# Multi-Response Optimization of WEDM Process Parameters for Machining of Superelastic Nitinol Shape-Memory Alloy Using a Heat-Transfer Search Algorithm

^{1}

^{2}

^{3}

^{4}

^{5}

^{*}

## Abstract

**:**

## 1. Introduction

_{on}), pulse off time (T

_{off}), spark gap voltage (SV), wire tension (WT), wire feed rate (WF) has been studied on material removal rate (MRR), surface roughness (SR) and surface characteristics of material. They found that MRR and SR values increase significantly with the increase in T

_{on}whereas MRR and SR values decrease with an increase in SV and T

_{off}. Micro-cracks, craters, and debris were observed on the machined surface. The defect could be eliminated by more precise controlling of WEDM process parameters. Sharma et al. [17] conducted the parametric optimization of Ni40Ti60 alloy using the WEDM process. MRR, SR and the dimensional shift have been considered as an output response variables under the influence of input variables such as T

_{on}, T

_{off}, peak current (IP) and servo voltage (SV). Output responses were optimized using desirability approach for SMA alloy and close correlation between predicted and experimented values were obtained. T

_{on}of 124 µs, T

_{off}of 25 µs, SV of 30 V, and IP of 110 mu was the obtained optimal parameter setting for multi-response optimization with desirability value of 0.708. In another study by Soni et al. [18], WEDM machining of Ti50Ni40CO10 SMA has been explored. The final result revealed formation of microcracks can be avoided and recast layer thickness can be reduced by setting pulse on time lower than 125 µs and servo voltage larger than 20 V. Majumder and Maity [19] conducted a similar study wherein microhardness (MH) and SR were considered as output response variables and they are optimized with the help of a fuzzy technique for the SMA alloy Ni55Ti45. T

_{on}was identified as the main significant input process parameter as compared to other input variables. Manjaiah et al. [20] used a L

_{27}orthogonal array to perform the experiment and optimized output responses of MRR and SR during the machining of SMA. The study highlighted the significant effect of T

_{on}and T

_{off}and SV for the maximization of MRR and minimization of SR under the influence of brass wire and zinc-coated brass wire. B. Jabbaripour et al. [15] states that the electrical discharge machining (EDM) process is suitable for machining titanium alloys. They used Ti6Al4V to investigate various output performance characteristics. Increase in T

_{on}resulted in increase in MRR. In another study by Ramamurthy et al. [21], machining of Ti6Al4V alloy was conducted using the EDM process by using Taguchi L9 orthogonal array. They observed that T

_{off}has more influent nature on the output performances of machining characteristics because the T

_{off}influences the discharge energy in WEDM.

_{on}, T

_{off}and the current are the three most notable input process parameters while MRR, SR, and MH as the output response variables. The prime requirement after machining of SMA is its shape-memory effect. Shape-memory effect has been correlated to MH [32]. The differential scanning calorimetry (DSC) test is one of the techniques to ensure shape memory effect. Along with this, either single or multi-objective optimizations with limited consideration to actual industrial requirements are targeted in past published studies. However, to the best of the author’s knowledge, generated Pareto curves are targeted only for two responses for the study of SMAs using the WEDM process [33]. Thus, the present study addresses an evident research gap by using pareto curves incorporating three simultaneous responses generated using a novel HTS algorithm.

## 2. Materials and Methods

_{on}, T

_{off,}and current along with 3 different levels which have been selected on the basis of existing literature, machining capability and their influence on selected output response parameters. Ni55.8Ti was used as a workpiece (anode) and 0.18 mm diameter molybdenum wire was used as a tool electrode (cathode). Experiments (3 number of trials at each parameter setting) have been conducted following the Box-Behnken (BBD) technique of RSM as shown in Table 3. Response surface methodology has been used to minimize the number of trials which reduces the cost of material as well as reduces the machining time.

^{3}/s.

