Optimal Abrasive Mass Flow Rate for Rock Erosion in AWJ Machining Petr Jandaˇ cka 1(B ) , Jiˇr튡 cuˇ cka 1 , Petr Martinec 1 , Miloslav Lupták 2 , Ivan Janeˇ cek 1 , S. M. Mahdi Niktabar 1 , Michal Zele ˇ nák 1 , and Petr Hlavᡠcek 1 1 Institute of Geonics of the Czech Academy of Sciences, Ostrava, Czechia petr.jandacka@ugn.cas.cz 2 Faculty of Materials, Metallurgy and Recycling, Technical University of Košice, Košice, Slovakia Abstract. Erosion process of the Abrasive Water Jet (AWJ) machining on a rock material depends on various parameters. A brittle rock material is removed pre- dominantly by the deformation wear. Abrasive grains can enhance the machining since their hardness and therefore material removal is better than work of pure water. However, to this day, determination of an optimal dosage of the abrasive matter entering into the mixing chamber was rather neglected. Based on the laws of conservations of momentum and energy combined with some empirical facts, it is possible to derive an equation for erosion of the material and subsequently another relation that provides estimation of the optimal mass flow rate of an abrasive mat- ter. The main equation for erosion consists of six experimental coefficients, for an intensive AWJ only four, describing the effectivity of the water jet k w and abra- sive jet k a impacting the material. It seems that the energy that is used for erosion is very small and the ideal dosage of the abrasive material is approximately ˙ M a ≈ ˙ m w ·(1 - 2k w /k a ), where ˙ M a and ˙ m w are the abrasive and water mass flow rates. Such an equation could be used for setting of AWJ machines. The econom- ical optimum (eo) for cutting is proposed via the relation eo = E/E max - R/R max , with the erosion E and its maximum value and the resistivity R and its maximum value. Keywords: AWJ · Erosion · Rock material · Erosion model Nomenclature (SI unit system) a (m) size of the cubic abrasive grain (length of the side) A ( m 2 ) change of the surface area of the material b (m) interatomic distance in a crystal D (m) nozzle diameter D f (m) focusing tube diameter e (Pa) young modulus of the material E (kg/s) erosion of the material (removed mass of material per time) E rel (kg/kg) relative erosion of the material (removed mass of the material/mass of abrasives) © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 D. Klichová et al. (Eds.): Water Jet 2019, LNME, pp. 81–90, 2021. https://doi.org/10.1007/978-3-030-53491-2_9