Squeeze-film-dampers (SFDs) used to couple rotor dynamic systems to linear static structures, such as those in aircraft engines and turbochargers, are often approximated as linear connections in dynamic simulations. Linearized stiffness and damping coefficients of the SFDs can be reasonably estimated for circular centered orbits. Selection of linearized properties for the SFD is challenged under more general whirling conditions, such as those occurring in non-centered dampers with steady gravity loading. In this paper, an efficient method for coupling the rotor system to a static structure modeled as frequency-response-functions (FRFs) through nonlinear SFDs is illustrated. The harmonic balance method (HBM) with arc length continuation technique is employed in the frequency domain to obtain the system periodic response. Degrees-of-freedom participating in the non-linear SFD model, when separated from the remaining linear degrees-of-freedom, are expanded in terms of Fourier coefficients. The algorithm allows the Fourier coefficients approximating the nonlinearity to be iteratively determined at each frequency of interest. The approach has a tremendous time advantage over a traditional nonlinear transient analysis. The method can be used to efficiently predict vibration response on the engine static structure to typical imbalance on the rotors to assess the risk of meeting the low vibration requirements typical of new designs. The prediction includes the primary driving frequencies and their harmonics in the vibration estimate. A flexible rotor system connected to structure through an SFD is used to demonstrate the approach and discuss the impact of results.
The generalized harmonic balance method for determining the combination resonance in the parametric dynamic systems
