Multi-attribute recursive optimization (MARO) for EDM of D3 tool steel

ABSTRACT

Electric Discharge Machining (EDM) is one of the most effective unconventional material removal techniques that mill electrically conductive objects, despite their hardness using electrical discharge. This elite method provides excellent accuracy and surface finish within short duration. The presented research envisages to study the effect of process variables of EDM namely Pulsating Current (I), Pulse-on-time (Ton) and Pulse-off time (Toff) on machining performance measures namely Tool Wear Rate (TWR), Surface Roughness (SR) and Material Removal Rate (MRR). The best possible condition for specimen selection is presented by a new technique known as Multi Attribute Recursive Optimization (MARO). The optimal experimental conditions were found with Ton 100 s, Toff 49.82 s, and I 4.99 A, with ideal responses of SR 0.057 µm, MRR 0.036 g/min, and TWR 3.301 g/min. For the best run identification, the METHod for Enrichment Evaluation, Preference Ranking Organization METHod (PROME-THEE) was used while Historical Data Design (HDD) was used to validate the result obtained. The integration of PROMETHEE and HDD known as MARO is identified to appreciate degree of the methods analyzed. The close convergence of PROMETHEE and HDD at 97% guarantees the accuracy of the proposed MARO technique.

Keywords:
Electric discharge machining; material removal; process parameters; multi-attribute recursive optimization; historical data design

1. INTRODUCTION

A cutting-edge thermoelectric machining process is Electrical Discharge Machining (EDM) which is gaining popularity, as it doesn’t need complicated cutting tools and permits the machining of thin, brittle, hard and complex geometries. The ability to machine any material that conducts electricity, despite of its good tensile strength, toughness and hardness, together with the precision in dimension for intricate configurations, satisfy the demands of contemporary manufacturing industries. This non-traditional machining process eliminates the common machining issues including mechanical stress and vibration since the electrode and the workpiece are not in direct contact. As a result, EDM is extensively employed in a variety of significant applications, including those found in the aerospace and automotive, die and mould, microelectronics, and biomedical sectors [¹,²,³].The process of EDM involves the localized melting and vaporization of material to remove material from the workpiece. When two electrodes placed in a dielectric medium are held closely together and are subjected to a significant potential difference, electric sparks produced between the electrodes. The sparks that develop between the two electrode surfaces produce specialized areas of high temperatures [⁴,⁵,⁶].The material of the workpiece melts and vaporizes in the restricted zone. The dielectric flow removes the majority of the melted and vaporized material as debris particles from the specimen electrode gap.

Enhancing the surface finish, subsurface integrity and material removal rate (MRR) in EDM was the objective of various investigations. The entire potential application of this process is still not fully known, though, owing to its complexity and several process controllable factors. Rajender KUMAR et al. [⁷] in the research work enhanced the WEDM characteristics for ZE41A magnesium alloy by employing Grey Relational Analysis (GRA). L16 orthogonal array employed to optimize the corrosion rate, MRR, and the surface characteristics with respect to servo voltage, peak pulse-on time, pulse-off time and current. The best possible process parameters of WEDM were ascertained by means of GRA technique and the current and peak pulse-on time were found to be the highly significant parameter. The L9 orthogonal array of tests was explored by LODHI and AGARWAL [⁸] to improve the process parameters for AISI D3 steel during WEDM. Surface roughness was found to be highly affected by Pulse-on-time and discharge current. Artificial neural network (ANN) and Response Surface Methodology (RSM) were employed to develop a model by MONDAL et al. [⁹] to forecast MRR and SR in EDM of stainless steel AISI 304. It has been reported that ANN predicted pattern was high in accuracy, in addition both patterns were produced good accuracy with the experimented data. The Taguchi technique was employed in the investigation by RADHIKA et al. [¹⁰] to examine the impacts of and flushing pressure, Pulse-on-time and Pulse-on current on the performance measures. The tool wear ratio, SR and rates of material loss were measured and computed. Using EDM, GATTO et al. [¹¹] performed investigations on the machinability of Aluminium (Al) alloys. The study investigated the efficiency of EDM machining in terms of workpiece surface quality, dimensional and geometrical precision, and electrode wear mechanism. To enhance the quality of the machining surface, MIR et al. [¹²] carried out modelling along with experimental investigations on powder mixed EDM of H11 steel. Investigations analyses the process variables, viz. Al content in the dielectric fluid, discharge current and Pulse-on-time. It has been demonstrated that the addition of Al powder enhances the quality of surface. The parameters Pulse-on current and Pulse-on-time were varied from 6 to 12 A and 60 to 200 s, respectively. Two different dielectric materials and a graphite electrode used for conduction the experiments.Al6061 alloy was examined in relation to EDM machining [¹³]. The impacts of process parameters of wire EDM on SR, cutting rate and MRR were studied by SINGH and PRADHAN [¹⁴]. Brass wire electrodes and an L27 orthogonal array of tests were used to mill AISI D2 steel specimens. SR was influenced by Pulse-on-time and servo voltage, although Pulse-on-time and Pulse-off-time considerably influenced cutting rate and MRR.

