Heat flow induced alteration of rotor response

摘要

This licentiate thesis is concerned with rotor dynamics, tribology and to some extent control theory. The common factor is development of thermal bends in a rotor shaft. Rotors, in particular those in large machines such as steam turbines, sometimes exhibit a behaviour referred to as 'spiraling', which means that they constantly change their synchronous vibrations. This can lead to problems such as difficulties in performing proper balancing and, in serious cases, to a situation where it is impossible to operate. The phenomenon is associated with an asymmetric temperature distribution in the shaft and a feedback coupling from this to the vibration. Contacts between rotating and stationary parts, for instance in seals, may be one explanation. Another is that vibrations in the bearings cause asymmetric heating of the journal and a consequent shaft bend (or bow). A small residual unbalance after ordinary balancing can result in a shaft bow which increases vibrations considerably. The time constant is large, it can take hours before a bow reaches steady state (provided that it is stable). It is observed that balancing under these circumstances is complicated. Assume a harmonic, synchronous vibration. Now a certain position on the shaft surface in the bearing will experience the same temperature variation, revolution after revolution. However, different positions on the shaft in the peripheral direction experience different temperatures, and an asymmetric temperature distribution follows. In the next step asymmetric heat is conducted in the shaft, resulting in a temperature field. In turn a volume integral of this gives a shaft bow. Here dynamic aspects must be regarded. The three-dimensional transient heat conduction is quite arduous to solve. Multiple bearings are coupled through the rotor dynamic response. One contribution to the vibration comes from mass unbalances and another from the bows (geometrical unbalances). Due to difference in time scales between bow development and vibrations, the steady-state solution for the vibration response of the rotor can be used. The work includes a new analytic model of the heat conduction in the shaft and the resulting shaft bend. Multivariate control theory is used for stability and unbalance response analysis. Results from a multiple-bend case are presented for the first time. It is observed that development of thermal bends due to asymmetric heating can lead to severe vibration problems 13 refs, 3 figs