Dissipated energy and boundary condition effects associated to dry friction on the dynamics of vibrating structures

Abstract

In turbomachines, dry friction devices (under platform dampers, shrouds, and tie-wire) are usually introduced to reduce resonant responses of bladed disks. Dry friction between rubbing elements induces a highly nonlinear dynamic behaviour which flattens the frequency response functions. It is clear that such behaviour requires an optimisation process to find the optimum parameters that lead to the minimum forced response amplitudes. However, different interpretations still remain concerning the explanation of the physical origin of this type of flattening. The most common one is based on dissipated energy. In this case, heat resulting from the relative frictional motion between contacting surfaces is supposed to bring sufficient dissipation to flatten response functions. On the other hand, a different approach considers that a decrease in vibrational amplitudes is explained by changes in boundary conditions induced by a stick/slip behaviour. In this study, a single degree-of-freedom system is used and analysed both in time and in frequency domains (Harmonic Balance Method) in order to show the contribution of respectively energy dissipation and change of contact state on peak levels.

Experiments and numerical simulations of nonlinear vibration responses of an assembly with friction joints – Application on a test structure named “Harmony”

“…This is the reason why this method has been chosen for the present study. In the recent years, many efforts have also been done to increase the numerical efficiency of this nonlinear approach for vibration damping by dry friction [8][9][10][11][12][13]. Among them, we can cite the Dynamic Lagrangian Frequency Time method (DLFT), proposed by Nacivet et al [14] that enables to handle directly the non-smooth unilateral and frictional contact laws.…”

Non-linear models for Rotor-AMB system drop

“…This peak flattening could be due to the out-ofphase between the friction force and the displacement generated by the stick-slip phenomenon, as explained in [7]. Thus, the damping provided by the ribbon when a rotor drops onto its TDBs would come mainly from the alternation of stick and slip motion of each bump of the ribbon, rubbing along the inner-race and housing surfaces, generating this force-deflection out-of-phase.…”

“…A first approach is the modelling of the ribbon damper with the Masing macroslip model, used in [7] in parallel with a purely elastic restitution force, see equation (1). The contact parameters are assessed thanks to the experimental force-deflection loops, plotted in dotted lines in figure 4.…”

Nonlinear vibrations of a mechanical system with non-regular nonlinearities and uncertainties

“…The last case considers the rubbing phenomena with friction dissipation mechanism and stick-slip motion [18,19], as illustrated in Figures 3(b) and (e). The nonlinear forces f nl 1 (t) due to friction is expressed, according to the Coulomb law, as:…”