The genesis of this thesis is physical observations of slow alterations of synchronous rotor vibrations over time. It can lead to problems such as difficulties in performing proper balancing and unacceptably high vibration levels. The cause is often asymmetric heating of the rotor shaft. Contacts between rotating and stationary parts, for instance in seals, or vibrations in fluid-film bearings may cause asymmetric heating of the shaft and a consequent shaft bow. A small residual unbalance after ordinary balancing can result in a shaft bow which increases vibration levels considerably. The time constant is large, it can take hours before a bow reaches steady state (if this at all exists). It is observed that balancing under these circumstances is complicated.

A shaft bow will change the unbalances of the rotor shaft. The new vibration pattern will alter the asymmetric heating and this alters the bow and so on.

Heat generation in an oil film is strongly dependent on the film height, the smaller the height the higher the temperature. Different positions on the shaft will experience different film heights if the shaft performs a synchronous vibration, giving asymmetric heating to the shaft.

In case of shaft-seal contact combined with synchronous vibrations, different positions on the shaft will not experience the same rub, so that the shaft also in this case is asymmetrically heated. The main difference between asymmetric heating in a bearing and in a seal is that the relation between vibration and asymmetric heating can be regarded as linear in the bearing case, but not in the seal case (as there is a gap between shaft and seal).

The linear case may be divided into solutions which are stable or unstable, but the non-linear case is more complicated as a solution may be unstable at one vibration level but stable at another. Often this leads to so-called limit cycles, where the shaft bow undergoes a cyclic alteration.

The scientific basis for this work spans over different fields such as rotordynamics, tribology and heat conduction.