WEDM process parameters optimization by preference-based CS & PSO algorithm for LCP

Locking Compression Plates (LCP) are typically made of Ti6Al4V alloy. LCP is used to heal fractures of the bone. This article uses Wire Cut Electric Discharge Machining (WEDM) to machine Ti6Al4V alloy. Responses are optimized by two metaheuristic algorithms, the cuckoo search algorithm (CS) and particle swarm optimization (PSO). The cuckoo search algorithm shows that the maximum MRR is 59.4312 mg/min & the maximum cutting speed is 5.0625 mm/min. The single-objective PSO shows a maximum MRR of 59.3632 mg/min & the maximum cutting speed is 5.0155 mm/min. The GRA revealed that the optimum weight for MRR and cutting speed is 48.868% and 51.132% respectively. Scanning electron microscope analysis indicates proper biocompatibility after machining. This article compares CS and PSO with similar calculations for the t-test and found that the p-values for MRR and Cutting speed are 0.9432 and 0.9919.

Keywords: Optimization; manufacturing; biocompatibility; Ti6Al4V alloy; machining

Introduction

Ti6Al4 V has outstanding qualities like high mechanical potency, corrosion limit, and a strength-to-mass ratio.[[1]] Because of these features, Ti6Al4 V alloys are employed in the automobile, aviation, chemical, and biomedical sectors.[[2]] When Ti alloy is transplanted into the person's body, a layer of TiO2 is formed on it. Hence it has good biocompatibility.[[3]] Therefore, Ti alloys are widely used in biomedical device materials.

However, along with some advantages of Ti alloy, it also has disadvantages like advanced chemical interaction, poor thermal conductivity, and lesser modulus of elasticity, which makes the material difficult to cut and therefore limits its use.[[4]] When titanium alloys are machined by conventional machining, the temperature of the machining area increases rapidly. This became the cause of the formation of serrated chips and the phenomenon of sticking.[[5]] This requires some advances in traditional machining.

Wire Cut EDM is unconventional machining.[[6]] This WEDM develops a high potential thermally assisted spark between the workpiece and the conductive wire. At the same time, the material is flushed with deionized water.[[7]]

WEDM also has advantages, such as non-contact machining. Thus, the difficulty of Ti alloy machining (due to the low elastic modulus and its mechanical and physical properties) is overcome using WEDM.[[8]] However, WEDM has a few disadvantages, such as lesser MRR, expensive, and the need for conductive materials for machining.[[9]] Some advanced machining and response optimization techniques can eliminate the disadvantages of WEDM.

Optimization is nothing but maximizing desired responses and minimizing unwanted responses. Optimization is done after modeling the responses. While in engineering, these responses are multimodal, non-linear, and complex constraints in nature. The real-life optimization problems cannot be solved by local search algorithms or traditional optimization techniques like hill climbing or the Nelder-Mead downhill simplex method.[[10]] In contrast, metaheuristic optimization algorithms can quickly solve these real-life optimization problems. Metaheuristic algorithms evolved from some natural biological system that has become so strong and efficient that millions of years have passed to make them the fittest to survive. In multi-objective optimization, different responses are optimized simultaneously.[[11]] In this paper, the CS and PSO of the priori approach were used to find the best optimal setting of WEDM to simultaneously maximize MRR and cutting speed to improve the manufacturing of LCP by WEDM. The novelty of this paper is to boost the manufacturing aspect of various biomedical devices such as LCPs by maximizing the MRR and cutting speed.

An LCP is a metal implant used for internal fixation fractures where the bone can't be repaired by an exterior method like casting. LCP consists of a combination of conventional screw holes with a locking screw hole. Before the development of LCP, a dynamic compression plate (DCP) existed, which was used as conventional plating. In DCP, the bone's fixation occurs through friction amidst the bone and the plate. The DCP plate contacts the bone and can cause disturbances in the blood supply. The limited contact type DCP was then developed to limit interaction with the bone and preserve the blood supply. But the disadvantage of LC-DCP is that the screws are held only vertically, whereas the screws are at different angles to a conventional plate.[[13]] So, the hole of the locking head screw and the conventional hole need to be combined. These combined holes in the LCP make it versatile for use in various bone fracture treatments.[[14]]

This paper analyzes the effect of WEDM process parameters on Ti6Al4 V alloy by SEM images and MRR and Cutting Speed analysis. The manufacturing aspect of LCP is understood using two optimization methods (CS & PSO).

MD Al-Amin et al. explored the potential of powder mixed EDM (PMEDM) on biomaterials (like Mg-based alloys, Ti-based alloys, Co-Cr-Mo-based alloys, etc.). They found that the PMEDM coating improves the biocompatible surface and mechanical properties.[[15]] Miller and Goswami studied LCP as an internal fixator in fracture healing.[[16]] Deprey et al. executed an in-vitro comparison of a great angle stabilized interlocking nail and LCP in compression, bending, and torsion. They found that the stable angle nail is more stable than the LCP due to the better distribution of stresses.[[17]] Niemeyer et al. found that LCP is more stable and reliable, especially in osteopenic and osteoporotic bone, providing more options for internal fixation.[[18]] Viberg et al. revealed a poor correlation amid biomechanical and clinical approaches to the proximal femur LCP. They found that biomechanical analyses may be unable to establish new implants. But its clinical studies are also essential to establish them as new implantable devices.[[19]] McDonald et al. studied Synthes variable angle LCP for distal femoral fractures on 113 patients and found it to have an acceptable failure rate for promoting union rate.[[20]] Sommer et al. studied 4 cases of LCP loosening and plate rupture. They have found that treatment failure is attributed to incorrect selection of the LCP or its fixation technique rather than the LCP's characteristic.[[21]] Hasenboehler et al. performed a minimally invasive plate osteosynthesis technique (MIPO) for LCP fixation in diaphyseal and distal tibial fractures for 32 patients. They found that 26 out of 32 have excellent secondary bone healing, and thus, MIPO using LCP instead of intramedullary nailing is a good technique for diaphyseal and distal tibia shaft fractures.[[22]] Zhou et al. studied a sophisticated 3D finite element model of middle femoral comminuted fracture to study the newly desired assembly LCP (NALCP) and conventional LCP. They found that NALCP could provide sufficient mechanical stability for comminuted fractures.[[23]]