- t = duration of the machining process in second,
- ρ = 6.5 g/cm
^{3}the density of the workpiece

_{c}) was selected as 0.8 mm with the evaluation length of 7 mm. Ra values were recorded and analyzed to indicate the surface quality of the cut. A mirror finish was developed on the machined sample for the micro-hardness testing. A Vickers microhardness tester (MVH-S Auto Omintech, Pune, India) was used to calculate microhardness of the surface at 500 gf load at 10 s. The measured values of MRR, SR, and MH are analyzed and shown in Table 3 and the mathematical correlation was developed for each response. Further, the optimization route was followed as given in Figure 2. Validation of the shape-memory effect was conducted by the DSC technique. The DSC test was used to study the phase transformation behavior for both machined/unmachined surfaces and the results were compared. Using a Netzsch DSC 214 polyma machine (Netzsch, Selb, Germany), the DSC test was performed with a sample weight of 20 g at heating/cooling rate of 10 °C/min and a constant flow of nitrogen. The sample was place in a pan and a small spear hole was drilled on the top of the pan. This pan was kept within the machine for testing.

## 3. Results and Discussion

#### 3.1. Generation of Mathematical Model

^{3}/s to 0.5414 mm

^{3}/s respectively were obtained. SR value ranging from 4.944 µs to 6.82 µs and MH ranging from 275.2 HV to 383.9 HV were achieved. It can be observed from Table 3 that a different set of output responses was obtained at a different input set of parameters. The output response values mentioned in Table 3 were analyzed using Minitab software (Version 17) to generate in terms of input variables as shown in Equations (2)–(4):

_{on}, T

_{off}and Current) and their interactions on the dependent quality parameter (MRR, SR and MH). The ANOVA technique is used to investigate the significant and non-significant process parameters. The significance of input process parameter on the output response is indicated by F value and P value. The significance of process parameter on output response can be known from either higher F value or lower P value. The value of P must be lower than 0.05 to keep the particular process parameter significant for the 95% confidence level. The significance of T

_{on}and T

_{off}and current is shown in Table 4 on MRR, SR, and MH. T

_{off}and current are found to be significant for the output response of MRR while T

_{off}for SR and current for MH is considered to be the significant process parameters. Lack of fit was observed to be insignificant for all the responses which mean that the model is adequate for predicting the output responses under any combination of the process parameters considered in the range [34]. The 20% difference between R-squared and Adjusted (Adj) R-squared values means that the model is the best fit for selected responses [17]. For all the output responses considered in this study a difference of less than 20% was achieved.

^{3}/s) can be obtained when T

_{off}value is near to 10 µs and for any value of T

_{on}(between 35 µs to 55 µs). The effects of T

_{on}and T

_{off}also predict that MRR value increases with a decrease in T

_{off}. Similarly, MRR increases with the decrease in T

_{off}value and increase in current for the effect of contour for current and T

_{off}. This is due to the fact that the number of spark decreases with an increase in pulse off time which thereby lowers MRR and discharge energy increase with an increase in current which thereby increases MRR [35,36]. The effect of T

_{on}and current predicts the higher value of MRR when the current is in between 3.2 to 4 A and for any value of T

_{on}(between 35 µs to 55 µs).Figure 7 shows the contour plots for SR with the variation of two alternative input variables keeping the third variable as constant. Effect of T

_{on}and T

_{off}predicts the lower value of SR when T

_{on}value is in between 35 µs to 50 µs and T

_{off}value is near to 10 µs. A lower value of SR is observed at a lower value of T

_{on}and current and maximum SR is obtained at a higher value of T

_{on}and current. The discharge of higher pulse energy penetrates into the surface by forming a deep crater and leads to higher SR [20]. Furthermore, a contour plot for current and T

_{off}shows the least value of SR when T

_{off}varies from 10 to 12 µs and for the current value of 2 A. Figure 8 shows the contour plots for MH. Higher MH is obtained at the three different conditions viz. of T

_{on}35 µs and T

_{off}16 to 19 µs, current near to 4 A and T

_{on}40 µs to 55 µs, and again current 4 A and T

_{off}near to 10 µs.

#### 3.2. Optimization of Case Studies and Its Validation

#### 3.2.1. Conduction Phase

_{max}is the maximum number of generation specified; CDF is the conduction factor; R is the probability variable; R $\in $ {0, 0.3333}; r

_{i}$\in $ {0, 1} is a uniformly distributed random number.

#### 3.2.2. Convection Phase

_{i}$\in $ {0, 1} is a uniformly distributed random number; X

_{s}be the temperature of the surrounding and X

_{ms}be the mean temperature of the system; TCF is a temperature change factor.

#### 3.2.3. Radiation Phase

_{i}$\in $ {0, 1} is a uniformly distributed random number.

