Experimental analysis and optimization of machining parameters for Nitinol alloy: A Taguchi and multi-attribute decision-making approach

: The automotive and aerospace sectors have a strong demand for Nitinol alloy machined parts; therefore, optimizing machining parameters is essential to achieving better process performance results in terms of cost and product quality. In general, the process variables that in ﬂ u-ence machining include feed ( f ), depth of cut ( t ), and spindle speed ( S ). Material removal rate (MRR), tool wear (TW), and surface roughness (Ra) are pertinent output performance indicators. Analysis of variance has been performed to assess the e ﬀ ect of process variables on the aforesaid output performance. It has been found that feed has a signi ﬁ cant e ﬀ ect on MRR and surface roughness with a contribution of 50.65 and 33.62%, respectively, whereas spindle speed has a major contribution on TW with a contribution of 51.9%. This study assesses how well the Nitinol 56 machining process works overall. In this work, the Taguchi method has been used to determine the e ﬀ ect of aforesaid process variables on the output performance indices. To satisfy previously stated con ﬂ icting performance indices, a variety of multi-attribute decision-making approaches were used, such as utility, TOPSIS, and grey, to determine the optimal process variables. The optimal process variable combination has been achieved as f = 0.133 mm·rev − 1 , d = 0.06, and S = 835 RPM. This combination has been achieved using all methods.


Introduction
An essential group of shape memory alloy are NiTi alloys.The observation of the shape memory effect (SME) dates back to 1938, initially documented in copper-zinc alloys (Cu-Zn) and copper-tin alloys.However, the formal recognition of Nitinol, a nickel-titanium alloy with unique pseudoelasticity, strong damping capabilities, and an SME, came later in 1965 when the first patent application for this alloy developed by the Naval Ordnance Laboratory [1][2][3][4].Renowned for their outstanding properties, including fatigue strength, thermal stability, and corrosion resistance under extreme conditions, Ni-based superalloys are employed in manufacturing critical components of aero-engines and gas turbines that frequently endure high velocity, high pressure, and high temperature [5][6][7][8].Nevertheless, the presence of y′ and y′′ precipitates makes these materials challenging to machine, creating a persistent obstacle in the field of Ni-based superalloy machining [9][10][11].
Ni-based superalloys are categorized depending on their chemical makeup [12].Buehler and Wang [13] successfully improved the drilling and mechanical cutting Dev Sureja: Department of Mechanical & Aerospace Engineering, Institute of Infrastructure, Technology, Research and Management (IITRAM), Ahmedabad 380026, Gujarat, India Soni Kumari: Department of Mechanical Engineering, GLA University, Mathura 281406, U.P., India Basireddy Bhavani: Department of Civil Engineering, Institute of Aeronautical Engineering, Hyderabad, India machinability of NiTi alloys.An optimal drilling performance was observed using a tungsten-carbide twist drill with a rotational speed of 163 rpm and a feed rate of 0.07 mm•rev −1 .This configuration exhibited favorable values for machining time, cutting forces, and tool service life.Shyha et al. [14] conducted machinability improvement tests during the drilling of Kovar SMAS.To minimize cutting temperature and improve surface integrity, the experiments, which were conducted on unbacked and backed Kovar alloy workpieces at speeds ranging from 450 to 3,750 rpm in dry conditions, recommended using smaller drill sizes, lower feed rates, and reduced cutting speeds.These modifications result in lower burr size, lower thermal hardening, and a decreased risk of microcrack formation.
Kaynak et al. [15,16] investigated cryogenic machining as a viable tactic to improve NiTi SMAS machining performance in a different study.We used liquid nitrogen as the cryogenic coolant, which we kept at 1.5 MPa.Preheated machining involved a preheating temperature of 175°C, while minimum quantity lubrication (MQL) was applied with a flow rate of 60 ml•h −1 and an air pressure of 0.4 MPa at various machining parameter combinations.The study revealed that cryogenically machined samples exhibited superior surface integrity compared to dry samples at high speeds.Thermal distortion and reduced tool wear (TW) were found to be the primary factors contributing to this improvement, which resulted in smoother surface generation during cryogenic machining at elevated cutting speeds.
Grguraš et al. [17] carried out a comparative investigation with carbide end tools in milling SS 316L and Inconel 718 under varied lubrication conditions, and they introduced full-body ceramic tools for machining Inconel 718.The study evaluated cost, surface integrity, and tool life.The findings showed that ceramic tools outperform carbide tools in terms of material removal rate (MRR) and productivity; however, further investigation is necessary due to economic factors.Using an improved PVD-coated (AlTiN) carbide tool, Venkatesan et al. [18] accomplished dry turning on Inconel 718.Low cutting depths, low feed rates, and high cutting speeds produce the best results with the least amount of Ra and cutting forces, according to studies on surface finish, cutting forces, and tool life.A desirability function was used for parameter optimization.
Using SEM analysis of chip roots, Parida [19] machined Inconel 718 and investigated the effect of heating temperature on the workpiece surface.The researched attributes decreased as the heating temperature increased, according to the results.In their exploration of the machining difficulties of shape memory alloys based on Ni and Ti, Huang [20] found that, at speeds lower than 200 m•min −1 , greater cutting rates result in lower TW, improved surface smoothness, and lower cutting force.But after this point, the impact is negligible.Additional factors that affect machining characteristics are the feed rate and depth of cut.
In their investigation on the turning of Inconel 825, Gandhi et al. [21] measured the machining force, Ra, rate of metal removal, and chip thickness ratio.Better surface finishes were produced using C-type inserts, and machining force and the chip thickness ratio decreased with increased spindle speed, utilizing a CVD-coated tungsten carbide tool.Yadav et al. [22] machined Inconel 718 with an emphasis on MRR and TW, utilizing DEFORM 3D software for modeling [23][24][25][26].
The Taguchi method has been widely applied in previous state-of-the-art studies, offering efficiency by minimizing the number of trials through the application of the orthogonal array (OA) concept in the design of experiments (DOE).Renowned among academics and scientists, this approach excels in predicting the optimal configuration of machine parameters within a discrete domain.However, it falls short when confronted with multi-response optimization challenges [27][28][29][30][31][32].
To address these limitations, researchers have sought to enhance the Taguchi methodology by integrating it with various techniques, such as TOPSIS [33], utility concept [34], grey relation theory [35], MOORA [36], and desirability function [37].The combination of these approaches resolves the optimization challenges associated with multiple responses.By generating a unified performance index that encompasses various performance characteristics, these methods leverage the strengths of the Taguchi method for direct optimization.Consequently, optimization methodologies like MOORA-Taguchi, grey-Taguchi, TOPSIS-Taguchi, Utility-Taguchi, desirability-Taguchi, MOORA-Taguchi, and others have gained substantial recognition for real-time optimization across diverse qualities of processes or products [38,39].
The present study aims to investigate TOPSIS, utility, and grey multi-attribute decision making (MADM) approaches in order to find the best machine setup for Nitinol 56.
Adin [40,41] explored the impact of drilling parameters and cryogenic treatment on the M35 HSS drill bit, employed for drilling AA2024-T3 aluminum alloy under dry conditions.The investigation centered on predetermined drilling parameters based on the Taguchi experimental design and conducted subsequent analyses using both analysis of variance (ANOVA) and regression analysis methodologies [42].

