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This paper is aimed at providing a comprehensive analysis of the contact problem in orthogonal cutting based on the simple assumption that contact is governed by a Coulomb law. Effects of the sliding friction coefficient and of the cutting conditions are analyzed in details. The problem is analyzed numerically by using an Arbitrary Lagrangian Eulerian Finite Element technique. In parallel, analytical models are developed allowing us to interpret the numerical data and to make them more meaningful. Distributions along the tool-chip interface are analyzed for stresses, temperature and sliding velocities. The shear stress exerted along the sticking zone is found to be equal to the shear flow stress of the work-material. Of particular significance is the investigation of the interface heating as the chip temperature appears to be a key factor governing the contact regime. The increasing of the chip temperature along the tool rake face appears to be mainly controlled by the mean value of the shear stress on the rake face and the Peclet number taking into account the phenomena of advection and heat diffusion. At low values of the friction coefficient the contact is governed by chip-tool sliding for the whole range of cutting speeds considered here (1 ms(-1) <= V <= 50 ms(-1)). For larger values of the sliding friction coefficient, a transition to a contact dominated by sticking is found when the cutting speed is increased...