- For Pulse on time: 1 µs ≤ Pulse on time ≥ 110 µs
- For Pulse off time: 1 µs ≤ Pulse off time ≥ 32 µs
- For Current: 1 A ≤ Current ≥ 6 A

#### Case: I Optimization of Microhardness (MH)

#### Case: II Optimization of MH and Material Removal Rate (MRR)

#### Case: III Optimization of MH and Surface Roughness (SR)

#### Case: IV Simultaneous Optimization of MH, SR, and MRR

#### 3.3. Differential Scanning Calorimetry (DSC) Test

#### 3.4. Generation of Pareto Optimal Set

^{3}/s and 1.28 µm (as shown by red points) respectively. This shows that when maximum MRR needs to be achieved for higher production rate, the SR values are also at higher side showing the conflicting occurrence. Hence a Pareto point with its corresponding input parameters will be selected which would be a trade-off between these two values. A similar conclusion can be drawn from Figure 13 for the 2D view of MRR vs. MH which also shows that when maximum MRR needs to be achieved for higher production rate, the MH values are at lower side showing the conflicting occurrence. Whereas when maximum MH is considered as an output, MRR value is at a minimum. The maximum and minimum values of MRR and MH are 1.95 mm

^{3}/s and 870.86 HV (as shown by red points), respectively. Figure 14 gives the maximum and minimum values of SR and MH as 1.28 µm and 870.86 HV (as shown by red and yellow points) respectively for the 2D view of SR vs. MH. For some Pareto points, when SR is at its peak value, corresponding values of MH are not at its peak. This might be due to the effect of the third response parameter evident on the generated 2-D graphs. The selection of input and output variable values in the actual WEDM process is very complex, which requires true dependencies for the decision of input process parameter selection. In the current study, MH value becomes more important considering the fact that the possession of a shape memory effect is a must after machining.

## 4. Conclusions

- The regression models generated for the selected output response variables were found to be robust, verified using ANOVA. Residual plot analysis confirmed the prediction capability of the generated models of MRR, SR and MH.
- T
_{off}and current were found to be most significant parameters influencing SR and MH respectively, where as T_{off}and current were significantly influencing MRR. Contour plots analyses were used to identify the significance of input variables on the individual output responses. - The heat-transfer search (HTS) algorithm was found effective in predicting and optimizing the input values for four different case studies under consideration. The same was confirmed using validation tests. A close correlation between predicted and achieved values was obtained.
- DSC tests carried out for case IV indicated negligible difference between A
_{f}temperature for the machined and unmachined surface which confirmed the retention of shape memory effect even after WEDM. This can be considered as one of the most notable outcomes of the study. - 3-D Pareto curves were generated which effectively presented the solution for the simultaneous optimization of three output responses such as MRR, SR, and MH. A multi-objective version of HTS termed the MOHTS algorithm was successfully implemented for this.
- The complex relationship and conflicting nature of between input parameters, their interactions and output responses was evident from the scattered nature of the 2-D Pareto fronts.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Nomenclature

