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Abstract

NiTi is a shape memory alloy, mostly employed in cardiovascular stents, orthopedic implants, orthodontic wires, micro-electromechanical systems and so on. The effective and net shape machining of NiTi is very critical for excellent response of this material in medical and other applications. The present experimental work on wire electrical discharge machining process identifies the influence of process parameters that affect the cutting rate, dimensional shift and surface roughness while machining of porous nickel–titanium (Ni₄₀Ti₆₀) alloy. Porous Ni₄₀Ti₆₀ alloy was produced in-house using powder metallurgy technique. Response surface methodology–based central composite rotatable design has been used for the planning of experiments on wire electrical discharge machining. Empirical relations have been developed between the process parameters (pulse on-time, pulse off-time, servo voltage and peak current) and response variables. Desirability approach has been used for optimizing the three response variables simultaneously. Confirmation experiments were also performed at the optimized settings and reflect a close agreement between the predicted and experimental values (percentage error varies from −6.13% to +6.85%). Using wire electrical discharge machining, NiTi alloy can be machined easily and successfully in single-cutting operation, but after the first cut in wire electrical discharge machining, a surface projection appears on work surface which is the unmachined material on work surface.

Keywords

Central composite rotatable design multi-response optimization porous NiTi alloy response surface methodology unmachined area wire electric discharge machine

Introduction

NiTi alloy is a smart material because of its specific characteristics such as shape memory effect (SME), super elasticity and biocompatibility.¹ Therefore, this material is mostly employed in orthopedic implants, cardiovascular stent technology, orthodontics, micro-electromechanical systems (MEMS) in aerospace and electrical switching applications and so on. The unique characteristics of NiTi can be modified and improved by controlling the chemical composition and microstructure. Upon a specific temperature change, the equiatomic NiTi can undergo a reversible solid-state transformation from ordered cubic crystal structure (B2) called austenite to distorted monoclinic (B19′) called martensite.

Additive manufacturing methods^2,3 are advanced techniques used to fabricate net shape geometries of NiTi alloy with controlled microstructures. But these methods are highly expensive and still not commercialized. NiTi alloy can be produced in cylindrical shapes and rectangular sheets with controlled composition using vacuum induction melting⁴ and powder metallurgy process with sintering under vacuum or inert gas atmosphere.⁵ After fabrication, NiTi alloy is machined in final geometry for end use. Machining of NiTi with conventional machining methods (such as turning, milling and drilling) is very difficult because of strain hardening of surface, poor surface finish, high tool wear rate and burr formation at machined surface.^6–8 The most appropriate and widely accepted nontraditional machining method is numeric controlled wire electrical discharge machining (WEDM), which is spark-erosion, thermo-electric machining method to cut hard and conductive metal and alloys.⁹ The electrode or wire tools used in this process are of brass, copper and molybdenum wire with 0.05–0.30 mm diameters which continuously travel through the work-piece during machining.

The metal removal in WEDM occurs due to the generation of discrete sparks between the small gap of tool and work-piece which is controlled by the electrical pulses generated by power supply. The spark plasma generates very high temperature at work surface which vaporizes the localized area of work material. Deionized water as dielectric flows between the spark gap to flush all the debris. High surface finish, machining of complex shapes, higher dimensional accuracy and automated un-interrupted continuous operation are the main features of WEDM process.^10,11

Past research work on machining of NiTi alloys

Weinert and Petzoldt⁸ machined the NiTi (nearly stoichiometric composition) with the help of CNC lathe using coated cemented carbide and an emulsion consisting of 5% “Avantin 335” as coolant and 95% water was used as a lubricant. Tool wear, process force and hardening of machined surface were the response variables, while cutting rate (CR) and feed rate were the input process parameters. Poor chip breaking and burr formations were observed during machining. Lin et al.⁷ experimentally analyzed the machinability of equiatomic NiTi in drilling process using three types of drills made of WC, high-speed steel (HSS) and TiN-coated HSS. Same work material was also processed with emery blade and diamond blade. TiN-coated HSS drill shows better drill characteristics than other two. Emery blade represents better machining ability due to new cutting edges of SiC and Al₂O₃ powders. Kaynak et al.^12,13 used liquid nitrogen (LN₂) as a lubricant while machining NiTi on CNC lathe using cutting tool insert of grade KC 5410 with TiB₂ coating. Wear rate of tool reduces to 50% in a cryogenic environment. Surface roughness (SR) on machined NiTi surface increases with tool wear. Cryogenic machining resulted in better surface but for a short machining time (upto 5min.)., After this short machining time of 4-5 min., dry, cryogenic and minimum quantity lubrication (MQL) machining has equivalent SR.

To overcome the problems such as burr formation and tool wear in machining of NiTi alloys with conventional machining processes, nontraditional machining have been attempted. In an attempt made by Abedi et al¹⁴ on electrical discharge machining (EDM) process, material removal rate (MRR) of TiNi was found to be increased with the increase in the value of pulse current and pulse duration. The micro-hardness at machined surface reached up to 750 Hv due to the presence of white layer.⁶ The SR during the machining first decreases and then increases with the increase in pulse off-time (T_off) and current. The most significant parameter for MRR was pulse current and that for SR was pulse on-time (T_on).¹⁴ Alidoosti et al.¹⁵ processed NiTi with EDM using different electrode materials. Results show that MRR in copper electrode and tungsten–copper (W-Cu) electrode are the same. Work stability in the case of W-Cu electrode is higher, while the impurity level on the machined surface processed by Cu electrode is lower.

