Parametric Investigation of Die-Sinking EDM of Ti6Al4V Using the Hybrid Taguchi-RAMS-RATMI Method

Abstract

Ti6Al4V is a widely used alloy due to its excellent mechanical qualities and resistance to corrosion, which make it fit for automotive, aerospace, defense, and biomedical sectors. Due to its high strength and limited heat conductivity, it is difficult to machine. Both the workpiece’s and the electrode’s conductivity are important factors that impact the electro-discharge machining (EDM) process. In this case, the machining efficiency is also influenced by the electrode selection. As a result, choosing the right electrode and machining parameters is essential to improving EDM performance on the Ti6Al4V alloy. Research on EDM for Ti6Al4V is limited, with little focus on electrode material selection and shape. The impact of EDM settings on MRR, TWR, and surface roughness is complex, and a comprehensive optimization strategy is needed. Copper electrodes are widely used, but further investigation is needed on EDM’s effects on Ti6Al4V’s surface properties and surface integrity. Addressing these research gaps will improve the understanding and application of EDM for Ti6Al4V, focusing on parameter optimization, surface integrity, and thermal and mechanical effects. By employing copper tools to optimize four crucial EDM process parameters—peak current, duty cycle, discharge current, and pulse-on time—this research aims to increase surface integrity and machining performance. A comprehensive Taguchi experimental design is used to systematically alter the EDM settings. By optimizing parameters using tolerance intervals and response modelling, the recently developed RAMS-RATMI approach improves the dependability of the EDM process and increases machining efficiency. With the optimized EDM settings, there were notable gains in depth of cut enhancement, surface roughness minimization, tool wear rate (TWR) reduction, and material removal rate (MRR). The results of the surface integrity examination showed fewer heat-affected zones, fewer microcracks, and a thinner recast layer. Analysis of variance was used to verify the impact and resilience of the optimized parameters. Superior machining performance, higher surface quality, and increased operational dependability were attained with the Ti6Al4V-optimized EDM process, providing industry practitioners with insightful information and useful recommendations.

1. Introduction

Because it can precisely mill hard materials and intricate forms, electrical discharge machining (EDM) has gained popularity. Because EDM uses electrical discharges instead of standard machining processes to remove material from the workpiece, it is especially effective on materials that are challenging to machine. Titanium Grade 5 alloy (Ti6Al4V), renowned for its remarkable strength, low density, and superior corrosion resistance, is one such material. Ti6Al4V is the perfect material for important applications in the aerospace, biomedical, and automotive sectors because of these qualities [1]. Its great strength and low heat conductivity, however, provide serious difficulties for traditional machining methods, resulting in quick tool wear and subpar surface smoothness [2]. Ti6Al4V, an α + β titanium alloy with 4% vanadium and 6% aluminum, provides a special blend of corrosion resistance and mechanical qualities [3]. The aerospace industry uses this alloy extensively for items like fasteners, turbine blades, and aircraft structural elements for its high strength-to-weight ratio and superior performance at high temperatures. In the biomedical field, Ti6Al4V is extensively used for medical implants and prosthetics because of its biocompatibility and resistance to body fluids [4]. Despite its desirable properties, the machinability of Ti6Al4V is a major concern. Traditional machining methods often struggle with rapid tool wear, high cutting forces, and the generation of excessive heat, which can adversely affect the material’s microstructure and mechanical properties [5]. By using thermal energy to erode material without the tool and workpiece coming into close touch, EDM provides a competitive substitute. As a consequence, there are fewer mechanical stresses and difficult-to-reach places and complex geometries may be machined [6]. The selection of electrode material and process parameters has a considerable impact on EDM efficacy. Critical elements that impact the effectiveness of the EDM process include electrode wear, surface roughness, material removal rate (MRR), and dimensional accuracy. Copper, graphite, and copper-tungsten are a few of the electrode materials that have been researched to maximize EDM performance for various workpiece materials, including Ti6Al4V [7].

Copper is a versatile material with high electrical and thermal conductivity, making it ideal for EDM processes. Its high electrical conductivity ensures stable sparking, reduces electrode wear, and maintains surface integrity. Copper electrodes are easy to machine, allowing for intricate shapes. Despite moderate wear resistance, copper electrodes are crucial in EDM due to potential dimensional inaccuracies and increased costs. Despite challenges like electrode wear and cost, copper electrodes are suitable for the precision machining of complex geometries and high-quality surfaces. Copper electrodes offer superior surface finish and dimensional accuracy due to their high conductivity, resulting in precise control of spark energy. They are versatile and suitable for both roughing and finishing operations in the EDM process. Copper also works well with various dielectric fluids, enhancing flushing efficiency and reducing the risk of arcing and short circuits. Overall, copper electrodes are ideal for high-quality applications. Copper electrodes are more expensive than graphite electrodes in high-energy EDM processes, leading to faster wear and increased operational costs. They are also more prone to contamination, leaving residue on the workpiece surface, which may require additional cleaning processes, especially in applications with strict cleanliness standards. These factors can be particularly significant for large-scale or long-duration EDM operations. Copper electrodes are utilized in various industries, including tool and die making, aerospace, medical devices, and automotive. They are used in tool and die making for producing precision components, in aerospace for high-strength alloys, in medical devices for fabricating complex shapes and fine features in biocompatible materials, and in automotive for machined components like fuel injection nozzles, valve seats, and transmission parts. Copper electrodes ensure high precision and surface finish in these applications.

