Abstract

One of the critical components of turbomachinery is the bladed disk assembly (BDA). BDAs operate in a harsh environment and under dynamic pressure during operation. In aero engines, the pressure inhomogeneities in airflow and friction forces due to contact at different locations can cause vibrations of the blades and disk. These vibrations result in a range of damages to the machine, from damage to the blade and casing, such as wear, to catastrophic engine failure. The following two factors may have a critical influence on the vibrations of BDAs: (i) the contact between the blade root and disk, (ii) the unavoidable imperfections in manufacturing or mounting of the blades, referred to as mistuning. The former leads to friction forces between the blade root and disk, while the latter adds a significant amount of uncertainty to the system and may lead to the localization of vibration energy to a few blades. The friction forces at the joints and other contact areas introduce nonlinear terms into the governing equations. The analysis of nonlinear vibrations of BDAs is a time-consuming process. Many studies have focused on the separate effects of nonlinearity and mistuning on the vibration characteristics of BDA in turbomachinery. The combined effects of these two phenomena, however, are not well understood. This area has attracted great interest in recent years, and engineers are working to uncover the correlation between mistuning and nonlinearity and their effects on the vibration characteristics of BDAs.
This study is concerned with the mathematical modeling, numerical analysis, and statistical analysis of vibration characteristics of BDAs, including both nonlinear forces and mistuning. The governing equations are written for a lumped parameter model replicating the behavior of BDA with six blades. The nonlinear forces are due to the dry friction between the roots of the blades and the disk. The nonlinear governing equations are then solved for the tuned BDA. The steady-state forced response of the mistuned nonlinear system is then computed, with mistuning introduced as a small blade-to-blade deviation in the elasticity of the blades with respect to the tuned BDA. The effects of changing the mistuning and excitation levels are investigated. Two different mistuning realizations are considered to study the effect of mistuning on the vibrations of a BDA. A preliminary statistical analysis is then performed on an ensemble of 150 realizations of mistuned BDAs.