Residual stresses are very important for the lifetime of pieces in their mechanisms. These kind of damages are mainly caused by mechanical, thermal, and metallurgical affectations of the machined material. To control these affectations, we need to link the cutting parameters to the residual stress state observed onto the workpiece surface and depth. These connections can be made with analytical works, experimental works or numerical works. In our case, it has been chosen to work with a numerical support in order to observe and understand precisely the phenomenon involved during cutting operation. While this way of study is really popular, we proposed to model the residual stress generation in a original way by keeping aside the chip formation. This new approach presented in a previous paper was simple and only use a 2D model. This first model moves thermo mechanical loadings onto the workpiece surface to recreate the relative motion between the tool and the workpiece. The new 3D model, presented in this paper, is now improved with an original friction law. It underlines the impact of each passage of the tool onto the others. The physical properties are thermo dependant and the flow stress model is based on a Johnson cook behaviour.