A | Ampere |

A_{f} | Austenitic start |

A_{f} | Austenitic finish |

ANOVA | Analysis of variance |

BBD | Box-Behnken design |

DSC | Differential scanning calorimetry |

HTS | Heat transfer search |

IP | Peak current (Ampere) |

M_{f} | Martensitic start |

M_{s} | Martensitic finish |

MH | Microhardness (HV) |

MOHTS | Multi-objective heat transfer search |

MRR | Material removal rate (mm^{3}/s) |

RSM | Response surface methodology |

SMA | Shape memory alloy |

SMAs | Shape memory alloys |

SR | Surface roughness (µm) |

SV | Spark gap voltage |

T_{on} | Pulse on time (µs) |

T_{off} | Pulse off time (µs) |

WEDM | Wire electric discharge machine |

## References

- Jani, J.M.; Leary, M.; Subic, A.; Gibson, M.A. A review of shape memory alloy research, applications and opportunities. Mater. Des.
**2014**, 56, 1078–1113. [Google Scholar] [CrossRef] - Henderson, E.; Buis, A. Nitinol for prosthetic and orthotic applications. J. Mater. Eng. Perform.
**2011**, 20, 663–665. [Google Scholar] [CrossRef] - Elahinia, M.H.; Hashemi, M.; Tabesh, M.; Bhaduri, S.B. Manufacturing and processing of NiTi implants: A review. Prog. Mater. Sci.
**2012**, 57, 911–946. [Google Scholar] [CrossRef] - Kannan, T.D.; Pegada, R.; Sathiya, P.; Ramesh, T. A comparison of the effect of different heat treatment processes on laser-welded NiTinol sheets. J. Braz. Soc. Mech. Sci. Eng.
**2018**, 40, 562. [Google Scholar] [CrossRef] - Marattukalam, J.J.; Balla, V.K.; Das, M.; Bontha, S.; Kalpathy, S.K. Effect of heat treatment on microstructure, corrosion, and shape memory characteristics of laser deposited NiTi alloy. J. Alloys Compd.
**2018**, 744, 337–346. [Google Scholar] [CrossRef] - Elahinia, M.H.; Ahmadian, M. An enhanced SMA phenomenological model: II. The experimental study. Smart Mater. Struct.
**2005**, 14, 1309. [Google Scholar] [CrossRef] - Yuan, B.; Chung, C.Y.; Zhang, X.P.; Zeng, M.Q.; Zhu, M. Control of porosity and superelasticity of porous NiTi shape memory alloys prepared by hot isostatic pressing. Smart Mater. Struct.
**2005**, 14, S201. [Google Scholar] [CrossRef] - Markopoulos, A.; Pressas, I.; Manolakos, D. Manufacturing processes of shape memory alloys. In Materials Forming and Machining; Elsevier: Amsterdam, The Netherlands, 2016; pp. 155–180. [Google Scholar]
- Velmurugan, C.; Senthilkumar, V.; Dinesh, S.; Arulkirubakaran, D. Machining of NiTi-shape memory alloys—A review. Mach. Sci. Technol.
**2018**, 22, 355–401. [Google Scholar] [CrossRef] - Prabu, S.M.; Madhu, H.C.; Perugu, C.S.; Akash, K.; Kumar, P.A.; Kailas, S.V.; Anbarasu, M.; Palani, I.A. Microstructure, mechanical properties and shape memory behaviour of friction stir welded nitinol. Mater. Sci. Eng. A
**2017**, 693, 233–236. [Google Scholar] [CrossRef] - Weinert, K.; Petzoldt, V. Machining of NiTi based shape memory alloys. Mater. Sci. Eng. A
**2004**, 378, 180–184. [Google Scholar] [CrossRef] - Tripathy, S.; Tripathy, D. Multi-response optimization of machining process parameters for powder mixed electro-discharge machining of H-11 die steel using grey relational analysis and topsis. Mach. Sci. Technol.
**2017**, 21, 362–384. [Google Scholar] [CrossRef] - Dave, S.; Vora, J.J.; Thakkar, N.; Singh, A.; Srivastava, S.; Gadhvi, B.; Pate, V.; Kumar, A. Optimization of EDM drilling parameters for Aluminium 2024 alloy using Response Surface Methodology and Genetic Algorithm. In Key Engineering Materials; Transtech Publication: Stafa-Zurich, Switzerland, 2016; pp. 3–8. [Google Scholar]
- Kumar, P.; Parkash, R. Experimental investigation and optimization of EDM process parameters for machining of aluminum boron carbide (Al–B
