Parametric investigation in electrical discharge drilling of Ti-alloy using ANFIS

Abstract

The need for precise and efficient manufacturing processes is rapidly growing worldwide for the conversion of biomaterials into highly accurate and precise artificial implants and medical devices. Ti-based alloys are particularly used for implants and bone plate materials because they have good mechanical as well as biological properties. Predicting increased productivity during EDD of Ti-6Al-4V alloy with less tool damage and improved dimensional accuracy of the drilled hole is proposed in the study. Process performance was evaluated in terms of metal removal rate (MRR), tool wear rate (TWR), and hole taper (HT), as functions of discharge current, pulse-on time, pulse-off time, and dielectric pressure. A hybrid modeling approach combining Adaptive Neuro-Fuzzy Inference System (ANFIS) model integrating artificial neural networks (ANN) and fuzzy logic (FL) was employed to capture the non-linear relationships among variables. The model exhibited a close agreement with experimental results, with prediction errors 1.04% for MRR, 5.65% for TWR and 4.12% for HT. Discharge current and dielectric pressure were identified as the most influential parameters. While the proposed approach effectively predicts process behavior within the experimental range, its applicability beyond the tested parameter domain requires further validation. The study demonstrates the potential of hybrid modeling for achieving enhanced precision and efficiency in the fabrication of biomedical components.

Keywords

Ti-alloy electric discharge drilling intelligent modelling metal removal rate tool wear rate hole taper

Introduction

Titanium alloys are highly desirable structural materials that are widely used in various industrial applications due to their high strength, low density, and exceptional corrosion resistance. Their application is limited in parts exposed to frequent friction and wear due to their relatively low hardness and inadequate tribological properties. Ti-6Al-4V alloy is particularly most attracted metallic material for biomedical and aerospace applications due to its high strength-to-weight ratio, high temperature stability, and great corrosion resistance (Abu Qudeiri et al., 2018; Chen et al., 2011; Danişman et al., 2021; Krstić et al., 2024; Xu et al., 2021). Stainless steel is the first metallic biomaterial that was used successfully as an implant. Titanium and its alloys are the modern metallic biomaterials and have wide applications in medical and dental fields for making biomedical devices and implants due to better biocompatibility (Chen et al., 2020; Elias et al., 2008; Sharma et al., 2024; Yamanoglu, 2020). These alloys are also used in marine engineering and chemical industries because they have good cryogenic qualities (Singh et al., 2020; Thesiya et al., 2015). The need of efficient manufacturing processes is rapidly growing worldwide for the conversion of technologically advanced engineering materials into high standard components or products (i.e., turbine blades of aeroengines and artificial human body implants). Machining of Ti and its alloys is difficult with conventional methods as they possess low thermal conductivity, low machinability and react chemically at elevated temperatures during interaction with tool (Chetan et al., 2015; Hourmand et al., 2021; Muhammad et al., 2014). These problems can be avoided by using the advanced methods of machining.

Among all advanced machining processes (AMPs), electrical discharge machining (EDM) is the most acceptable process to remove the excess amount of material from the electrically conductive solids irrespective of their mechanical properties. On comparison with other AMPs, EDM offers high precision in dimensional accuracy and metal removal at low cost comparatively. It can be utilised for making complex geometry in hardened electrically conductive alloys with good quality. EDM is a non-contact type thermal process and extensively used for making large aspect ratio holes in electrically conductive modern engineering materials. In EDM, a series of high frequency sparks is produced between the tool and workpiece electrodes. These electrodes are required to submerge in dielectric fluid for growing the spark energy into the confined space between the electrodes which is termed as inter electrode gap (IEG). Due to this gap, there is no cutting force developed and mechanically induced stresses are absent in the workpiece material. The spark energy is responsible to melt and vaporize the material from the localized zone and further the molten materials is expelled from the machining zone in the form of debris by employing the effective flushing techniques. Dielectric liquid is supplied through the nozzle in machining zone for removing the by-products and for cooling purposes.