Ghate et al.[[24]] studied laser surface modification for Ti6Al4 V biomedical implants. They compared surface roughness, microhardness, and wettability for laser machined implants with desired implant properties and found that the properties are in range. At the same time, Shubham Jain and Vishal Parashar studied the effect of EDM on biomedical materials. They concluded that the biocompatibility of EDM mechanized biomaterials increases due to better cell growth.[[25]] Keles et al.[[26]] investigated additive manufacturing for Ti6Al4 V alloys. They found that its applications in biomedical fields are due to the excellent compatibility with human cells and the excellent mass-to-toughness proportion of the alloy. They also concluded that 3D printing could help to make dental implants because of the low friction coefficient.

Devarasiddappa and Chandrasekaran employed preference-based TLBO on Ti6Al4 V alloy during WEDM. They found that the optimization improves the MRR by 40.51% and reduces the SR by 15.66% when comparing the highest preference and equal weight.[[11]] Karthik et al.[[27]] developed new AlCoCrFeNiMo0.5 high entropy alloy (HEA) particles reinforced aluminum composite by powder metallurgy and observed the effect of WEDM on it. They found that reinforcement % is the critical factor in HEA. TON contributes most to MRR, SR, and KW by ANOVA.

Chakala et al.[[28]] adopted the RSM and desirability approach to optimize the WEDM parameters for nitinol alloy. They found that TON and peak current are significant factors for SR and MRR. Payla et al.[[29]] examined the influence of WEDM parameters on MRR and power consumption. They concluded that TON increases power consumption, while wire tension does not affect power consumption. Jahare et al.[[30]] used a full factorial design when examining the WEDM parameters' effect on responses, such as MRR and Kerf width (kW). They found that when WEDM is performed on CoCrMo alloy, optimum KW is achieved at lower levels of Ton.

Phate et al. applied an adaptive neuro-fuzzy inference system (ANFIS) and response surface methodology (RSM) for modeling SR during WEDM on a newly fabricated 5% graphite-reinforced aluminum base composite.[[31]] K. Mouralova et al.[[32]] conducted 33 rounds of experiments by WEDM on the abrasion-resistant steel Creusabro 4800. Unwanted subsurface defects, such as burn cavities, were found. They also concluded that better surface quality was achieved at 60 V voltage, TON 8 microseconds, TOff 40 microseconds, discharge current 25 amps, and wire speed 12 m/min. Roy and Mandal modeled the responses to WEDM. At the same time, TON, Vgap, and flow rate were selected as input parameters. He verified the RSM model by the Monte Carlo method for 100,000 runs.[[33]]

Dey and Pandey selected a gray-based hybrid method to optimize surface roughness, kerf width, and cutting speed when performing WEDM on Al matrix composites. They found an improvement of 3.243% for kerf width and 7.053% for surface roughness.[[34],[35] Ubale and Deshmukh inspected the consequence of WEDM parameters such as Ton, Toff, Ip, wire tension, spark gap, and voltage on MRR and SR. They found that Ton is the most critical factor for WEDM on W-30 Cu metal matrix composites.

Kumar et al.[[36]] performed a WEDM analysis on titanium-based biomaterials. They found that voltage is an essential factor for surface quality.

Bharti optimized electric discharge machining through Taguchi's orthogonal array and then trained the data using a neural network-based approach. After obtaining 24 Pareto optimal solutions, they are ranked by the TOPSIS method.[[37]] Kandpal et al.[[38]] fabricated AA6061/10% Al2O3 aluminum metal matrix composites by stir casting. MMC was characterized using an energy dispersion X-ray analysis (EDX) and scanning electronic microscope (SEM). Then using Taguchi and the utility concept, the responses were optimized. They have found that overcut, SR, Tool Wear Rate (TWR), and MRR increase with an increase in TON and IP. But the duty factor has little effect on these responses.

Raj and Prabhu[[39]] analyzed WEDM on Ti alloy using GRA with PCA. They have found that a high pulse current level is the most critical factor in maximizing MRR. Pramanik et al.[[7]] have optimized WEDM on Ti alloy. At the same time, the responses are the characteristics of dimensional accuracies, such as cylindricity, circularity, and dimensional error. They have found that flushing pressure is the most critical factor for dimensional accuracy.

Kumar and Raj analyzed the rake face texture of a tool manufactured by WEDM while turning AISI4340 steel. The turnings are then compared by the textured tool and the untextured tool. They have found that the textured tool is superior to the untextured tool because of flank wear, cutting zone temperature, chip trace area, cutting force, and surface finishes.[[40]]

Singh et al. analyzed the improvement of EDM by powder mixed EDM with optimization. They obtained that MRR, TWR, and poor surface roughness could be improved using PMEDM compared to conventional EDM.[[9]] Bisaria and Shandilya have processed curve profiles on shape memory alloys. They found that during WEDM, the low pulse parameters reduced the corner error compared to the high pulse parameters.[[41]]

Sen et al.[[6]] analyzed the surface integrity of maraging steel 300 while performing WEDM. They have found that silver-coated brass wire is the best electrode material to achieve good surface integrity among various wire materials. They also concluded that good surface integrity is achieved at low discharge energy levels due to the uniform distribution of discharge energy. Khan[[42]] et al. analyzed the machinability of Inconel-800 considering various process parameters such as Ton, Zn layered brass wire, wire tension, cryogenic cooled Zn layered brass wire, and wire feed. At the same time, the responses were MRR and SR. They have found that cryogenic cooled wire and increased wire tension are the best conditions for WEDM on the Inconel-800.

