Modal Synthesis Method for Inter-Blade Dry-Friction Surface Angle Design of Turbine Wheel for Vibration Suppression

Abstract New calculation approach based on modal synthesis method is proposed for evaluation of structural and dry-friction damping effect on self-excited vibrations due to aero-elastic instability in the bladed turbine wheels. The aerodynamic excitation arises from the spatially periodical flow of steam through the stator blade cascade. The self-excited aero-elastic forces of blades are described by Van der Pol model. The proposed method as reduced order method (ROM) simplified approach is computationally efficient solution allowing to estimate effect of many important blade cascade parameters of such a complex non-linear mechanical system. The paper is aimed at the narrow frequency range of nozzle excitation and on the case when a slip motion is prevailing in the contacts. The method is applied herein to an industrial turbine wheel design with 66 blades. For evaluation of damping effect, the tie-boss and shroud couplings are applied. Therefore, neighboring blades are interconnected by rigid arms that are on one side fixed to one blade and are in friction contact on their free side with the other blade. Static normal contact forces are prescribed in contact point pairs at the initial state. Due to relative normal motions in contacts, the prescribed contact forces vary in time. Friction forces in contacts are driven by the modified Coulomb friction law. The effect of the angles of inter-blade contact surfaces on the wheel dynamics and on level of friction damping is discussed.