DETERMINING THE BALANCE CONFIGURATION, IN CASE OF THE OSCILLATING MOVEMENT OF THE MAIN SPINDLE AT CNC LATHE

In the paper we present a mathematical model through which are determined the balance conditions, needed for the stability analysis of the oscillating movement of the main spindle at CNC lathe. We take into account Hamilton's variation principle, the axiom of impulse derivative and the axiom of kinetic moment derivative. We present the general movement equations that generate the oscillations based on the calculus hypotheses, performing the introduction of the external solicitations. Establishment of the balance configuration is done by imposing the conditions that the system of forces that act upon the ensemble spindle – bearings - tool causes a deformation of the spindle, without producing spindle vibration. We obtain the new differential equations of the movement, in which the forces and moments are determined from the static case, based on which we can determine the integration constants in the characteristic points of the main spindle.