Sharma et al[[43]] optimized WEDM for Ti6Al4 V alloy. Cutting speed and surface roughness were chosen as responses. The Taguchi L9 orthogonal array was used to plan the experiments. They have found that the optimum cutting speed is 0.2044 mm/min, and SR is 2.162 micrometer. They have found from the analysis of surface morphology that the crack intensity is higher due to higher discharge energy.

Sharma et al[[44]] investigated WEDM on a biomedical alloy namely Ti6Al4 V alloy. They have optimized the MRR and Rz using the Gray harmony search method. They found that the maximum MRR is 6.4 mm3/min and SR is 13.84 µm.

Materials & methods

The concept of the LCP plate evolved from the Dynamic Compression Plate (DCP). The AO Group developed the DCP plate during the 1960s.[[13]] DCP is used for conventional plating through friction between bone and plate. This obstructs the blood supply. However, DCP is a good decision when we fix simple fractures. After DCP, limited contact type DCP (LC-DCP) has come into play. This maintains the blood supply, and the bone is healed by reducing contact with the bone. However, the LCP became a versatile plate that reduces friction, allows the plate to move, and converts the axial force into compressive force. Hence LCPs are used for comminuted fractures. A combination hole is developed in the LCP. One hole is for the conventional screw, while the other locking hole is used to fix the locking screw, which has a threaded part on the head. So, when we use the LCP plate, it gives many combinations of the plate to fit. Hence according to the fracture type, the LCP plate is selected with the desired combinations. Hence it is necessary to study the LCP plate using different lengths and holes for the specific problem type. Hence LCP is one of the best plates for fracture. However, it has some drawbacks when used for simple fractures.[[16]]

ASTM std F-382 is the test method of the metal bone plate. While the following are the specifications for surgical implants of different materials, such as those for alloyed Ti, Ti6Al4 V extra low interstitial, and wrought, Ti-6Al-7Nb are F-67, F-136, and F-1295 respectively.[[45]]

All surfaces of the LCP bone plate are machined by CNC milling, while the sixth surface, which comes into contact with the bone, is machined by EDM. Therefore, in this study, the LCP profiles have been cut by WEDM to see the manufacturing aspect of WEDM for LCP plates. The CAD model of the LCP is shown in Fig. 1.

Graph: Figure 1. CAD model of LCP plate.

MRR is the response that shows how much material is eliminated from the sample per unit period by WEDM. Measurement of MRR as a response is done by measuring the weight of the sample formerly and after machining. At the same time, time is computed with the help of a stopwatch. Therefore, MRR is measured by the following equation 1:

(1)

Graph

$MRR=\frac{W_i-W_f}{Time}$

Here,

Graph

$W_i$ is the initial weight of the specimen,

Graph

$W_f$ is the weight of the specimen after machining, and Time is the machining time.[[46]]

The cutting speed is the speed that shows the length of the sample to be cut per unit of time. It points directly at the CNC WEDM monitor. The machining setup for the WEDM is shown in Fig. 2:

PHOTO (COLOR): Figure 2. WEDM set up.

Therefore, MRR and Cutting Speed have been chosen as the responses in this study. The LCP manufacturing aspect is observed in these responses.

LCP comes under Biomedical Implant. These biomedical implants are often made from Ti6Al4 V alloy. The properties required for a biomedical implant are surface roughness, biocompatibility, bifunctionality, and corrosion resistance. However, the Ti6Al4 V alloy meets a biomedical implant's properties.[[47]] Ti alloys also have a variety of combinations. Ti was first developed as a biomedical implant in the 1940s. After that, commercially pure Ti began to be used. Conversely, it has low strength and adverse wear resistance. Therefore, this limits the use of commercially pure Ti. This encourages the development of Ti alloys for biomedical implants.

Different Ti alloys are now available based on the microstructure at room temperature. Ti alloys have alpha phase Ti, beta phase Ti, and alpha+beta phase Ti. Whereas in the 1970s, ELI Ti6Al4 V alloy was formed. It was suitable for dental implants. But after some time, it was found that Ti6Al4 V has some toxic effects, but it is not entirely proven that this toxicity is due to vanadium (V). Then this V in Ti6Al4 V alloy was changed using Nb. Hence Ti6Al7Nb has been developed for biomedical use.[[47]]

Titanium is the fourth most ample material on the Earth's crust. But this is expensive because of its machining and extraction difficulty. Titanium-based minerals were first found in the late 18th century. After about 120 years, its extraction process changed significantly. Previously the Kroll process was used to obtain Ti metal by thermal reduction of TiCl4. Nowadays, there is more mass automation and continuous development. In the 21st century, Frey et al. developed an electrolytic process, but its stability and efficiency are still unavoidable. Therefore, self-propagating high-temperature synthesis (SHS) is a good option for Ti alloy extraction. However, even then, the widespread use of Ti alloys requires a cheap extraction process.[[48]] However, after extraction, there are also issues related to reducing the cost of Ti implants in machining. Some problems include maintaining high strength even at elevated temperatures, thin and serrated type chips, high power consumption, high chemical reactivity with tools, low modulus of elasticity, chattering, deflection, and rubbing. Due to these properties of Ti alloy, it is machined by unconventional machining like Spark EDM, WEDM, Laser Machining, etc.[[5]]

The Box Behnken Design (BBD) was applied in this study to design the experimental runs as the Response Surface Method (RSM). The BBD has a central point and other points at the center of the sides. This BBD is an almost rotatable design. The BBDs for the three factors and the three levels are shown in Fig. 3. This paper selects three levels of three parameters and two responses to design the experimental run.[[49]] This paper carried out 17 experimental runs, and a quadratic model (Eq. 2) was developed to predict the responses.

