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In the present study, a mathematical model has been developed to predict the abrasive wear behavior of Al 6061. The experiments have been conducted using central composite design in the design of experiments (DOE) on pin-on-disc type wear testing machine, against abrasive media. A second order polynomial model has been developed for the prediction of wear loss. The model was developed by response surface method (RSM). Analysis of variance technique at the 95% confidence level was applied to check the validity of the model. The effect of volume percentage of reinforcement, applied load and sliding velocity on abrasive wear behavior was analyzed in detail. To judge the efficiency and ability of the model, the comparison of predicted and experimental response values outside the design conditions was carried out. The result shows, good correspondence, implying that, empirical models derived from response surface approach can be used to describe the tribological behavior of the above composite.

Wear is related to interactions between surfaces and more specifically the removal and deformation of material on a surface as a result of mechanical action of the opposite surface [

The objective of this work is to perform the statistical analysis for the abrasive wear behavior of Al 6061 at different orientation and at different loads and to form the equation wear.

In order to carry out the experimental work the following procedure is adopted: 1) specimen preparation; 2) materials selection; 3) response surface methodology (RSM).

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. [

where A is constant of equation. B_{1}, B_{2}, B_{3}, B_{4}, … B_{n} are the unknown regression coefficients and X_{1}, X_{2}, … 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.

. Important factors and their levels for abrasive wear

S.N. | Factors | Notation | Unit | Levels | ||
---|---|---|---|---|---|---|

1. | Orientation | A | Deg | 0 | 45 | 90 |

2. | Applied load | L | N | 10 | 15 | 20 |

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

By analyzing the estimated regression coefficients of CCD (Full Model-Uncoded Units) as shown in

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 ^{2}) 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

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

. Analysis of variance for wear (full model)

Source | DF | Seq SS | Adj SS | Adj MS | F | P |
---|---|---|---|---|---|---|

Regression | 5 | 0.298476 | 0.298476 | 0.059695 | 86.50 | 0.000 |

Linear | 2 | 0.261252 | 0.261252 | 0.130626 | 189.27 | 0.000 |

Square | 2 | 0.034929 | 0.034929 | 0.017465 | 25.31 | 0.000 |

Interaction | 1 | 0.002294 | 0.002294 | 0.002294 | 3.32 | 0.106 |

Residual error | 8 | 0.005521 | 0.005521 | 0.000690 | ||

Lack-of-fit | 3 | 0.004770 | 0.004770 | 0.001590 | 10.59 | 0.013 |

Pure error | 5 | 0.000751 | 0.000751 | 0.000150 | ||

Total | 13 | 0.303997 |

. Estimated regression coefficients for wear using data in uncoded units

Term | Coef |
---|---|

Constant | 0.779142 |

Angle | −0.00168839 |

Load | 0.0166802 |

Angle × angle | −4.81743 × 10^{−}^{5} |

Load × load | −3.02118 × 10^{−}^{4} |

Angle × load | 0.000106444 |

. Estimated regression coefficients of wear (full model)

Term | Coef. | SE coef. | T | P | Description |
---|---|---|---|---|---|

Constant | 0.859688 | 0.01007 | 85.334 | 0.000 | Significant |

Angle | −0.199233 | 0.01072 | −18.577 | 0.000 | Significant |

Load | 0.062033 | 0.01072 | 5.784 | 0.000 | Significant |

Angle × angle | −0.097553 | 0.01561 | −6.251 | 0.000 | Significant |

Load × load | -0.007553 | 0.01561 | −0.484 | 0.641 | Non-significant |

Angle × load | 0.023950 | 0.01314 | 1.823 | 0.106 | Non-significant |

. Estimated regression coefficients for wear (coded units)

Term | Coef | SE | T | P |
---|---|---|---|---|

Constant | 0.85780 | 0.009986 | 85.902 | 0.000 |

Angle | 0.19923 | 0.011531 | −17.279 | 0.000 |

Load | 0.06203 | 0.011531 | 5.380 | 0.000 |

Angle × angle | −0.10070 | 0.015254 | −6.602 | 0.000 |

. Estimated regression coefficients for wear using data in uncoded units

Term | Coef. |
---|---|

Constant | 0.770233 |

Angle | 4.81481 × 10^{−5} |

Load | 0.0124067 |

Angle × angle | −4.97284 × 10^{−5} |

Normal probability plot of the residuals

Residual versus order of the data

The goodness of fit of the mathematical models was also tested by coefficient of determination (R^{2}) and adjusted coefficient of determination (R^{2} adj). The R^{2} is the proportion of the variation in the dependent variable explained by the regression model. On the other hand, R^{2} adj is the coefficient of determination adjusted for the number of independent variables in the regression model. Unlike R^{2}, the R^{2} adj may decrease if the variables are entered in the model that does not add significantly to the model fit. The R^{2} and R^{2} 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

Residuals versus the fitted values

. Comparison of the predicted and measured results

Parameters | Wear loss | |||
---|---|---|---|---|

A | L | Measured | Predicted | Deviation (%) |

0 | 5 | 0.811 | 0.832 | 2.622 |

30 | 5 | 0.761 | 0.786 | 3.294 |

60 | 5 | 0.653 | 0.650 | 0.405 |

30 | 10 | 0.867 | 0.848 | 2.180 |

60 | 10 | 0.766 | 0.712 | 6.999 |

30 | 15 | 0.899 | 0.910 | 1.238 |

60 | 15 | 0.799 | 0.774 | 3.076 |

30 | 20 | 0.965 | 0.972 | 0.743 |

60 | 20 | 0.854 | 0.836 | 2.054 |

Avg. deviation | 2.512% |

The present study has used central composite design of experiments to develop a second-order polynomial equation for describing abrasive wear behavior of Al 6061. The relationship of abrasive wear loss with orientation and applied load has been successfully obtained by using RSM at the 95% confidence level. This model is valid within the ranges of selected experimental parameters of orientation and applied load. The accuracy of the Response Surface Model was verified with three sets of experimental data which were never used in modeling and average percentage deviation calculated as 2.512%. The results obtained are in accordance with the work done on Statistical Analysis for the Abrasive Wear Behavior of Bagasse Fiber Reinforced Polymer Composites [