In case of electric discharge drilling (EDD), dielectric is injected through the tool electrode for efficient removal of the eroded material. Commonly used dielectric fluids are hydrocarbons, mineral oils, and deionized water. These are the very efficient to concentrate the spark energy. Generally, kerosene and deionized water are used to create the miniature features in the aerial and biomaterials. The application of different types of dielectric fluids influences the process performance in a different way. With the application of kerosene in EDD, gases bubbles are formed, and this can be avoided by mixing certain additives in the dielectric (Tiwary et al., 2018). Deionized water has the wide acceptance as dielectric liquid to produce miniature features and micro holes while machining of hard-to-cut materials. It was observed that high MRR and low TWR can be obtained with the use of purified water in place of kerosene as dielectric fluid (Kagaya et al., 1990).

Several investigations have been carried out in the past to improve the efficiency and performance of conventional EDM process. The modification in tool electrodes reduces tool wear and hence increases productivity, also researcher found that cryogenically treated copper is the most effective electrode for EDM of Ti-6Al-4V in terms of MRR, surface finish, and tool life, but TiC layer formation is a key metallurgical change affecting surface integrity (Rahul et al., 2018) . The improvement was found in MRR and surface quality of the workpiece by providing the rotation of the tool with high frequency vibrations (Khatri et al., 2016). Purna et al. (2015) investigated the influences of dielectrics such as kerosene and deionized water on the MRR, TWR, overcut and surface integrity during EDM of titanium alloy. It has been noted that kerosene-based dielectrics generally provide superior surface finish and higher material removal rates (MRR) due to their better spark stability and insulating strength. However, they also tend to produce thicker recast layers and higher tool wear ratios because of carbon deposition and localized overheating. Conversely, deionized water offers improved flushing and reduced carbon contamination, yielding cleaner surfaces but sometimes causing microcracks or lower MRR due to its higher cooling rate and lower viscosity. Valaki et al. (2016) investigated the possibility of Jatropha curcas oil-based biofluid as a dielectric medium to make the EDM process sustainable. They found that jatropha biodiesel improves the surface properties of machined components.

Niamat et al. (2017) conducted the experiments on Al6061-T6 alloy to analyse the effects of kerosene and water on MRR, electrode wear rate (EWR), surface irregularities and micro-structure. They found higher MRR with the application of kerosene because of arcing phenomena is occurred with the distilled water. Yadav and Yadava (2015) used electro-discharge diamond drilling process for making the holes in nickel-based superalloy and found improvement in hole circularity and surface finish. Machinability of titanium alloy (Ti–6Al–4V) has been investigated in EDM process by (M Kumar et al., 2019). The influences of discharge current and pulse on time on MRR, tool wear rate (TWR), and surface quality have been observed by them and concluded that the pyrolysis of the dielectric media is responsible for migrating the carbon contents on machined surface and formed the carbide layer which increases the microhardness of machined surface. Senthilkumar and Omprakash (2011) investigated the influences of TiC particles on MRR and TWR during EDM of metal matrix composites (Al/TiC). They found that TiC significantly improves MRR and TWR during the process by improving arc stability in the IEG. However, scaling down EDM processes for precise micro-machining applications in biomedical, aerospace, and MEMS industries, with focus on precision and repeatability has been found a research gap.

To understand the process behaviour with better prediction and optimize the machining results, various intelligent and statistical techniques have been used in EDM operation. Abhilash and Chakradhar (2020) developed an artificial neural network (ANN) model to analyse the influences of process variables on machining failures such as spark absence and wire breakage. Sengottuvel et al. (2013) used the Fuzzy Logic to optimize EDM performance parameters such as MRR, TWR, and SR precisely during machining of Inconel718. Ashok et al. (2017) employed fuzzy logic and the ANN approaches to optimize the MRR in W-EDM of hybrid nanocomposites. Kumar and Dhanabalan (2019) used grey relational analysis (GRA) and fuzzy logic to optimize the productivity and dimensional accuracy of holes in EDM of Inconel718. They employed multi-hole Cu electrodes for drilling and found improvement in process performance. Hascalık and Caydas (2007) investigated the effect of discharge current and pulse time on the MRR, recast layer and tool wear ratio during electric discharge machining of Ti-6Al-4V. It was reported that the MRR, SR, TWR, and recast layer thickness increased with the increase of discharge current and pulse time.