(2)

Graph

$Y=J_0+J_1{X}_1+J_2{X}_2+J_3{X}_3+J_{12}{X}_1{X}_2+J_{13}{X}_1{X}_3+J_{23}{X}_2{X}_3+J_{11}{X}_1^2+J_{22}{X}_2^2+J_{33}{X}_3^2$

PHOTO (COLOR): Figure 3. Box-Behnken Design for three process parameters.

Here Y, is the responses. X1, X2, and X3 are the distinct variables. There are X1X2, X1X3, and X2X3 interaction effects.

Graph

$X_1^2$ ,

Graph

$X_2^2$ , and

Graph

$X_3^2$ are quadratic effects. J0 is an intercept. J1-J33 are the regression coefficients.[[50]]

This article selects Ton, SV, and WT as process parameters. Cutting Speed & MRR are chosen as two responses. The process parameters' levels are shown in Table 1. The experimental chart for MRR and Cutting Speed is exposed in Table 2 below.

Table 1. Coded level of Process Parameters.

					Coded Value
Factor	Name	Units	Type	Sub Type	Low (−1)	Mean (0)	High (+1)
A	Pulse ON Time	Micro Seconds	Numeric	Continuous	9	11	13
B	Servo Voltage	Volts	Numeric	Continuous	20	30	40
C	Wire Tension	Gram	Numeric	Continuous	1000	1600	2200

Table 2. Experimental Chart for MRR & CS.

Std.	A: Pulse on Time	B: Servo Voltage	C: Wire Tension	Material Removal Rate	Cutting Speed	GRC MRR	GRC CS
Micro Seconds	Volts	Gram	mili gram/min	mm/min
1	9	20	1600	15.76	2.48	0.333333	0.441077
2	13	20	1600	38.4	1.04	0.643004	0.333333
3	9	40	1600	16.26	2.39	0.336917	0.432343
4	13	40	1600	38.04	1.08	0.633643	0.335611
5	9	30	1000	25.4	4.85	0.41932	0.942446
6	13	30	1000	42.78	3.41	0.783892	0.557447
7	9	30	2200	29.74	4.97	0.474417	1
8	13	30	2200	47.1	3.77	1	0.620853
9	11	20	1000	19.46	1.58	0.36181	0.366947
10	11	40	1000	20.16	1.7	0.367754	0.375358
11	11	20	2200	27.38	2.01	0.44278	0.398985
12	11	40	2200	22.46	2.09	0.388737	0.405573
13	11	30	1600	36.24	3.12	0.590652	0.515072
14	11	30	1600	28.16	3.23	0.452759	0.530364
15	11	30	1600	34.26	2.84	0.549632	0.479853
16	11	30	1600	34.62	2.9	0.556661	0.486989
17	11	30	1600	28.26	2.88	0.454071	0.484587

Grey relational analysis (GRA)

In this paper, Cutting Speed and MRR are taken as responses. For manufacturing purposes, both Cutting Speed and MRR must be maximized together. In single objective optimization, only one response must be optimized. But in multi-objective optimization, both the responses are optimized by assigning different weights to these responses. The weights for these responses are given by the gray relational analysis method.[[51]] The advantage of the GRA is that its test results govern it. So, a fitness function for multi-objective optimization can be given as (Eq.3):

(3)

Graph

$FitnessFunction=w_1\ast \left(\frac{1/MRR}{1/MR{R}_{max}}\right)+w_2\ast \left(\frac{1/CuttingSpeed}{1/CuttingSpee{d}_{max}}\right)$

Here, 1/MRR and 1/Cutting Speed are taken as single objective functions, while MRRmax and Cutting Speedmax are the maximum estimates of single objective MRR and Cutting Speed, respectively. 1/MRR and 1/Cutting Speed are taken because algorithms do the minimization while we must maximize these responses.

Whereas w1 and w2 are gray relational weights for MRR and Cutting Speed, respectively.[[52]] These are calculated by following Table 3.

Table 3. Weight calculation for objectives by GRA.

	MRR (milligram/min.)				Cutting Speed (mm/min.)
level	TON (micro seconds)	Vs (volts)	Wire Tension (gram)	level	TON (micro seconds)	Vs (volts)	Wire Tension (gram)
−1	0.39099	0.44523	0.4831	−1	0.703966	0.385	0.5605
0	0.46276	0.58682	0.5056	0	0.449303	0.624	0.4488
1	0.76513	0.43176	0.5764	1	0.461810	0.387	0.6063
R	0.37413	0.1550	0.0932	R	0.25466	0.239	0.1575
∑R	0.6224			∑R	0.6513
Weight	0.48868			Weight	0.51132

Cuckoo search algorithm

In the cuckoo search algorithm, the concept of cuckoo breeding behavior is used to optimize the responses. However, cuckoos are known for their captivating voice. The cuckoo replaces its eggs with eggs of some other species. First, the cuckoos lay their eggs in another species of bird's nest (See Fig. 4). The cuckoo then removes the host egg. The time of laying the cuckoo is also perfect. After that, when the cuckoo's chick explodes. Then it removes the host eggs and tries to imitate the host chicks to get more food. After that, if the host bird knows about the cuckoo, they throw the cuckoo's eggs or build a new nest at other locations using levy flight.[[12]] This way, CS is used to improve the responses.