Precipitates of TiC were found on the melted zone during the EDM of NiTi using W-Cu electrode. These precipitates diminished the SME of material. To retain SME, these surfaces were further processed either by slow energy process or by removal of melted zone by electrochemical action.¹⁶ Alloys of NiTi consisting Cr and Zr were also processed with EDM, and it has been found that with the increase in pulse duration and discharge current, MRR and SR increase due to the strike of discharge more intensely onto the surface, and hence, erosion effect is more.¹⁷

The presence of recast layer decreases the shape recovery effect, but machined TiNiZr exhibits a good shape recovery.^18,19 TiNiCr and TiNiZr were machined with the help of WEDM, and it was found that higher pulse duration diminishes the surface finish. The hardness up to 875 Hv was reached due to the presence of oxide of TiO₂, TiNiO₃, ZrO₂ and Cr₂O₃.²⁰ Narendranath et al.²¹ investigated that the SR was more sensitive toward the T_on at low peak current (IP) compared to high IP during the WEDM of NiTiCu. MRR was also found to increase with increase in T_on. LotfiNeyestanak and Daneshmand²² investigated the machining of Nitinol-60 on WEDM. A recast layer of 10–20 μm has been found on Nitinol-60 surface, which contains CuZn, Ti₂Ni, NiO and Cu₂O metal oxide. These metal oxides enhance the micro-hardness several times on the surface up to the depth of 20 μm when compared to micro-hardness before WEDM.

The specific properties of NiTi alloys creates difficulty in conventional machining due to strain hardening effect, cyclic hardening, intermetallic compound and rapid tool wear rate. WEDM can be proved to be a better alternative to machine the complex geometry in NiTi alloys. But the literature available on machining of NiTi on WEDM is very limited. Therefore, in the present work, an attempt has been made for an experimental study of NiTi on WEDM process.

Experimentation

Work material

Although NiTi alloy is biocompatible material best suited for orthopedics and orthodontics, the minor possibility of release of Ni⁺ ions into human bodies cannot be ignored. Therefore, a protective and noncorrosive layer on NiTi alloy is required for medical applications. But in NiTi alloy, a protective coating of TiO₂ is generated by the reaction of atmospheric oxygen which stops the release of Ni⁺ ions into human bodies. Therefore, in the present work, weight % of Ti is considered more when compared to Ni, and Ni₄₀Ti₆₀ is produced using powder metallurgy process.

Porous NiTi alloys are gaining more importance in medical applications due to their low elastic moduli that closely match with human bone and high bone tissue ingrowth in pores of metallic implants. Thus, porous NiTi alloys are promising biomaterials for hard tissue replacement.²³ Therefore, in the present work, porous NiTi is fabricated using low-temperature additives and low-compaction pressure in powder compaction stage. Figure 1 shows the scanning electron microscopic (SEM) image of porous structure of the present work sample. This figure shows that the pores are of irregular sizes distributed over larger areas, and many pores are interconnected. The chemical composition of titanium and nickel powder is given in Table 1.

Figure 1.

SEM micrograph of porous NiTi.

Table 1.

Chemical composition of titanium and nickel powder.

Sr. no.	Titanium powder		Sr. no.	Nickel powder
Sr. no.	Elements	Observation (wt. %)	Sr. no.	Elements	Observation (wt. %)
1.	Ni	0.086	1.	Fe	0.031
2.	Fe	0.930	2.	Cr	0.024
3.	V	0.341	3.	Co	0.09
4.	Mo	0.05	4.	Ni	99.84
5.	Ti	98.59

Process variables

In the present work, experiments were performed on five-axis Sprintcut ELPULS 40 manufactured by Electronica Machine Tool Ltd, India. Based on previously published work on WEDM of high-strength and high-temperature resisting materials,^24,25 four input variables, namely, T_on, T_off, servo voltage (SV) and IP, have been selected for investigation. Response variables which are to be measured at various settings of process parameters are CR, dimensional shift (d_sh) and SR. Based on trial experiments and previously published work on WEDM, the range of variable process parameters is selected as follows: T_on = 105–124 μs, T_off = 25–55 μs, SV = 30–80 V and IP = 110–190 machine unit (mu). Different levels are depicted in Table 2. Zinc-coated brass wire of 0.25 mm diameter is used due to its capability to uphold high discharge energy.

Table 2.

Process variables, their units and levels.

Sr. no.	Process parameter	Units	Levels
Sr. no.	Process parameter	Units	−2	−1	0	1	2
1.	Pulse on-time (T_on)	μs	98.52	105	114.5	124	130.48
2.	Pulse off-time (T_off)	μs	14.77	25	40	55	65.23
3.	Servo voltage (SV)	V	12.96	30	55	80	97.04
4.	Peak current (IP)	mu	82.73	110	150	190	217.27
Fixed process parameters
Sr. no.	Work-piece			Ni₄₀Ti₆₀
1.	Work-piece thickness			5 mm
2.	Wire tension			7 N
3.	Wire feed			6 m/min
4.	Water pressure			7 kg/cm²
5.	Servo feed			2010 mm/min
6.	Dielectric			Distilled water
7.	Dielectric conductivity			20 S
8.	Dielectric temperature			20 °C–24 °C

The work-piece profile to be cut is shown in Figure 2(a). The wire entered through the work-piece at point A (10, 5). It will travel a clockwise path along AB, BC, CD, DE and EA and will exit the work-piece from point A (10, 5).

Figure 2.

(a) Work-piece profile and (b) d_sh representation on WEDM.