The aim of the present work is to predict the higher productivity with minimum tool damage and better dimensional accuracy of the drilled hole during EDD of Ti-6Al-4V alloy. Experiments were conducted in predefined range of process variables. The process has been modelled using the hybrid approach of ANN and fuzzy logic to predict the uncertainty and complex relationships of the process and to understand the behaviour of drilling process in relation to Ti-6Al-4V. The approach is termed as ANFIS modelling, which has a capability of predicting uncertainty with better accuracy as compared to fuzzy logic. Further, the effects of variables on process performance have been analysed using surface plots.

Materials and experimentation

Around 70%–80% of bio-implants are fabricated by using the metallic biomaterials. Ti-based alloys are particularly well suitable for implants and bone plate materials, because they have the exceptional combination of mechanical and biological properties. Ti-based alloys have the excellent chemical stability which helps to avoid the toxicity metallic ions release into the human body induced by poor osseointegration and clinical failure (Saptaji et al., 2018). In the present work, titanium alloy (Grade 5) is used as workpiece material of 5.5 mm thickness for the experimentation and its chemical composition (by weight %) is shown in Table 1. Copper is used as tool electrode material because of its high thermal conductivity and wide acceptance. With the proper parameter selection of process variables, good surface finish can be obtained by using Cu electrode. Diameter of tubular electrode is 0.8 mm. In place of conventional dielectric medium (i.e., kerosene oil), deionized water has been used to conduct the spark erosion process. Conventional dielectric medium releases toxic fumes and gases in drilling process which will be harmful for experimenter health and environment. Deionized water leads the sustainable machining of biocompatible materials. It also offers several advantages over kerosene like non-flammable, non-toxic, eco-friendly and also have higher thermal conductivity and lower viscosity. Higher MRR can be obtained with deionized water comparatively.

Table 1.

Chemical composition of Titanium alloy.

Element	Al	V	Fe	O	C	Ti
Weight (%)	6.11	3.98	0.18	0.18	0.01	Rest

In this study, four process variables such as discharge current (I_p), pulse-on time (T_on), pulse-off time (T_off), and dielectric pressure (P_d) have considered for experimentation and the influences of these variables on process performance parameters such as metal removal rate (MRR), tool wear rate (TWR) and hole taper (HT). Experiments were performed on EDM drill setup supplied by Sparkonix, Pune (India) in Jaypee University of Engineering and Technology, Guna. Ranges of the process variables have been decided after conducting the pilot experiments and these are tabulated in Table 2. During pilot experiments, it was observed that through hole is obtained within the range of process variables. However beyond the range of variables, metallurgical damages were experienced in the specimens and below the range through holes were not obtained. The pulsed discharge current is used here to erode the excess amount of material. A low current may increase the machining time unnecessarily and a very high current may damage the workpiece surface and consume more electrodes. Such experimental conditions have been examined for obtaining the favourable outputs by using the EDM drill setup.

Table 2.

Process variables range for experimentation.

Process variable	Symbol	Unit	Minimum value	Maximum value
Discharge current	I_p	Ampere	5	14
Pulse-on time	T_on	μsec	11	32
Pulse-off time	T_off	μsec	5	16
Dielectric pressure	P_d	kgf/cm²	40	50

The experiments were conducted by using the straight polarity for obtaining the higher material removal rate with low TWR. These characteristics have been calculated using equations (1) and (2) by measuring the differences in weights of the workpiece and tool electrode before and after drilling. Digital weighing balance of 0.1 mg least count has been used for taking the weight readings. EDM drilled holes diameters were measured by using a Tool Maker’s Microscope (TMM). Thread shapes, gear teeth, angles, and other fine details can all be precisely measured with the TMM. Without coming into direct contact with the workpiece, it achieves micron-level accuracy by combining optical magnification with a measuring stage. A total of eight readings were taken to measure the four diameters (D₁, D₂, D₃ and D₄) of the hole on top side as shown in Figure 1, and similar measurements were taken on the bottom side of the hole at respective positions. The average of four diameters was used to calculate the hole diameter at top and bottom side. Afterwards, the dimensional accuracy of hole has been computed in terms of hole taper, and it should be minimum for straight hole. It can be computed using the equation (3).

MRR (mg / \sec) = \frac{w_{1} - w_{2}}{t}

(1)

TWR (mg / \sec) = \frac{C_{1} - C_{2}}{t}

(2)

HT (degree) = \tan^{- 1} \frac{(Top diameter - Bottom diameter)}{2 * Plate thickness}

(3)

where

w_{1} a n d w_{2}

are the weights of work material before and after drilling and

C_{1} a n d C_{2}

are weights of tool electrode before and after drilling in

m g

respectively and t is the time of drilling in seconds. Table 3 shows the experimental values.

