Dynamic Consequences of Bearing Radial Clearance in Jeffcott Rotors

Abstract: Earlier research on bearing radial clearance on a vertical Jeffcott rotor is rare, but an interesting and realistic point of view in a rotor system. Applying this force to the system produces interesting results for a vertical Jeffcott rotor.  The target of this thesis is to investigate how a simplified model of a rotor system is affected when bearing radial clearance is applied. A mathematical model for the rotor system and its motion is developed in both polar coordinates and Cartesian coordinates. Through this mathematical model, a dynamical system of differential equations with dimensionless quantities is constructed, and simulations for various different parameters and initial conditions are performed. The results indicate that the considered system is sensitive to changes in both the values of its fundamental parts, but also in the positioning of its initial conditions. The damped natural frequency and final motion, stability, and behaviour for different levels of the bearing radial clearance is further investigated through simulations. A large amount of initial conditions and variations in different parameters are studied, to seek patterns in the behaviour of this dynamical system. Non-local stability has been investigated in different solutions, and it's concluded that bifurcation exist in the system when bearing radial clearance is applied.  The results from this thesis could be used as a base in a deeper and more detailed research for bearing radial clearance in Jeffcott rotors. It could also be used to further investigate non-circular periodic motion, and determine the implication and effect that these solutions might have to an actual rotating machine.