An Analysis of Nonlinear Differential Equations Describing the Dynamic Behavior of an Unbalanced Rotor

The present paper investigates the dynamic behavior of an unbalanced rotor mounted in a balancing machine. Differential equations of motion are derived without linearization using Lagrange equations of the second kind to determine the nonlinear nature of the system. This study proposes a method for using differential equations in balancing to determine important parameters, such as the coordinates of the center of mass and the products of inertia of the rotor. An analysis of the interactions between the periodicities of the individual terms in the differential equations is carried out in order to eliminate terms with difficult-to-determine moments of inertia.