Table 3.

Experimental results of EDD.

S. No	Ip (A)	Ton (μsec)	Toff (μsec)	P_d (kgf/cm²)	MRR (mg/sec)	TWR (mg/sec)	Hole taper (degree)
1	5	11	16	40	0.0633	0.0117	0.0657
2	5	13	15	40	0.0389	0.0093	0.0686
3	6	13	15	40	0.0388	0.0136	0.0636
4	8	13	15	40	0.0490	0.0083	0.0368
5	16	13	15	40	0.0878	0.0063	0.0448
6	12	18	15	50	0.1509	0.0320	0.0434
7	12	20	15	50	0.1479	0.0398	0.0269
8	12	22	15	50	0.1892	0.0521	0.0108
9	12	25	15	50	0.2030	0.0454	0.0179
10	12	30	15	50	0.1671	0.0443	0.0316
11	12	32	15	50	0.1324	0.0395	0.0434
12	12	32	12	50	0.2005	0.0223	0.0458
13	12	32	10	50	0.3154	0.0263	0.0302
14	12	32	5	50	0.2642	0.0849	0.0156
15	10	32	5	50	0.2951	0.0537	0.0024
16	10	13	15	40	0.1147	0.0205	0.0382
17	12	13	15	40	0.2144	0.1327	0.0231
18	14	13	15	40	0.1325	0.0607	0.0865
19	14	32	5	50	0.3287	0.1217	0.0108
20	14	32	10	50	0.1452	0.0161	0.0075
21	10	32	10	50	0.2944	0.1199	0.0311
22	6	11	10	50	0.0285	0.0118	0.0621
23	6	20	12	40	0.0312	0.0248	0.0584
24	8	20	10	40	0.0375	0.0267	0.0374
25	8	25	15	50	0.0498	0.0286	0.0328
26	10	20	12	50	0.1895	0.0322	0.0398

Hybrid approach of modelling: ANFIS

In present scenario, artificial intelligence (AI) based systems such as the ANN and fuzzy interference units are very popular to solve the complicated and real-world challenges. Jang suggested a Neuro-fuzzy system (NFS) in 1983, which comprises of an ANN (artificial neural network) and fuzzy logic approach. The ANFIS technique is stochastic method and used for mapping relation between input and output parameters by using hybrid learning method to find the optimal values of membership functions (Karakuzu, 2009). The technique is well suitable for random data input, which is utilised to train the networks, resulting in a variety of outputs. The ANFIS model training was performed in MATLAB R2014a, utilizing the software’s default random initialization for data partitioning, wherein 21 datasets were used for training and 5 for validation. This randomization ensures unbiased parameter learning and prevents overfitting by maintaining statistical independence between training and validation subsets. The network’s performance is increased by increasing the number of hidden layers, modifying the activation function, increasing the number of neurons in the hidden layer, and randomising the weight. Hence, the effect of randomization has been minimised (Hasçalik and Çaydaş, 2007) The employed system combines the interpretation of fuzzy system with the architecture of neural networks. In ANFIS the function parameters are revised by using back propagation (S Kumar et al., 2019).

An adaptive Neuro-fuzzy inference system is a prediction pattern that is composed of five levels. Each of them is described by node functions as shown in Figure 2. Each layer of ANFIS is built by preceding layer nodes, such as ANN. The output of an adaptive network is determined by the node parameters and the performance of the system/process has been maximized during parametric training of the model. ANFIS system may be seen as having two inputs, x and y, and one output, u. To compute the outcome, there are five layers or stages, presented by if then fuzzy rules based on the Sugeno model.

Rule 1 : if x is M_{11} and y is M_{21}; then f_{1} = p_{1} x + q_{1} y + r_{1}

Rule 2 : if x is M_{12} and y is M_{22}; then f_{2} = p_{2} x + q_{2} y + r_{2}

where the fuzzy sets are M₁₁, M₂₁, M₁₂, and M₂₂ and the modifiable parameters are represented by p_i, q_i, and r_i; f_i indicates separated outputs for respective rule. Total numbers of rules are decided based on the number of input variables and their membership functions.

