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Chatter is a self-excited vibration that can occur during machining operations. This undesirable phenomenon is one of the most common limitations when it comes to improving productivity and part quality. Notwithstanding its importance, chatter stability analysis in metal cutting is an unsolved problem at low cutting speeds due to the Process Damping (PD) phenomenon, were vibrational energy is dissipated through impacts between tool flank and workpiece. Despite the great amount of literature on this issue, some basic claims exploited by the most widespread modelling approaches are weak and unsound. The adopted fomulations are not able to provide a reliable prediction of cutting stability limit without being tuned by adhoc experimental campaigns that usually require a complex set-up and need to be repeated for every combination of tool wear status, machined material and lubrication strategy. Such effort, typically time-consuming and requiring specialized knowledge, is usually incompatible with the industrial context. In the present article, a critical investigation on PD is carried out, analysing PD mechanics by means of FE analysis of cutting. The results lead to a new analytical formulation of PD force, more coeherent with the experiences obntained in material science field, whose generality suffices for a wide range of cases of technological interest. Besides, it is pointed out how the damping force is also influenced by tool-workpiece relative dynamics, so that the sole local mechanics of the contact between tool and workpiece cannot describe completely the real sistuations. Then, the PD model is included in a time domain milling simulation model, enabling a complete functional simulation of cutting taking into account machine-process dynamic interaction and, hence, regenerative chatter occurrence. Thereafter, for a given milling operation, the stability lobes diagram can be computed numerically, in time domain, by scanning a proper grid of spindle speeds and depths of cut; in this way, the effect of the proposed PD model can be evaluated. Finally, the proposed modelling analysis of PD is used to interpret the results of a milling tests campaign in an industrial context.