In the present work, three response variables have been observed in WEDM process. CR is measured as linear movement of table per minute (in mm/min) which is displayed on machine tool monitor screen. d_sh (in mm) is the gap between work surface and wire periphery as revealed in Figure 2(b). “D” denotes the wire diameter. d_sh helps to predict accurate wire offset for higher dimensional precision. In most of the research, SR value (in μm) is measured in terms of mean absolute deviation (Ra). A few researchers used the term total deviation (Rz). In this research, SR value is measured in terms of Rz using the digital surface tester Mitutoyo 201P (least count: 0.01 μm). SR value represent the average of readings of roughness taken at six places perpendicular to the direction of cut.

Experimental planning

Experiments were performed on a random basis (run order) using response surface methodology (RSM). RSM is a collection of statistical and mathematical techniques that requires sufficient number of experimental data used for the modeling and analysis of a problem in which responses are affected by several input parameters, and the main objective is to optimize these responses individually and collectively.²⁶ The process of RSM is as follows:

Selection of the important input parameters and their working range;

Selection of experimental design to reduce the total number of experiments to be conducted for the evaluation of influence of input variables on response variables;

Regression analysis to generate the statistical model between input parameters and response variables;

ANOVA and lack of fit test to investigate the significant parameters, adequacy of the regression model;

Selection of optimal settings of input parameters for highest possible values of response variables;

Correspond to optimal settings, confirmation of the predicted values of response variables and calculation of experimental errors;

If regression model is not acceptable, then screening of input parameters is carried out, and the process is repeated.

In the present work, according to the first step in RSM, four important input variables have been selected. In WEDM, process parameters can be categorized into three major categories, namely, discharge parameters (IP, T_on, T_off and SV), wire electrodes (wire material, wire diameter, wire feed rate, wire tension and wire electrode coating) and dielectric conditions (type of dielectric, dielectric flow rate and conductivity). Based on trial experiments and previous literature on WEDM of hard to machine materials, only discharge parameters, namely, IP, T_on, SV and T_off, have been selected as input variable parameters, while parameters under the category of wire electrode and dielectric conditions have been assigned a constant value as listed in Table 2.

According to the second step of RSM, face-centered composite rotatable design (CCRD) has been selected. A well-designed experimental layout can reduce the total number of experiments. Using Design-Expert 7.0 (DX-7), a statistical tool, an experimental matrix has been generated for CCRD for four input variables as shown in Table 3. Second-order central composite design is the most efficient tool in RSM to create the mathematical relation of the response surface using the smallest possible number of experiments without losing its accuracy.²⁷ The response variable (y) can be modeled as in equation (1)

y = β_{0} + \sum_{i = 1}^{k} β_{i} x_{i} + \sum_{i = 1}^{k} β_{ii} x_{i}^{2} + \sum_{i < j} β_{ij} x_{i} x_{j} + ε

(1)

Table 3.

Design of experiment (run-order basis) and experimental results.

Standard order	Run order	T_on	T_off	SV	IP	CR (mm/min)	d_sh (mm)	SR (μs)
7	1	105	55	80	190	0.0753048	0.07493	1.69
5	2	124	25	30	190	0.683724	0.1197	2.99
14	3	114.5	40	97.04	150	1.0869	0.0972	3.64
16	4	114.5	40	55	217.27	0.170931	0.1127	2.34
2	5	124	55	30	110	0.273486	0.1083	2.19
12	6	114.5	65.23	55	150	0.474086	0.1098	2.75
17	7	114.5	40	55	150	1.18686	0.1027	4.05
9	8	98.52	40	55	150	0.218308	0.0741	2.49
4	9	105	55	30	190	0.0434682	0.0623	1.62
20	10	114.5	40	55	150	1.13472	0.1099	3.79
8	11	105	25	30	110	0.170273	0.0519	1.83
18	12	114.5	40	55	150	1.12977	0.1101	3.65
21	13	114.5	40	55	150	0.960557	0.1113	3.66
11	14	114.5	14.77	55	150	0.640991	0.0531	3.01
1	15	124	55	80	110	1.25001	0.0889	3.77
6	16	105	25	80	110	0.436617	0.1009	2.75
19	17	114.5	40	55	150	1.13037	0.1085	3.63
10	18	130.48	40	55	150	1.97815	0.1391	5.75
15	19	114.5	40	55	82.73	0.982853	0.0843	3.37
3	20	124	25	80	190	1.58111	0.0813	4.93
13	21	114.5	40	12.96	150	0.113509	0.0779	1.33

T_on: pulse on-time; T_off: pulse off-time; SV: servo voltage; IP: peak current; CR: cutting rate; d_sh: dimensional shift; SR: surface roughness.

where x_i, x_j and x_k are the input or independent process parameters; β₀, β_ii and β_ij are the unknown parameters or regression coefficients; and ε is the random error.

According to CCRD with four process parameters at smaller set of experiments, a total of 21 experiments are required to be performed as given in Table 3. The next step of RSM, that is, regression analysis and ANOVA, has been performed for response variables in section “Results and discussion.” The selection of optimal parameter setting and confirmation results is discussed in section “Multi-response optimization: desirability approach.”