_{4}C) composite. Mach. Sci. Technol.**2016**, 20, 330–348. [Google Scholar] [CrossRef] - Jabbaripour, B.; Sadeghi, M.H.; Faridvand, S.; Shabgard, M.R. Investigating the effects of EDM parameters on surface integrity, MRR and TWR in machining of Ti–6Al–4V. Mach. Sci. Technol.
**2012**, 16, 419–444. [Google Scholar] [CrossRef] - Bisaria, H.; Shandilya, P. Experimental studies on electrical discharge wire cutting of Ni-rich NiTi shape memory alloy. Mater. Manuf. Process.
**2018**, 33, 977–985. [Google Scholar] [CrossRef] - Sharma, N.; Raj, T.; Jangra, K.K. Parameter optimization and experimental study on wire electrical discharge machining of porous Ni
_{40}Ti_{60}alloy. Proc. Inst. Mech. Eng. Part B J. Eng. Manuf.**2017**, 231, 956–970. [Google Scholar] [CrossRef] - Soni, H.; Sannayellappa, N.; Rangarasaiah, R.M. An experimental study of influence of wire electro discharge machining parameters on surface integrity of TiNiCo shape memory alloy. J. Mater. Res.
**2017**, 32, 3100–3108. [Google Scholar] [CrossRef] - Majumder, H.; Maity, K. Application of GRNN and multivariate hybrid approach to predict and optimize WEDM responses for Ni-Ti shape memory alloy. Appl. Soft Comput.
**2018**, 70, 665–679. [Google Scholar] [CrossRef] - Manjaiah, M.; Narendranath, S.; Basavarajappa, S.; Gaitonde, V.N. Effect of electrode material in wire electro discharge machining characteristics of Ti
_{50}Ni_{50−x}Cux shape memory alloy. Precis. Eng.**2015**, 41, 68–77. [Google Scholar] [CrossRef] - Ramamurthy, A.; Sivaramakrishnan, R.; Muthuramalingam, T.; Venugopal, S. Performance analysis of wire electrodes on machining Ti-6Al-4V alloy using electrical discharge machining process. Mach. Sci. Technol.
**2015**, 19, 577–592. [Google Scholar] [CrossRef] - Shabgard, M.; Farzaneh, S.; Gholipoor, A. Investigation of the surface integrity characteristics in wire electrical discharge machining of Inconel 617. J. Braz. Soc. Mech. Sci. Eng.
**2017**, 39, 857–864. [Google Scholar] [CrossRef] - Kuruvila, N. Parametric influence and optimization of wire EDM of hot die steel. Mach. Sci. Technol.
**2011**, 15, 47–75. [Google Scholar] [CrossRef] - Dang, X.-P. Constrained multi-objective optimization of EDM process parameters using kriging model and particle swarm algorithm. Mater. Manuf. Process.
**2018**, 33, 397–404. [Google Scholar] [CrossRef] - Somashekhar, K.; Ramachandran, N.; Mathew, J. Optimization of material removal rate in micro-EDM using artificial neural network and genetic algorithms. Mater. Manuf. Process.
**2010**, 25, 467–475. [Google Scholar] [CrossRef] - Prabhu, S.; Vinayagam, B. Optimization of carbon nanotube based electrical discharge machining parameters using full factorial design and genetic algorithm. Aust. J. Mech. Eng.
**2016**, 14, 161–173. [Google Scholar] [CrossRef] - Patel, V.K.; Raja, B.D. A comparative performance evaluation of the reversed Brayton cycle operated heat pump based on thermo-ecological criteria through many and multi objective approaches. Energy Convers. Manag.
