| Summary: | 碩士 === 國立臺灣科技大學 === 機械工程系 === 93 === Rotor-bearing systems are widely used in all kinds of machinery. During operation, the rotor system is frequently subjected to axial forces due to external resistance. The axial forces bring about parametric instability under certain situations.
This thesis study the dynamic stability of a rotor-bearing system subjected to axial random forces. In this thesis, the rotor-bearing system consists of a shaft, disk and a pair of bearings. The shaft is modeled as a Timoshenko beam; the disk is assumed as a rigid disk with eccentricity, and the bearings are assumed as flexible supports having orthotropic stiffness and damping coefficients. First the discretized equations of motion can be derived by using the finite element method. The set of discretized system equations is partially uncoupled by the modal analysis procedure suitable for gyroscopic systems. Next, the stochastic averaging method is adopted to obtain Ito’s equations for the response amplitudes of the system. Finally the stability criteria are derived by the aid of Ito’s differential rule.
Numerical results show that the eccentricity of the disk will create a parametric excitation to the rotor bearing system. If the axial vibration is neglected, the effects of the mass eccentricity and the axial random force will cancel out each other, which makes some of the summed-type instability regions disappear.
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