Results and discussion

A total of 21 experiments were planned and performed according to the experimental layout.²⁸ The average values of CR (in mm/min), d_sh (in mm) and SR (in μm) are listed in Table 3. The analysis of data, including test for significance on model and its coefficients, percentage contribution of process parameters have been performed using ANOVA.²⁹

Analysis of CR

Fit summary of analysis suggests that the quadratic model for CR is significant with F-value = 103.53 and p-value < 0.0001,. The results are depicted in the ANOVA Table 4. A larger F-value corresponds to a smaller p-value and more percentage contribution. Backward elimination with 95% confidence level is used to remove the nonsignificant terms. During this, the model of CR is not hierarchical, so T_off (B in coded form) is hierarchically added. A model is said to be hierarchical if the presence of higher-order terms (such as interaction and second-order terms) requires the inclusion of all lower-order terms contained within those of higher order.

Table 4.

Pooled analysis of variance (CR).

Source	SS	df	MS	F-value	p-value	PC = (SS_i/SS_t) × 100
Model	5.97	11	0.54	103.53	<0.0001		Significant
A-T_on	1.55	1	1.55	295.23	<0.0001	25.74751
B-T_off	0.014	1	0.014	2.66	0.1376	0.232558
C-SV	1.06	1	1.06	202.56	<0.0001	17.60797
D-IP	0.33	1	0.33	62.84	<0.0001	5.481728
T_on × T_off	0.25	1	0.25	47.1	<0.0001	4.152824
T_on × SV	0.31	1	0.31	59.17	<0.0001	5.149502
T_on × IP	0.036	1	0.036	6.84	0.028	0.598007
T_off × IP	0.065	1	0.065	12.45	0.0064	1.079734
$T_{off}^{2}$	0.54	1	0.54	103.27	<0.0001	8.9701
SV²	0.46	1	0.46	87.52	<0.0001	7.641196
IP²	0.5	1	0.5	95.97	<0.0001	8.305648
Residual	0.047	9	5.25E–03			0.780731
Lack of fit	0.018	5	3.51E–03	0.47	0.7831	0.299003	Nonsignificant
Pure error	0.03	4	7.41E–03			0.498339
Corresponding total (model SS + residual SS)	6.02	20
R²		0.992159		Predicted R²		0.963656
Adjusted R²		0.982575		Adequate precision		36.80081

T_on: pulse on-time; T_off: pulse off-time; SV: servo voltage; IP: peak current; SS: sum of square; df: degree of freedom; MS: mean square; PC: percentage contribution.

The lack of fit determines the measure of failure of model to represent data in the experimental domain at which points are not included in the regression variation that cannot be accounted for random error. A nonsignificant lack of fit is desired, while in significant lack of fit indicated by a larger F-value, response predictor is discarded.²⁷

In the pooled ANOVA of CR (Table 4), the lack of fit is nonsignificant, and p-value is 0.7831. The value of R² is 0.9921, which shows that 99.21% variations can be explained by this model and only 0.79% variation cannot be explained, indicating a good accuracy. The difference between adjusted R² and predicted R² is less that 0.2, which is also a sign of good model. Adequate precision measures the ratio of significant factors to nonsignificant factors, that is, signal to noise. This value (i.e. adequate precision) must be larger than 4 for an adequate model. Here, the value is 36.80, indicating a significant signal-to-noise ratio. Using DX-7, a statistical tool, multiple regression analysis on the experimental data has been performed, and the empirical relation in terms of actual factors is obtained as follows

\begin{matrix} CR = - 6.99548 + 0.045027 \times T_{on} + 0.24853 \times T_{off} \\ - 0.053022 \times SV - 0.012411 \times IP - 1.91606 E - 003 \\ \times T_{on} \times T_{off} \\ + 8.29332 E - 004 \times T_{on} \times SV + 2.73844 E - 004 \\ \times T_{on} \times IP \\ + 2.33951 E - 004 \times T_{off} \times IP - 8.44310 E - 004 \\ \times T_{off}^{2} - 2.79817 E - 004 \\ \times {SV}^{2} - 1.14455 E - 004 \times {IP}^{2} \end{matrix}

(2)

Figure 3(a) and (b) shows the normal probability plot (i.e. normality test) of residuals and predicted versus actual plot for CR. Most of the residuals fall on a straight line, which means that errors are normally distributed. Figure 3(c) reflects the variation of process parameters on CR. Increase in T_on and IP increases, the CR. Increasing pulse current (IP) for a longer duration (Ton) increases the discharge energy, which causes the high erosion of work material. T_off has an opposite effect on CR as compared to T_on. The main mechanism lies behind this is that if T_off increases, then the intensity of discharge energy decrease, due to reduction of erosion rate.³⁰ Lower SV value favors the CR as observed from Figure 3(c) during the machining of NiTi alloy. The probable reason for this is that at lower value of SV, lower will be the discharge waiting time, which favors productivity. Figure 3(d) shows the percentage contribution of various process parameters on CR. The percentage contribution of each factor is investigated as

% Contribution = \frac{{SS}_{i}}{{SS}_{t}} \times 100

(3)

Figure 3.

(a) Normal plot of residual for CR, (b) predicted versus actual plot for CR, (c) process parameter effect on CR and (d) percentage contribution of parameters for CR.

where SS_i is the sum of square of respective factor and SS_t is the total sum of square.

Here, T_on as the major contributor with contribution 25.75%, followed by SV (17.6%) and IP (5.5%), the percentage contribution of all other factors, that is, quadratic terms and interactions, is given in ANOVA table of CR (Table 4).