Layer 1 (Fuzzification): In this layer μ_M1i and μ_M2i are the membership function of the two input variables x and y respectively and each node produces the MF’s of the input values. Each node may have same/different number of membership function and of similar/different types of membership function. The equation describes the MF’s of the triangular function taken for the study (Talpur et al., 2017):

μ_{t r i a n g l e} = \max (\min (\frac{x - a}{b - a}, \frac{c - x}{c - b}), 0)

(4)

where a, b, and c – parameter set and these set changes the FMS form in between 0 and 1 value.

Layer 2 (Product layer): Multiplication of the incoming signals by applying Fuzzy operator.

Π = μ_{M 1 i} (x) * μ_{M 2 i} (y)

(5)

where i = 1,2……

Layer 3 (Normalized Layer): The normalization of the node firing strength is calculated by equation.

\bar{w} = \frac{w_{i}}{w_{1} + w_{2} + \dots \dots \dots . + w_{n}}, i = 1, 2, 3 \dots \dots \dots \dots n

(6)

Layer 4 (Defuzzification): Defuzzification is used to forecast the correct value from a fuzzy quantity. Every node in layer 4 is an adaptive node with a node function. During network training, the node functionalities are identified. Defuzzification combines the MF’s with the Takagi-Sugeno (if-then rules) rules to produce the outcomes.

\bar{w_{i}} * u_{i} = \bar{w_{i}} \cdot (p_{i} * x + q_{i} * y + r_{i})

(7)

where

p_{i}, q_{i} {a n d r}_{i}

are the consequent parameter set of each node.

Layer 5 (Output layer): It is the summation of all incoming node where output is calculated by using the equation:

O u t p u t = \sum_{i} \bar{w_{i}} \cdot u_{i} = \frac{\sum_{i} \bar{w_{i}} * u_{i}}{\sum_{i} \bar{w_{i}}}

(8)

The root mean square error is calculated in this layer for inspection of the performance of trained model.

Results and discussion

In the proposed work, hybrid modelling approach of ANN and fuzzy logic (i.e., ANFIS) is employed to predict the process performance. The model has been developed by using the twenty-one experimental results out of twenty six for testing and training and five data set was kept for validation of model. The pre-existing algorithm in MATLAB R2014a has been used to achieve perfect training and prediction of results. Initial ANFIS model parameters are tabulated in Table 4.

Table 4.

Initial ANFIS model parameters.

Output characteristics	MRR	TWR	HT
Membership functions (MF’s)	Triangular	Triangular	Triangular
No. of MF’s	3 3 3 3	3 3 3 3	3 3 3 3
No. of epochs	300	350	100
Method of training	Hybrid	Hybrid	Hybrid
Output function	Constant	Constant	Constant

The hybrid algorithm was utilised in this ANFIS structure, which consist of combination of forward and backward propagation. The input and output MF’s shapes of the model are not uniform. Triangular membership functions (Trimf MF’s) were chosen for the analysis because they have increment and decrement characteristics with one specific value. The benefits of triangular membership function are: it is simple and efficient in computation, easy to interpret, perform well for limited data-set, less sensitive to small variations in input data. The lowest test error and the lower value of mean absolute percentage error have been noticed in the Trimf than other MF’s. The training curves obtained for the MRR, TWR and HT have been shown in Figure. 3(a)–(c), respectively.

The obtained value of training error is found as 4.45 × 10⁻³ for MRR, 1.8 × 10⁻³ for TWR and 4 × 10⁻³ for HT. A set of fuzzy inference systems was chosen for the training phase to predict the process characteristics. The predicted results of process quality characteristics using ANFIS model have been compared with the experimental results and it has been shown in Figure 4. Figures 4(a), 4(b), and 4(c) show the experimental and predicted values for MRR, TWR, and HT, respectively. Further, these results are tabulated in Table 5. The predicted results of all the output characteristics have shown the good agreement with the experimental results as depicted in Figure 5. Further model was validated with another set of data which was shown in Table 6. It shows the model is well trained for prediction the process performance parameters. Since ANFIS is an adaptive model and root mean square error is so small for the responses. The model can be used to predict the responses within the predetermined range of process variables that may not be possible to get with experimental setup.

Table 5.

Comparison of experimental and predicted training data for MRR, TWR and HT.

