This paper presents a theoretical approach to analyse the macroscopic thermo-mechanical behaviour of labyrinth seal fins (knife edges) during and after a rubbing event. The study helps to understand the mechanism behind radial cracking in labyrinth fins and identifies its driving parameters. To begin with, a generic analytical model is developed in order to determine the elastic thermo-mechanical stresses in a thin rotating disk representing the seal fin for a given radial temperature distribution and contact pressure. Secondly, the analytical model is used to explain the high tensile stresses which may result from a rubbing process in labyrinth seals and which are a prerequisite for radial cracks to occur. The driving parameters and simple criteria to compare different materials with respect to cracking are discussed in detail. Crack initiation criteria and fracture mechanics are not considered in this paper.
Finally, the analytical model is validated for various seal fin geometries and rub conditions using a three-dimensional Finite-Element model. The interaction of the seal fin with the stator is not taken into account in this numerical simulation. Instead, the rubbing process is modeled by assuming a time-constant surface friction heat flux and contact pressure on the seal fin tip. Both friction heat flux and contact pressure were varied in a sensitivity study in order to account for different rubbing conditions.