Open AccessThe milling process inherently is on/off, and therefore inevitably there is vibration excitation in the Machine/Fixture/Tool/Part (MFTP) system, which results in a different quality of the treated surface, depending on the machining conditions. The objective is to identify effective operation conditions to cut a part on the 3-way easy class machines when there is no unwanted regenerative self-oscillation, leading to a significant deterioration in the quality of the surface machined. The paper describes vibrations arising during a milling process and their effect on the surface shape and the working tool. To solve this problem we apply a numerical simulation method of cutting dynamics, which consist of 4 modules. The main module is an algorithm of the geometric simulation. The second module is a phenomenological model of the cutting forces. Two remaining modules are responsible for dynamics simulation of the part machined and the cutting tool under time-varying cutting forces. The calculated values are transferred back to the geometric modelling algorithm at each step in time. Thus, the model is closed and allows us to take into account an effect of delay in a dynamic system. A finite element machine model to perform calculation in 3DCUT software has been a selected and compiled. The paper presents geometrical mapping of the machining process and natural frequencies and shapes found for the finite element model. Conducting multivariate calculations allowed us to analyse the dependences of a dynamic behaviour of the system on changing spindle speed. The multivariate modelling results are presented as the Poincare maps for a moving free end of the tool. These Poincare maps allow us to select the operation conditions domains coming both with forced vibration and with self-excited oscillations. On the Poincaré map for two operation conditions of different domains there are graphics of the cutting forces, a thickness of the cutting layer, tool movements, and a shape of the machined surface to demonstrate differences in the dynamic behaviour of the system. A milling process modelling technique considered in the paper, taking into account a dynamics of the cutting 3-way machine of easy class allows us to estimate the nature and the level of vibration in the processing system, depending on the operation conditions selected for machining through building the Poincaré maps based on the results of multivariate modelling. These results can be used to select the effective milling operation conditions that enhance the quality and processing performance.