Contact Stiffness and Dry Friction Damping to Mitigate Turbomachinery Vibrations

This thesis deals with the problem of modeling dry friction contacts, that is a crucial aspect of the design of "dry friction dampers"; these devices are responsible for the absorption and dissipation of the energy of the turbomachinery blades vibrations. A numerical method for the contact problem solution was developed and implemented in a MATLAB program. The tangential force-displacements curves were derived for the cylinder on a plane and for the two planes contacts using the proposed method. The corresponding tangential contact stiffness and the representation of the frictional hysteresis loops were computed. In particular, for the cylindrical contact, the influence of diameters and lengths were investigated, instead the behavior of these loops for non-uniform normal pressure distribution were also analyzed for the planar contact. With the flexibility of the proposed method, it was possible to formulate two "numerical" equations for the normal and the tangential displacements of the cylindrical contact using multiple models with different dimensions. It is worth mentioning that no analytical solutions are available in the literature for the tangential displacement, so the solution presented in this thesis can be considered original.