments. It leads to reduction of material costs and processing time. However, there are some differences between the optimal results of C* using Topsis-Taguchi and using ANOVA analysis. Therefore, there is a need to have more future works to enhance the suitability of Topsis and Taguchi for multi-response optimization in PMEDM.