Acceleration of Unbalanced Rotors

Abstract

AbstractA lot of work in rotordynamics is done in the evaluation of the Laval rotor. By accelerating this type of rotor, described by a single rigid disc centred in the middle of a slim shaft modelled as spring, one can observe the sticking of the rotational speed at the first bending eigenfrequency of the system, also named critical speed. This phenomenon only appears when the rotor is unbalanced and a small external torque accelerates the rotor. Taking a look at higher critical speeds one will notice that the Laval rotor model is insufficient accurate to take this eigenfrequencies into account. Therefore the equations of motion are derived using the Projection Equation in subsystem representation leading to Partial Differential Equations (PDE). Using the Timoshenko beam theory enables one to include the discs not only as rigid body but as real elastic part of the beam system. Applying the Transfer-Matrix-Method (TMM) to the system's linearized equations delivers adequate shape functions for the nonlinear PDE. The advantage of using the TMM is the possibility to calculate multidisc rotors and systems where the border between disc and shaft related to the diameter to length ratio cannot be defined clearly. Furthermore, the excentricity which is responsible for the unbalance of the rotor, has to be taken into account. The modeling is again done with the Projection Equation. Numerical simulation solutions are presented and compared to experimental results.