An experimental investigation on Ti6Al4V was carried out by Paulson et al. [1] to assess the effect of machining factors on wire EDM. The findings demonstrated that peak current and pulse-off duration were the primary factors influencing surface roughness when utilizing the GRA optimization approach. As the peak current increased, so did the surface roughness. Peak current and pulse-off time were found to be the two main factors that influenced MRR. While machining Ti6Al4V, Suresh et al. [2] carried out an experimental optimization of EDM die-sinking electrode materials, including copper, brass, and graphite. They designed and machined electrodes using statistical techniques, noting surface roughness, fluctuations in surface hardness, and dimensional stability. The results showed graphite electrodes produced a better surface finish with minimal dimensional variation, indicating higher resistivity toward current. The depth of machining significantly impacted surface hardness variations post-machining. Using Ti-5Al-2.5Sn alloy as the workpiece, Bhaumik and Maity’s [3] experiment investigated the effects of several electrode types (copper, brass, and zinc) on the EDM process. According to the results, copper electrodes generated a smoother surface and exhibited less tool wear than brass and zinc electrodes, which both achieved greater MRR. According to research by Jain and Pandey [4], multi-performance parameters in titanium alloy drilling are highly impacted bypulse-on time. The investigation discovered that the genetic algorithm was the most efficient, improving quality attributes by 59%. The effects of machining factors on tool wear rate (TWR) during EDM of Ti6Al4V were investigated by Choudhary et al. [5]. They examined the ideal circumstances for the lowest possible TWR and discovered that cryogenic copper had a greater TWR than untreated copper, with more noticeable impacts on current, pulse-on time, and tool electrode type. The effect of EDM on surface integrity in Ti6Al4V has been investigated by Kushwaha et al. [6]. Peak current improves MRR, the TWR, and Ra, while longer pulse-on times shorten the pulse and degrade the surface quality. EDM produces oxides and carbides, which increase wear resistance. Using WEDM, Madyira and Akinlabi et al. [7] tested the fracture toughness of compact tension specimens made of Ti6Al4V. The average toughness value, 111.82 MPa.m0.5, was 4.4% less than what was stated in the literature. The fracture surfaces met the criteria for plane strain, suggesting that compact tension specimens may be safely pre-cracked by WEDM in order to measure the fracture resistance of Ti6Al4V. The work by Sivam et al. [8] uses a graphite tool electrode with negative polarity to optimize the EDM parameters for Ti6Al4V. Surface roughness, variation between entrance and exit, titanium machining rate, and graphite wear rate are all heavily influenced by electrical factors.

Peak current and pulse-on time were identified by Krishnaraj’s [9] research as the two main influencing variables in EDM machining using a copper tool electrode. Maximal MRR, minimum TWR, and minimum hole taper were the ideal characteristics, improving mathematical models for micro-EDM performance. Current and pulse-on time were determined to be essential factors in Sivam et al.’s [10] investigation of sink electric discharge machining of Ti6Al4V, with pulse-on time having the most significant impact—apart from MRR. According to Perumal et al.’s [11] research, MRR is greatly impacted by spark-on time, discharge current, and tool diameter when it comes to machining reactions in EDM for Ti6Al4V alloy. In Ti6Al4V ELI (Grade 23), Kumar et al.’s [12] investigation discovered a direct relationship between discharge current and surface morphology, MRR, and surface polish. Superior surface quality is achieved with lower current intensity and higher discharge energy, which diminishes the surface finish. Gap voltage, peak current, and pulse-on time were shown to be the most efficient parameters in Bhaumik and Maity’s [13] experiment on Ti-5Al-2.5Sn alloy electro-discharge machining. This suggests that RSM combined with the GRA method may efficiently handle multi-response optimization issues in EDM. The goal of Singh and Kumar’s study [14] was to improve the surface finish on Ti6Al4V by optimizing EDM settings. They tested with pulse time, pulse off, and current using spark erosion EDM (EDM). The findings indicated that pulse-off time is the factor that has the greatest impact on surface roughness, with the current coming in second. Using the L-9 orthogonal array, Verma and Sajeevan [15] optimized die-sinking EDM on Ti6Al4V. Microcracks and a recast layer were discovered on the machined surface by SEM imaging and XRD investigation. Surface roughness, TWR, and MRR were the ideal process variables. The structure of the work material was changed by thermal heating and cooling. In their study, Bhaumik et al. [16] investigated the best parameter settings to get high-quality results while utilizing a brass electrode for electrical discharge machining titanium Grade 6 alloy. Grey relational grade and relative closeness coefficient improvements were observed in confirmation trials. According to Meena and Azad’s [17] study, voltage is the most important input parameter for output performance parameters, improving metal removal rate, TWR, and overcut during micro-electric discharge machining (micro-EDM) of Ti6Al4V alloy.

In Ti6Al4V planetary electrical discharge machining, Mathai et al. discovered that the duty factor selection is critical and that pulse-ON time and current had a substantial influence on reactions [18]. For a greater wear ratio and a lower TWR, the tool electrode should have a negative polarity. The study shows that total wire resistance in Ti6Al4V planetary EDM is influenced by machining settings and tool actuation, with copper electrodes exhibiting reduced material loss [19]. The electrode material has a considerable impact on the ideal process parameters, according to Huu et al.’s [20] work on micro EDM. Taguchi-MOORA, which is based on ratio analysis, achieves high machining quality and precision. In research by Verma and Sahu [21], MRR increased with peak current, gap voltage, pulse-on time, and dielectric fluid flow pressure when die-sinking EDM was used to machine Ti6Al4V. Alongside these factors comes an increase in surface roughness. On the machined surface, the scientists also discovered craters and tiny fissures. Pramanik et al.’s [22] study of titanium alloy machining techniques identified low thermal conductivity and excessive heat generation as EDM process problems, with hybrid approaches becoming more popular. According to Rahul et al.’s [23] study, electrode selection has a major influence on the effectiveness of electro-displacement machining (EDM) on Ti6Al4V. Copper electrodes that have undergone cryogenically treated conditions exhibit improved performance, lower SCD, and higher WLT. Graphite powder was added to kerosene dielectric liquid in Unses and Cogun’s [24] study to improve EDM performance in the aerospace sector. This resulted in higher MRR, surface roughness, and lower relative wear, demonstrating the suitability of graphite powder to EDM applications. Palanisamy et al. [25] used orthogonal array and grey relational analysis to optimize the EDM process for titanium alloy, resulting in improved performance and optimum parameters. In the research on EDM in Ti6Al4V ELI processing, Karmiris-Obratański et al. [26] discovered that machining parameters had an impact on MRR, TMRR, and TWR, with pulse-on current having a greater influence. The goal of Gangil and Pradhan’s [27] study was to use RSM and VIKOR techniques to predict optimal EDM settings for optimum productivity and lowest surface integrity. The outcomes validated EDMed products’ improved accuracy and MRR. The work by Balamurali et al. [28] shows that cryogenic treatment improves the mechanical and thermal characteristics of titanium alloys, indicating a useful technique for EDM machining of titanium Grade 2 alloy. The work by Baroi et al. [29] shows that during EDM of titanium Grade 2, current and pulse-on time have a substantial influence on MRR, TWR, and surface roughness. According to research by Khan et al. [30] on surface finish characteristics in Ti-5Al-2.5Sn titanium alloy EDM, the best surface structure is produced using copper-tungsten electrodes. Using the Taguchi approach, Azad and Puri’s [31] work on micro-EDM for titanium alloy machining discovered that important factors like voltage and current had little effect on quality features. The MRR, TWR, and surface roughness are all highly impacted by current and pulse-on time, according to Baroi et al.’s [32] study on titanium Grade 2 alloy electric discharge machining. The wear rate and machinability of tools can be improved by surface modification, grain refinement, and cryogenic treatment, according to Gupta et al.’s [33] work on EDM of titanium and titanium alloys. Hybrid techniques may also be advantageous. Through the use of micro-electric discharge drilling, Kebede et al. [34] discovered decreased burr formation, recast layer error, and capacitance and voltage levels in titanium Grade 2 alloy. Ti6Al4V ELI Grade 23 alloy machining for biomedical applications was enhanced by Asif et al.’s [35] research on environmentally safe surfactant additives, leading to improvements in MRR, TWR, surface roughness, overcut, and corrosion resistance.

