It has been shown consistently that traditional machining method has been inefficient and cumbersome in the manufacturing of a material with high strength and high temperature resistance capacity (Rizwee et al., 1807; Soundhar et al., 2019; Rizwee et al., 2020; Singaravel et al., 2020; Boopathi, 2022). Ti-13Zr-13Nb is a titanium alloy very suitable for bone implant (Shah et al., 2017; Soundhar et al., 2019; Majchrowicz et al., 2019; Ossowska et al., 2020; Kumar et al., 2021) and its fabrication quite demanding compared to other materials because of its mechanical strength and the required complex shape for biomedical implant. Electrical discharge machining method (EDM) has replaced the traditional method in the manufacturing of a complex shape and high strength material due to its high manufacturing efficiency (Zia et al., 2019; Myilsamy & Sampath, 2021). Many studies have been conducted on the use of EDM for the manufacturing of material, to mention few as follows. Świercz & Oniszczuk-Świercz (2017) machined tool steel with EDM and investigated the surface layer properties of the tool steel. Garg & Sharma (2017) examined how accurate the EDM method was in the manufacturing of metal matrix composite (MMC). Gowthaman et al. (2018) made a study on the employement of EDM in machining monel-super alloy. Kavimani et al. (2019) investigated the influence of EDM parameters on surface integrity of reduced graphene oxide/magnesium composite. Muthuramalingam (2019) examined the effect of discharge energy on white layer thickness of EDM process. Grigoriev et al. (2020) studied the machining of oxide nanocomposite using EDM technique. Ming et al. (2021) studied how to minimize energy consumption and exhaust emissions during the machining of Al 6061 and SKD 11 when with EDM technique. Despite several studies on the use of EDM in the manufacturing of materials, optimization of machining conditions for multiple performance characteristics has been a point of concern. This studies employed the use of grey relational analysis as a unique assistance for response surface methodology.
Response surface method (RSM) is a collection of mathematical and statistical techniques for exploring the relationships between several inputs as design variables and one or more response variables as an outcome. RSM uses a sequence of suitably designed experiments to fnd an optimal response that is only an approximation of experimental model. This approximated model is adequate to estimate and apply, even when little is known about the process. Statistical and mathematical approaches such as RSM can be used to extract a model that present optimized operational factors (Dadrasi et al., 2019). Although there have been several studies in the fabrication of biomedical materials, such as bioceramics (Obada et al., 2020; Abifarin et al., 2019; Abifarin, 2021; Obada et al., 2021a; Obada et al., 2021b; Abifarin et al., 2021a; Abifarin et al., 2021b); biodegradable polymers (Oladapo et al., 2019; Tafaoli-Masoule et al., 2019; Oladapo et al., 2021a; Abifarin et al., 2021c; Oladapo & Zahedi, 2021; Oladapo et al., 2021b; Oladapo et al., 2021c); biocompatible metallic implants (Montani et al., 2017; Prakash & Uddin, 2017; Prakash et al., 2018; Prakash et al., 2019; Prakash et al., 2020), these studies had relatively insufficient information in the employment of optimization techniques for a lasting solution in the fabrication of biomedical materials, especially metallic implants like Ti alloy. Stanić et al. (2014) employed CCD technique to optimize operating conditions of antimicrobial activity for the synthesized fluorine doped HAp (FHAp). The operating conditions considered were exposure time, pH of saline, and fluoride concentration and fluoride concentration in apatite samples. The design revealed that there was close agreement in antimicrobial activities of both the experimental and the predicted results. It was further revealed that reduction in pH salinity and increase in fluoride concentration enhanced antimicrobial activities of the synthesized FHAp. Farombi et al. (2018) prepared catfish derived HAp (CHAp) at optimized synthesis conditions, namely; temperature (300-1000 oC), heating time (1-2 h)s using CCD. It was revealed from the design that optimization of the synthesis conditions for quality HAp was gotten. Eosoly et al. (2010) fabricated poly-ε-caprolactone doped HAp (PHAp) and used CCD technique to optimize laser fill power, outline laser power, scan spacing, and part orientation for high performance PHAp. The obtained result from the design revealed that the fabricated HAp depends on the manufacturing direction and scan spacing. It was further established from the result that the mechanical behavior was a function of manufacturing direction. Foroutan et al. (2020) employed CCD to investigate the effect of pH (2-10), temperature (25-45 oC), contact time (10-50 min), initial methyl violet (MV) concentration (5-25 mg/L), and Bio-HAp/MgO quantity (0.5-2.5g/L) on the composite adsorption efficiency. It was revealed that Bio-HAp particles and Bio-HAp/MgO mesoporous composites efficiently reduced the dye content of the pure sample. Pathak & Pandey (2020) employed pressure-less microwave sintering assisted by CCD technique to fabricate zinc–hydroxyapatite (ZHAp) biodegradable composite for load bearing orthopedic application. The CCD was used to investigate the effect and to optimize process factors, namely; wt% of hydroxyapatite, compaction pressure, and microwave sintering factors such as sintering temperature, heating rate, and soaking time on the compressive yield strength and sintered density. The regression analysis in the CCD technique brought out tthe optimum processing conditions and the conditions were validated through confirmation analysis. It was further noted that the fabricated ZHAp correlated with the human native bone required mechanical and degradation characteristics. Ebrahimi et al. (2021) employed CCD to optimize pH, temperature, and hydrothermal treatment time for high yield, size, and crystallinity. It was observed that pH is the most influencing factor affecting the yield, size, and crystallinity of the synthesized HAp. Fern & Salimi (2021) employed CCD technique to examine the effect of processing temperatures (30-50 ˚C), stirring time (30-60 min) and stirring rates (300-500 rpm) on the crystallite size of HAp. The variance analysis from the design revealed R2 coefficient to be 0.8736 and established processing temperature to be the most influencing factor affecting the crystallite size of HAp. Coşkun et al. (2016) employed CCD technique to examine the effect of solution temperature and applied potential on the in vitro corrosion performance of hydroxyapatite coated CoCrMo biomedical alloys. The experimental processing conditions were temperature (10-74°C) and potential (−1.2-−1.9 V). The result revealed that the predicted and experimental values correlated with an R 2 value of 0.9481. The optimized processing conditions were obtained to 32.33°C solution temperature and −1.55 V potential. It was also noted that the HAp coated CoCrMo alloys at optimum conditions displayed excellent crystal formation and high in vitro corrosion resistance.
Grey relational analysis technique has been proven to assist a complex situation and to determine the optimal manufacturing conditions for multiple performance characteristics (Yazdani et al., 2019; Li et al., 2019; Abifarin, 2021). Hence, this study employed grey relational analysis to assist response surface optimization analysis in the manufacturing of Ti-13Zr-13Nb alloy.