Compact models for squeezed-film dampers with inertial and rarefied gas effects

A modified Reynolds equation where the gas inertia effect is included is derived from the Navier-Stokes equation. Continuum and slip-flow regions are modelled. Small flow velocity is assumed, and border effects are not considered. By introducing an effective flow rate coefficient including the inertial and rare gas effects, existing linearized analytic squeezed-film damping models can be reused. Equivalent-circuit mechanical impedance and admittance implementations for a rectangular parallel-plate damper are given. The model response is compared against 2D and 3D FEM time-domain and frequency-domain simulations with an excellent agreement. The validity and limitations of the models are discussed extensively.