The majority of EDM investigations, according to earlier research, concentrated on how process variables affected surface integrity and MRR when machining various steel workpieces. Due to its outstanding wear resistance, enhanced hardening capabilities, increased impact strength, high compressive strength and good resistance to tempering back, High Carbon High Chromium die steel is the perfect choice for making punches [¹⁵]. In manufacturing industries, the profiles are generated using the EDM technique after being hardened between 62 and 65 HRC, primarily for tool and dies. Using traditional machining techniques to make the profile for such punches is fairly difficult. In spite of widespread research on the process parameters of EDM, machinist skill and trial-and-error methods were still used in industries to determine the ideal machining settings for EDM of HCHCr steel. The method was time consuming and person dependent. Instead, it has been discovered that Design of Experiments (DoE) along with RSM is a successful strategy for developing mathematical models to identify the desired process parameter. Experimental study utilizing orthogonal array facilitates the simultaneous investigation of the results of many parameters using the least number of trials, the best use of time, and the least quantity of material. The genetic algorithm, simulated annealing, GRA, differential and particle swarm optimization [¹⁶,¹⁷] are popular multi-response optimization tools. Improving surface finish, subsurface integrity, and material removal rate (MRR) in EDM has been the focus of numerous studies. However, due to the complexity of the process and the many controllable factors involved, its full potential applications remain largely unexplored.

To optimize the EDM performance of HCHCr die steel, this research focuses on developing mathematical models RSM. A novel hybrid approach, Multi-Attribute Recursive Optimization (MARO), is employed to integrate multiple optimization techniques, where one optimization strategy is validated and evaluated by another higher-order methodology [¹⁸]. In this study, the optimal parametric combination is first identified through ranking using PROMETHEE, a Multiple Criteria Decision Making (MCDM) technique. This combination is then rigorously validated for reliability through another optimization method, Historical Data Design (HDD), a subset of RSM. The overall research framework is depicted as a block diagram in Figure 1, providing a clear and structured visualization of the concept.

Figure 1
Research framework.

2. EXPERIMENTAL WORK AND METHODS

2.1. Materials

Metallic flats made of hardened AISI D3 steel (47 1 HRC) which is a high carbon, high chromium tool steel and air hardened were employed as the work material in the current work. Due to its widespread usage and application, it was chosen and it possesses great compressive strength, outstanding dimensional stability, and excellent abrasion/wear resistance. It can be heat treated and will have hardness between 58 and 64 HRC. A wide range of tools and gauges, including burnishing dies or rolls, cold trimmer dies or rolls, lamination dies, forming and seaming rolls, slitting cutters, blanking, stamping, and cold-forming dies and punches, etc., are made from D3 steel. Due to its high electrical and thermal conductivity, ease of machinability, increased wear resilience, affordability, ease of availability, etc., copper is employed as the electrode material in the present EDM setup. In a vertical milling machine, a copper rod measuring 10 mm was turned into a hexagonal rod. Figure 2 (a) represents the material of the workpiece, whereas Figure 2 (b) shows the material of the tool.

Figure 2
(a): Die sinker EDM machine set up. (b): Hexagonal shaped copper rod as electrode. (c): Setting of EDM machining parameters. (d): AISI D3 steel workpiece before machining. (e): Experimental setup. (f): AISI D3 steel workpiece after machining.

2.2. Experimental setup

On a die sinker EDM machine, the trials were carried out. The used dielectric fluid was EDM oil. 10 kg/cm² of flushing pressure was maintained. Figures 2 (c) to (f) depict the experimental setup and an EDM copper tool, respectively. The studies were done using a precision die-sinking EDM of type D7125 for 30 minutes in order to get a more accurate result. Work piece materials of size 40 mm × 40 mm × 12 mm and an electrolytic hexagonal copper electrode were used. During the tests, deionized water was employed as the dielectric fluid, and the eroded particles from the machining zone were removed using an impulse jet cleaning system. The range for the process parameters was determined to be 4 to 6 A for current, 40 to 60 s for Pulse-off-time, and 80 to100 s for Pulse-on-time. The purpose of the exploratory machining trials was to narrow down the range of process variables that were acceptable, classify the appropriate upper and lower bounds of parameters, and ensure that the machining surface quality was sufficient with a minimal heat impacted zone and little debris [¹⁸]. Three degrees of process parameter variation were used, and the Taguchi L₉ orthogonal array was chosen to perform the WEDM trials. Each trial was conducted with a consistent space amid the electrode and work piece.

Some of the quality traits that were measured include the Electrode Wear Rate (EWR), MRR, and SR. The measurement of electrode wear and material removal were done with a digital weighing scale of 0.001 g precision. The difference in mass between the work piece and electrode before and after the machining is determined. The degree of roughness on the machined surface corresponds to the surface’s texture were also accounted for each run. The Mitutoyo SJ 210 (SR tester) was used to gauge the samples’ SR. Table 1 displays the EDM process parameters and its responses (mean value of three repeated experimental trials) and parametric combinations throughout numerous machining trials.

Table 1
Experimental results of EDM of AISI D3 steel.