Analysis of d_sh

Fit summary suggests a significant quadratic model for d_sh with F-value = 27.1 (p-value < 0.0001) and lack of fit p-value = 0.085, which is nonsignificant as desired for a good model. IP is added to the model to make it hierarchical. From Table 5, it is shown that the terms T_on, T_off and SV; interactions of T_on and T_off, T_on and IP, T_on and SV and IP and SV; and quadratic terms of T_off, IP and SV are significant. Out of these, T_on = 34.6%, T_off = 16.1%, interaction of T_on and IP = 17.8%, interaction of T_on and SV = 12.3% and quadratic term of T_off = 14.4% contribution in d_sh as clarified in the “PC” column of Table 5. The contribution of other parameters is also given in Table 5.

Table 5.

Pooled analysis of variance (d_sh).

Source	SS	df	MS	F-value	p-value	PC
Model	0.01	11	9.18E–04	27.1	<0.0001		Significant
A-T_on	3.46E–03	1	3.46E–03	102.24	<0.0001	34.6
B-T_off	1.61E–03	1	1.61E–03	47.45	<0.0001	16.1
C-SV	9.64E–05	1	9.64E–05	2.85	0.1259	0.964
D-IP	4.03E–04	1	4.03E–04	11.9	0.0073	4.03
T_on × T_off	3.26E–04	1	3.26E–04	9.62	0.0127	3.26
T_on × SV	1.78E–03	1	1.78E–03	52.63	<0.0001	17.8
T_on × IP	1.23E–03	1	1.23E–03	36.35	0.0002	12.3
SV × IP	3.83E–04	1	3.83E–04	11.31	0.0083	3.83
$T_{off}^{2}$	1.44E–03	1	1.44E–03	42.47	0.0001	14.4
SV²	8.75E–04	1	8.75E–04	25.82	0.0007	8.75
IP²	2.12E–04	1	2.12E–04	6.27	0.0336	2.12
Residual	3.05E–04	9	3.39E–05			3.05
Lack of fit	2.59E–04	5	5.18E–05	4.5	0.085	2.59	Nonsignificant
Pure error	4.60E–05	4	1.15E–05			0.46
Corresponding total	0.01	20
R²		0.9707		Predicted R²		0.7365
Adjusted R²		0.9349		Adequate precision		19.208

T_on: pulse on-time; T_off: pulse off-time; SV: servo voltage; IP: peak current; SS: sum of square; df: degree of freedom; MS: mean square; PC: percentage contribution.

The value of R² is 0.9707, which shows that 97.07% variations can be defined by this model and 2.93% variations cannot be explained, which reflects a good accuracy of model. Lack of fit; nonsignificant, difference between adjusted and predicted R² is less than 0.2 and adequate precision is greater than 4 (i.e. 19.208), confirms the adequacy of the proposed model. After regression analysis on the experimental data, the empirical relation in terms of actual factors is obtained as follows

\begin{matrix} d_{sh} & = + 0.41118 - 5.25938 E - 003 \times T_{on} - 3.36173 E - 003 \times T_{off} \\ + 9.68520 E - 003 \times SV - 4.51170 E - 003 \times IP + 6.95763 E - 005 \times T_{on} \times T_{off} \\ - 6.28579 E - 005 \times T_{on} \times SV + 5.07323 E - 005 \times T_{on} \times IP - 6.92125 E - 006 \times SV \times IP \\ - 4.35120 E - 005 \times T_{off}^{2} - 1.22136 E - 005 \times {SV}^{2} - 2.35132 E - 006 \times {IP}^{2} \end{matrix}

(4)

Figure 4(a) shows the normality test of residuals for d_sh and Figure 4(b) represents the predicted versus actual values. In this figure, residual clustered on a straight line, which indicates that residuals are normally distributed. d_sh is the material removed perpendicular to the direction of table feed, which depends on the discharge energy. Figure 4(c) depicts the effect of variation of process parameters on d_sh. With the increase in T_on, T_off and IP, a significant increase in d_sh has been observed. With the increase in T_on, IP and SV, discharge energy increases which increases melting and evaporation of work surface due to large ionization of the spark gap.^30,31 Increase in T_off at high discharge energy results in complete flushing of eroded debris and therefore a low re-deposition of melted material which increases the d_sh. Percentage contribution of process parameters is shown in Figure 4(d), in which it is clearly defined that T_on and T_off have the maximum contribution as compared to SV and IP.

Figure 4.

(a) Normal plot of residual for d_sh, (b) predicted versus actual plot for d_sh, (c) process parameter effect on d_sh and (d) percentage contribution of parameters for d_sh.

Analysis of SR

Pooled version of ANOVA is shown in Table 6, which suggests that quadratic model is statistically significant for SR.

Table 6.

Pooled version of analysis of variance (SR).

Source	SS	df	MS	F-value	p-value	PC
Model	23.68	10	2.37	31.78	<0.0001		Significant
A-T_on	9.64	1	9.64	129.34	<0.0001	39.45968
B-T_off	0.034	1	0.034	0.45	0.5159	0.139173
C-SV	5.16	1	5.16	69.25	<0.0001	21.12157
D-IP	0.53	1	0.53	7.12	0.0236	2.169464
T_on × T_off	0.51	1	0.51	6.85	0.0257	2.087597
T_on × SV	0.8	1	0.8	10.74	0.0083	3.274662
T_on × IP	0.35	1	0.35	4.74	0.0545	1.432665
$T_{off}^{2}$	1.7	1	1.7	22.76	0.0008	6.958657
SV²	3.4	1	3.4	45.61	<0.0001	13.91731
IP²	1.79	1	1.79	23.98	0.0006	7.327057
Residual	0.75	10	0.075			3.069996
Lack of fit	0.62	6	0.1	3.34	0.1314	2.537863	Nonsignificant
Pure error	0.12	4	0.031			0.491199
Corresponding total	24.43	20
R²		0.9695		Predicted R²		0.8706
Adjusted R²		0.939		Adequate precision		20.378

T_on: pulse on-time; T_off: pulse off-time; SV: servo voltage; IP: peak current; SS: sum of square; df: degree of freedom; MS: mean square; PC: percentage contribution.

