59283 - Mistuning and Damping of a Radial Turbine Wheel. Part 1: Fundamental Analyses and Design of Intentional Mistuning Pattern 

The radial turbine impeller of an exhaust turbocharger is analyzed in view of both free vibration and forced response. Stator vane rings located upstream between engine and turbine wheel are applied to guide the exhaust gases in optimized flow directions. Hence, turbine wheels are subjected to aerodynamic excitations causing forced vibrations of blades and the whole turbine. Due to random blade mistuning resulting from unavoidable inaccuracies in manufacture or material inhomogeneities, localized modes of vibration may arise, which involve the risk of severely magnified blade displacements and inadmissibly high stress levels compared to the tuned counterpart. In consequence, damages may occur along with a dramatic decrease of efficiency or even a total failure during engine operation as worst-case scenarios. Contrary, the use of intentional mistuning has proved to be an efficient measure to mitigate the forced response. 

Independently, the presence of aerodynamic damping is significant with respect to limit the forced response since structural damping ratios of blade integrated disks (blisks) typically take extremely low values. Thus, a detailed knowledge of respective damping ratios would be desirable while developing a robust blisk design. For this, far-reaching experimental investigations are carried out to determine damping curves of a comparative wheel within a wide pressure range by simulating operation conditions in a pressure tank. They are the basis to develop empirical formulas for damping estimation which could be be taken into account during future design processes. In order to get an idea of the real structural behaviour, further measurements are conducted to determine the present mistuning of the turbine wheel, which facilitates to update structural models and finally allows to compute the forced response in an accurate manner.

Reduced order models are built up for designing suitable intentional mistuning patterns by using the subset of nominal system mode (SNM) approach introduced by Yang and Griffin [1], which conveniently allows for accounting both differing mistuning patterns and the impact of aeroelastic interaction. For this, the aerodynamic damping curves are determined by means of computational flow simulations. The SNM approach finally provides appropriate mistuning patterns by conducting optimization studies based on genetic algorithms. The robustness of the found solutions is proved by additionally superimposing both random mistuning and experimentally determined mistuning of the original wheel.

Finite element analyses are carried out in order to identify appropriate measures to implement intentional mistuning patterns, which are featuring only two different blade designs. In detail, the impact of specific geometric modifications on blade natural frequencies is investigated. After implementation of the intentional mistuning pattern, which will be described in Part 2 of this paper later on, the success of taken measures will be reviewed based on both, experimental testing at standstill conditions and in a test stand by running the wheel under realistic operational conditions.

[1] Yang, M. T., Griffin, J. H., „A Reduced-Order model of Mistuning Using a Subset of Nominal System Modes“. J Eng Gas Turb Power, 123, pp. 893-900 (2001).