Ex.No.	Ton (µs)	Toff (µs)	I (A)	SR (µm)	MRR (g/min)	TWR (g/min)
1	80	40	4	3.864	0.01	0.001
2	80	50	5	3.593	0.02	0.003
3	80	60	6	3.521	0.066	0.007
4	90	40	4	3.954	0.02	0.003
5	90	50	5	3.848	0.016	0.001
6	90	60	6	3.732	0.05	0.003
7	100	40	4	3.474	0.036	0.002
8	100	50	5	3.293	0.06	0.004
9	100	60	6	3.137	0.06	0.007

3. SELECTION OF BEST POSSIBLE SPECIMEN USING PROMETHEE II

The top specimens are rated using the Preference Ranking Organization Method for Enrichment Evaluation (PROMETHEE). Brans developed the comprehensive MCDM technique known as PROMETHEE in 1982, and Vincke and Brans enhanced it in 1985 [¹⁹]. PROMETHEE is a better way to rank and choose among a limited number of possible courses of action. The alternatives were fully ranked in PROMETHEE II, from the greatest to the worst. The alternatives are ranked using the net flow. It is presumed that the solution with the higher net flow is preferable. Preferences and discrepancies are included (pre-order) (GOSWAMI [²⁰]). PROMETHEE II, an upgradation of PROMETHEE was first postulated by DOUMPOS and ZOPOUNIDIS in 2004 and further enriched by HAJKOWICZ and HIGGINS in 2008 manages discrete choices for both quantitative and qualitative criteria. The approach compares the alternatives pair-wise to determine a preference function for each criterion (SINGH et al. [²¹]).Using the preference function, a preference index that favours alternative ‘a’ over alternative ‘b’ was calculated. The preference index serves as a gauge to confirm the claim that option ‘a’ is favoured over alternative ‘b’. In comparison to other MCDM approaches, the PROMETHEE method has a number of advantages, since it discovers non-comparable alternatives, which are alternatives that are challenging to evaluate because of a trade-off connection between evaluation standards (ABEDI et al. [²²]).

3.1. Procedural steps

Step 1: Creating the decision matrix.

Determine the criteria ( j = 1, 2,…,n) alias the goal of output responses for a set of given alternatives (i = 1,2, ..., m). ‘m’ alternatives are arranged row-wise and ‘n’ criteria were placed column-wise. The decision matrix [Eq. (1) & (2)] was constructed with variable elements that indicate values/test results of each criterion for each alternative (BRANS and DE SMET [²³]).

(1) $$Decisionmatrix,aij=\left[\begin{array}{ccc}{a}_{11}& \cdots & a_{1n}\\ ⋮& \ddots & ⋮\\ a_{m1}& \cdots & a_{mn}\end{array}\right]$$

(2) $$a_{ij}=\left(\begin{array}{ccc}0.010& 0.001& 3.864\\ 0.020& 0.003& 3.593\\ 0.066& 0.007& 3.521\\ 0.020& 0.003& 3.954\\ 0.016& 0.001& 3.848\\ 0.050& 0.003& 3.372\\ 0.036& 0.002& 3.474\\ 0.060& 0.004& 3.293\\ 0.060& 0.007& 3.137\end{array}\right)$$

Step 2: Determine the weight factor ‘w_j’ for each criterion [Eq. (3)].

(3) $${\displaystyle \sum _{i-1}^n{w}_j}=1$$

Considering the current study, MRR will the beneficiary criteria (Larger-the-better), where as the other two responses considered as non-beneficiary criteria. The relative importance (w_j) for MRR and SR considered as 0.35, whereas for TWS it was reckoned as 0.3.

Step 3: Normalization of the decision matrix

The formula for normalizing the elements for the beneficial criterion is as follows [Eq. (4)]:

(4) $$N_{ij}=\frac{x_{ij}-\min (x_{ij})}{\max (x_{ij})-\min (x_{ij})}$$

where, the performance indicator for the i^th alternative in relation to the j^th criterion is x_ij.

The above equation can be modified to include the non-beneficial criterion as follows[Eq. (5)]:

(5) $$N_{ij}=\frac{\max (x_{ij})-x_{ij}}{\max (x_{ij})-\min (x_{ij})}$$

The normalized values of decision matrix detailed below[Eq. (6)].

(6) $$\left(\begin{array}{ccc}0.000& 1.000& 0.110\\ 0.179& 0.667& 0.442\\ 1.000& 0.000& 0.530\\ 0.179& 0.667& 0.000\\ 0.107& 1.000& 0.130\\ 0.714& 0.667& 0.272\\ 0.464& 0.833& 0.588\\ 0.893& 0.500& 0.809\\ 0.893& 0.000& 1.000\end{array}\right)$$

Step 4: The evaluation of the differences between the row items of the i^th alternative and the other alternatives is carried out (BRANS and DE SMET [²³]). The stage entails calculating pair-wise differences in criterion values between several possibilities. The difference values for the ‘m’ choices will be (m–1). The difference between the criteria values of each of alternatives from 1 to 9 with other alternatives are detailed in Table 2.

