## 1 Introduction
As the mass flow rate increases, so does the depth of cut and the quality of the machined surface. A higher concentration of abrasive particles in the jet allows moreefficient material removal, resulting in a smoother and more accurate cut. However, this flow rate increase is limited by the critical mass flow rate. Beyond this threshold, the depth of cut will decrease. This decrease is because the excess particles collide with each other, leading to the loss of kinetic energy that would otherwise contribute to cutting the material [16,26]. Changing the traverse speed affects the shape and depth of the cut and, hence, its profile and quality. Slower speeds cause visible unwanted milling on the surface, affecting the surface appearance and accuracy. Conversely, higher traverse speed results in a more precise and smoother cut, though it may result in higher cost and other technological challenges. [PERSON] [27] and [PERSON] [16] have defined the required amount of particles (Equation (2)):  
\[\textbf{PDD}=\frac{\mathbf{m_{a}}}{\mathbf{v_{f}}}\left[\text{kg/m}\right], \tag{2}\]  
where the following is true:  
**PDD** (Particle Dosing Density) is the abrasive particle density division (the amount of particles necessary to generate a groove of nominal length under specific conditions) [kg/m];  
**m\({}_{\textbf{a}}\)** is abrasive mass flow rate [kg/s];  
**v\({}_{\textbf{f}}\)** is the traverse speed of water jet movement against material [m/s]. Additionally, the energy density division (EDD) of abrasive particles may be defined according to Equation (3):  
\[\textbf{EDD}=\frac{1}{2}.\textbf{PDD}.\mathbf{v_{a}}^{2}\left[\text{J/m}\right], \tag{3}\]  
where the following is true:  
**EDD** is the energy density division of abrasive particles (the amount of energy reverted to a unit of the generated groove length) [J/m];  
**v\({}_{\textbf{a}}\)** is the speed of abrasive coming from the nozzle [kg/s]. These equations are essential for industrial practices, as they can be used to optimize the cutting processes for specific materials and required properties [23]. Beech plywood was chosen due to its widespread use in Eastern and Central Europe and the need to improve the machinability of this material. Cutting bech plywood using technical methods with AWJ is crucial in the furniture and construction industry, as it enables high precision and quality. This technology uses a high-pressure water stream enriched with abrasive particles, which enables precise and clean cuts in rigid materials (such as beech plywood). In this article, the focus is on optimizing the AWJ cutting parameters for technical beech plywood to minimize potential negative impacts. Despite the potential advantages of this method, there is a lack of systematic studies in the current literature analyzing the influence of AWJ cutting parameters on the long-term durability of beech plywood. This gap limits the ability to optimize cutting processes and fully exploit the technology's potential in industrial applications. Furthermore, the growing need for environmentally friendly manufacturing technologies must be emphasized, with AWJ representing an ecological alternative to traditional cutting methods, as it does not generate thermally damaged waste or harmful emissions. For these reasons, scientific investigation into AWJ cutting of beech plywood is essential for expanding current knowledge, optimizing manufacturing processes, and supporting sustainable development in the woodworking industry. This study has the potential to fill identified gaps in the scientific literature and contribute to both technical and environmental advances in material processing. The core hypothesis of the article is whether it is possible to assume the existence of a combination of cutting parameters (traverse speed, abrasive mass flow rate, and material thickness) that minimizes AWJ lag without negatively affecting surface quality.