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In modern production, milling is considered the widespread cutting process in the formatting field. It remains important to study this manufacturing process as it can be subject to some parasitic phenomena that can degrade surface roughness of the machined part, increase tool wear and reduce spindle life span. In fact, the best quality work piece is obtained with a suitable choice of parameters and cutting conditions. In another hand, the study of tool vibrations and the cutting force attitude is related to the study of bearings as they present an essential part in the spindle system. In this work, a modeling of a High Speed Milling (HSM) spindle supported by two pair of Active Magnetic Bearings (AMB) is presented. The spindle is modeled by Timoshenko beam finite elements where six degrees of freedom are taken into account. The rigid displacements are also introduced in the modeling. Gyroscopic and centrifugal terms are included in the general equation. The bearings reaction forces are modeled as linear functions of journal displacement and velocity in the bearing clearance. A cutting force model for peripheral milling is proposed to estimate the tool-tip dynamic responses as well as dynamic cutting forces which are also numerically investigated. The time history of response, orbit, FFT diagram at the tool-tip center and the bearings dynamic coefficients are plotted to analyze dynamic behavior of the spindle.

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The high speed milling represents the most important process to produce parts in different fields such as aeronautics, automotive and mould. It allows obtaining parts with complex form and with the best surface quality. So, it remains essential to understand the impact of both the cutting force model and its parameters on the tool tip response. Consequently, the mastering of chatter vibration in milling and surface properties of the work piece is essential. In this paper, the simulation of machining is applied to determine the cutting forces distribution. A spindle system modeling is presented using a new approach: Both rigid and flexible modes of the spindle's shaft are taken into account. The shaft is discretized with the Timoshenko beam finite elements with different circular sections. Nonlinear electromagnetic loads exerted by AMBs are computed in terms of the nominal air gap between bearings and spindle, the control current and the displacement of each node. A parametric study is performed to determine the influence of some parameters, such as the feed rate, the tangential cutting coefficient, the spindle speed and the axial depth of the cut on the cutting forces and the chatter vibrations in milling.

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