The effect of coupled lateral and torsional vibrations of an unbalanced Jeffcott rotor supported by roller bearings

Abstract

In this paper, an unbalanced Jeffcott rotor supported by the roller bearings is modelled, and the dynamic differential equations are obtained by the Lagrange’s equations. The fourth order Runge–Kutta method is employed to simulate this system in two cases. Simulation results show the combined effect of the coupled lateral and torsional vibrations and the variable compliance vibration of the rotor. In the case of that only a large and constant radial force is applied, the sum and difference between variable compliance and rotational frequency components of the torsional vibrations of the disk are induced because of the roller bearings’ rotation. And when they are near to the natural frequency of the torsional vibration, the resonance peaks appear. In the case of that a large and constant radial force and a harmonic torque are simultaneously applied, the two components, the sum and difference between rotational frequency and the frequency of the external torque, of the lateral vibrations of the disk are induced. When the frequency of the external harmonic torque approximatively equal to a special value, the two frequency band lines, variable compliance and the sum of rotational frequency and the frequency of external torque, intersect near the natural frequency of the lateral vibration, and the vibration may aggravate.