**2.1. Parametric design using Taguchi techniques**

In this study, parametric optimization was achieved using Taguchi L18 fractional factorial DOE to evaluate the parameters of the electroplating process used for depositing the Ni/Al2O3 composite coating for improved hardness and wear resistance. The main process parameters evaluated were cathode current density and agitation/stir rate (A), the pH level of the solution (B), particle concentration (C), and bath temperature (D). The parameter settings used, shown in Table 1, were determined through preliminary investigation and represent three different level settings (levels 1–3). The orthogonal array is presented in Table 2 and shows the param‐ eter combination for each of the 18 experimental runs using the level settings, as shown in Table 1 [27].

The optimization can be achieved by calculating the signal-to-noise (S/N) ratio as a quality tool for evaluating the performance of the coatings produced. The S/N ratio (*η*) represents the degree of predictable performance of the coatings in the presence of noise factors. To calculate the S/N ratio, the average and variation of the experimental results can be determined using Equation 1 [6].

$$
\eta = \text{ -10 } \log(\text{MSD}).\tag{1}
$$

where MSD is the mean square deviation for the output characteristic. As the aim of this study is to minimize the wear loss of the coating, the smaller-is-better quality characteristic was selected and can be calculated using Equation 2 [28].

$$\text{Smaller is better} - \text{MSD} = \frac{1}{n} \sum\_{i=1}^{n} y\_i^2 \tag{2}$$


**Table 1.** Experimental levels used for electrodeposition process.


**Table 2.** Taguchi L18 orthogonal array.

On the other hand, given the relationship between hardness and wear resistance [3], the larger-the-better characteristic was used to optimize the coating for hardness, as shown in Equation 3:

$$\text{Largeristic better} - \text{MSD} = \frac{1}{n} \sum\_{l=1}^{n} \frac{1}{y\_l^{2^{\prime}}} \tag{3}$$

where *yi* is the value of wear resistance for the *i*th test; and *n* is the number of tests.

The average value of the response variable at each parameter level was determined by applying Equation 4 to each parameter level for each factor [24]:

$$m\_{A1} = \frac{1}{3}(\eta\_1 + \eta\_2 + \eta\_3). \tag{4}$$

#### **2.2. ANOVA**

h

selected and can be calculated using Equation 2 [28].

**Table 1.** Experimental levels used for electrodeposition process.

**Level Current density (A/mm2 )**

190 Electrodeposition of Composite Materials

**Experiment**

**Table 2.** Taguchi L18 orthogonal array.

where MSD is the mean square deviation for the output characteristic. As the aim of this study is to minimize the wear loss of the coating, the smaller-is-better quality characteristic was

> 1 1 *<sup>n</sup> <sup>i</sup> <sup>i</sup> y n* <sup>=</sup>

**Bath pH (B)**

**Controlled parameters A B C D E**

 1 1 1 1 1 1 1 2 2 2 1 1 3 3 3 1 2 1 1 2 1 2 2 2 3 1 2 3 3 1 1 3 1 2 1 1 3 2 3 2 1 3 3 1 3 2 1 1 3 3 2 1 2 1 1 2 1 3 2 2 2 2 1 2 3 2 2 2 3 1 2 2 3 1 2 2 3 1 3 2 2 3 2 1 3 2 3 3 2 1

Smaller is better MSD = <sup>2</sup>

**Stir rate (rpm)**

**1** 2.3 440 4.0 10 40 **2** 2.5 600 4.45 20 50 **3** – 800 4.6 30 60

**(A)**

= -10 log(MSD), (1)


**Al2O3 concentration (g/L) (C)**

**Bath temperature**

**(°C) (D)**

> The analysis of variance (ANOVA) was carried out to examine the influence of each process parameter on quality characteristics. If some parameters do not significantly affect wear rate, they can be fixed to a minimum level and excluded from the optimization process. The percent contribution of each parameter was calculated by determining the total sum of squared deviation and the individual contribution of each parameter to the sum of squared deviations. These variables were calculated using Equations 7:

$$\text{SS}\_{\text{T}} = \frac{1}{\mathcal{U}} \sum\_{l=1}^{9} \left( \eta\_{l} - \overline{\eta} \right)^{2} \tag{5}$$

$$\overline{\eta} = \frac{1}{\mathcal{G}} \sum\_{l=1}^{9} \eta\_{l} \tag{6}$$

$$\text{SS}\_d = \text{3x} \left( \eta\_{A1} - \overline{\eta} \right)^2 + \text{3x} \left( \eta\_{A2} - \overline{\eta} \right)^2 + \text{3x} \left( \eta\_{A3} - \overline{\eta} \right)^2 \tag{7}$$

The percentage contribution (*ρ*) of each factor to the overall response is determined using Equation 8:

$$
\rho = \frac{\mathbf{SS}\_d}{\mathbf{SS}\_\Gamma} \times 100.\tag{8}
$$