**2019**, 183, 252–265. [Google Scholar] [CrossRef] - Raja, B.D.; Jhala, R.; Patel, V. Multiobjective thermo-economic and thermodynamics optimization of a plate–fin heat exchanger. Heat Transf.—Asian Res.
**2018**, 47, 253–270. [Google Scholar] [CrossRef] - Patel, V.K. An efficient optimization and comparative analysis of ammonia and methanol heat pipe for satellite application. Energy Convers. Manag.
**2018**, 165, 382–395. [Google Scholar] [CrossRef] - Tawhid, M.A.; Savsani, V. ∊-constraint heat transfer search (∊-HTS) algorithm for solving multi-objective engineering design problems. J. Comput. Des. Eng.
**2018**, 5, 104–119. [Google Scholar] [CrossRef] - Raja, B.; Patel, V.; Jhala, R. Thermal design and optimization of fin-and-tube heat exchanger using heat transfer search algorithm. Therm. Sci. Eng. Prog.
**2017**, 4, 45–57. [Google Scholar] [CrossRef] - LotfiNeyestanak, A.A.; Daneshmand, S. The effect of operational cutting parameters on Nitinol-60 in wire electrodischarge machining. Adv. Mater. Sci. Eng.
**2013**, 2013, 1–6. [Google Scholar] [CrossRef] - Magabe, R.; Sharma, N.; Gupta, K.; Davim, J.P. Modeling and optimization of Wire-EDM parameters for machining of Ni
_{55.8}Ti shape memory alloy using hybrid approach of Taguchi and NSGA-II. Int. J. Adv. Manuf. Technol.**2019**, 1–15. [Google Scholar] [CrossRef] - Zhao, D.; Wang, Y.; Wang, X.; Wang, X.; Chen, F.; Liang, D. Process analysis and optimization for failure energy of spot welded titanium alloy. Mater. Des.
**2014**, 60, 479–489. [Google Scholar] [CrossRef] - Mahanta, S.; Chandrasekaran, M.; Samanta, S.; Arunachalam, R.M. EDM investigation of Al 7075 alloy reinforced with B
_{4}C and fly ash nanoparticles and parametric optimization for sustainable production. J. Braz. Soc. Mech. Sci. Eng.**2018**, 40, 1–17. [Google Scholar] [CrossRef] - Tonday, H.; Tigga, A. Analysis of effects of cutting parameters of wire electrical discharge machining on material removal rate and surface integrity. IOP Conf. Ser. Mater. Sci. Eng.
**2016**, 115, 012013. [Google Scholar] [CrossRef] - Patel, V.K.; Savsani, V.J. Heat transfer search (HTS): A novel optimization algorithm. Inf. Sci.
**2015**, 324, 217–246. [Google Scholar] [CrossRef] - Buehler, W.J.; Gilfrich, J.; Wiley, R. Effect of low-temperature phase changes on the mechanical properties of alloys near composition TiNi. J. Appl. Phys.
**1963**, 34, 1475–1477. [Google Scholar] [CrossRef] - La Roca, P.; Isola, L.; Vermaut, P.; Malarría, J. Relationship between grain size and thermal hysteresis of martensitic transformations in Cu-based shape memory alloys. Scr. Mater.
**2017**, 135, 5–9. [Google Scholar] [CrossRef] - Kato, H.; Yasuda, Y.; Sasaki, K. Thermodynamic assessment of the stabilization effect in deformed shape memory alloy martensite. Acta Mater.
**2011**, 59, 3955–3964. [Google Scholar] [CrossRef] - Raja, B.D.; Jhala, R.; Patel, V. Thermal-hydraulic optimization of plate heat exchanger: A multi-objective approach. Int. J. Therm. Sci.
**2018**, 124, 522–535. [Google Scholar] [CrossRef] - Patel, V.; Savsani, V.; Mudgal, A. Many-objective thermodynamic optimization of Stirling heat engine. Energy
**2017**, 125, 629–642. [Google Scholar] [CrossRef] - Patel, V.; Savsani, V.; Mudgal, A. Efficiency, thrust, and fuel consumption optimization of a subsonic/sonic turbojet engine. Energy
**2018**, 144, 992–1002. [Google Scholar] [CrossRef]

