Modeling heat treatment process variables for 3-inch cast steel balls-mineral grinding balls

Abstract

A model is sought from the variables of the production process to forecast the surface hardness of 3-inch diameter steel balls. The DI indicator in replacement of chemical composition is considered as an independent variable. The analyzed data corresponds to 43 controls. In which 10 independent variables and a dependent variable are initially considered as the surface hardness of the ball (HRC). The data treatment begins with a descriptive analysis of the type of relationship between the independent and dependent variables, and then reduces the independent variables, then applies the multiple linear regression method. The initial model to be considered is of the type Y = β0 + ΣβiXi + ε to later be Y = β1X1 + β2X2 + β3X3 + β4X4 + β5X5 + β6X6 + β7X7 This model was evaluated, multicollinearity, between independent variables by the inverse matrix method of correlations. Normality and homoscedasticide of residues were also tested. The value found for R2 = 0.97056, The test of global significance of the coefficients rejects null hypothesis H0: β1 = βi = 0 and accepts alternative hypotheses, at least one coefficient is different from zero because it has p-value <0.05.