Variable impedance bearings for large rotating machinery

This thesis describes an investigation which was carried out under the Interdisciplinary Higher Degres (IHD) Scheme of The University of Aston in Birmingham. The investigation, which involved joint collaboration between the IHD scheme, the Department of Mechanical Engineering, and G.E.C. Turbine Generators Limited, was concerned with hydrostatic bearing characteristics and of how hydrostatic bearings could be used to enable turbine generator rotor support impedances to be controlled to give an improved rotor dynamic response. Turbine generator rotor critical speeds are determined not only by the mass and flexibility of the rotor itself, which are relatively easily predicted, but also by the dynamic characteristics of the bearing oil film, pedestal, and foundations. It is because of the difficulty in accurately predicting the rotor support characteristics that the designer has a problem in ensuring that a rotor's normal running speed is not close to one of its critical speeds. The consequence of this situation is that some rotors do have critical speeds close to their normal running speed and the resulting high levels of vibration cause noise, high rotor stresses, and a shortening of bearing life. A combined theoretical and experimental investigation of the effects of mounting the normal rotor journal bearing in a hydrostatic bearing was carried out. The purpose of the work was to show that by changing the oil flow resistance offered by capillaries connecting accumulators to the hydrostatic bearing, the overall rotor support characteristics could be tuned to enable rotor critical speeds to be moved at will. Testing of a combined journal and hydrostatic bearing has confirmed the theory of its operation and a theoretical study of a full size machine showed that its critical speed could be moved by over 350 rpm and that its rotor vibration at running speed could be reduced by 80%.

Kineto-elastodynamic analysis of high-speed four-bar mechanism

This thesis addresses the kineto-elastodynamic analysis of a four-bar mechanism running at high-speed where all links are assumed to be flexible. First, the mechanism, at static configurations, is considered as structure. Two methods are used to model the system, namely the finite element method (FEM) and the dynamic stiffness method. The natural frequencies and mode shapes at different positions from both methods are calculated and compared. The FEM is used to model the mechanism running at high-speed. The governing equations of motion are derived using Hamilton's principle. The equations obtained are a set of stiff ordinary differential equations with periodic coefficients. A model is developed whereby the FEM and the dynamic stiffness method are used conjointly to provide high-precision results with only one element per link. The principal concern of the mechanism designer is the behaviour of the mechanism at steady-state. Few algorithms have been developed to deliver the steady-state solution without resorting to costly time marching simulation. In this study two algorithms are developed to overcome the limitations of the existing algorithms. The superiority of the new algorithms is demonstrated. The notion of critical speeds is clarified and a distinction is drawn between "critical speeds", where stresses are at a local maximum, and "unstable bands" where the mechanism deflections will grow boundlessly. Floquet theory is used to assess the stability of the system. A simple method to locate the critical speeds is derived. It is shown that the critical speeds of the mechanism coincide with the local maxima of the eigenvalues of the transition matrix with respect to the rotational speed of the mechanism.