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.

Study on the lateral and torsional vibration of single rotor-system using an integrated multi-body dynamics and finite element analysis

“…Where: q is the generalized coordinate, F is the equilibrium equation in the direction of generalized coordinate q, L is the Lagrangian (T-V), T is kinetic energy; V is potential energy, Φ is algebraic constraint equations, λ is Lagrange multiplier, Q is generalized Force, n is of generalized coordinates, m is of constraint equations (<or = n). The derivation of equations of motion of such as SRS was explained clearly by Yu 16 based on Lagrange’s equations.…”

“…Shen et al 15 derived equations of motion of the coupled torsional-lateral vibration model with six degrees of freedom and using Lagrange approach and two kinds of unbalance. Yu et al 16 derived equations of motion for the mechanical model of unbalanced Jeff coat rotor supported by roller bearings by using Lagrangian approach. Gosiewski 17 established a rotor dynamic model under case of unbalance that accounts both lateral displacement and torsional angle by using the Evans method.…”

Vibration analysis of air-bearing work-stage under micro-scale effect

“…Yamamoto et al 9 pointed out that the natural frequency of the gas bearing spindle agrees well with the experimental data by taking membrane stiffness and damping into the motion equation of elastic vibration. Yu et al 10 solved the non-equilibria of roller bearing support with dynamic difference method and found the coupling effect of the coupling transverse and the torsional vibration. Cappa et al 11 proved that increasing the number of delivery holes will reduce radial hydrostatic bearing radial movement error.…”

“…Yu et al. 10 solved the non-equilibria of roller bearing support with dynamic difference method and found the coupling effect of the coupling transverse and the torsional vibration. Cappa et al.…”