A New Approach for Thermo-Elastic Equations to Predict Spiral Vibrations in Turbogenerator Shafts

The phenomenon of vibration vector rotation caused by thermally induced unbalance changes, referred to as the “spiral vibration” (SV), is frequently observed in large rotating machinery. Since the SV is a consequence of an interaction between mechanical and thermal unbalance of the rotor, a set of standard rotordynamic equations must be extended by the additional thermal equation. For the case of rotor deformation caused by a hot spot on a slip ring of turbo-generator a new thermo-elastic model has been formulated. A solution for the thermal mode response of a simplified system has been derived analytically using the non-dimensional form of the thermal equation. This paper provides formulae for stability threshold and spiral period corresponding to the newly developed model of thermal excitation. The presented theoretical results have been adopted in more detailed numerical models and used to effectively extend stability margin of the SV in turbo-generator shaft trains.