Experimentation
Nitinol 56 was produced using the Banka 40, a manual lathe shown in Figure 1.Samples having a length of 10 mm and a diameter of 16 mm were cut from a total length of 150 mm.The TNMG160408 from KYOCERA (single-point cutting tool) was used in the machining process.
The literature reveals that various parameters influence machining characteristics.Drawing from the literature and considering the adjustable parameters in turning specifically the spindle speed, feed, and depth of cut, have been chosen.As indicated in Table 1, several arrangements of process variables, including S (RPM), t (mm), and f (mm•rev −1 ), were used for the machining.Table 2 shows how the experimental trials were methodically arranged using Taguchi's L9 OA.
Material removal rate was assessed by comparing the workpiece weight before and after machining, along with recording the duration of the operation.An electronic weighing scale was utilized to measure the weight, and a digital watch was employed to measure the time.Equation ( 1) was utilized to evaluate the MRR: where M 1 is the initial wt. of the workpiece (g), M 2 is the weight after machining the workpiece's weight (g), ρ is the workpiece density, and m t is the machining time (s).The surface roughness (Ra) of the machined workpiece was calculated using a Taylor Hobson's surface roughness tester (Figure 2).Due to continuous usage, TW is the progressive degradation of cutting tools.The assessment of TW was conducted using a toolmaker microscope, specifically the Mitutoyo TM Series, as depicted in Figure 3.