Table 2
Difference between the criteria values of each of alternatives from 1 to 9 with other alternatives.

DIFFERENCE BETWEEN THE CRITERIA VALUES OF ALTERNATIVE 1 AND OTHER ALTERNATIVES			DIFFERENCE BETWEEN THE CRITERIA VALUES OF ALTERNATIVE 2 AND OTHER ALTERNATIVES			DIFFERENCE BETWEEN THE CRITERIA VALUES OF ALTERNATIVE 3 AND OTHER ALTERNATIVES			DIFFERENCE BETWEEN THE CRITERIA VALUES OF ALTERNATIVE 4 AND OTHER ALTERNATIVES			DIFFERENCE BETWEEN THE CRITERIA VALUES OF ALTERNATIVE 5 AND OTHER ALTERNATIVES
–0.179	0.333	–0.332	0.179	–0.333	0.332	1.000	–1.000	0.420	0.179	–0.333	–0.110	0.107	0.000	0.020
–1.000	1.000	–0.420	–0.821	0.667	–0.088	0.821	–0.667	0.088	0.000	0.000	–0.442	–0.071	0.333	–0.312
–0.179	0.333	0.110	0.000	0.000	0.442	0.821	–0.667	0.530	–0.821	0.667	–0.530	–0.893	1.000	–0.400
–0.107	0.000	–0.020	0.071	–0.333	0.312	0.893	–1.000	0.400	0.071	–0.333	–0.130	–0.071	0.333	0.130
–0.714	0.333	–0.162	–0.536	0.000	0.170	0.286	–0.667	0.258	–0.536	0.000	–0.272	–0.607	0.333	–0.142
–0.464	0.167	–0.477	–0.286	–0.167	–0.146	0.536	–0.833	–0.058	–0.286	–0.167	–0.588	–0.357	0.167	–0.458
–0.893	0.500	–0.699	–0.714	0.167	–0.367	0.107	–0.500	–0.279	–0.714	0.167	–0.809	–0.786	0.500	–0.679
–0.893	1.000	–0.890	–0.714	0.667	–0.558	0.107	0.000	–0.470	–0.714	0.667	–1.000	–0.786	1.000	–0.870
DIFFERENCE BETWEEN THE CRITERIA VALUES OF ALTERNATIVE 6 AND OTHER ALTERNATIVES			DIFFERENCE BETWEEN THE CRITERIA VALUES OF ALTERNATIVE 7 AND OTHER ALTERNATIVES			DIFFERENCE BETWEEN THE CRITERIA VALUES OF ALTERNATIVE 8 AND OTHER ALTERNATIVES			DIFFERENCE BETWEEN THE CRITERIA VALUES OF ALTERNATIVE 9 AND OTHER ALTERNATIVES
0.714	–0.333	0.162	0.464	–0.167	0.477	0.893	–0.500	0.699	0.893	–1.000	0.890
0.536	0.000	–0.170	0.286	0.167	0.146	0.714	–0.167	0.367	0.714	–0.667	0.558
–0.286	0.667	–0.258	–0.536	0.833	0.058	–0.107	0.500	0.279	–0.107	0.000	0.470
0.536	0.000	0.272	0.286	0.167	0.588	0.714	–0.167	0.809	0.714	–0.667	1.000
0.607	–0.333	0.142	0.357	–0.167	0.458	0.786	–0.500	0.679	0.786	–1.000	0.870
0.250	–0.167	–0.316	–0.250	0.167	0.316	0.179	–0.167	0.537	0.179	–0.667	0.728
–0.179	0.167	–0.537	–0.429	0.333	–0.222	0.429	–0.333	0.222	0.429	–0.833	0.412
–0.179	0.667	–0.728	–0.429	0.833	–0.412	0.000	0.500	–0.191	0.000	–0.500	0.191

Step 5: Calculating P_j(a,b), the preference function.

The main categories of generalized preference functions are six. However, in real-time applications, it will be difficult for the problem solver to decide which particular type of preference function is suitable for each criterion[Eq. (7) & (8)].

(7) $${\text{P}}_j(\text{a,b})={\text{0, if R}}_{\text{aj}}\le {\text{R}}_{\text{bj}}$$

(8) $${\text{P}}_j(\text{a,b})={\text{R}}_{\text{aj}}-{\text{R}}_{\text{bj}},\text{if}{\text{R}}_{\text{aj}}>{\text{R}}_{\text{bj}}$$

The above condensed preference function can be used to get around the issue [²⁴]. The preference function of each of the alternatives with other alternatives are illustrated in Table 3.

Table 3
Preference function of each of the 9 alternatives with subsequent alternatives.

