The objective of this study is to develop a practical mathematical model for prediction of the depth of cut in the course of Abrasive Water Jet (AWJ) machining. Semi-empirical method which is an integration of theoretical derivation and statistical analysis is used for process description. A theoretical model was constructed based on kinetic energy conservation equation, physical relationship among operating parameters, abrasive size, material properties and cutting results. Then, correlation between the depth of cut and operational parameters was analyzed in order to improve the theoretical model. Finally, a regression equation representing 1000 samples was constructed.

Three statistical criteria were considered synthetically to determine the final form of the regression equation. These criteria include multiple correlation coefficient R², the plot of a standard residual GI, and the number of GI >±2.

The multiple correlation coefficients for evaluation of the accuracy of the constructed equation range from 0.95 to 0.99. Prediction error in 92% of cases did not exceed ±2 mm for samples having thickness up to 30 mm. The constructed equation was also used for process examination. It was evaluated, for example, that water contribution to the material removal is roughly 10 times less than particles contribution.