Although a great deal of research has been conducted on EDM of different materials, there are still certain gaps in our understanding of Ti6Al4V that need to be filled. A thorough optimization framework is still required despite the fact that several studies have examined the impact of EDM settings on MRR, TWR, and surface roughness for Ti6Al4V. Previous studies have frequently concentrated on discrete characteristics like voltage, pulse length, and current. A more comprehensive optimization strategy is necessary, nevertheless, due to the intricate relationships between these variables and how they all interact to affect performance indicators. There has been little published research on Ti6Al4V and copper electrodes. The electrode material selection and shape have a significant influence on the EDM process’s effectiveness and caliber. While research concentrating on the performance of copper electrodes especially with Ti6Al4V is scarce, copper electrodes are widely employed. Further investigation is needed on how EDM affects the subsurface properties and surface integrity of Ti6Al4V. Although surface roughness is commonly recorded, other features, like TWR, MRR, machined depth of cut, etc., have not been well studied. Their application to Ti6Al4V is, however, somewhat unexplored. Tool life, surface quality, and MRR might all be significantly increased by looking at these factors. Addressing these research gaps will significantly enhance the understanding and application of EDM for Ti6Al4V. Comprehensive studies focusing on parameter optimization, surface integrity, thermal and mechanical effects are essential for advancing the state of the art in EDM technology for this critical material.

By addressing the challenges associated with machining Ti6Al4V and exploring the potential of optimized EDM processes, this research seeks to advance the application of EDM in high-performance materials and pave the way for more efficient and reliable manufacturing practices in industries that rely on Ti6Al4V. By employing copper tools to optimize four crucial EDM process parameters—peak current, duty cycle, discharge current, and pulse-on time—this research aims to increase surface integrity and machining performance. A comprehensive experimental design based on the Taguchi approach is used to systematically alter the EDM settings. Through the use of tolerance intervals and response modelling to optimize parameters, the recently developed RAMS-RATMI technique boosts machining efficiency and enhances the reliability of the EDM process. The robustness and significance of the improved parameters were confirmed using ANOVA.

2. Experimental Methodology

2.1. Work Material

Ti6Al4V, is a popular titanium alloy that is well known for its exceptional corrosion resistance, low weight, and high strength (

Table 1. Composition and properties of Ti6Al4V [2].

Composition	Properties
Titanium (Ti): Balance	Ultimate tensile strength: ~950 MPa
Aluminum (Al): 6%	Yield strength: ~880 MPa
Vanadium (V): 4%	Elongation: ~14%
Iron (Fe): ≤0.25%	Modulus of elasticity: ~110 GPa
Oxygen (O): ≤0.20%	Density: ~4.43 g/cm3
Carbon (C): ≤0.08%	Melting point: ~1660 °C
Nitrogen (N): ≤0.05%	Thermal conductivity: ~6.7 W/m K
Hydrogen (H): ≤0.015%	Coefficient of thermal expansion: ~8.6 × 10−6/°C

). For high-performance applications, its remarkable mechanical qualities, resistance to corrosion, and biocompatibility make it the ideal choice. It is still relevant and significant in a variety of sectors due to continuous improvements in processing and application techniques. It is utilized in exhaust systems, offshore constructions, maritime gear, surgical implants, orthopedic devices, high-performance engine components, aviation parts, chemical processing equipment, and heat exchangers. Ti6Al4V may be produced via a number of industrial processes, including powder metallurgy, casting, and forging. However, because of its great strength and limited heat conductivity, machining this alloy can be difficult. To accomplish accurate and effective machining, methods such as EDM are frequently used. A workpiece measuring 120 × 100 × 7 mm was utilized in its base form in the machining process. Four workpieces of the same size were used to accommodate each run (Figure 1).

2.2. Selection of Tools and Parameters for Machining

A cylindrical copper tool of 20 mm diameter and 60 mm length was used for machining (Figure 2).

Table 2. Copper tool material properties [3].

Bulk Modulus	140 GPa
Density	8.96 g/cm3
Melting point	1084.62 °C
Poisson ratio	0.34
Shear modulus	48 GPa
Thermal conductivity	401 W/m K
Thermal expansion	16.5 µm/m K (at 25 °C)
Vickers hardness	343–369 MPa
Young’s modulus	110–128 GPa

shows the properties of the copper tool used for EDM. After careful consideration, the best suitable factors and their levels were chosen based on the analysis of previous studies and as per the EDM machine specification.

Table 3. Machining parameters and their levels.

Parameters	Coded Form	L1	L2	L3
Pulse-on time (Ton), µs	A	500	750	1000
Duty cycle, %	B	8	9	10
Peak current, Amp	C	40	45	50
Voltage, V	D	20	25	30

shows the machining parameters and their levels.