PREFERENCE FUNCTION OF 1ST ALTERNATIVE OVER OTHER ALTERNATIVES			PREFERENCE FUNCTION OF 2ND ALTERNATIVE OVER OTHER ALTERNATIVES			PREFERENCE FUNCTION OF 3RD ALTERNATIVE OVER OTHER ALTERNATIVES			PREFERENCE FUNCTION OF 4TH ALTERNATIVE OVER OTHER ALTERNATIVES			PREFERENCE FUNCTION OF 5TH ALTERNATIVE OVER OTHER ALTERNATIVES
0.000	0.333	0.000	0.179	0.000	0.332	1.000	0.000	0.420	0.179	0.000	0.000	0.107	0.000	0.020
0.000	1.000	0.000	0.000	0.667	0.000	0.821	0.000	0.088	0.000	0.000	0.000	0.000	0.333	0.000
0.000	0.333	0.110	0.000	0.000	0.442	0.821	0.000	0.530	0.000	0.667	0.000	0.000	1.000	0.000
0.000	0.000	0.000	0.071	0.000	0.312	0.893	0.000	0.400	0.071	0.000	0.000	0.000	0.333	0.130
0.000	0.333	0.000	0.000	0.000	0.170	0.286	0.000	0.258	0.000	0.000	0.000	0.000	0.333	0.000
0.000	0.167	0.000	0.000	0.000	0.000	0.536	0.000	0.000	0.000	0.000	0.000	0.000	0.167	0.000
0.000	0.500	0.000	0.000	0.167	0.000	0.107	0.000	0.000	0.000	0.167	0.000	0.000	0.500	0.000
0.000	1.000	0.000	0.000	0.667	0.000	0.107	0.000	0.000	0.000	0.667	0.000	0.000	1.000	0.000
PREFERENCE FUNCTION OF 6TH ALTERNATIVE OVER OTHER ALTERNATIVES			PREFERENCE FUNCTION OF 7TH ALTERNATIVE OVER OTHER ALTERNATIVES			PREFERENCE FUNCTION OF 8TH ALTERNATIVE OVER OTHER ALTERNATIVES			PREFERENCE FUNCTION OF 9TH ALTERNATIVE OVER OTHER ALTERNATIVES
0.714	0.000	0.162	0.464	0.000	0.477	0.893	0.000	0.699	0.893	0.000	0.890
0.536	0.000	0.000	0.286	0.167	0.146	0.714	0.000	0.367	0.714	0.000	0.558
0.000	0.667	0.000	0.000	0.833	0.058	0.000	0.500	0.279	0.000	0.000	0.470
0.536	0.000	0.272	0.286	0.167	0.588	0.714	0.000	0.809	0.714	0.000	1.000
0.607	0.000	0.142	0.357	0.000	0.458	0.786	0.000	0.679	0.786	0.000	0.870
0.250	0.000	0.000	0.000	0.167	0.316	0.179	0.000	0.537	0.179	0.000	0.728
0.000	0.167	0.000	0.000	0.333	0.000	0.429	0.000	0.222	0.429	0.000	0.412
0.000	0.667	0.000	0.000	0.833	0.000	0.000	0.500	0.000	0.000	0.000	0.191

Step 6: Consider the weights of the criterion while calculating the aggregated preference function, where w_j is relative weight of the j^th criterion.

Preference function aggregated as [Eq. (9)],

(9) $$\pi (a,b)=\frac{{\displaystyle {\sum }_{(j=1)}^n{w}_j\times P_j(a,b)}}{{\displaystyle {\sum }_{j=1}^n{w}_j}}$$

The total of all weights/relative importance factors given to each criterion must equal 1 [²⁵]. The aggregate preference functions are illustrated in Table 4.

Table 4
Calculation of aggregate preference functions.

