The article presents research on the erosion of the metamorphic rock - marble by the Abrasive Water Jet (AWJ). The fragmentation of abrasive grains during the erosion process is demonstrated. The effect of the cutting process's most important parameters as traverse speed, nozzle ID, and abrasive mass flow rate, on the maximum cutting depth, is shown. To create a mathematical-statistic model of the erosion process, the methodology of the response surface (RSM) was used for modeling. The polynomial equation of the second degree is chosen for developing the regression model. Studies have shown the optimal parameters of the process, to reach the highest depth of the cut. Additionally, the erosion wear of a focusing tube under different process conditions is presented.

The size and distribution of abrasive particles have a significant influence on the effectiveness of the cutting process by the high-speed abrasive water jet (AWJ). This paper deals with the disintegration intensity of abrasive materials in AWJ cutting during the creation of the abrasive jet. An evaluation of the abrasive materials was performed after forming in the cutting head was carried out and grain distribution was evaluated using the geometric and logarithmic Folk and Ward method. The influence of the abrasive concentration of abrasive materials such as alluvial garnet, recycled garnet, corundum, and olivine on grain distribution was studied. A recovery analysis was also carried out and the recycling coefficient was determined for each abrasive material tested.

In the case of advanced manufacturing technologies, which include Abrasive Water Jet Machining, optimization of control parameters is necessary to achieve appropriate efficiency and quality. One of the optimization methods used in the presented research is SAW, from the Multi-Criteria Decision Making (MCDM) group. In multi-criteria decision-making (MCDM) situations, the criterion weights are crucial components that have a big impact on the outcomes. A novel technique called MEREC (MEthod based on the Removal Effects of Criteria) was presented to find the objective weights of the criteria. The research covered cutting high-alloy steel using AWJ, under the Design of Experiment (DoE) within the L9 orthogonal table. Abrasive flow rate, pressure, and feed were selected as control parameters. The cutting depth (beneficial) and the roughness of the cut surface Sa (non-beneficial) were taken as the output parameters. The result of the research is the determination of the impact of individual control parameters and the determination of a set of control parameters from the point of view of efficiency and quality.