The F-value of model is 31.78 (significant) with lack of fit value 0.1314 (nonsignificant). T_on, IP, SV, T_on × T_off, T_on × SV, $T_{off}^{2}$ , IP² and SV² are the significant terms identified by ANOVA. The percentage contribution of each term is shown in Table 6; Model-significant, lack of fit-nonsignificant, difference between adjusted and predicted R² less than 0.2 and adequate precision 20.378 (i.e. greater than 4) confirm all requirements of a desired model. After regression analysis, the equation in terms of actual factors is obtained as follows

\begin{matrix} SR & = - 5.28349 - 3.50415 E - 003 \times T_{on} + 0.42973 \times T_{off} \\ - 0.044131 \times SV - 0.041330 \times IP - 2.75418 E - 003 \times T_{on} \times T_{off} \\ + 1.33158 E - 003 \times T_{on} \times SV + 8.59083 E - 004 \times T_{on} \times IP - 1.49413 E - 003 \times T_{off}^{2} \\ - 7.61333 E - 004 \times {SV}^{2} - 2.15636 E - 004 \times {IP}^{2} \end{matrix}

(5)

Figure 5(a) and (b) represents the normal plot of residuals and predicted versus actual value plot. The residuals in this figure are observed on a straight line. This verifies the normality test and signifies that the residuals are normally distributed. Mean value of the five Rz_i (Rz_i is the sum from the height of the highest profile peak and the depth of the lowest profile valley within a sampling length) values from the five sampling length (lr_i) over the total measured length (ln) is termed as overall SR (Rz). The variation of SR with process parameters is shown in Figure 5(c). The SR increases with the increase in T_on. This is due to the fact that with the increase in T_on, discharge energy increases which increases the melting of material and increases the crater size and hence increases SR. The SR decreases with the increase in T_off due to decrease in discharge energy.³² In the present work, the influence of SV and IP on SR is contradicting in comparison to previous studies on WEDM. With the increase in IP from 110 to 150, SR remains constant, but it decreases further with the increase in IP up to 190 A. The probable reason for this fact may be the porosity of the material. At high value of IP, the melted work material may fill the voids or pores of the surface due to high pressure energy in the spark zone which decreases the SR.

Figure 5.

(a) Normal plot of residual (SR), (b) predicted versus actual plot (SR), (c) process parameter effect on SR and (d) percentage contribution of parameters (SR).

The percentage contribution of process parameters on SR is shown in Figure 5(d). T_on has maximum effect (i.e. 39.46%) on SR, followed by SV (21.12%) and IP (2.16%). T_off is nonsignificant with percentage effect 0.14% on SR. The percentage contribution of all interactions and quadratic terms is given in Table 6.

Multi-response optimization: desirability approach

Every machining process carries multiple response variables that may be conflicting in nature. The optimal setting for each response variable may vary depending on its importance for a particular application. In the present work, CR is the “larger the better” type of response while SR and dsh is “lower the better“ type of response. These types of problems can be easily solved by desirability approach. Here, three responses, namely, CR, d_sh and SR, are simultaneously optimized by this approach. The desirability approach uses an objective function D(X), named desirability function. These functions translate a projected value into scale-free value (d_i), called desirability. In this approach, desirability function for each response (Y_i) is investigated. The value of desirability varies from 0 to 1, a value close to 1 is desired. Value of d_i varies over the range and 1. If response Y_i is at goal or target, then d_i = 1. Response outside the satisfactory region is d_i = 0.

The value of importance is selected depending upon the required preference of the response. If any response gives a priority, then its importance is selected as 5. By default, the value of importance for a response is 3. The weighted geometric mean of individual desirability for the responses is compound desirability. Parameter setting having the maximum value of compound desirability gives optimal results of response variables. In the present investigation, the response variables CR, d_sh and SR are chosen to maximize the overall desirability. The optimal setting of process parameters is investigated by attaining maximum compound desirability.³³ The procedure optimization takes place as follows³⁴

Investigating the individual desirability (d_i) for each response;

Coalescing the individual desirability for getting the compound desirability (D);

Maximizing the compound desirability and finding the optimal settings of the process parameters.

The simultaneous objective function is a geometric mean of all transformed responses

D = {(d_{1} \times d_{2} \times d_{3} \times \dots \times d_{n})}^{1 / n} = {(Π_{i = 1}^{n} d_{i})}^{1 / n}

(6)

where n is the number of responses in the measure. If any of the response falls outside the desirability range, the overall function becomes zero. Equation (6) can be modified as equation (7) by incorporating the concept of assigning different importance to responses and can be extended to

D = {(d_{1}^{I_{1}} \times d_{2}^{I_{2}} \times \dots \times d_{n}^{I_{n}})}^{1 / n}

(7)

to reflect the possible difference in the preference of different responses, where the importance satisfies 0 < I_i < 1 and

\sum_{i = 1}^{n} I_{i} = 1

(8)

As defined in the previous text, it is clearly mentioned that the objective function (i.e. desirability) varies from zero (outside the limit) to one (at the goal). Importance is selected according to the preference of a response. If there are numerous responses, then all goals coalesced into one desirability function. The “Goal” field for responses contain five choices: “none,”“maximum,”“minimum,”“target” or “in range.” Out of these, one is selected for simultaneous optimization. Process parameters are always in design range by default. The meanings of goals are as follows:

