Multi response Particle Swarm Optimization of Wire Electro Discharge Machining parameters of Nitinol alloys

The conventional process of Machining of Nitinol alloy leads to extensive wear on the tool and deprived surface quality. Wire electro discharge machining (WEDM) is widely accepted for machining this alloy involving various input factors, namely, P, (pulse-on-duration), Q, (pulse-o ﬀ -duration), C, (maximum-current), and V, (voltage). The factor’s effect on MRR (metal removal rate) and SR (surface roughness) responses and multi-response optimization of the WEDM process by employing PSO (particle swarm optimization) method are studied. The relationship model between factors and response characteristics were generated by ANOVA and optimized by response surface methodology has shown more signicant factors (A and C). Though the effect of WEDM process factors on SR and MRR are contradictory when studied individually. MRPSO method was employed to get the best optimum condition for minimizing SR and maximizing MRR. MRPSO results improved the responses for vast combination of optimal setting of factors to meet the product requirements.


Introduction
The present development of science and technology demands the parts made of materials having strong (higher strength) and lightweight (low density) in the form of newer materials. Various alloys are available, especially the combination of Nickel and Titanium forms Nitinol alloy has been widely used as one of such favorable metal possessing the desired properties. These properties shape remembering effect, pseudo adaptability, creep, and corrosion resistance, etc. along with them adding other blending material such as Cu enhances phase changing temperature levels, immediate response to stimulation, cyclic, and vibration damping characteristics. These alloys are innovative metallic alloys nd their applications mostly in aerospace and automobile elds, medicinal as well as dental elds [1]. Apart from the above said major elds.
Their direct application is found in couplers, sealings, simulators, turbine components, scramjet combusting chamber, etc. Traditional machining process on these alloys with a good surface nish to a higher order of precision for attaining their outstanding characteristics make di cult, laborious, and expensive to apply. Advanced machining plays an important role in reckoning properties of the alloys, saving labor, production cost, quick and simpli cation of the process to be implemented.
One of the signi cant characteristics of alloys of low thermal conductivity materials is undergoing Strain hardening in Nickel and Titanium-based alloys, Super and shape memory alloys, etc. as they are complicated to apply xed machining processes like turning, drilling, boring, milling, etc., as well as causing excessive wear and sticking of chips on the tool. Various advanced machining processes like ECM (electro-chemical), EDM (electro-discharge), AJM (abrasive-jet), WEDM (wire-electro-discharge), laser, hybrid machining processes, etc. in which WEDM has proved most adaptable un-conventional machining procedures to hard metals and their alloys in any proportions forming different alloys discharging is affected by breakdown voltage as the wire (made of Cu, brass, Mo, Al, and Graphite) is bolstered through workpiece [2]. Graphite wire because of its high melting point temperature Material Removal rate (MRR) is higher compared to Cu wire, which increases hardness due to Titanium carbide developed on the surface. In contrast, the Aluminium wire provides a good surface nish. As WEDM develops high temperature procedure produces reformed and subdued surfaces affected by heating introduce residual tensile stresses, causing rupture [3,4]. The surfaces produced with short and long pulses of discharge current had shown the same surface roughness even with the constant pulse energy. Still, the distribution of surface nish found different [5,6]. Response features (MRR and SR) on input factors of shape memory alloy (Ti50Ni42.4Cu7.6) were investigated.
A combination of low values of maximum-current (C) and instant Pulse-on-duration (P) become more helpful for maximizing MRR than to minimize SR with a large amount of Pulse on duration is needed. The effect of WEDM factors during machining the Ti50Ni49Co1 surface of SMA developing poor surface quality at a higher value of P and rich surface nish at high speed. Response surface methodology (RSM) for modeling and optimizing WEDM factors of Nickel-based superalloy using the desirability approach has been carried out [7]. On Nimonic-80A, optimization of MRR and wear a fraction of wire using Taguchi with performed experiments of the WEDM process [8]. RSM optimization of the outputs of SR and measurement variation of the WEDM process used in pure titanium performed [9,10].
The fuzzy controller, along with its magni cent economic algorithm for handling the intricacies in solving regular manufacturing optimization challenges, was suggested [11,12]. But surveys of the sources show no systematic studies of the input factors affecting the surface nish and MRR through the WEDM process applied on Nitinol (Nickel-Titanium) alloy. Consequently, this study emphases evaluating the effect of input factors, namely P, Q, C, and V, on Nitinol alloy machining characteristics (MRR and SR). So, in current research, the plan of the experiment was prepared with CCD standards to elucidate the combined impact of factors on response features of Nitinol alloy consuming electrode wire made of "molybdenum." Hence, important regression models were generated for investigating the in uence of P, Q, C, and V on responses utilizing RSM involved higher degree models. Optimization essentially looks for the probable superior set of factors either for maximizing/ minimizing the responses [13]. Various ways of optimizing the input factors of other processes and WEDM have been employed in the earlier work for single/multiple responses, namely, Taguchi design, RSM, Grey relation approach. Such techniques can suitably handle the single optimization response but not for multi-factor multi objectives as their results contradict in concluding [14]. In 1995, Kennedy and Eberhart offered PSO technique as a tool for transforming evolutionary procedure to the optimization of the performance characteristics very rst time [15]. The PSO algorithm used for solving reliable non-linear updating problems after recognizing the actions of the ecological swarm bird returning to settle back, which detected in several categories of aerial organisms [16]. PSO generates top score measures within a short estimation time, as well as a steady combination of factors [17]. Since the capability of the PSO system for executing the top score of the process, many engineers/researchers realize it as a fruitful decision over many issues, especially while managing multiple-goal updating matters [18].
Advanced and evolving procedures attaining success in solving multi-dimensional objectives with several con ned targets and one of them is the PSO approach (stochastic optimization) which make use of a population of random solutions to search the optimum one from the various generations developed by initial community similar to management of a bird ock. It falls in the category of evolution algorithms like a statistical search mechanism. Additionally, the PSO is extending to deal with multi-objective optimization (MOO) problems, and PSO procedures are easy to implement due to their simple mathematical and logical operators, which make itself computationally less complicated [19]. Swarm information is considered as a genetic, and arti cial intelligence depends on the joint performance in regionalized self-prepared structures.
Excellent surface nish and the high metal removable rate of Nitinol alloy is a stimulating topic in the eld of production. The study available on this WEDM machining method is limited. In this scenario, the prevailing study is on investigating the impact of factors on machining characteristics (SR and MRR). Furthermore, multi-output/ objective PSO involving genetic algorithm with multi outputs along with Pareto font is applied to acquire the top-scored optimum set of factors for maximizing and minimizing the MRR and SR, respectively. Presently no research work about the application of PSO for multi objectives of the WEDM method of Nitinol alloy. Using a set of strategic trials, the tness function to optimize responses were changed in the mathematical model form and using ANOVA, the importance of it in the way of the RSM model is examined. The optimum setting of WEDM process factors was achieved by employing a multi-output genetic algorithm based PSO, and PSO performances of Pareto front solutions were compared and validated.