S. No	Experimental	Predicted	Experimental	Predicted	Experimental	Predicted
S. No	MRR (mg/sec)	MRR (mg/sec)	TWR (mg/sec)	TWR (mg/sec)	Hole taper (degree)	Hole taper (degree)
1	0.0633	0.0633	0.0117	0.0117	0.0657	0.0657
2	0.0389	0.0375	0.0093	0.0106	0.0686	0.0688
3	0.0388	0.0403	0.0136	0.0104	0.0636	0.0636
4	0.0490	0.0489	0.0083	0.0102	0.0368	0.0390
5	0.0878	0.0878	0.0063	0.0063	0.0448	0.0448
6	0.1509	0.1420	0.0320	0.0313	0.0434	0.0436
7	0.1479	0.1630	0.0398	0.0411	0.0269	0.0264
8	0.1892	0.1840	0.0521	0.0504	0.0108	0.0110
9	0.2030	0.2030	0.0454	0.0474	0.0179	0.0170
10	0.1671	0.1620	0.0443	0.0424	0.0316	0.0348
11	0.1324	0.1360	0.0395	0.0404	0.0434	0.0424
12	0.2005	0.2000	0.0223	0.0223	0.0458	0.0421
13	0.3154	0.3150	0.0263	0.0263	0.0302	0.0337
14	0.2642	0.2640	0.0849	0.0849	0.0156	0.0146
15	0.2951	0.2950	0.0537	0.0537	0.0024	0.0024
16	0.1147	0.1150	0.0205	0.0205	0.0382	0.0344
17	0.2144	0.2140	0.1327	0.1330	0.0231	0.0246
18	0.1325	0.1330	0.0607	0.0606	0.0865	0.0865
19	0.3287	0.3290	0.1217	0.1220	0.0108	0.0108
20	0.1452	0.1450	0.0161	0.0161	0.0075	0.0075
21	0.2944	0.2940	0.1199	0.1200	0.0311	0.0311
Avg	0.1702	0.1701	0.0458	0.0458	0.0355	0.0355

Table 6.

Experimental and predicted data for MRR, TWR and HT for validation.

S. No	Experimental	Predicted	Experimental	Predicted	Experimental	Predicted
S. No	MRR (mg/sec)	MRR (mg/sec)	TWR (mg/sec)	TWR (mg/sec)	Hole taper (degree)	Hole taper (degree)
1	0.0285	0.0264	0.0118	0.0173	0.0621	0.0586
2	0.0312	0.0345	0.0248	0.0252	0.0584	0.0545
3	0.0375	0.0343	0.0267	0.0274	0.0374	0.0358
4	0.0498	0.0456	0.0286	0.0265	0.0328	0.0335
5	0.1895	0.1992	0.0322	0.0345	0.0398	0.0385
Avg	0.0673	0.068	0.0248	0.0262	0.0461	0.0442

Effects of process variables on MRR

The surface plots in Figure 6(a)–(c) illustrate the variation of material removal rate (MRR) with dielectric pressure in combination with different electrical parameters—discharge current, pulse off time, and pulse on time, respectively. In Figure 6(a), MRR increases notably with both discharge current and dielectric pressure, reaching a maximum at high current and moderate pressure. This occurs because higher discharge current enhances spark energy, leading to greater material erosion, while moderate dielectric pressure promotes effective debris flushing without destabilizing the plasma channel. In Figure 6(b), MRR decreases with increasing pulse off time, as a longer off period reduces the number of discharge events per second. The influence of dielectric pressure shows an optimum region, where sufficient flushing supports stable machining, but excessive pressure slightly diminishes MRR. Figure 6(c) demonstrates that MRR rises with increasing pulse on time and moderate dielectric pressure. A longer pulse duration allows greater energy transfer to the workpiece, enhancing material removal, while optimal pressure maintains efficient debris evacuation. Overall, the plots reveal that maximum MRR is achieved under high discharge energy (high current and long pulse on time), low pulse off time, and moderate dielectric pressure, ensuring a balance between spark stability and effective debris removal.

