Precision comparison of analytical and statistical-regression models for AWJ cutting

The article is focused at the comparison of results calculated using analytical model for determination of abrasive water jet cutting and equations prepared via application of the statistical-regression approach. The statistical-regression model (SRM) is based on measurement of a set of column holes cut in a plan-parallel brass plate according to Box-Behnken design. The material and respective range of factors were selected so that they cover the largest possible scale of varying kerf shapes; brass 2.0402 (CuZn40Pb2), water pressure from 280 to 380 MPa, abrasive mass flow rate from 150 to 450 g/min and variable traverse speed from 25 to 75 mm/min. The main results arising from the experiments were the ideal diameters of the holes' sections in several selected depths of material and the cylindricity, i.e. the difference of the real shape of the “column” hole from the ideal one represented by a column with ideal diameter. The statistical-regression equations for calculation of the selected parameters were set-up. The comparison of the analytical model and the one created via statistical-regression was performed for bottom diameters of the produced holes. The reliability of the statistical-regression model is high within the tested scope of factors. However, its precision can be significantly reduced beyond the selected range of factors or by changes that cannot be involved in the regression (change of material wear character, etc.). Statistical processing of the measured data yields interesting relations between certain factors (abrasive mass flow rate, pressure) and respective results (diameters of holes, cylindricity). Therefore, the respective statistical-regression equations are also presented graphically. The comparison proved that the analytical model also has a very high accuracy and, moreover, its application is not limited by the selected ranges of factors.