ESTABLISHING THE EQUATIONS THAT GENERATE THE VIBRATION MOVEMENT OF THE MAIN SPINDLE IN TRANSVERSAL DIRECTION AT CNC LATHE

The paper presents a mathematical model for determining the movement equations that generate the transversal vibration of the main spindle at CNC lathe. For this purpose, we take into account the general equations which generate the vibration of the spindle, obtained by means of Hamilton's Variational Principle as well as the impulse derivative and kinetic moment axioms. The solutions to the movement equations are arranged under the form of a system of first order partial derivatives equations, for which we determine the integration constants. This original way of establishing these equations allows further analysis of the main spindle vibrations in transversal direction and finding ways to decrease the vibration amplitude.