Materials And Methods
Workpieces made of commercially available material Nitinol alloy (Nickel-Titanium alloy) were prepared for machining using WEDM. The development of numerical models is very critical in the production process to develop parts in a short time at the lowest machining cost. The realistic model using RSM can develop a compromising relationship of input factors and responses [11]. In RSM, the noticeable interaction between input factors and output is expressed as follows. (1) Where Z, the output characteristic to be optimized and h, the objective function consists of both dependent and independent factors a1, a2, a3 . . . . . . . . . . an, along with xing errors. The optimization of WEDM factors involved in the machining of an Aluminium alloy 5754 produced by friction-stir-welding using the Taguchi design method, for experimentation planning in an orthogonal array format to take all various possible combinations of factors and their levels . To improve the quality and accuracy of the WEDM process, Taguchi parametric design and RSM were employed. In this attempt, face-centered composite design (CCD) was used to develop mathematical models for the MRR and SR and to study parameters in uence on accuracy. RSM seems to be a suitable method to analyze and optimize the input factors. This method increases not only e ciency but also product authority [8,9,20]. The process factors in uencing signi cantly on the MRR and SR responses are Pulse-on-duration, P, Pulse-off-duration, Q, maximum-Current, C, and Voltage, V. Table 1 details the chosen process factors at the various range. The mathematical model using RSM will be used to develop the tness function required for the PSO technique. In PSO, Multi-object optimization, along with a genetic algorithm, will be performed by MATLAB optimization toolbox using Pareto front solver.