Range

d_i = 0 if low value > response > high value

d_i = 1 if response changes from low to high

Target

d_i = 0 if response < low value

0 ≤ d_i ≤ 1 because response changes from low to target

1 ≥ d_i ≥ 0 because response changes from target to high

d_i = 0 if response > high value

Minimum

d_i = 1 if response < low value

1 ≥ d_i ≥ 0 because response changes from low to high

d_i = 0 if response > high value

Maximum

d_i = 0 if response < low value

0 ≤ d_i ≤ 1 because response changes from low to high

d_i = 1 if response > high value

The d_i for “in range” are included in the product of desirability function D but not counted in determining n

D = {(Π d_{i})}^{1 / n}

Three-dimensional (3D) interaction plot (T_on and T_off) of desirability is shown in Figure 6(a). It is clear that with the increase in T_on, the desirability increases and attains a value of 0.710. This is a maximum value of desirability at which T_on is at 124 and T_off is at 25. A decrement in the desirability is observed when T_off increases. Higher value of T_on and smaller value of T_off favor desirability. Figure 6(b) shows the histogram of desirability, in which red bars are the desirability of the input process parameters (which is always equal to 1), while blue bars represent the individual desirability of response variables. The lowest blue bar is the combined or compound desirability of response variables. The individual desirability of CR, d_sh and SR are 0.6004, 0.9800 and 0.6082, respectively. DX-7 with RSM is used to optimize the machining parameters. As shown in Table 7, experiments are performed by varying the importance of response variables. First of all, same importance (i.e. 3) is given to all response variables. The obtained predicted response variables are compared with the experimental responses at the given parameter setting. This is also known as confirmation experiment for a specified parameter setting.

Table 7.

Predicted values of response variables.

Importance	Solution	T_on	T_off	SV	IP	CR	d_sh	SR	Desirability
CR: 3, d_sh : 3, SR: 3	1	124	25	30.2	110	1.2113	0.053	3.07	0.710	1
	2	123.67	25	30.47	110.02	1.2027	0.053	3.07	0.708
	3	123.66	25	30	110.59	1.1880	0.054	3.04	0.706
CR: 5, d_sh : 1, SR: 1	1	122.09	25	80	110	1.9781	0.048	4.67	0.817	2
	2	122.12	25	79.26	110	1.9781	0.049	4.68	0.816
	3	122.16	25	78.48	110	1.9781	0.049	4.68	0.816
CR: 1, d_sh : 5, SR: 1	1	123.56	25	30	110.05	1.1819	0.053	3.03	0.853	3
	2	124	25.23	30	110.01	1.2034	0.054	3.06	0.848
	3	124	25.46	30.01	110	1.2024	0.055	3.06	0.843
CR: 1, d_sh : 1, SR: 5	1	112.27	25	30	110	0.5933	0.051	2.33	0.695	4
	2	112.81	25.13	30.13	110	0.6265	0.052	2.37	0.694
	3	111.61	25	30.47	110	0.5698	0.051	2.31	0.693

T_on: pulse on-time; T_off: pulse off-time; SV: servo voltage; IP: peak current; CR: cutting rate; d_sh : dimensional shift; SR: surface roughness.

Figure 6.

(a) 3D interaction plot of T_on and T_off and (b) desirability histogram.

In the second set of experiments, importance 5 is given to CR, while all others are kept at importance 1. Predicted response is again compared with the experimental values at the optimal setting of maximum desirability. Similarly, in the third and fourth sets of experiments, importance level 5 is given to d_sh and SR, respectively. Confirmation experiment for each optimal setting is performed and is given in Table 8 along with the percentage error between the predicted value and experimental value. The percentage error between the experimental and predicted values of all response variables is calculated as per equation (9), and it varies from −6.13 to +6.85. This represents the excellent result reproducibility

\begin{matrix} Percentage error (%) \\ = \frac{(Experiemntal value - Predicted value)}{Experimental value} \times 100 \end{matrix}

(9)

Table 8.

Experimental results at the optimal settings.

Importance		CR	d_sh	SR
CR: 3, d_sh: 3, SR: 3	Predicted value	1.2113	0.053	3.07	1
	Experimental value	1.20	0.0569	3.16
	% Error	−0.94	6.85	2.84
CR: 5, d_sh: 1, SR: 1	Predicted value	1.9781	0.048	4.67	2
	Experimental value	2.06	0.0507	4.42
	% Error	3.97	5.32	−5.65
CR: 1, d_sh: 5, SR: 1	Predicted value	1.1819	0.053	3.03	3
	Experimental value	1.13	0.0563	3.18
	% Error	−3.74	5.86	4.71
CR: 1, d_sh: 1, SR: 5	Predicted value	0.5933	0.051	2.33	4
	Experimental value	0.559	0.049	2.26
	% Error	−6.13	−4.08	−3.09

CR: cutting rate; d_sh: dimensional shift; SR: surface roughness.

SEM analysis after WEDM

Although WEDM is a best alternative to generate intricate and complex profiles in hard metal alloys and metal matrix composites, with high degree of accuracy, but damaged surface layer with poor surface integrity is a major disadvantage of WEDM. After WEDM, machined surface of NiTi alloy, generally, consists of a white layer which constitutes precipitates of TiC and metal oxides. The micro-hardness of this white layer reaches up to 875 Hv which is several times greater than bulk hardness of NiTi alloy. This white or brittle layer diminishes the SME and degrades the biocompatibility of NiTi alloy.^16,20,22

In the present work, a white layer or recast layer of thickness 10–15 μm was found on work samples. Figure 7 shows the SEM image of recast layer on machine surface of Ni₄₀Ti₆₀. Higher the thickness of white layer, higher the probability of diminishing of specific characteristics of Ni₄₀Ti₆₀.