2.3. Machining Setup

The experiment was carried out using a copper tool and MET-L-COOL EDM 30 oil (submerged with flushing) as the electrolyte on a die-sinking NC EDM machine (ELECTRONICA EMS-5535, Electronica India Limited, Kolkata, India). The flushing pressure was set at 0.5 kg/cm² (7.1 psi). For each material, spark gaps of 50 µm on either side are taken into account for the electrode diameter. For finishing activities, the aforementioned structure is typically taken into account. In order to achieve a larger material removal rate when the discharge energy increases, a transistor pulse (TP) power circuit method—which is the most versatile circuit according to previous research—is applied. The oscillation circuit that is chosen determines the current setting, voltage setting, duty cycle (the percentage of the on time compared with the overall cycle time), and the on time (during this period the voltage is applied across the wire electrode and job). Thousands of pulses are produced every second by a TP circuit, which also results in shorter pulse intervals. The work’s surface hardness, material removal, and surface polish are largely determined by the interaction of these three variables. Given that the material Ti6Al4V has a high hardness value, a maximum current of 50 Amps is specified. In order to obtain the appropriate surface smoothness and to avoid arcing or burning of the sparked surface, the spark gap, also known as the arc gap, must be maintained. The operation’s speed is also determined by the spark gap. Greater and coarser material removal and a rougher operation are associated with larger spark gaps. Where a finer finish is needed, a smaller spark gap is maintained, which takes more time. For every run, the same 5 min of machining time were used. Additionally, a 0.1 mm overcut was preserved. Leica M50 optical microscope (Leica, Wetzlar, Germany) equipped with depth measuring capabilities was used to quantify the depth of the incision, and MRR was computed by taking TWR, the beginning and final weight of the tool and workpiece after machining, the dimensions of the workpiece area to be machined, and the machined cavity after the EDM process; the surface roughness was assessed using a surface roughness tester (Mitutoyo SURFTEST SJ-410, Mitutoyo, Kawasaki, Japan) (Figure 3). A total of twenty-seven experimental runs were planned utilizing the parameters in Taguchi’s plan. SEM micrographs analysis was performed JEOL JSM-6480 LV (JEOL Ltd., Tokyo, Japan) scanning electron microscope (SEM).

3. RAMS-RATMI Method

Abdulaal et al. [36] developed the RAMS-RATMI method in 2022 to address complex engineering issues. First, options are divided into advantageous and non-benefit categories using the RAMS approach, which is an extension of the ranking alternatives by perimeter similarity (RAPS) method. By comparing the perimeter of the triangle formed by the advantageous components with the ideal alternative, the optimal alternative is narrowed down. By comparing the triangle’s median to the best option, RAMS rates the alternatives [37]. Uroševićc et al. [38] introduced the RATMI method, which is an expansion of the RAMS and multiple criteria ranking by alternative trace (MCRAT) techniques. The majority index is a novel metric for rating alternatives that is created by combining the alternative trace and the median similarity of the alternatives.

Step 1: A relevant decision matrix is created with ‘m’ no. of experimental runs and ‘n’ no. of. responses:

$$M=\left[\begin{array}{cc}\begin{array}{cc}{x}_{11}& x_{12}\\ x_{21}& x_{22}\end{array}& \begin{array}{cc}\dots & x_{1n}\\ \dots & x_{2n}\end{array}\\ \begin{array}{cc}\dots & \dots \\ x_{m1}& x_{m2}\end{array}& \begin{array}{cc}\dots & \dots \\ \dots & x_{mn}\end{array}\end{array}\right]$$

(1)

The value that was obtained of the ‘j-th’ response during the ‘i-th’ experimental trial is denoted by ‘x_ij’.

Step 2: Due to the multidimensionality of the problem data, making decisions is difficult. The multidimensional decision space must be converted into a nondimensional space in order to prevent issues. It is best to maximize certain characteristics and minimize others. The answer values in the original choice matrix could have varied scales and dimensions, thus two equations must be used to convert them into dimensionless elements:

$$r_{ij}=f\left(x\right)=\left\{\begin{array}{c}{\displaystyle \frac{x_{ij}}{max{x}_{ij}}}, i=\mathrm{1,2},\dots ,m (for maximization)\\ {\displaystyle \frac{{minx}_{ij}}{x_{ij}}}, i=\mathrm{1,2},\dots ,m (for minimization)\end{array}\right.$$

(2)

Step 3: The weighted normalized decision matrix is created by constructing a decision matrix based on the normalized decision matrix and its corresponding criteria weights.

$$U={\left[u_{ij}\right]}_{m\times n}=w_j{r}_{ij}; \left\{\begin{array}{c}i=\mathrm{1,2},\dots ,m\\ j=\mathrm{1,2},\dots ,n\end{array}\right.$$

(3)

where ‘w_j’ is the weight of criteria ‘j’, which can be ascertained using the AHP approach or by consulting a panel of experts. Each weight must add up to a total of one.

Step 4: The optimal alternative can be determined by analyzing each component of the solution:

$$q_{ij}=max\left(u_{ij}\right); \left\{\begin{array}{c}i=\mathrm{1,2},\dots ,m\\ j=\mathrm{1,2},\dots ,n\end{array}\right.$$

(4)

The optimal alternative is represented by the following set:

$$Q=\left\{q_1,q_2,\dots .,q_n\right\}$$

(5)

Step 5: The optimal alternative can be decomposed into two sets or two components:

$$Q=Q^{max}\cup Q^{min}$$

(6)

$$Q=\left\{q_1,q_2,\dots .,q_k\right\}\cup \left\{q_1,q_2,\dots .,q_h\right\};k+h=j$$

(7)

where ‘k’ denotes the total number of criteria that must be maximized and ‘h’ the total number of criteria that mustbe minimized.

Step 6: The experimental trials are further divided into two sets or components, following the same process as the previous step:

$$U_i=U_i^{max}\cup U_i^{min};i=\mathrm{1,2},\dots ,m$$

(8)

$$U_i=\left\{U_{i1},U_{i2},\dots .,U_{ik}\right\}\cup \left\{U_{i1},U_{i2},\dots .,U_{ih}\right\};i=\mathrm{1,2},\dots ,m$$

(9)

Step 7: The formula may be used to determine each component of the ideal alternative’s magnitude:

$$Q_k=\sqrt{Q_1^2+Q_2^2+\dots +Q_k^2}$$

(10)

$$Q_h=\sqrt{Q_1^2+Q_2^2+\dots +Q_h^2}$$

(11)

Similarly, it may be calculated as follows for every experimental trial:

$$U_{ik}=\sqrt{u_{i1}^2+u_{i2}^2+\dots +u_{ik}^2};i=\mathrm{1,2},\dots ,m$$

(12)

$$U_{ih}=\sqrt{u_{i1}^2+u_{i2}^2+\dots +u_{ih}^2}$$

(13)

Step 8: MCRAT (ranking by alternatives trace). Here, matrix ‘F’ with the best possible alternative components is constructed:

$$F=\left[\begin{array}{cc}{Q}_k& 0\\ 0& Q_h\end{array}\right]$$

(14)

