The specimen for wear studies was cut from the Al alloy bar. The specimen cross section used was 1 cm × 1 cm with a length of 4.5 cm. The top and bottom surfaces of specimen were made planer by polishing against emery papers of appropriate grits. For the preparation of the surface to be used for wear studies, the final grit size of the emery paper was the same as the one to be used for the wear studies.

For wear study, the material selected is Al 6061 alloy. The wear studies were conducted against grinding disc for different load at different orientation. The selection of load and orientation discussed later.

For wear studies the following loads were selected 1) 5 N, 2) 10 N, 3) 15 N, 4) 20 N. For each load the orientation of the specimen was kept at 0˚, 30˚, 45˚, 60˚ and 90˚ respectively.

RSM is a collection of mathematical and statistical techniques that are useful for the modeling and analysis of problems in which output or response is influenced by several input-variables and objective is to find the correlation between the response and the input-variables. Farias et al. [16] studied the sliding wear of austenitic stainless steels. They adopted to obtain an empirical model of wear rate as a function of applied load and sliding velocity using RSM. A polynomial model of second order type was proposed to represent the relationship between wear loss and tribo test independent variables. In the present work, the input variables are angle of orientation (A) measured in degree and normal applied load (L) measured in Newtons and the output (response) is wear loss (W) measured in milligram (mg). A response surface model given in Equation (1) is usually expressed as:

where A is constant of equation. B₁, B₂, B₃, B₄, … B_n are the unknown regression coefficients and X₁, X₂, … X_k are the input variables that influence the response Y, k is the number of input factors. The method of least square is used to estimate the coefficients of the second order model. The response surface analysis is then done in terms of the fitted surface. The degree of significance of the model was tested by analysis of variance (ANOVA) using the software MINITAB-15.

A central composite design (CCD) is used with two design factors of each of three levels to describe response of the wear loss and to estimate the parameters in the second-order model. Table 1 shows important factors and their levels for abrasive wear. A central composite design (CCD) has following parameters.

Central composite design of full factorial was used, a total of 14 experiments are conducted and regression coefficients were calculated as shown in Table 2.

By analyzing the estimated regression coefficients of CCD (Full Model-Uncoded Units) as shown in Table 3. The mathematical model of wear loss (W) can be expressed in term of the un-coded values of the independent variables in the Equation (2) given below:

Analysis of variance (ANOVA) and the F-ratio test have been performed to check the adequacy of the model as well as the significance of the individual model coefficients. The ANOVA was carried out on the model for a confidence level of 95%. The results of ANOVA tables for wear loss are listed in Table 2 and Table 4. Table 2 presents the ANOVA table for the second order model propose for wear loss given in Equation (2). It can be appreciated that the P-value is less than 0.05 which means that the model is significant at 95% confidence level. Furthermore, the significance of each coefficient in the full model was examined by the t-values and P-values and the results are listed in Table 4. The larger values of t-test and smaller values of “P” indicate that the corresponding coefficient is highly significant [17] . Hence, the results given in Table 4 suggest that the influence of load (L²) and orientation × load (A × L) are non-significant and therefore can be removed from the full model to further improve the model. By doing so, the full model for the wear loss is expressed in Equation (3).

ANOVA was performed on the reduced model and the results are presented in Table 5 in coded units and Table 6 in un-coded units and found that the model is highly significant. Thus, Equation (4) represents the un-coded form of final empirical model for wear loss of Al 6061. It should be noted that the above equations are valid over the range of conditions 0˚ ≤ orientation (angle) ≤ 90˚ and 10 N < normal applied load < 20 N for abrasive wear of above composite against 400 grit size.

By taking regression coefficient values for reduced model, the full model for the wear loss can be reduced as:

The regression model is used for determining the residuals of each individual experimental run. The difference between the measured values and predicted values are called residuals. The residuals are calculated and ranked in ascending order. The normal probabilities of residuals are shown in Figure 1. The normal probability plot is used to vary the normality assumption. As shown in Figure 1, the data are spread roughly along the straight line. Hence it can be concluded that the data are normally distributed [18] .

Figure 2 is used to show the correlation between the residuals and from this, it is emphasized that a tendency to have runs of positive and negative residuals indicates the existence of a certain correlation. Also the plot shows that the residuals are distributed evenly in both positive and negative long the run. Hence the data can be said to be independent.

Figure 3 indicates the residuals versus fitted values, which shows only the maximum variation of −0.04 to +0.04 gm in wear loss between the measured and the fitted values. This plot does not reveal any obvious pattern and hence the fitted model is ample.

The goodness of fit of the mathematical models was also tested by coefficient of determination (R²) and adjusted coefficient of determination (R² adj). The R² is the proportion of the variation in the dependent variable explained by the regression model. On the other hand, R² adj is the coefficient of determination adjusted for the number of independent variables in the regression model. Unlike R², the R² adj may decrease if the variables are entered in the model that does not add significantly to the model fit. The R² and R² adj values of mathematical models are found 0.974 and 0.967 respectively which clearly indicate the very good correlation between the experimental and the predicted values of the responses.

The performance of the developed model was tested using five experimental data which were never used in the modeling process. The results predicted by the developed model were compared with the measured values and also average percentage deviation (φp) was calculated and presented in the Table 7. The results indicate that the model predicted wear loss has good validity with acceptable percentage deviation.