Experimental Details
All trials on Nitinol parts using CNC Wire cut EDM were carried out, having a 0.2 mm diameter wire made of molybdenum (Mo) as electrode material. Mo wire has various advantages like high molten temperature as well as ultimate strength while producing complex shapes parts of aerospace and missile. Care must be taken about the wire diameter and the deionized water's pressure to use it as a dielectric liquid, keeping at around 2.6 kg/cm2, which should not vary. The trials were collected targeting CCD full fraction for all factor combinations occurring at higher (3) and lower (1), i.e., two levels and multi-responses (MRR and SR) of the WEDM process were tabulated in Table 2.
Where the Measurement of Surface roughness is done by employing the surface roughness tester (Taylor Hobson pro lometer) conducting at three different portions of the surface, and the average value of it presented in micrometers. Multi-Objective Optimization (MOO) using PSO Every particle in the group having a velocity vj(f) with that it can ee into the illustration area and can be characterized by a velocity vj(f) and position xj(f) vector. Their elements are well-expressed by the various input factors in the optimizing process. Modi cations of the particle location are done by employing its preceding position data and its present velocity. Thus Where vj(f) and xj(f) are the velocities and current position at iteration f; Pbestj and Gbestj are the personal and the global best position of particle j respectively; rand, w, c1, and c2 are the random number (from 0 to 1), the weighting function, the cognition, and social learning rate respectively.
The random numbers produce velocities updated in PSO are statistical may instigate an uncontrollable rise in velocity as well as the uncertainty of the search algorithm. This is prevented using the Pareto front algorithm along with a genetic algorithm by carrying out multiobjective PSO.
Multi-objective states yield an optimum set of solutions for input factors in the place of a single solution. They often include disagreeing responses such that one objective gets improved by causing a decline in solution. Two universal methods to MOO either by combining each objective function into a solo compound function or change entirely, leaving one response to the constraint group. The key gain of such a "weighted-sum" method is allowing an open application as well as numerically effective. The second universal method is to establish a complete Pareto front-optimum solutions group or an illustrative subgroup. The solution that can improve any response by deteriorating individual or more responses is known as nondominated (ND) solutions. The purpose of executing a MOO is to obtain a set of ND solutions, stabilizing the transaction among disagreeing responses called a Pareto set. The proposed work involves maximizing MRR along with minimizing SR.

Results And Discussion
In uence of Input factors on Responses MRR and SR Experimental results obtained based on CCD were investigated to nd the in uence of various input factors on the responses (MRR and SR) using ANOVA at 0.05 level signi cant. ANOVA for MRR and SR (refer to Table 3 and 4) with the small value of probability indicates a larger value of correlation coefficient. According to the RSM investigation, the quadratic model used is statistically signi cant for both MRR and SR. The "coefficient of determination" R2 attaining 1 indicates the output characteristics tting the real data, and this even helps in checking predicted and adjacent R2 (i.e., Pred-R2 and Adj-R2) reached unity. Above 90% for R2 as well as Adj-R2 of both machining characteristics (MRR and SR) shows that the mathematical model developed by regression has a good relationship between process factors and output results. The inputs like P, square terms -CXC, and interaction terms-PxC, are found to be most signi cant. V, Q, and C are found to an insigni cant process parameter for MRR. Similarly, the ANOVA table for SR shows that C, P, and Q, and square term-CxC are essential to process parameters. V is found to be insigni cant input factors for SR.    to 4A) may severely decrease the MRR without even increasing the Pulse on time as it encourages swift melting along with alloy vaporization. But the mid-side value of C might improve MRR up to A=37.5 µs and remains same up to 45 µs and then MRR increase further irrespective of A and C change after 45 µs because high value of C directs a large amount of energy hooked on the targeted area to remove the higher amount of metal along with impulsive forces in the dielectric uid for taking away molten metal of targeted area. The MRR also gets increased due to change of shape as well as the size of surface pits, pores, etc., with an increase in C., whereas factors B and D have a counter effect on MRR, i.e., they contribute to MRR value only if A and C are also changing. The interactions of the input factors on SR are depicted in Figures 3 (a) to (f). At a low value of C, SR reduces with increasing A because of low impulsive forces retaining longer time. But at higher C, SR increases along with the A because high impulsive forces along with sparks and maintaining a more extended time would damage the surface, and hence SR increases. The pits, pores increase due to the high rate of erosion of an alloy. It is also noticed that low thermal conductivity and melting point gives a higher SR .
The decisive empirical formed equations of machining characteristics (MRR and SR) are characterized in Eq. (4) Table 6. The desirability need not always be equal to one, but its value discloses the proximity of the margins set pertaining to the real optimum values. An optimal set of factors using Minitab 19 software was evaluated and presented in Table 5. Once the optimum values are achieved, it becomes necessary to validate to check the con rmation with experiments at these optimal values. Table 6 gives % error for con rming with experimentation results of WEDM and found very small, which is acceptable by the researchers.  The desirability gradient and line graph of the WEDM process (refer Figure 4) shows the di value obtained for each response generated between low and high values. If the targeted responses di value is closer to 1 show having good desirability, then the desirability is good. The global desirability D = 0.8748 shows closeness of responses to the target set.