PREFERENCE FUNCTION 1*CRITERION-WISE WEIGHT FACTOR			AGGREGATED PREFERENCE FUNCTION 1	PREFERENCE FUNCTION 2*CRITERION-WISE WEIGHT FACTOR			AGGREGATED PREFERENCE FUNCTION 2	PREFERENCE FUNCTION 3*CRITERION-WISE WEIGHT FACTOR			AGGREGATED PREFERENCE FUNCTION 3	PREFERENCE FUNCTION 4*CRITERION-WISE WEIGHT FACTOR			AGGREGATED PREFERENCE FUNCTION 4	PREFERENCE FUNCTION 5*CRITERION-WISE WEIGHT FACTOR			AGGREGATED PREFERENCE FUNCTION 5
0.000	0.100	0.000	0.100	0.063	0.000	0.116	0.179	0.350	0.000	0.147	0.497	0.063	0.000	0.000	0.063	0.038	0.000	0.007	0.044
0.000	0.300	0.000	0.300	0.000	0.200	0.000	0.200	0.288	0.000	0.031	0.318	0.000	0.000	0.000	0.000	0.000	0.100	0.000	0.100
0.000	0.100	0.039	0.139	0.000	0.000	0.155	0.155	0.288	0.000	0.185	0.473	0.000	0.200	0.000	0.200	0.000	0.300	0.000	0.300
0.000	0.000	0.000	0.000	0.025	0.000	0.109	0.134	0.313	0.000	0.140	0.453	0.025	0.000	0.000	0.025	0.000	0.100	0.045	0.145
0.000	0.100	0.000	0.100	0.000	0.000	0.060	0.060	0.100	0.000	0.090	0.190	0.000	0.000	0.000	0.000	0.000	0.100	0.000	0.100
0.000	0.050	0.000	0.050	0.000	0.000	0.000	0.000	0.188	0.000	0.000	0.188	0.000	0.000	0.000	0.000	0.000	0.050	0.000	0.050
0.000	0.150	0.000	0.150	0.000	0.050	0.000	0.050	0.038	0.000	0.000	0.038	0.000	0.050	0.000	0.050	0.000	0.150	0.000	0.150
0.000	0.300	0.000	0.300	0.000	0.200	0.000	0.200	0.038	0.000	0.000	0.038	0.000	0.200	0.000	0.200	0.000	0.300	0.000	0.300
Preference Function 6*criterion-wise weight factor			Aggregated Preference Function 6	Preference Function 7*criterion-wise weight factor			Aggregated Preference Function 7	Preference Function 8*criterion-wise weight factor			Aggregated Preference Function 8	Preference Function 9*criterion-wise weight factor			Aggregated Preference Function 9
0.250	0.000	0.057	0.307	0.163	0.000	0.167	0.330	0.313	0.000	0.245	0.557	0.313	0.000	0.311	0.624
0.188	0.000	0.000	0.188	0.100	0.050	0.051	0.201	0.250	0.000	0.129	0.379	0.250	0.000	0.195	0.445
0.000	0.200	0.000	0.200	0.000	0.250	0.020	0.270	0.000	0.150	0.098	0.248	0.000	0.000	0.165	0.165
0.188	0.000	0.095	0.283	0.100	0.050	0.206	0.356	0.250	0.000	0.283	0.533	0.250	0.000	0.350	0.600
0.213	0.000	0.050	0.262	0.125	0.000	0.160	0.285	0.275	0.000	0.238	0.513	0.275	0.000	0.305	0.580
0.088	0.000	0.000	0.088	0.000	0.050	0.111	0.161	0.063	0.000	0.188	0.251	0.063	0.000	0.255	0.317
0.000	0.050	0.000	0.050	0.000	0.100	0.000	0.100	0.150	0.000	0.078	0.228	0.150	0.000	0.144	0.294
0.000	0.200	0.000	0.200	0.000	0.250	0.000	0.250	0.000	0.150	0.000	0.150	0.000	0.000	0.067	0.067

Step 7: Determination of the entering and exiting surpassing flows:

Exiting (or favourable) flow for i^th alternative [Eq. (10)],

(10) $${\phi }_a^{+}=\frac{1}{m-1}\times \left[{\displaystyle \sum _{p=1}\pi (a,b)}\right],asa\ne b$$

Incoming (or unfavourable) flow for i^th alternative [Eq. (11)],

(11) $${\phi }_a^{-}=\frac{1}{m-1}\times \left[{\displaystyle \sum _{p=1}\pi (b,a)}\right],asb\ne a$$

where ‘m’ is the number of alternatives.

In this case, each alternative must compete with (m–1) alternatives. The outgoing/leaving flow illustrates the extent to which one alternative dominates the other alternatives, and the incoming/entering flow illustrates the extent to which one choice is subjugated by the others. The positive and negative flow were detailed in Table 5.

Table 5
Positive and negative flow.

ALTERNATIVES	A1	A2	A3	A4	A5	A6	A7	A8	A9	LEAVING POSITIVE FLOW, ϕ+a
A1	0.000	0.100	0.300	0.139	0.000	0.100	0.050	0.150	0.300	0.142
A2	0.179	0.000	0.200	0.155	0.134	0.060	0.000	0.050	0.200	0.122
A3	0.500	0.320	0.000	0.470	0.450	0.190	0.188	0.038	0.038	0.274
A4	0.060	0.000	0.200	0.000	0.025	0.000	0.000	0.050	0.200	0.067
A5	0.044	0.100	0.300	0.145	0.000	0.100	0.050	0.150	0.300	0.149
A6	0.310	0.188	0.200	0.283	0.262	0.000	0.088	0.050	0.200	0.198
A7	0.330	0.201	0.270	0.356	0.285	0.161	0.000	0.100	0.250	0.244
A8	0.557	0.379	0.248	0.533	0.513	0.251	0.228	0.000	0.150	0.357
A9	0.624	0.445	0.165	0.600	0.580	0.317	0.294	0.067	0.000	0.386
Entering Negative Flow, ϕ–a	0.325	0.217	0.235	0.335	0.281	0.147	0.112	0.082	0.205

The PROMETHEE II approach can provide the entire pre-order based on these outranking flows by employing a net flow (ϕ_a) [Eq. (12)].

(12) $${\mathrm{\varphi }}_a={\mathrm{\varphi }}_a^{+}-{\mathrm{\varphi }}_a^{-}$$

Step 8: Based on the value of ϕ_a, rank of each alternative was derived. The calculated results were presented in Table 6. The best option is provided by the highest value.

Table 6
Ranking of alternatives.