**Figure 9.**Flow chart of heat-transfer search (HTS) algorithm. Adapted from [31], with permission from © 2017 Elsevier.

**Figure 10.**Differential scanning calorimetry (DSC) curve of NiTi alloy for (

**a**) unmachined sample (

**b**) machined sample at optimized parameter.

Element | Ti | Ni | Co | Cu | Cr | Fe | Nb | C | H | O | N |

Content (wt.%) | Balance | 55.78 | 0.005 | 0.005 | 0.005 | 0.012 | 0.005 | 0.04 | 0.001 | 0.035 | 0.001 |

Factors | Process Parameters | Level 1 | Level 2 | Level 3 |
---|---|---|---|---|

A | Pulse on time (T_{on}), µs | 35 | 45 | 55 |

B | Pulse off time (T_{off}), µs | 10 | 15 | 20 |

C | Discharge current, Ampere | 2 | 3 | 4 |

Run | Pulse on Time (µs) | Pulse off Time (µs) | Current (Ampere) | MRR (mm^{3}/s) | SR (µm) | Microhardness (HV) |
---|---|---|---|---|---|---|

1 | 35 | 10 | 3 | 1.230948122 | 5.637 | 330.2 |

2 | 55 | 10 | 3 | 1.065245598 | 5.986 | 342.3 |

3 | 35 | 20 | 3 | 0.714888337 | 6.453 | 275.2 |

4 | 55 | 20 | 3 | 0.756738988 | 6.82 | 342.8 |

5 | 35 | 15 | 2 | 0.675983558 | 5.322 | 308.6 |

6 | 55 | 15 | 2 | 0.666859456 | 6.58 | 301 |

7 | 35 | 15 | 4 | 1.066357739 | 6.595 | 346.5 |

8 | 55 | 15 | 4 | 1.103461538 | 5.577 | 351.3 |

9 | 45 | 10 | 2 | 0.845274725 | 4.944 | 341.7 |

10 | 45 | 20 | 2 | 0.541463415 | 5.925 | 354.2 |

11 | 45 | 10 | 4 | 1.23034188 | 5.638 | 383.9 |

12 | 45 | 20 | 4 | 0.874333587 | 5.762 | 374.6 |

13 | 45 | 15 | 3 | 0.92275641 | 6.053 | 326.3 |

14 | 45 | 15 | 3 | 0.925 | 5.484 | 309.5 |

15 | 45 | 15 | 3 | 0.921634615 | 6.098 | 316.3 |

ANOVA for MRR | |||||

Source | SS | MS | F | P | Significance |

T_{on} | 0.001149 | 0.001149 | 1.07 | 0.328 | - |

T_{off} | 0.275425 | 0.275425 | 256.99 | 0.000 | Significant |

Current | 0.298345 | 0.298345 | 278.37 | 0.000 | Significant |

R–Sq = 98.41 %, R–Sq (Adj) = 97.53% | |||||

ANOVA for SR | |||||

Source | SS | MS | F | P | Significance |

T_{on} | 0.11424 | 0.11424 | 2.51 | 0.157 | - |

T_{off} | 0.94875 | 0.94875 | 20.85 | 0.003 | Significant |

Current | 0.08020 | 0.08020 | 1.76 | 0.226 | - |

R–Sq = 91.71 %, R–Sq (Adj) = 83.41% | |||||

ANOVA for MH | |||||

Source | SS | MS | F | P | Significance |

T_{on} | 739.2 | 739.2 | 3.14 | 0.120 | - |

T_{off} | 329.0 | 329.0 | 1.40 | 0.276 | - |

Current | 2842.6 | 2842.6 | 12.07 | 0.010 | Significant |

R–Sq = 85.52 %, R–Sq (Adj) = 71.03% |

Condition | MRR (mm^{3}/s) | SR (µm) | Microhardness (HV) |
---|---|---|---|

Predicted by HTS Algorithm | 1.6938 | 8.62 | 679.05 |

Experimentally measured values | 1.5921 | 8.89 | 654.32 |

% ERROR | 6 | 3.13 | 3.64 |

Condition | MRR (mm^{3}/s) | SR (µm) | Microhardness (HV) |
---|---|---|---|

Predicted by HTS Algorithm | 0.81324 | 1.28 | 870.21 |

Experimentally measured values | 0.77271 | 1.35 | 855.55 |

% ERROR | 4.98 | 5.46 | 1.68 |

Nitinol Sample | A_{s} (°C) | A_{f} (°C) | M_{s} (°C) | M_{f} (°C) | Hysteresis, |A_{s} − M_{f}| (°C) |
---|---|---|---|---|---|

Unmachined | −58 | −39.7 | −88.5 | −110.4 | 52.4 |

Machined | −61.3 | −40.1 | −98.9 | −118.3 | 57 |

Objective Function | Design Variables | Objective Function Value | ||||
---|---|---|---|---|---|---|

Pulse on Time | Pulse off Time | Current | MRR (mm^{3}/s) | MH (HV) | SR (µm) | |

Maximum MRR | 10 | 5 | 5 | 1.9503 | 423.05 | 13.70 |

Maximum MH | 63 | 32 | 6 | 0.7803 | 870.86 | 1.29 |

Minimum SR | 65 | 32 | 6 | 0.8132 | 870.21 | 1.28 |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Chaudhari, R.; Vora, J.J.; Mani Prabu, S.S.; Palani, I.A.; Patel, V.K.; Parikh, D.M.; de Lacalle, L.N.L. Multi-Response Optimization of WEDM Process Parameters for Machining of Superelastic Nitinol Shape-Memory Alloy Using a Heat-Transfer Search Algorithm. *Materials* **2019**, *12*, 1277.
https://doi.org/10.3390/ma12081277

**AMA Style**

Chaudhari R, Vora JJ, Mani Prabu SS, Palani IA, Patel VK, Parikh DM, de Lacalle LNL. Multi-Response Optimization of WEDM Process Parameters for Machining of Superelastic Nitinol Shape-Memory Alloy Using a Heat-Transfer Search Algorithm. *Materials*. 2019; 12(8):1277.
https://doi.org/10.3390/ma12081277

**Chicago/Turabian Style**

Chaudhari, Rakesh, Jay J. Vora, S. S. Mani Prabu, I. A. Palani, Vivek K. Patel, D. M. Parikh, and Luis Norberto López de Lacalle. 2019. "Multi-Response Optimization of WEDM Process Parameters for Machining of Superelastic Nitinol Shape-Memory Alloy Using a Heat-Transfer Search Algorithm" *Materials* 12, no. 8: 1277.
https://doi.org/10.3390/ma12081277