In a similar manner, a second matrix, ‘G_i’, is constructed that contains components of the experimental trial:

$$G_i=\left[\begin{array}{cc}{U}_{ik}& 0\\ 0& U_{ih}\end{array}\right];i=\mathrm{1,2},\dots ,m$$

(15)

Now, matrixes ‘F’ and ‘G_i’ are multiplied to create the matching matrix ‘T_i’:

$$T_i=A\times B_i=\left[\begin{array}{cc}{T}_{11;i}& 0\\ 0& T_{22;i}\end{array}\right];i=\mathrm{1,2},\dots ,m$$

(16)

The trace of the matrix ‘T_i’ above may be used to determine the MCRAT score, as demonstrated below:

$$t\left(T_i\right)=T_{11;i}+T_{22;i}; i=\mathrm{1,2},\dots ,m$$

(17)

Step 9: The RAPS method ranks alternatives based on their perimeter similarity, with the optimal alternative’s perimeter representing the right angle’s base and perpendicular side:

$$P=Q_k+Q_h+\sqrt{Q_k^2+Q_h^2}$$

(18)

Every alternative’s perimeter is computed in the same manner.

$$P_i=U_{ik}+U_{ih}+\sqrt{U_{ik}^2+U_{ih}^2}$$

(19)

Alternatives are sorted in descending order based on their perimeter similarity, which is the ratio of each alternative’s perimeter to the ideal one:

$${PS}_i={\displaystyle \frac{P_i}{P}};i=\mathrm{1,2},\dots ,m$$

(20)

Step 8: The RAMS method ranks alternatives based on their median similarity like the RAPS method (Step 7) where the ideal alternative’s median is represented by an expression:

$$M=\sqrt{{\displaystyle \frac{Q_k^2+Q_h^2}{2}}}$$

(21)

Likewise, the following formula is used to determine the median for every experimental trial:

$$M_i=\sqrt{{\displaystyle \frac{U_{ik}^2+U_{ih}^2}{2}}}; i=\mathrm{1,2},\dots ,m$$

(22)

The median of each trial is divided by the median of the ideal response values to determine the RAMS score (or “MS_i”) for each experimental trial. The ratio between the optimal answer and the alternative’s perimeter is known as median similarity

$${MS}_i={\displaystyle \frac{M}{M_i}};i=\mathrm{1,2},\dots ,m$$

(23)

The RAMS score is used to rate the experimental trials in descending order, while alternatives are ranked in descending order based on the ‘MS_i’.

Step 10: The RATMI score (E_i) is a ranking method that calculates the combination of the MCRAT and RAMS scores.

$$E_i=v{\displaystyle \frac{t\left(T_i\right)-mint\left(T_i\right)}{max{MS}_i-min{MS}_i}}+\left(1-v\right){\displaystyle \frac{{MS}_i-min{MS}_i}{max{MS}_i-min{MS}_i}}, i=\mathrm{1,2},\dots ,m$$

(24)

The majority index ‘E_i’ between MCRAT’s strategy and RAMS’s strategy is determined by assigning a weight ‘$v$’ to each strategy, with α ranging from 0 to 1. The RATMI score’s declining values are used to rate the experimental trials from best to worst.

4. Results and Discussions

Table 4. Experimental design and outputs.

Run No.	A (Pulse on Time (Ton), µs)	B (Duty Cycle, %)	C (Peak Current, Amp)	D (Voltage, V)	MRR mm3/ min	Depth of Cut, mm	Surface Roughness, µm	TWR mm3/ min
R1	500	8	40	20	5.48	0.087	9.07	0.000000223
R2	500	8	40	25	5.30	0.084	8.97	0.00000111
R3	500	8	40	30	5.20	0.083	8.72	0.00000223
R4	500	9	45	20	2.37	0.038	9.24	0.00000223
R5	500	9	45	25	2.20	0.035	9.14	0.00000446
R6	500	9	45	30	2.09	0.033	8.89	0.00000223
R7	500	10	50	20	3.49	0.056	10.33	0.00000223
R8	500	10	50	25	3.31	0.053	10.24	0.00000223
R9	500	10	50	30	3.21	0.051	9.99	0.00000223
R10	750	8	45	20	1.60	0.026	7.66	0.00000223
R11	750	8	45	25	1.43	0.023	7.57	0.00000223
R12	750	8	45	30	1.32	0.021	7.32	0.00000223
R13	750	9	50	20	1.71	0.027	11.53	0.00000111
R14	750	9	50	25	1.53	0.024	11.43	0.00000111
R15	750	9	50	30	1.43	0.023	11.18	0.00000111
R16	750	10	40	20	2.89	0.046	8.65	0.00000111
R17	750	10	40	25	2.72	0.043	8.55	0.00000111
R18	750	10	40	30	2.61	0.042	8.31	0.00000223
R19	1000	8	50	20	3.94	0.063	9.89	0.00000111
R20	1000	8	50	25	3.77	0.060	9.79	0.00000111
R21	1000	8	50	30	3.66	0.058	9.55	0.00000223
R22	1000	9	40	20	4.11	0.066	9.78	0.000000111
R23	1000	9	40	25	3.94	0.063	9.69	0.00000111
R24	1000	9	40	30	3.84	0.061	9.44	0.00000223
R25	1000	10	45	20	2.02	0.032	7.19	0.00000334
R26	1000	10	45	25	1.85	0.029	7.09	0.00000223
R27	1000	10	45	30	1.74	0.028	6.84	0.00000223

displays the experimental plan (Taguchi L₂₇) using four controlled parameters along with the output responses, i.e., MRR, depth of cut, surface roughness, and TWR.

4.1. Optimization Using the RAMS-RATMI Method

Since MRR and a depth of cut must be maximized while surface roughness and TWR must be minimized, normalization was achieved using Equation (2) followed by the addition of weights (0.5405 for MRR, 0.1802 for depth of cut, 0.0688 for surface roughness, and 0.2015 for TWR) calculated by using the AHP method. Furthermore, an optimal alternative for all response criteria was calculated followed by the construction of a decomposition matrix (

Table 5. Decomposition of alternatives.