PHOTO (COLOR): Figure 4. Cuckoo behavior & the nest.

The pseudocode and flow chart for the cuckoo search algorithm is shown in Figs. 5 and 6.

Graph: Figure 5. The pseudocode for the CS.

Graph: Figure 6. The cuckoo search algorithm flowchart.

PSO

PSO is a swarm intelligence technology. Kennedy and Eberhart established it. In this algorithm, a set of foraging behaviors of birds are used to optimize responses (see Fig. 7). In this, the position and velocity of each unit are first defined by Equations 4 and 5. Then the best particle solution and global solution are obtained. The velocity of each bird varies as the number of iterations increases. pbest and gbest get updated as iterations go on. The weight of velocity is updated according to equation 6.

PHOTO (COLOR): Figure 7. Particle behavior in PSO.

When the particle weight for velocity is greater, the algorithm is explored. In contrast, the weight of the velocity is less. So, it converges. The position and velocity of a particle are revised by the following equations 7 & 8.[[53]]

(4)

Graph

$Y\left(k,l\right)=lb\left(k\right)+randomnumber\ast \left(ub\left(k\right)-lb\left(k\right)\right)$

(5)

Graph

$\mathrm{V}\left(\mathrm{k},\mathrm{l}\right)=0$

(6)

Graph

$weight\left(k\right)=w_{max}-\left(\left(\frac{w_{max}-w_{min}}{ite{r}_{max}}\right)\ast iter\right)$

(7)

Graph

$X\left(k,l\right)=X\left(k,l\right)+V\left(k,l\right)$

(8)

Graph

$V\left(k,l\right)=weight\left(k\right)\times V\left(k,l\right)+Ph{i}_{01}\times randomno.\times \left(Ps\left(l,:\right)-S\left(:,l\right)\right)+Ph{i}_{02}\times randomno.\times \left(gs-S\left(:,l\right)\right)$

Here,

Y (k, l) is the position of the lth particle at kth iteration, and V (k, l) is the velocity of a lth particle at kth iteration. Phi01 & Phi02 are non-negative learning factors. Ps (l, :) is the personal best position of an lth particle at kth iteration, while gs is the global best position at kth iteration.

The PSO's pseudocode and flow chart are shown in Figs. 8 and 9.

Graph: Figure 8. The particle swarm optimization pseudocode.

Graph: Figure 9. The flowchart for the Particle Swarm Optimization.

Results & discussion

Experimental study of MRR

MRR was selected as the response in this paper. The quadratic model is best suited for MRR with an R2 value of 0.9466, which is very close to 1. Here, the difference amid adj R2 and pred R2 is smaller than 0.2. So, it is found that the quadratic model can estimate the MRR very accurately. As stated by ANOVA, the linear consequence of TON and the quadratic impact of V & TON is the most critical factor effect of MRR. The ANOVA table and regression result for MRR is shown in the following Table 4 and equation number 9:

(9)

Graph

$MaterialRemovalRate=+1.07485-18.64008\times PulseONTime+6.16682\times ServoVoltage+0.014573\times WireTension-0.010750\times PulseONTime\times ServoVoltage-4.16667E-06\times PulseONTime\times WireTension-0.000234\times ServoVoltage\times WireTension+1.08713\times PulseONTim{e}^2-0.095415\times ServoVoltag{e}^2-1.11528E-06\times WireTensio{n}^2$

Table 4. Analysis of Variance for MRR.

Source	Sum of Squares	df	Mean Square	F-value	p-value
Model	1285.81	9	142.87	13.77	0.0011	significant
A-Pulse ON Time	783.29	1	783.29	75.52	<0.0001
B-Servo Voltage	2.08	1	2.08	0.2006	0.6678
C-Wire Tension	44.56	1	44.56	4.30	0.0769
AB	0.1849	1	0.1849	0.0178	0.8975
AC	0.0001	1	0.0001	9.642E-06	0.9976
BC	7.90	1	7.90	0.7613	0.4118
A2	79.62	1	79.62	7.68	0.0277
B2	383.33	1	383.33	36.96	0.0005
C2	0.6787	1	0.6787	0.0654	0.8054
Residual	72.60	7	10.37
Lack of Fit	14.39	3	4.80	0.3297	0.8056	not significant
Pure Error	58.21	4	14.55
Cor Total	1358.42	16

The normal plot of residuals indicates that the regression model is the best fit (Fig. 10). The residual versus predicted plot shows no pattern across experiments (Fig. 11). Therefore, no transformation is required for the regression model of MRR (Fig. 12).

Graph: Figure 10. MRR Residuals vs Normal Plot.

Graph: Figure 11. MRR Residuals vs Predicted plot.

Graph: Figure 12. MRR Box-Cox plot.

The perturbation plot (Fig. 13) for MRR shows that with a rise in Ton, MRR increases. Because of greater discharge energy at elevated Ton, higher molten material is removed, hence higher MRR. Whereas at some optimal value of servo voltage, MRR rises. Because of good flushing at optimum servo voltage, MRR is high. In comparison, wire tension has a very negligible effect on MRR.

Graph: Figure 13. MRR Perturbation plot.