Methodology
The methodology employed in this study involved a systematic approach (illustrated in Figure 4) to optimize the machining process for Nitinol alloy.First, Nitinol alloy was selected as the material.The identification of input parameters, including the spindle speed (S), feed (f), and depth of cut (d), has been based on their significance in the machining process.DOE, specifically the Taguchi methodology, was used to systematically vary these input parameters and analyze their effects  on the output performance indices, namely TW, MRR, and surface roughness (Ra).The workpiece's weight before and after machining were compared to calculate the MRR, while TW and Ra were measured using appropriate tools and devices.The utility function approach, TOPSIS, and grey analysis are three examples of MADM approaches that were used to achieve optimal process variables, which were taken into consideration during a detailed analysis and discussion of the experiment outcomes.The flowchart illustrating the aforementioned techniques is presented in Figures 5-7.Within Figure 5, the grey relation analysis (GRA) is depicted as a systematic procedure presented in a stepby-step flow chart.The sequence initiates with data collection, followed by normalization to standardize the scale.A reference series is established for comparative analysis with other variables.Grey values are computed based on their proximity to this reference series.Subsequently, the calculation of grey relation coefficients exposes the strength of relationships.The ranking of variables provides insights into their relative significance.The ensuing results undergo a comprehensive analysis, leading to interpretations that contribute to decision-making processes.
In Figure 6, the utility function approach is depicted through a succinct flow chart detailing crucial steps.The process commences with the identification of decision criteria and the assignment of weights based on their significance.Subsequently, utility functions are crafted to quantify preferences, enabling the computation of overall utility scores for alternatives.A sensitivity analysis is conducted to evaluate the repercussions of variations in criterion weights.This method provides decision-makers with a structured and systematic approach to assess and compare alternatives grounded in utility considerations.In Figure 7, the flow chart outlines the multi-response optimization using the TOPSIS-Taguchi approach.It begins with identifying multiple responses and their optimization goals, employing Taguchi's experimental design to establish optimal factor levels.The TOPSIS method is then utilized to rank alternative factor combinations based on their proximity to the ideal solution.A subsequent sensitivity analysis evaluates the robustness of the optimized solutions.This systematic approach, as depicted in the flow chart, provides practitioners with a structured methodology for the simultaneous optimization of multiple responses, leveraging the synergistic combination of TOPSIS and Taguchi techniques.

Results and discussion
ANOVA was used in the study's findings section to evaluate the impacts of three machining factors: feed (f), depth of cut (d), and spindle speed (S).An analysis of the effects of each variable and their interactions on the output performance measures was made easier by this statistical method, which also gave important insights into how these characteristics affect the machining process.Furthermore, a comprehensive examination of the chips generated throughout the machining procedure was carried out in order to understand the behavior of the material and the relationship between the tool and the workpiece.Since chip formation directly affects productivity, surface smoothness, and TW, understanding it is critical to improving machining results.
Furthermore, employing MADM techniques, the study descended into the optimization phase.The best mix of machining variables that concurrently satisfy competing performance indices was found by using a variety of MADM approaches, such as utility, TOPSIS, and grey.Among these measures were TW, the MRR, and surface roughness (Ra) (Table 3).The study combined the findings of ANOVA with the insights from chip formation analysis to identify the most productive and effective machining settings (Table 3).

Effects of machining variables on output characteristics
To explore the individual impact of all input variables on the output responses, the ANOVA technique was implemented.Tables 4-6 list the percentage contributions of each variable for MRR, Ra, and TWR. Figure 8 represents the percentage contribution of the spindle speed, depth of cut, and feed with respect to the MRR, Ra, and TWR.It is obvious that the MRR is highly impacted by the feed, with a share of 50.65%., followed by the depth of cut (6.18%) and spindle speed (29.69%).The same has been calculated for other output characteristics, namely Ra and TW, as presented in Figure 8(b) and (c), respectively.For Ra, feed tops the chart, with a share of 33.62%, followed by the

Chip formation
The study highlighted several crucial observations related to chip formation and its impact on the machining process.First, the depth of cut emerged as a pivotal factor, as it directly influenced the chip thickness; higher depths of cut led to an increase in the chip diameter, underscoring the importance of this parameter in determining the size and shape of the generated chips, which is illustrated in Figure 9. Additionally, the study revealed that chip thickness was positively correlated with cutting velocity and feed amount in dry conditions, indicating that these factors played a significant role in chip formation dynamics.Moreover, the research findings indicated that chips produced under all dry-cutting conditions exhibited a continuous pattern, emphasizing consistency in the machining process.It was also noted that during dry-turning operations, the generation of chips was accompanied by the dissipation of heat energy, contributing to heat-related losses.
Importantly, the study emphasized the critical implications of chip characteristics on the lifespan of tools and the overall surface quality of the machined components, highlighting the need for a comprehensive understanding of chip formation for optimizing tool longevity and product quality in machining processes.