Run No.	MRR	Depth of Cut	Surface Roughness	TWR
R1	0.2921	0.0325	0.0031	0.0406
R2	0.2739	0.0304	0.0032	0.0016
R3	0.2631	0.0292	0.0033	0.0004
R4	0.0548	0.0061	0.0030	0.0004
R5	0.0470	0.0052	0.0030	0.0001
R6	0.0426	0.0047	0.0032	0.0004
R7	0.1185	0.0132	0.0024	0.0004
R8	0.1070	0.0119	0.0024	0.0004
R9	0.1003	0.0112	0.0025	0.0004
R10	0.0250	0.0028	0.0043	0.0004
R11	0.0199	0.0022	0.0044	0.0004
R12	0.0170	0.0019	0.0047	0.0004
R13	0.0284	0.0032	0.0019	0.0016
R14	0.0229	0.0026	0.0019	0.0016
R15	0.0199	0.0022	0.0020	0.0016
R16	0.0814	0.0091	0.0034	0.0016
R17	0.0719	0.0080	0.0035	0.0016
R18	0.0665	0.0074	0.0037	0.0004
R19	0.1513	0.0168	0.0026	0.0016
R20	0.1383	0.0154	0.0026	0.0016
R21	0.1306	0.0145	0.0028	0.0004
R22	0.1649	0.0183	0.0026	0.1639
R23	0.1513	0.0168	0.0027	0.0016
R24	0.1433	0.0159	0.0028	0.0004
R25	0.0397	0.0044	0.0049	0.0002
R26	0.0332	0.0037	0.0050	0.0004
R27	0.0295	0.0033	0.0054	0.0004

). This matrix was further used to construct two sets of components and their magnitude. Finally, the components and their magnitude were used to compute the MCRAT score and the RAPS score, which were used to compute the RATMI majority index (

Table 6. MCRAT, RAMS and RATMI score.

Run No.	Uik	Uih	MCRAT				RAMS			RATMI
			T11	T22	t(Ti)	Rank	Mi	MSi	Rank	t(Ti)	MSi	Ei	Rank
R1	0.5697	0.2090	0.3246	0.0860	0.4106	2	0.3034	0.8635	1	0.4106	0.8635	0.9981	1
R2	0.5517	0.0692	0.3143	0.0285	0.3428	3	0.2780	0.7912	3	0.3428	0.7912	0.8302	3
R3	0.5407	0.0612	0.3081	0.0252	0.3332	4	0.2721	0.7743	4	0.3332	0.7743	0.8014	4
R4	0.2467	0.0581	0.1405	0.0239	0.1645	16	0.1267	0.3606	16	0.1645	0.3606	0.2019	16
R5	0.2286	0.0560	0.1303	0.0230	0.1533	17	0.1177	0.3349	17	0.1533	0.3349	0.1635	17
R6	0.2177	0.0601	0.1240	0.0247	0.1487	19	0.1129	0.3213	18	0.1487	0.3213	0.1454	18
R7	0.3628	0.0527	0.2067	0.0217	0.2284	10	0.1833	0.5217	10	0.2284	0.5217	0.4324	10
R8	0.3448	0.0531	0.1965	0.0219	0.2183	11	0.1744	0.4964	11	0.2183	0.4964	0.3961	11
R9	0.3338	0.0543	0.1902	0.0223	0.2125	12	0.1691	0.4813	12	0.2125	0.4813	0.3748	12
R10	0.1666	0.0687	0.0949	0.0283	0.1232	23	0.0901	0.2564	23	0.1232	0.2564	0.0529	23
R11	0.1486	0.0695	0.0846	0.0286	0.1132	25	0.0820	0.2334	25	0.1132	0.2334	0.0186	25
R12	0.1376	0.0717	0.0784	0.0295	0.1079	27	0.0776	0.2208	27	0.1079	0.2208	0.0010	27
R13	0.1776	0.0596	0.1012	0.0245	0.1257	22	0.0936	0.2665	22	0.1257	0.2665	0.0649	22
R14	0.1595	0.0598	0.0909	0.0246	0.1155	24	0.0852	0.2424	24	0.1155	0.2424	0.0294	24
R15	0.1486	0.0606	0.0846	0.0249	0.1096	26	0.0802	0.2283	26	0.1096	0.2283	0.0086	26
R16	0.3008	0.0709	0.1714	0.0292	0.2006	13	0.1545	0.4398	13	0.2006	0.4398	0.3228	13
R17	0.2828	0.0714	0.1611	0.0294	0.1905	14	0.1458	0.4150	14	0.1905	0.4150	0.2870	14
R18	0.2718	0.0639	0.1549	0.0263	0.1811	15	0.1396	0.3973	15	0.1811	0.3973	0.2578	15
R19	0.4100	0.0650	0.2336	0.0268	0.2604	6	0.2076	0.5907	6	0.2604	0.5907	0.5386	6
R20	0.3920	0.0654	0.2233	0.0269	0.2502	8	0.1987	0.5655	8	0.2502	0.5655	0.5023	8
R21	0.3810	0.0565	0.2171	0.0232	0.2403	9	0.1926	0.5480	9	0.2403	0.5480	0.4725	9
R22	0.4281	0.4081	0.2439	0.1679	0.4118	1	0.2957	0.8415	2	0.4118	0.8415	0.9829	2
R23	0.4100	0.0659	0.2336	0.0271	0.2607	5	0.2076	0.5909	5	0.2607	0.5909	0.5394	5
R24	0.3990	0.0570	0.2274	0.0235	0.2508	7	0.2015	0.5736	7	0.2508	0.5736	0.5096	7
R25	0.2102	0.0713	0.1197	0.0294	0.1491	18	0.1110	0.3158	19	0.1491	0.3158	0.1418	19
R26	0.1921	0.0738	0.1095	0.0304	0.1398	20	0.1029	0.2929	20	0.1398	0.2929	0.1087	20
R27	0.1812	0.0763	0.1032	0.0314	0.1346	21	0.0983	0.2797	21	0.1346	0.2797	0.0898	21
Qk	0.5697
Qh	0.4115

). It was noted that the RATMI majority index (E_i) was higher in the case of R1 while it was lowest in R12. Hence, it can be concluded that the T_on of 500 µs, duty cycle of 8%, peak current of 40 Amp, and voltage of 20 V can be considered for optimizing the machining characteristics.

4.2. Infuential Factors

Figure 4 displays the main effect plot of means for the RATMI majority index (E_i) with respect to four machining parameters (A (pulse-on time (Ton), µs); B (duty cycle, %); C (peak current, Amp); and D (voltage, V)). Since the RATMI majority index (E_i) must be maximized, the maximum value fetched in the factor configuration is to be considered. Hence, according to the plot, the Ton of 500 µs, duty cycle of 8%, peak current of 40A, and voltage of 20 V can be considered for optimizing the machining characteristics.