Experimental study of cutting speed

Cutting Speed is a response to WEDM. It indicates how much length is cut by WEDM in a unit of time. ANOVA shows that the quadratic model is finest suited for Cutting Speed. The difference between Adj R2 and Pred R2 is significantly less (Table 5). Therefore, the model can accurately predict Cutting Speed. ANOVA also suggests a linear effect of Ton and WT. At the same time, the quadratic effect of Ton, WT, and V is the most critical factor for Cutting Speed. The ANOVA table (Table 6) and regression equation for Cutting Speed (eq. no.10) are shown below:

(10)

Graph

$CuttingSpeed=+13.44930-3.65150\times PulseONTime+1.08212\times ServoVoltage-0.006245\times WireTension+0.001625\times PulseONTime\times ServoVoltage+0.000050\times PulseONTime\times WireTension-1.66667E-06\times ServoVoltage\times WireTension+0.144813\times PulseONTim{e}^2-0.018257\times ServoVoltag{e}^2+1.87986E-06\times WireTensio{n}^2$

Table 5. Fit statistics for Cutting Speed.

Std. Dev.	0.1419
R2	0.9932
Predicted R2	0.9726
Adjusted R2	0.9844
C.V. %	5.20
Adeq Precision	36.7953
Mean	2.73

Table 6. Analysis of Variance for Cutting Speed.

Source	Sum of Squares	df	Mean Square	F-value	p-value
Model	20.45	9	2.27	112.88	<0.0001	significant
A-Pulse ON Time	3.63	1	3.63	180.42	<0.0001
B-Servo Voltage	0.0028	1	0.0028	0.1397	0.7196
C-Wire Tension	0.2112	1	0.2112	10.50	0.0143
AB	0.0042	1	0.0042	0.2099	0.6607
BC	0.0004	1	0.0004	0.0199	0.8919
AC	0.0144	1	0.0144	0.7154	0.4256
A2	1.41	1	1.41	70.19	<0.0001
B2	14.04	1	14.04	697.30	<0.0001
C2	1.93	1	1.93	95.81	<0.0001
Residual	0.1409	7	0.0201
Lack of Fit	0.0238	3	0.0079	0.2707	0.8443	not significant
Pure Error	0.1171	4	0.0293
Cor Total	20.59	16

From one factor at a time, it is concluded that the Cutting Speed decreases marginally as the pulse on time increases (Fig. 14 (a), (b) & (c)). Because more energy is discharged at higher Ton and more molten material is handled, the Cutting Speed is reduced due to higher Kerf Width. Whereas the Cutting Speed increases at the optimum value of V, there is a reasonably good discharge of the molten material. When the tension of the wire increases, Cutting Speed decreases. But when the tension of the wire is further increased, the Cutting Speed increases significantly due to the less loosening of the wire. The perturbation plot (Fig. 15) and 3D plot for Cutting Speed (Fig. 16(a) & (b)) are shown below:

Graph: Figure 14. Cutting Speed One factor plot with (a) Pulse on Time (b) Servo Voltage (c) Wire Tension.

Graph: Figure 15. Cutting Speed Perturbation Plot.

Graph: Figure 16. Cutting Speed surface plot for (a) Ton vs SV, (b) Ton vs WT.

Microstructure Analysis

Surface analysis of Ti6Al4 V alloy before WEDM and after WEDM is described in this section. The scanning electron microscope (SEM) is a high-resolution field emission scanning electron microscope (HR-FESEM).[[39]] This setup is of ZEISS model name ULTRA PLUS and is from Germany. This SEM setup is used to take pictures to analyze surface quality. All SEM micrographs were taken at a magnification of 1.5 K. The SEM micrographs are shown by Figs. 17(a) and 17(b). These data are associated with the experimental results without EDM conditions and with EDM at maximum MRR conditions.

Graph: Figure 17. SEM image of Ti6Al4 V alloy for (a) without machining and (b) after WEDM at maximum MRR optimized condition.

The surface morphology of WEDM machined Ti alloy is investigated by analyzing craters, voids, debris, small cracks, and globules. Whereas these surface characteristics can be changed by various machining input parameters such as tonnage, Vgap and wire tension. It is found that the EDM machined surface morphology is much worse than that without EDM machining. This is achieved at high Ton, moderate interval voltage, and high wire tension. Here a rougher biocompatible surface is obtained at 13 microsecond ton, 30 volt voltage, and 2200 g tension.

The SEM result is shown in Fig. 17(a). It shows that without machining conditions, the surface is smoother. Whereas Fig. 17(b) shows some cracks and debris vacancies, which are used to increase the biocompatibility. As it is the fact that a relatively rough surface is helped to improve biocompatibility. So, it is determined that WEDM enhances the biocompatibility of Ti alloy.

Multi-objective results

This article compares the CS and PSO on preference-based multi-objective optimization. This PBMOO is used to optimize multi-responses like MRR and Cutting Speed.[[11]] At the same time, in equations (9) and (10), the regression equation for MRR and Cutting Speed is presented. These regression equations are prepared by experimental analysis of DOE software. The multi-objective optimization function is formulated in Equation 3.

Here, (In equation 3) preference factors (w1) & (w2) are considered in the range of 0 to 1 in the step of 0.05, as w1+w2 = 1. The composite function was analyzed. A modern PC with a 1.6 GHz CPU, 64-bit OS, & 8 GB RAM was used for the analysis. For the CS and PSO, the tuning parameters are shown in Table 7 below.

Table 7. Tuning Parameters for CS & PSO.

Cuckoo Search Algorithm	Particle Swarm Optimization
Population 20	Population 20
Iteration 1000	Iteration 1000
Discovery Rate 0.25	Learning Factor Phi01 0.5 Phi02 0.5
Levy Exponent 3/2	Weightage of velocity 1 to 0.3

The optimization algorithm was executed ten times at each level of the weight combination, and the desired optimal (max) values are assumed to be the best value for that weight. Here the individual results for optimal MRR and optimal Cutting Speed are shown in the table below (Tables 8 & 9). 19 combinations of step weights, two varieties of the single objective, and GRA method-derived weights are used to optimize the responses.

