In this paper an algorithm is developed where Reynolds' equation, equilibrium equations and non-negativity of pressure are formulated as a system of equations, which are not differentiable in the usual sense. This system is then solved using Pang's Newton method for B-differentiable equations.

By using balancing balls constrained to move in a circular groove filled with oil, the vibration of rotating machinery can, under certain circumstances, be reduced. This paper shows that the damping from the oil reduces the instability region, i.e., the conditions when the balancing balls don't find their equilibrium positions. However, the instability region seems to increase with increasing number of balancing balls. The critical ball damping ratio is highest just above the natural frequency and then rapidly decreases. Consequently, since the region between instability and critical damping is quite small, the ball damping should be made as small as possible without getting too close to the instability threshold. Bearing damping has a large effect on the instability region. High bearing damping will suppress the instability. The time it takes to reach the asymptotically stable position seems to increase with increasing number of balls. Keeping this time low is one of the most important things when designing a balancing ring.

The paper is concerned with material and microslip damping in a rotor The horizontal rotor is carried by anisotropic bearings, which means that the shaft feels three different frequencies, the rotational frequency and the difference and the sum of the rotational and vibrational frequencies. When material damping is studied, these three frequencies lead to three different equivalent viscous damping constants and the dissipated energy can be solved analytically. The rotor slot wedges in a turbine generator are used as an example of microslip damping. In this case the damping is nonlinear and the results are obtained through numerical simulations. The results show that these two different internal damping sources give both similarities and dissimilarities. The sign change and different magnitude of the dissipated energy running sub- or supercritical are the same. However the dissipated energy for material damping is nor affected by gravity which microslip damping is.

In the present paper, an explicit beam element for non-symmetric thin-walled composite shafts is developed. The element is developed from the WS element which normally demands numerical integration. It allows circumferential changes of the radius but takes advantage of the fact that it is only the second term in a Fourier series expansion that has a major influence on the dynamic behaviour of the rotor. The element allows transverse shear and moreover the mass is not distributed on the centre line.

The present doctoral thesis is concerned with three different rotordynarnic applications; composite rotors, internal damping and microslip in a turbine generator. When a composite shaft has an imperfection, such as differences in the filament winding angle, the eigenfrequencies of the non-rotating shaft depend only on the material stiffness. However, for composite shafts in high speed applications the eigenfrequencies also depend on the new geometry caused by centrifugal forces. The difference between these two cases is negligible, which means that the change in the stiffnesses has a much larger influence than the change in the geometry. For a composite rotor with a delamination the effects on the eigenfrequenciesdue to the delamination increase with increasing thickness of the composite shaft. The position of the delamination and its length are also important. However, compared to other imperfections, the effect of the delamination will probably be negligible and it will be difficult to detect for instance with diagnostic techniques for condition monitoring.

The thesis is also concerned with the influence of different kinds of internal damping. The material damping for a shaft made from a high-modulus carbon fiber in epoxy resin has been investigated for different angles of filament winding. The effects from internal viscous damping have been studied on a horizontal rotor with a flexible shaft supported in flexible bearings. The shaft and bearings may have damping and asymmetric/anisotropic stiffnesses. Major instabilities appear near the imbalance resonance. These instabilities can often be avoided with the right combination of viscous damping and asymmetric stiffness of the shaft and the damping and anisotropic stiffnesses of the bearings.

To be able to solve the same kind of vibrational problems with hysteretic damping as with viscous damping, the dissipative behavior due to multi-frequency excitation has been studied. It is shown theoretically and verified experimentally that it is possible to treat the frequencies separately. Practically, this leads for instance to the conclusion that for sub-critical rotational speeds the material damping in a rotor with anisotropic bearings can be treated as a complex stiffness. For super-critical rotational speeds the complex stiffness approach only has good accuracy if the rotor orbital is close to a circle.

Finally, the thesis is concerned with dynamic instability of a turbine generator due to friction between the rotor slot wedges and the rotor. The energy transferred due to friction can be reduced by increasing wedge length, coefficient of friction or normal force or by reducing the cross-section area of the wedge.