ALTERNATIVES	ϕ+a	ϕ–a	ϕa = ϕ+a – ϕ–a	RANK
A1	0.142	0.325	–0.183	8
A2	0.122	0.217	–0.094	6
A3	0.274	0.235	0.039	5
A4	0.067	0.335	–0.268	9
A5	0.149	0.281	–0.132	7
A6	0.198	0.147	0.050	4
A7	0.244	0.112	0.132	3
A8	0.357	0.082	0.275	1
A9	0.386	0.205	0.182	2

The optimal alternative combination reported in Table 7.

Table 7
Optimized solution.

EXPERIMENTAL COMBINATION/RUN	FACTORS			RESPONSES
	Ton (µs)	Toff (µs)	I (A)	SR (µm)	MRR (g/min)	TWR (g/min)
8	100	50	5	0.06	0.004	3.293

4. VALIDATION OF THE OPTIMIZED RESULTS OBTAINED FROM PROMETHEE II USING HISTORICAL DATA DESIGN

Historical Data Design (HDD) was a user-friendly, software-based approach within RSM that relied on regression and correlation techniques [²⁶, ²⁷]. The method was used to identify both the individual and combined effects of process characteristics on output responses. Input factors were treated as independent variables, while output responses were considered dependent variables (MAGUTEESWARAN et al. [²⁸]). A regression equation was formulated for each response, with correlation expressing the degree of similarity between dependent and independent variables, as described by ATHAWALE et al. [²⁹]. The software Design Expert V.10 employed to identify the optimal combination of factors and responses, providing the best possible solution.

4.1. Process parameter effects on MRR

Figure 3 presents 3D surface plots illustrating the interaction effects between key factors on MRR: two groups of experiments were conducted: (a) MRR as a function of Ton and Toff; (b) MRR as a function of Ton and the pulsating current. These plots graphically provide an understanding of the amount of interaction between all these parameters to enable efficient handling of the process. Initially, the MRR decreases as Pulse-on-time was increased. At Pulse-on-time 90 ms, the parabolic curve starts to change from descending trend to ascending trend. The MRR starts to increase with increase in T_on. But, MRR faces a steeper increase with higher values of Pulse-off-time. With pulsating current, MRR shares an almost flat contour, as it remains steady without increase or decrease for an increasing MRR.

Figure 3
3D surface plot indicating the interaction between factors (a) T_on and T_off with MRR (b) T_on and pulsating current with MRR.

The model is apparently significant given its Model F-value of 5.88 (Table 8). A “Model F-Value” this large could only happen owing to noise 4.28% of the time. When “Prob > F” is less than 0.05, model terms are considered significant [²⁴, ²⁵]. The model term B is important considering MRR. The regression equation for predicting MRR is presented in Eq. (13).

Table 8
Analysis of Variance (ANOVA) table for MRR.

SOURCE	SUM OF SQUARES (SS)	DEGREES OF FREEDOM (DoF)	MEAN SQUARE (MS)	F VALUE	p-VALUE PROB > F	DECLARATION
Model	0.00297	3	0.0009	5.8833	0.0428	Significant
A	0.0006	1	0.0006	3.5629	0.1177
B	0.0020	1	0.0020	11.9754	0.0180	Most influencing
A2	0.0004	1	0.0004	2.1114	0.2059
Residual	0.0008	5	0.0002
Correlation Total	0.003814222	8
Standard Deviation		0.0129		R2		0.8792
Mean		0.0376		Adjusted R2		0.7468
C.V. %		34.5539		Predicted R2		0.6860
PRESS		0.0027		Adequate Precision		6.9354

(13) $$MRR=0.9227-0.023\times T_{on}+0.0018\times T_{off}+0.00013\times T_{on}{}^2$$

4.2. Process parameter effects on TWR

Figure 4 presents 3D surface plots illustrating the interaction effects between key factors on TWR: hypothesis 1 is to investigate (a) the impact of Ton with respect to Toff on TWR and (b) the impact of Ton with pulsating current to TWR. These plots also show the effects of all of these parameters simultaneously to illustrate the relationship between them on tool wear. A V-shaped curve is obtained, when TWR was plotted against T_on. When pulse-off-time was made to interacted with TWR, an upward curve with positive trend was obtained. There was a slight increase in the values of TWR with every incremental value of pulsating current.

Figure 4
3D Surface Plot indicating the interaction between factors (a) T_on and T_off with TWR (b) T_on and Pulsating Current with TWR.

The model’s F-value of 5.179 (Table 9) suggest its significance. Only 1.22% of the time could noise account for a “Model F-Value”. The model term B ismore important concerning TWR.The regression equation for predicting TWR is presented in Eq. (14).

Table 9
ANOVA table for TWR.