Table 8. Optimum Results of PBMOO-CSA.

S.No.	W1 (MRR)	W2 (Cutting Speed)	Parametric Settings	Optimum MRR (mg/min)	Optimum Cutting Speed (mm/min)	Minimum Fitness value
1.	0.48868	0.51132	13 µ sec, 29.876 V, 2200 g	59.3377	3.7980	1.1710
2.	0	1	9 µ sec, 29.935 V, 2200 g	39.5428	5.0625	5.0625
3.	1	0	13 µ sec, 28.88 V, 2200 g	59.4312	3.7715	59.4312
4.	0.05	0.95	9 µ sec, 29.900 V, 2200 g	39.3047	5.0059	1.0273
5.	0.10	0.90	9 µ sec, 29.854 V, 2200 g	39.5304	5.0245	1.0486
6.	0.15	0.85	9 µ sec, 29.8132 V, 2200 g	39.4330	5.0151	1.0759
7.	0.20	0.80	9 µ sec, 29.772 V, 2200 g	39.5687	5.0186	1.0996
8.	0.25	0.75	9 µ sec, 29.731 V, 2200 g	39.5108	5.0200	1.1249
9.	0.30	0.70	9 µ sec, 29.6903 V, 2200 g	39.5839	5.0198	1.1493
10.	0.35	0.65	9 µ sec, 29.649 V, 2200 g	39.5364	5.0194	1.1750
11.	0.40	0.60	13 µ sec, 29.937 V, 2200 g	59.1344	3.7853	1.1965
12.	0.45	0.55	13 µ sec, 29.904 V, 2200 g	59.3540	3.7874	1.1784
13.	0.50	0.50	13 µ sec, 29.867 V, 2200 g	59.3839	3.7675	1.1655
14.	0.55	0.45	13 µ sec, 29.825 V, 2200 g	59.4003	3.7852	1.1459
15.	0.60	0.40	13 µ sec, 29.777 V, 2200 g	59.3500	3.7877	1.1298
16.	0.65	0.35	13 µ sec, 29.7235 V, 2200 g	59.2977	3.7905	1.1138
17.	0.70	0.30	13 µ sec, 29.660 V, 2200 g	59.3080	3.7872	1.0980
18.	0.75	0.25	13 µ sec, 29.587 V, 2200 g	59.2630	3.7897	1.0821
19	0.80	0.20	13 µ sec, 29.499 V, 2200 g	59.1576	3.7913	1.0674
20.	0.85	0.15	13 µ sec, 29.394 V, 2200 g	59.3106	3.7972	1.0489
21.	0.90	0.10	13 µ sec, 29.264 V, 2200 g	59.3682	3.7667	1.0331
22.	0.95	0.05	13 µ sec, 29.100 V, 2200 g	59.2816	3.7947	1.0174

Table 9. Optimum Results of PBMOO-PSO.

S.No.	W1 (MRR)	W2 (Cutting Speed)	Parametric Settings	Optimum MRR (mg/min)	Optimum Cutting Speed (mm/min)	Minimum Fitness value
1.	0.48868	0.51132	12.993 µ sec, 29.749 V, 2199.3 g	59.2890	3.7930	1.1654
2.	0	1	9.001 µ sec, 29.361 V, 2198.5 g	39.5836	5.0155	5.0155
3.	1	0	12.994 µ sec, 28.973 V, 2198.7 g	59.3632	3.7704	59.3632
4.	0.05	0.95	9.003 µ sec, 30.887 V, 2199.6 g	39.3047	5.0059	1.0273
5.	0.10	0.90	9.000 µ sec, 29.9744 V, 2199.4 g	39.5304	5.0245	1.0486
6.	0.15	0.85	9.001 µ sec, 30.320 V, 2197.0 g	39.4330	5.0151	1.0759
7.	0.20	0.80	9.004 µ sec, 29.667 V, 2199.0 g	39.5687	5.0186	1.0996
8.	0.25	0.75	9.005 µ sec, 30.123 V, 2199.7 g	39.5108	5.0200	1.1249
9.	0.30	0.70	9.000 µ sec, 29.4891 V, 2199.1 g	39.5839	5.0198	1.1493
10.	0.35	0.65	9.003 µ sec, 29.876 V, 2198.5 g	39.5364	5.0194	1.1750
11.	0.40	0.60	12.9829 µ sec, 29.9044 V, 2196.8 g	59.1344	3.7853	1.1965
12.	0.45	0.55	12.9988 µ sec, 29.5415 V, 2197.9 g	59.3540	3.7874	1.1784
13.	0.50	0.50	12.9989 µ sec, 28.9757 V, 2197.1236 g	59.3839	3.7675	1.1655
14.	0.55	0.45	12.999 µ sec, 29.3163 V, 2199.205 g	59.4003	3.7852	1.1459
15.	0.60	0.40	12.9987 µ sec, 29.5635 V, 2197.9 g	59.3500	3.7877	1.1298
16.	0.65	0.35	12.9912 µ sec, 29.5889 V, 2199.5 g	59.2977	3.7905	1.1138
17.	0.70	0.30	12.9986 µ sec, 29.7341 V, 2196.6 g	59.3080	3.7872	1.0980
18.	0.75	0.25	12.996 µ sec, 29.9148 V, 2199.3 g	59.2630	3.7897	1.0821
19	0.80	0.20	12.9983 µ sec, 30.4519 V, 2198.0 g	59.1576	3.7913	1.0674
20.	0.85	0.15	12.9986 µ sec, 29.9285 V, 2199.6 g	59.3106	3.7972	1.0489
21.	0.90	0.10	12.993 µ sec, 28.845 V, 2199.5 g	59.3682	3.7667	1.0331
22.	0.95	0.05	12.998 µ sec, 29.9954 V, 2198.6 g	59.2816	3.7947	1.0174

By adopting this PBMOO, the mean of MRR and Cutting Speed is calculated, and a t-test is performed for both CS and PSO. For this t-test, the null hypothesis was assumed that both algorithms give the same result. At the same time, the alternative hypothesis is that the two algorithms give different results.[[54]] For this t-test of Cuckoo Search and PSO, Table 10 below shows the different parameters.

