Non-linear modelling of rotor dynamic systems with squeeze film dampers: an efficient integrated approach

Squeeze film dampers used in rotor assemblies such as aero-engines introduce non-linear damping forces into an otherwise linear rotor dynamic system. The steady state periodic response of such rotor dynamic systems to rotating out-of-balance excitation can be efficiently determined by using periodic solution techniques. Such techniques are essentially faster than time marching techniques. However, the computed periodic solutions need to be tested for stability and recourse to time marching is necessary if no periodic attractor exists. Hence, an efficient integrated approach, as presented in this paper, is necessary. Various techniques have been put forward in order to determine the periodic solutions, each with its own advantages and disadvantages. In this paper, a receptance harmonic balance method is proposed for such a purpose. In this method, the receptance functions of the rotating linear part of the system are used in the non-linear analysis of the complete system. The advantages of this method over current periodic solution techniques are two-fold: it results in a compact model, and the receptance formulation gives the designer the widest possible choice of modelling techniques for the linear part. Stability of these periodic solutions is efficiently tested by applying Floquet Theory to the modal equations of the system and time marching carried out on these equations, when necessary. The application of this integrated approach is illustrated with simulations and an experiment on a test rig. Excellent correlation was achieved between the periodic solution approach and time marching. Good correlation was also achieved with the experiment.