Figure 7.

White layer on Ni₄₀Ti₆₀ after WEDM.

Also, in WEDM, after the first cut, a small edge line is found on work surface which represents the unmachined material left on work surface. Jangra³⁵ has investigated this unmachined area left on work surface as represented in Figure 8. In Figure 8, the dotted line (OIF) shows the wire path starting form point O. D is the effective spark diameter which is the sum of wire electrode diameters (d) and spark gap (SG). According to the tool path profile, wire electrode should reach the point I to complete the machining job. But in actual practice, cutting takes place earlier at point F, and no spark occurs further. As a result, some unmachined area or projection left on work surface.

Figure 8.

Unmachined area on work surface after rough cut in WEDM.³³

In the present work, similar to Figure 8, an unmachined area in triangular shape appears on machined surface of Ni₄₀Ti₆₀ when the wire tool completes clockwise path A-B-C-D-E-A as mentioned in Figure 2. The height or shape of the unmachined area on work surface depends on the effective spark diameter (D) which is highly affected by the discharge energy. Therefore, at low discharge energy (T_on: 105 μs, T_off: 55 μs, SV: 80 V and IP: 150 mu), a sharp triangular shape is obtained at work surface, while deteriorated surface projections are obtained at higher discharge energy as shown in Figure 9(a)–(c) respectively.

Figure 9.

Unmachined surface area corresponding to (a) low discharge energy (T_on: 105 μs, T_off: 55 μs, SV: 80 V and IP: 150 mu; (b) medium discharge energy (T_on: 114 μs, T_off: 40 μs, SV: 55 V and IP: 150 mu); and (c) high discharge energy (T_on: 124 μs, T_off: 40 μs, SV: 80 V and IP: 190 mu).

Concluding remarks

In the present work, porous Ni₄₀Ti₆₀ alloy has been processed using WEDM process. The influence of four input discharge parameters, namely, T_on, T_off, IP and SV, has been investigated on response variables on porous Ni₄₀Ti₆₀ alloy. Using RSM, CCRD has been used for planning of experiments. The quadratic models have been developed to correlate the input parameters with response variables, namely, CR, d_sh and SR.

The present work concludes the following points:

Processing of porous NiTi alloy on WEDM yields better machining performance in terms of MRR, surface finish and dimensional accuracy if compared with conventional machining processes;

The CR of porous NiTi alloy on WEDM has been obtained in the range of 0.11–1.97 mm/min. The parameter setting that provides maximum CR is T_on = 130 μs, T_off = 40 μs, SV = 55 V and IP = 150 mu. The significant parameters that affect CR up to 95% confidence level are T_on, SV and IP;

d_sh varies from 0.0519 to 0.1397 mm. Minimum d_sh was obtained corresponding to the parameter setting of T_on = 105 μs, T_off = 25 μs, SV = 30 V and IP = 110 mu. The significant parameters that affect d_sh up to 95% confidence level are T_on, T_off and IP;

The SR (in terms of R_z) is obtained in the range of 1.33–5.75 μm. The optimal parameter setting for minimum SR is T_on = 114 μs, T_off = 40 μs, SV = 13 V and IP = 150 mu. The significant parameters that affect SR up to 95% confidence level are T_on, SV and IP;

ANOVA for response variables (i.e. CR, d_sh and SR) reveals that quadratic model is statistically significant for the analysis. The lack of fit is nonsignificant, and adequate precision is more than 4 at 95% confidence level. The coefficient of regression (R²) achieved in the developed model of CR, d_sh and SR is 0.9921, 0.9717 and 0.9695, respectively. Difference between the R² and adjusted R² is less than 0.20 in the analysis of all response variables, which satisfy the conditions of a good model;

To obtain a single setting of parameters for three response variables, multi-response optimization has been carried out using desirability approach. The optimal parameter setting for multi-response variables is obtained as T_on = 124 μs, T_off = 25 μs, SV = 30 V and IP = 110 mu, with desirability value of 0.708. Confirmation experiments were performed corresponding to the optimal parameter settings. The experimental values were compared with the predicted values, and the percentage error ranges between −6.13% and +6.85%;

After the first cut in WEDM, white layer and unmachined surface area are major surface defects that diminish the SME, pseudo-elasticity and biocompatibility of porous NiTi alloy and hence possess a serious challenge for its applications in medical and other fields. Therefore, elimination of white layer and unmachined area on NiTi surface is a future challenge during machining on WEDM. These surface defects can be partially eliminated by controlling the WEDM parameters in the first cut and then using trim cutting operation at optimized parameter setting.

Footnotes

Declaration of conflicting interests

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

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

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Parameter optimization and experimental study on wire electrical discharge machining of porous Ni 40 Ti 60 alloy

Abstract

Keywords

Introduction

Past research work on machining of NiTi alloys

Experimentation

Work material

Process variables

Experimental planning

Results and discussion

Analysis of CR

Analysis of dsh

Analysis of SR

Multi-response optimization: desirability approach

SEM analysis after WEDM

Concluding remarks

Footnotes

Declaration of conflicting interests

Funding

References

Analysis of d_sh