Optimal process combination using different MADM techniques 4.3.1 Grey analysis
First of all, experimental data will be normalized to exclude all the diversity of data as well as conflict requirements.
Here, Surface roughness and tool wear should be referred Experimental analysis and optimization of machining parameters  7 to as smaller is better and MRR as higher is better.The following equations will be used to normalize the experimental data: [27].Smaller is better (SB): The normalization for SB is performed (Table 7) using the following equation: Larger is better (LB): The normalization for LB is performed using the following equation: where p i (n) represents the normalized value, min.qi 0 (n) denotes the minimum response value of q i 0 (n), max.q i 0 (n) indicates the maximum response value of q i 0 (n), and q i 0 (n) represents the experimental value.The following formula determines the grey relational coefficient using the computed normalized response data: In the given context, where ξ i (n) signifies the Grey relational coefficient for the ith experiment, Ψ represents the identification coefficient (typically set at 0.5), Δ max corresponds to the maximum value of Δ 0i (n), and Δ min denotes the minimum value of Δ 0i (n).Overall, Grey's relational grade (R i ) Table 7 optimal combination using Taguchi (Figure 10).Experimental analysis and optimization of machining parameters  9

Optimal process combination employing utility analysis
The evaluation of the output feature involves the use of lower and higher values as benchmarks.In this context, two arbitrary arithmetic values, namely 0 and 9, which are commonly referred to as preferred numbers, have been designated for this purpose.The preference number (N p ) can be computed using an equation designed to assess the feature on a logarithmic scale (Table 8): In equation (7), the representation of the output characteristic x is denoted as B q .The lower value of the output characteristic x, labeled as B q′ , is expressed.M is a constant, and its calculation is determined by equation ( 8 The overall utility (equation 9) is specified as in Table 8 and optimal combination using Taguchi (Figure 11) In accordance with the conditions, (equation 10)

Optimal process combination employing TOPSIS
To initiate the process, the mentioned evaluation characteristics undergo normalization using equation 11, and the resultant normalized values are presented in Table 9.
where, for attribute X j. , r ij depicts the normalized perfor- mance of A i .
In the existing work, all the responses are supposed to have equivalent importance; therefore, an equal weight (0.25) has been assigned to each characteristic, and weighted values are calculated using equation (11) and tabulated in Table 9.
It is crucial to determine negative and positive ideal solutions, recognizing the inherent incompatibility of the  evaluation qualities mentioned earlier.In this context, the optimal values are identified as the lowest for qualities like TW and Ra, where lower values are preferable and conversely for others.Similarly, the positive ideal solution is characterized by the highest MRR, while the negative ideal solution exhibits the lowest MRR.Both negative and positive optimal solutions are detailed in Table 10.Subsequently, the separation distance from the negative and positive ideal solutions was computed using equations ( 13) and ( 14), respectively, and the results are documented in Table 11.Preference is accorded to proximity coefficient values that are closest, as determined by equation (15).Finally, the application of the Taguchi methodology to the proximity coefficient aids in identifying the optimal combination (Figure 12).

Confirmatory test
In a later stage, the confirmatory test was carried out for favorable machining conditions (i.e., at S = 835 RPM, f = 0.133 mm•rev −1 , and d = 0.06) obtained from the intended optimization model in order to validate the optimal conditions, and results are shown in Table 12.It was observed that overall output characteristics improved.

Conclusions
This study observes the machinability aspects of Nitinol 56 with a focus on TW, surface roughness, and MRR.The following is a summary of the main findings: i.A number of optimization techniques, including utility, grey, and TOPSIS, have been presented and combined to identify the proper machine parameters for Nitinol 56 cutting.ii.ANOVA was conducted to evaluate the impact of process variables on the mentioned output performance.The analysis revealed that the feed significantly influences the MRR and surface roughness, contributing 50.65 and 33.62%, respectively.Meanwhile, the spindle speed plays a significant role in TW, accounting for a major contribution of 51.9%.iii.The optimal output process responses for machining Nitinol 56 were observed at f = 0.133 mm•rev −1 , d = 0.6, and S = 835 RPM.iv.Significantly, all the previously mentioned methods result in the same optimal input settings.

Figure 8 :
Figure 8: Percentage contribution of machining parameters for (a) the MRR and (b) surface roughness.(c) TWR of all input variables.

Figure 9 :
Figure 9: Chip formed during different machining conditions.

Figure 10 :
Figure 10: Main effect plot for overall R.

9 p
), only if = B B* q(where A* is the optimal value), then = N

Figure 11 :
Figure 11: Main effect plot for O u .

Figure 12 :
Figure 12: Main effect plot for Cc.

Table 1 :
Process variables and their corresponding levels

Table 3 :
Experimental data

Table 4 :
ANOVA technique for the MRR

Table 5 :
ANOVA technique for surface roughness

Table 6 :
ANOVA technique for TW

Table 7 :
Normalized experimental data along with grey relational coefficients and corresponding grey relation grades

Table 8 :
Utility values for O u (overall utility) with S/N ratio and predicted SN ratio and corresponding output characteristics Sr. no.N p -Ra N p -MRR N p -TW O u

Table 11 :
Closeness coefficient corresponding to S/N ratios, predicted S/ N ratio for optimal setting, and positive and negative separation distances

Table 9 :
Weighted and normalized values corresponding to the output values