Table 10. T-test comparison of CS & PSO.

Algorithms	Mean optimized Results	Size of samples	DoF (Degree of freedom)	Standard Deviation	Types of Hypotheses	t-score	p-value	Results
MRR
CSA	52.16988 (µ1)	22	42	3	The null hypothesis is such that µ1=µ2	0.07158	0.9432	Null-Hypothesis cannot be rejected
PSO	52.10513 (µ2)	22	The alternative Hypothesis is µ1≠µ2
Cutting Speed
CSA	4.24246 (µ1)	22	42	3	The null hypothesis represents µ1=µ2	0.010127	0.9919	Null-Hypothesis cannot be rejected
PSO	4.23330 (µ2)	22			Alternative Hypothesis µ1≠µ2

From this t-test, it is obtained that for both CS and PSO, the p-value is greater than 0.05; hence, the null hypothesis cannot be excluded. This infers that MRR and Cutting Speed give almost identical results for both algorithms. But as the No Free Lunch Theorem (NFL) says, a particular algorithm produces improved results for a specific problem, and no one is perfect. Whereas for other problems, another algorithm is promising. The above table shows that CS gives somewhat better results than PSO. But the elapsed time for PSO is less than for CS. The time elapsed for the algorithm's execution depends on the algorithm's complexity and the operating system used.

The PBMOO for CS and PSO shows that when we prioritize the individual response. So, it gives a more favorable result for that response.

The convergence curve indicates how many iterations it gives the best optimal value. From the convergence curves of MO-PSO and MO-CS, it is clear that the cuckoo search algorithm converges the function much more quickly than the particle swarm optimization. Whereas the Pareto Front indicates how much the responses interacted with each other. The Pareto Front of MO-CS found that the cutting speed is lower at higher material removal rates (due to higher Kerf width at higher MRR). In comparison, the Pareto front of MO-PSO indicates that both the responses are scattered. The convergence curve and the Pareto front figure are shown in Figures 18 & 19 below.

Graph: Figure 18. Multi-objective Cuckoo Search Optimization Pareto front & convergence curve.

Graph: Figure 19. Multi-objective PSO Pareto front & convergence curve.

The MRR and cutting speed are chosen as the responses in the present work. Whereas these reactions are of better type. But comparatively cutting speed weightage is better type and MRR weightage is comparatively smaller better type, as kerf width should be minimum. MRR, kerf width, and cutting speed, are correlated as follows:

(11)

Graph

$\mathrm{M}\mathrm{R}\mathrm{R}\propto \left(\mathrm{K}\mathrm{e}\mathrm{r}\mathrm{f}\mathrm{W}\mathrm{i}\mathrm{d}\mathrm{t}\mathrm{h}\times \mathrm{C}\mathrm{u}\mathrm{t}\mathrm{t}\mathrm{i}\mathrm{n}\mathrm{g}\mathrm{S}\mathrm{p}\mathrm{e}\mathrm{e}\mathrm{d}\right).$

Because Ton is the most important factor for MRR, kerf width and cutting speed. When increasing Ton, MRR, and kerf width increases. But the width of the kerf should be minimum. So, the cutting speed should be better than the MRR.

Conclusion

The article compared PBMOO-based CS & PSO, while WEDM was performed on Ti6Al4 V alloy. It was found that CS gives somewhat better results than PSO. The critical conclusions are appended below:

• MRR is maximum at high Ton (13 micro-seconds), medium voltage (28.88 volts), and high tension (2200 g).
• Cutting Speed is maximum at lower Ton (9 microseconds), medium voltage (29.9359 Volts), & higher tension (2200 grams).
• PBMOO is considered for CS and PSO to optimize MRR and Cutting Speed. It is achieved that CS gives somewhat better results than PSO.
• The GRA sets a weighting of 48.869% for MRR and 51.13% for Cutting Speed.
• The multi-objective optimization by CS shows that at 13 micro-seconds, 29.876 volts, and 2200 g, the maximum MRR is 59.3377 milligram/min and Cutting Speed 3.7980 mm/min.
• Multipurpose optimization by GRA PSO shows that at 12.9932 microseconds, 29.7496 volts, and tension of 2199.3 g, the optimum MRR is 59.2890 mg/min, and Cutting Speed is 3.7930 mm/min.
• SEM images of the WEDM machined surface have more voids and craters than the unmachined surface. Therefore, WEDM can enhance biocompatibility.

The future scope of this work is to investigate other process parameters such as Toff, duty cycle, peak current, wire feed and various wire materials of WEDM on Ti6Al4 V alloy to analyze the machining, fabrication, and biomedical aspect. Furthermore, by developing more exploring metaheuristic algorithms and hybrid type metaheuristic algorithms, better and more accurate results can be obtained.

Disclosure statement

No potential conflict of interest was reported by the authors.

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By Shubham Jain and Vishal Parashar

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