The ANOVA findings for the RATMI majority index (E_i) are shown in

Table 7. Analysis of variance.

Factors	DoF	Adj SS	% Contribution	Adj MS	F-Value	p-Value
Ton, A	2	0.71058	30.89	0.355289	56.67	0.000
Duty cycle, B	2	0.21391	9.30	0.106957	17.06	0.000
Peak current, C	2	1.19068	51.77	0.595339	94.97	0.000
Voltage, D	2	0.07200	3.13	0.035998	5.74	0.012
Error	18	0.11284	4.91	0.006269
Total	26	2.30001
R-sq	95.09%	R-sq(adj)	92.91%	R-sq(pred)	88.96%

in order to examine the impact of the EDM settings on the machining output characteristics. The p-value of less than 0.05 (95% confidence interval) indicates that all four machining parameters are important and have an impact on obtaining the intended result. Among all, the peak current was found to be a more significant and influential parameter with 51.77% influence followed by pulse-on time, duty cycle, and voltage with a contribution of 30.89%, 9.30%, and 3.13%, respectively, which can help in achieving the desired machining output characteristics where MRR and the depth of cut can be maximized while surface roughness and TWR can be minimized. R² of 95.09% indicates that the model’s data fit the data well. However, after adjusting for the number of predictors in the model in relation to the number of observations, the adjusted R² value of 92.91% indicates the variance in the response that is explained by the model. The predicted R² value of 88.96% determines the fitness of the model for predicting the response to the observations.

The residual plot for the RATMI majority index (E_i) is displayed in Figure 5. The points fall close to the straight line, suggesting that the normal distribution fits the data well. The assumption that the residuals are randomly distributed and have constant variance is confirmed by the residuals versus fit plots. When you have around 20 or more data points, the residuals histogram helps you evaluate if the data are skewed or contain outliers despite the fact that the bell curve on the histogram indicates the sample distribution. The independent residuals do not display any trends or patterns in time order as the residuals versus the order graphic demonstrates. Nevertheless, given that the residuals fall randomly about the center line, patterns in the points may imply a correlation between the residuals, proving that they are not independent.

Figure 6 shows the contour plot of E_i vs. pulse-on time and duty cycle. It signifies that the majority index is reduced during medium-level settings for machining (dark red area) while the majority index increases when there is a lower-level setting for machining (purple area). In the experimental runs, it can also be seen that such factor setting causes lower MRR and high surface roughness values. Similar phenomena can be interpreted from Figure 7, which depicts the surface plot of E_i vs. pulse-on time and duty cycle where E_i decreases and increases according to a deeper area and a higher area, respectively. Figure 8 shows the contour plot of the RATMI majority index (E_i) vs. pulse-on time and peak current. It signifies that the majority index is reduced during the medium-level setting of pulse-on time and higher peak current for machining (dark red area) while the majority index increases when there is a lower-level setting for machining (purple area). In the experimental runs, it can also be seen that such factor setting causes lower MRR and high surface roughness values. Similar phenomena can be interpreted from Figure 9, which depicts the surface plot of E_i vs. pulse-on time and peak current where E_i decreases and increases according to a deeper area and a higher area, respectively. Figure 10 shows the contour plot of the RATMI majority index (E_i) vs. pulse-on time and voltage. It signifies that the majority index is reduced during the medium-level setting of pulse-on time and higher voltage for machining (dark red area) while the majority index increases when there is a lower-level setting for machining (purple area). In the experimental runs, it can also be seen that such factor setting causes lower MRR and high surface roughness values. Similar phenomena can be interpreted from Figure 11, which depicts the surface plot of E_i vs. pulse-on time and voltage where E_i decreases and increases according to a deeper area and a higher area, respectively. Figure 12 shows the contour plot of the RATMI majority index (E_i) vs. duty cycle and peak current. It signifies that the majority index is reduced during the medium-level setting of the duty cycle and higher peak current for machining (dark red area) while the majority index increases when there is a lower-level setting for machining (purple area). In the experimental runs, it can also be seen that such factor setting causes lower MRR and high surface roughness values. Similar phenomena can be interpreted from Figure 13, which depicts the surface plot of E_i vs. duty cycle and peak current where E_i decreases and increases according to a deeper area and a higher area, respectively. Figure 14 shows the contour plot of the RATMI majority index (E_i) vs. duty cycle and voltage. It signifies that the majority index is reduced during the high-level setting for machining (dark red area) while the majority index increases when there is a lower level setting for machining (purple area). In the experimental runs, it can also be seen that such factor setting displayed moderate enhancement in maximizing MMR and lower surface roughness compared with the results of previous plots. Similar phenomena can be interpreted from Figure 15, which depicts the surface plot of E_i vs. duty cycle and voltage where E_i decreases and increases according to a deeper area and a higher area, respectively. Figure 16 shows the contour plot of the RATMI majority index (E_i) vs. peak current and voltage. It signifies that the majority index is reduced during the medium-level setting of peak current and higher voltage for machining (dark red area) while the majority index increases when there is a lower-level setting for machining (purple area). In the experimental runs, it can be seen that such factor setting causes lower MRR and surface roughness values. Similar phenomena can be interpreted from Figure 17, which depicts the surface plot of E_i vs. peak current and voltage where E_i decreases and increases according to a deeper area and a higher area, respectively.

4.3. Surface Morphology

When machining Ti6Al4V using a copper tool in EDM, several main effects on the surface can be observed. In Figure 18a, small craters are present while Figure 18b shows large craters. EDM involves spark erosion, which results in crater formation on the machined surface due to the localized melting and evaporation of the material. R12 has higher surface roughness compared with R1 as Figure 18b shows a relatively high number of irregular craters and molten metal droplets solidified on the surface compared with Figure 18a. The roughness can vary depending on the EDM parameters. Higher discharge energy generally results in higher surface roughness.

The SEM image in Figure 19 shows how the recast layer (white layer) forms on the surface due to the molten material solidifying again. The EDM settings have an impact on the recast layer’s thickness. In this instance, a thinner recast layer is usually the consequence of decreased energy levels. Nonhomogeneous heat flow, plastic deformation, and metallurgical transformations are frequently encouraged by EDM operation. This leads to residual tension being created inside the machined object. It is commonly recognized that surface cracking is caused by residual tension that arises from fast cooling and phase shifts in the white layer. Under the recast layer, there is a heat-affected zone where the material undergoes structural alterations and thermal pressures without melting [23].

