Interdisciplinary Applied Mathematics

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18.2.1 Equivalent Circuit Models


Compact models for squeezed film damping based on equivalent circuit representation have the advantage of being incorporated into standard circuit simulators. The forces created by a squeezed gas film between vertically moving planar surfaces can be divided into spring and damping forces, which can be realized with frequency-dependent resistors and inductors (Veijola et al., 1995a). The second-order nonlinear Reynolds equation can be linearized when the motion of the plate(s) is small, the two plates are substantially parallel, and the motion is perpendicular to the surface of the plates. The linearized equation is written as


P092 V2 f P_ _ dL f P_ = F (H 12pe    poJ dt p0) dtg


where p is a small pressure change of the static pressure pQ. The variation of the plate spacing x is also assumed to be small compared with the static gap g; pe is the effective viscosity of the gas given by (Veijola et al., 1995a)





_P_


l + 9.638Kn1159


The linearized Reynolds equation (18.13) has two principal components in its solution, one in phase with the plate movement and the other out of phase, i.e., the spring term and the damping term, respectively. The force components can be calculated by integrating over the plate area, which for a rectangular plate is given (Blech, 1983) as an infinite series expansion

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