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The numerical analysis, based on the finite element modeling (FEM), presents nowadays an efficient computational tool. It allows a better understanding of several thermo-mechanical phenomena involved during the machining process. However, its reliability heavily depends on the accurate definition of the numerical model. In this regard, a FE analysis focused on the 2D modeling of the Ti6Al4V dry orthogonal machining was carried out in this study. The relevance of different numerical meshing approaches and finite elements topologies was studied. The effect of the friction coefficient on the numerical chip morphology, its geometry, the cutting and the feed forces was investigated. The adequacy of several compared adaptive meshing approaches, in terms of the modeling of severe contact conditions taking place around the cutting-edge radius, was underlined in the current study. However, numerical serrated chips, closer to the experimental ones, were only predicted when the pure Lagrangian formulation was adopted and a proper determination of the failure energy was carried out. The definition of different mesh topologies highlighted the efficiency of the 4-node quadrangular mesh, with a suitable edge length, in increasing the agreement with the experimental data, while reducing the computing times. [ABSTRACT FROM AUTHOR]