SOURCE	SUM OF SQUARES (SS)	DEGREES OF FREEDOM (DoF)	MEAN SQUARE (MS)	F VALUE	p-VALUE PROB > F	DECLARATION
Model	2.6389 × 10–5	3	8.7963 × 10–6	5.1794	0.01226	Significant
A	6.6667 × 10–7	1	6.6667 × 10–7	0.2410	0.6443
B	2.0167 × 10–5	1	2.0167 × 10–5	7.2892	0.0428	Most influencing
A2	5.5556 × 10–6	1	5.5556 × 10–6	2.0080	0.2157
Residual	1.3833 × 10–5	5	2.7667 × 10–6
Correlation Total	4.0222 × 10–5	8
Standard Deviation		0.0017		R2		0.7561
Mean		0.0034		Adjusted R2		0.6497
C.V. %		48.2902		Predicted R2		0.5842
PRESS		0.0001		Adequate Precision		5.1102

(14) $$TWR=0.12517-0.003\times T_{on}+0.0018\times T_{off}+0.000017\times T_{on}{}^2$$

4.3. Process parameter effects on SR

Figure 5 presents 3D surface plots illustrating the interaction effects between key factors on SR: two groups of experiments were conducted: (a) SR as a function of Ton and Toff; (b) SR as a function of Ton and the pulsating current. The SR increases as the Pulse-on-time increases. After reaching a threshold limit, the SR starts to decrease with increasing Pulse-on-time. There was a gradual decrease in the values of SR with higher Pulse-off-time. The above-mentioned trend was repeated for different values of pulsating current. There was a reduction in SR with increase in pulsating current.

Figure 5
3D Surface Plot indicating the interaction between factors (a) T_on and T_off with SR (b) T_on and Pulsating Current with SR.

Given the Model F-value of 86.96 (Table 10), the model is most likely significant. Only 0.01% of the time may a “Model F-Value” large be caused by noise. Most important model term in this situation was A.The regression equation for predicting SR is presented in Eq. (15).

Table 10
ANOVA for SR.

SOURCE	SUM OF SQUARES (SS)	DEGREES OF FREEDOM (DoF)	MEAN SQUARE (MS)	F VALUE	p-VALUE PROB > F	DECLARATION
Model	0.5933	3	0.1978	86.9620	< 0.0001	Significant
A	0.1922	1	0.1922	84.5310	0.0001	Most influencing
B	0.1356	1	0.1356	59.6239	0.0006
A2	0.2655	1	0.2655	116.7311	0.0003
Residual	0.0114	5	0.0023
Correlation Total	0.6047	8
Standard Deviation		0.0477		R2		0.9812
Mean		3.6018		Adjusted R2		0.9699
C.V. %		1.3240		Predicted R2		0.9377
PRESS		0.0376		Adequate Precision		26.5469

The optimized solution illustrated in Table 11 and the concurrence between the PROMETHEE II and HDD presented in Table 12.

Table 11
Optimized solution.

EXPERIMENTAL COMBINATION	Ton (µs)	Toff (µs)	I (A)	SR (µm)	MRR (g/min)	TWR (g/min)	PERCENTAGE OF ACCEPTANCE
1	100	49.82	4.99	0.057	0.0036	3.301	91

Table 12
Comparison of optimal solution obtained in PROMETHEE II and HDD.

FACTORS AND RESPONSES	PROMETHEE	HDD	% of DEVIATION	% of CLOSENESS
Ton (µs)	100	100	0	100
Toff (µs)	50	49.82	0.36	99.64
I (A)	5	4.99	0.2	99.8
SR (µm)	0.06	0.057	5	95
MRR (g/min)	0.004	0.0036	10	90
TWR (g/min)	3.293	3.301	0.24	99.76
Average deviation / closeness			2.63	97.37

5. conclusions

The recursive optimization aims at mixing two diverse optimization methods in order to arrive at a common solution. In the aforementioned research work, the best solution possible is achieved using a multi-attribute quantitative method named PROMETHEE and the results thus attained are tested and proved through the software Historical Data Design.

• By carrying out relevant tests to determine MRR, TWR, and SR, the optimum EDM process parameters of Ton, Toff and I for machining hardened AISI D3 steel with copper electrode are highlighted. By using the PROMETHEE approach the best set of EDM parameters is selected. EDM process parameters, including Pulse-on-time (Ton), Pulse-off-time (Toff), and Pulsating Current (I), have been chosen for machining hardened AISI D3 steel with copper electrode.

• The ideal EDM parameter combination is chosen using the PROMETHEE approach. The sample alternatives are successively arranged from best to worst based on the rating values: 8 > 9 > 7 > 6 > 3 > 2 > 5 > 1 > 4, where 8 is the maximum possibility of the pairing and 4 the least as far as the probability is concerned.

• A branch of RSM known as HDD provides evidence on its qualitative MCDM technique described above. The best experimental run was for Ton 100 s, Toff 49.82 s, and I 4.99 A with responses SR 0.057 (µm), MRR 0.036 (g/min), and TWR 3.301(g/min) are the optimal values for the experimental concentration.

• The results yielded by the techniques are almost the same with correspondingly low deviating error being less than 3%.

• Using HDD, the empirical model is developed with a higher reliability measure and may be used to locate the independents without the information search experimentation.

• The comparability between PROMETHEE and HDD established with 97% shows the credibility of the proposed MARO technique.

Since, the MARO technique has been effectively applied to determine the optimum process parameters for EDM of D3 tool steel than other techniques it can be applied to other manufacturing processes.

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Publication Dates

• Publication in this collection
  10 Feb 2025
• Date of issue
  2025

History

• Received
  22 Oct 2024
• Accepted
  06 Dec 2024