SEM micrographs showing the surface integrity of EDMed Ti6Al-4V specimens made with copper electrodes show poor surface morphology, including big surface fractures, microcracks, globules, pockmarks, and a white layer (Figure 20). Nevertheless, the degree of the aforementioned surface imperfections varies depending on the electrode material and spark energy input. The residual tension created while the EDM procedure is carried out is what causes surface cracking at the EDMed work surface. According to the literature on the EDMed part component’s residual stress [23], the residual stress seems to be the greatest at the surface. Additionally, it shows that when pulse energy increases, residual stress rises as well. Because of the way its size encourages surface cracking, such residual stress is detrimental. The process of EDM causes spark erosion, which leaves craters on the surface that has been machined. The material melts and vaporizes locally, creating these craters. Surface microcrack development can result from rapid cooling and solidification [15]. The machined part’s mechanical characteristics and surface integrity may be impacted by these microcracks. The machined surface’s microstructure may change as a result of the EDM’s heat cycles. This includes modifications to the phase composition and grain size, which can have an impact on the material’s characteristics. Because of the liquid metal droplets that settle on the surface and the uneven craters, the surface roughness of Ti6Al4V machined by EDM is often very high. The discharge current, duty cycle, and other EDM parameters may all affect how rough the surface is. Surface roughness often increases with discharge energy. Copper particles are deposited on the machined surface as a result of material transfer from the copper tool to the Ti6Al4V surface. Generally speaking, the elevated temperatures experienced during EDM might lead to the machined surface’s oxidation and carburization, which may result in the creation of titanium carbides or oxides.

4.4. Convergence of the Investigation

Peak current was revealed to be the most important regulating element for achieving a satisfactory machining outcome; nevertheless, a number of other research findings were also presented to support the current findings with regard to surface morphology and machining qualities. The most important aspect for regulating the surface roughness of EDMed Ti6Al4V with a copper electrode is currently identified by Singh and Kumar [14]. According to Kushwaha et al. [6], peak current utilizing a copper electrode has a beneficial impact on the MRR, TWR, and surface roughness of EDMed Ti6Al4V. Because of the high carbide deposition at the machined surface, longer pulse-on durations show truncation of TWR and MRR readings. The surface finish is greatly degraded by longer pulse-on times. According to Krishnaraj [9], in the EDMed Ti6Al4V utilizing a copper electrode, peak current and pulse-on time are the most important factors; peak current contributes the most to the MRR. Increased TWR is frequently the result of increased discharge energy density produced by higher currents. Choudhary et al. [5] have obtained similar results. Baroi et al. [32] discovered that because of the increasing heat energy in the inter-electrode gap, MRR and TWR rise with the current. However, because of carbon deposition and a long igniting delay, pulse-on time reduces MRR. Because of carbon deposition and longer heat transmission times, TWR falls with pulse-on time. Surface irregularity rises with the current and pulses punctually. According to Rahul et al. [23], deep cryogenic treatment of copper tool material results in reduced crystallite size, increased micro-hardness value, refined grain, and alleviation of stress. Additionally, it decreases tool wear and enhances surface smoothness when EDMing Ti6Al4V. White layer thickness and surface crack density were reduced by using cryogenically treated copper electrodes. According to Verma et al.’s [15] research, the input machine variable affected the density and severity of the microcracks and craters that formed. It was discovered that the primary factor influencing these attributes was pulse current.

5. Conclusions

Using a hybrid technique that combines Taguchi RAMS-RATMI optimization methodologies, this work gives a thorough parametric examination of the die-sinking EDM process applied to the Ti6Al4V alloy. The main goal of the EDM process optimization was to obtain increased machining performance and surface integrity of Ti6Al4V. For high-precision and high-performance manufacturing applications, the optimized process parameters obtained via this study greatly improve machining performance, surface integrity, and operational dependability. Important findings from this research include the following:

• The RATMI majority index (Ei) was found to be higher in R1 than in R12. To optimize machining characteristics, the Ton of 500 µs, duty cycle of 8%, peak current of 40Amp, and voltage of 20V can be considered. The main effect plot of means for the RATMI majority index (Ei) shows that the maximum value fetched in the same factor configuration should be considered.
• The ANOVA results show that all the machining parameters are significant in achieving the desired output characteristics. Peak current, with a 51.77% contribution, maximizes MRR and the depth of cut while minimizing surface roughness and TWR, thereby enhancing the machining output characteristics. Also, the residual plots show a good fit of the experimental data.
• The study reveals that the majority index (Ei) decreases during medium-level machining settings while increasing at lower-level settings, resulting in lower MRR and high surface roughness values. This phenomenon is also observed in surface plots, with the majority index decreasing in deeper areas and increasing in higher areas.
• The surface of Ti6Al4V is impacted by EDM using a copper tool. Small and large craters are present due to spark erosion, resulting from localized melting and vaporization. R12 has higher surface roughness than R1 due to irregular craters and molten metal droplets. The roughness can vary depending on EDM parameters, with higher discharge energy generally resulting in higher surface roughness.
• SEM micrographs show the recast layer formed on the surface of molten material due to solidification. EDM settings affect the recast layer’s thickness, with thinner layers often due to decreased energy levels. Inhomogeneous heat flow, metallurgical transformations, and plastic deformation are often encouraged by EDM operation, leading to residual tension and surface cracking. A heat-affected zone beneath the recast layer undergoes structural changes and thermal pressures without melting.
• Surface morphology of EDMed Ti6Al-4V specimens with copper electrodes shows poor surface integrity, including fractures, microcracks, globules, pockmarks, and a white layer. The degree of surface imperfections varies depending on electrode material and spark energy input.

This study suggests future research to improve the process efficiency, enhance material properties, and explore alternative dielectric fluids, tool electrode materials, and electrode coatings. It suggests hybrid and sequential EDM processes, combining EDM with other techniques for enhanced performance, and focusing on precision and surface quality in micro-components and medical implants. Real-time monitoring systems, environmental and economic aspects, life cycle analysis, cost-benefit analysis, and customization for specific applications can encourage interdisciplinary research and industry–academia partnerships.