Results of MOOPSO
The PSO technique was applied, keeping in mind that both should not be minimized as when SR reduces by minimizing the objective function, the MRR also gets reduced. But we need the maximization of MRR while minimizing the SR. To avoid con ict between objectives of MRR and SR and to achieve higher MRR and lower, the optimum set of input factors are to be located. Thus, the objective function of MRR is altered into minimization form in the following way as below: To achieve MO optimization as per speci c goal, a PSO toolbox of MATLAB program was employed to execute the source code of the anticipated algorithm. Distribution of Pareto front containing 100 optimum sets of factors satisfying the condition of both functions. Figure 5 showing the Pareto front distribution of top scored ND solutions out of the 100-optimum set of populations while performing optimizations of two functions. The best solution depends on product requirements or upon the choice of engineer for a speci cally designed process. MOOPSO forecasted the nest results within levels of factors. Top scored solutions come from 100 top global solutions, but only the nest 25 solutions are provided in Table 6. After both analysis and comparing with empirical outputs of MRR using Pareto front, the maximum value of 3.5420068 mm3/min is found at pulse-on-duration of 25.1118229 μs, pulse-off-duration of 12.3503394 μs, C of 2.009124 amp and V of 45.120498 volts, with corresponding to experiment no. 27 in Table 2 where the maximum MRR = 3.5663.23mm3/min at pulse-on-duration =25 μs, Q = 14 μs, C = 14 amp, and V = 50 volts. The MRR of the Pareto front optimal solution exhibits their values are slightly lesser than the experiment results. Furthermore, the 3-D MRR output plot (referring Figure 5) reveals that the MRR decreasing as the Pulse on time and C increases. The proper combination of input factor levels may yield a higher value of MRR. It is also found that minimum MRR of 2.508 mm3/min (refer Table 2) in experiments having s.no. 11 at pulse-on-duration =35 μs , Q =14 μs, C =3amp, and V =45volts. while Pareto front provided the minimum value of MRR of 2.66760113mm3/min at pulse-on-duration = 49.83780 μs , Q = 13.8012141 μs, C = 2.00763 amp, and V =45.50042649.614 Volts. A comparison of the minimum MRR provides the Pareto front result is 0.13 mm3/min higher experimental one, which is highly acceptable, and this difference is because of the factor level changes.
Similarly, Pareto front results revealed the minimum SR of 1.4855502 μm at P = 4549.83780 μs, Q = 13.801214 μs, C = 2.00763 amp, and V = 45.500426 volts and experiment output no. 5 (refer Table 2), the minimum SR of 1.501μm at P = 50 μs, Q = 14 μs, C = 2 amp, and V = 50 volts is slightly lower than the Pareto front analysis. Furthermore, the 3D response plots of SR (Fig. 6) show that the SR decreases with the increasing values of P, V and C. Therefore, by proper levels of input, factors yield the minimum SR, which is need of an hour. Further, experimental output no. 9, the maximum SR of 2.615 μm at P = 25 μs, Q = 8 μs, C = 4 amp, and V = 40volts. While Corresponding results of Pareto front seen with the maximum SR of 1.7886815 μm at P = 25.1118229 μs, Q = 12.3503394 μs, C = 2.009124amp, and V = 45.1204989 volts. Comparing the maximum SR of experimental is 0.4 μm higher than Pareto optimal results (refer Table 7). This may be because of factors level differences between these two methods. The ve most excellent pareto front results keeping minimum SR and maximum MRR are presented in the Table 8.

Conclusions
The particle swarm optimization (PSO) and RSM techniques based on CCD experimental plan were employed for multi-response optimization of input factors of the WEDM method of Nitinol alloy has been studied in this research. Using a composite desirability approach, optimization carried out yielding empirical model for evaluating the role of input factors on multi responses (MRR and SR). The inferences were made on the results of different methods for maximizing MRR and Minimizing SR are as follow: Experimental values presented P and C are highly contributing factors to machining responses during maximization of MRR/ minimization of SR such that minimum level of P and C discharge quick energy (electrical type) for alloy melting and vaporization. This yields maximum MRR and minimum SR as impulsive forces developed would be of lower intensity.
Composite desirability approach for optimizing the multi-responses yield the optimal combination for setting the level of factors for high MRR and Low SR very low percentage of error but acceptable are as follows: P = 25 µs, Q = 13.39 µs, C = 2.0 amp, and V = 48.59 volts.
The Pareto front solution from MRPSO also shown the response MRR increase and SR decrease with decreasing P and C rather than Q and V.
The MRPSO provided a vast combination of input factors in comparison to experimentation for allowing us to select very appropriate levels of factors to maximize MRR along with minimum SR for improving process e ciency.
The proper combinations of both high and low levels P, Q, C, and V are more suitable for maximum and minimum of MRR, and SR has been presented using MOOPSO.
The MRPSO presented a set of optimal solutions using the Pareto optimal front to enable the designers to have the set optimal solutions for selecting the optimal values of factors suitable for their product requirement.

Declarations
Availability of data and materials Tables   Desirability and optimal for input and responses Pareto optimal front diagram of two responses using MRPSO