ASYMPTOTIC EVALUATION OF NONLINEAR FRICTION EFFECTS IN REALISTIC LPT ROTORS

The study of the dynamical response of a bladed-disk usually requires finite element models with a very large number of degrees of freedom. In the case of the vibration produced by an external forcing, the dissipation associated with the nonlinear friction at the contact interfaces compensates the energy pumped into the structure and limits the growth of the vibration, producing a limit cycle oscillation. The small effect of nonlinear friction, which typically involves a very small subset of nodes, is therefore crucial for the calculation of the final response of the system. Friction laws are strongly nonlinear and can even show discontinuities, as a consequence, the equations of motion are numerically very stiff. On top of that, large integration times over many elastic cycles are typically needed to reach convergence. In the study of the forced response of a bladed-disk, this means that a quite significant computational effort goes into computing a single point of the resonance curve. Despite all these numerical difficulties, the resulting response is in most cases very similar to the one produced by a one dimensional nonlinear oscillator. In this work, we investigate the forced response of a realistic LPT rotor with 144 blades, and derive an asymptotically simplified model to directly capture this low dimensional dynamics. This asymptotic model is obtained using a multiple scales perturbation method, where the elastic time scale is filtered from the system, and only the evolution on the long time scale associated with the nonlinear friction is described. The resulting model consists of a single complex differential equation, and the computation of the resonance curve is reduced to just the evaluation of an analytical expression. The results of the asymptotic description show very good agreement with high fidelity time domain simulations of the full bladed-disk, and the computation times are reduced by several orders of magnitude.