Effects of process variables on TWR

Figure 7(a)–(c) shows the variation of TWR with respect to discharge current, pulse on time, pulse off time, and dielectric pressure. It was observed that TWR was higher at high dielectric pressure, high pulse on time, high pulse off time, and a discharge current of 12 A. A similar effect was observed in TWR as it affected MRR. High discharge current and high pulse-on time provide a high melting point for the tool wear, and high pulse-off time allows the evaporation of melted particles from the IEG. The removal of debris is carried out by the high dielectric pressure of the deionized water. The pulse-off time primarily determines the interval between two consecutive discharges, allowing the dielectric fluid to recover and flush away debris from the interelectrode gap. Within the tested parameter range, this interval is long enough to ensure adequate flushing even at lower values, so its variation does not drastically affect the overall discharge energy or spark frequency. Since T_off only indirectly influences the discharge process and mainly assists in maintaining gap cleanliness, its effect becomes secondary once flushing is already sufficient. Therefore, beyond a certain threshold, increasing or decreasing pulse-off time results in only minor variations in MRR/TWR, making it the least significant factor in the overall material removal mechanism.

Effects of process variables on HT

Figure 8(a) shows the variation of hole taper as a function of dielectric pressure and discharge current. It was observed that at low pressure and low discharge current, flushing is poor and discharge energy is low, resulting in a higher hole taper. Low discharge energy and poor flushing of debris create multiple sparks at the same location, causing uneven removal of materials, especially in the drilling process. In Figure 8(b), hole taper is observed to be lower at moderate dielectric pressure and varying pulse-on time, which can be explained as at the top surface flushing is efficient, but as the electrode progresses deeper into the hole, flushing is inappropriate and creates side sparking, thus increasing hole taper. Figure 8(c) shows higher hole taper at low dielectric pressure and high pulse off time, which can be attributed to lower pressure, which does not provide effective flushing, and high pulse off time, which has low discharge energy due to which material removal is poor.

Conclusions

In the present work, experiments were conducted for electric discharge drilling of titanium alloy, and a model was developed to predict the output characteristics beyond the range of the experimental setup. From the study, following observations have been made:

a. Optimum value of MRR, TWR and HT were found to correspond the discharge current of 12 A, pulse on time of 32μsec, pulse off time of 12μsec and a dielectric pressure of 50 kgf/cm².

b. Out of the four input parameters taken for the experimentation, discharge current and dielectric pressure are found as the two most affecting parameter for drilling operation and pulse-off time is the least significant.

c. The ANFIS model developed with the experimental results has very good predictability with minimum errors 1.04% for MRR, 5.65% for TWR and 4.12% for HT, which can be used to find the performance characteristics beyond the range of machining setup.

d. ANFIS works well within the range of training data but struggles with extrapolation beyond it. The model’s ability to generalize depends heavily on the type and number of membership functions; poor selection can lead to overfitting or underfitting.

e. Future research can be carried out by considering additional machining and material factors that may impact dimensional accuracy and surface quality, such as dielectric conditions, and work-tool interactions. Sensitivity analysis and comparison of different algorithms like ANN and RSM models can be done to further validate the model’s predictive strength for better accuracy and efficiency.

Footnotes

ORCID iDs

Md Tasnim Arif

Amit Sharma

Author contributions

“All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by Md Tasnim Arif (First Author). The first draft of the manuscript was written by Md Tasnim Arif and the draft was reviewed, modified and conceptualized by Dr. Amit Sharma (co-author). Both authors read and approved the final manuscript.”

Funding

The authors received no financial support for the research, authorship, and/or publication of this article.

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Data Availability Statement

Data is available in the manuscript for the study, if additional data will be required further. It will be provided as per the request.*

Author biographies

M. Mi Tasnim Arif completed his B.Tech. in Mechanical Engineering from Aligarh Muslim University, in 2008. He received his M.Tech from IIT Roorkee, with specialization in Industrial Metallurgy in 2010. He is currently a Ph.D. candidate at Jaypee University of Engineering and Technology, Guna. His research interests include the machining of advanced materials for aerospace and biomedical applications.

Dr. Amit Sharma completed his Master of Technology in 2007 from Aligarh Muslim University India with specialization of Industrial & Production Engineering. He was awarded Ph.D. degree from Motilal Nehru National Institute of Technology (MNNII) Allahabad, Prayagraj, India in October 2012. Presently, he is working as an Associate Professor in Department of Mechanical Engineering of Jaypee University of Engineering & Technology, Guna (MP), India. His research area includes the advanced machining of functional materials.

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