New models are developed for flexibly mounted stator (FMS) and flexibly mounted rotor (FMR) mechanical seals that incorporate the radial reaction force components produced by supporting O-rings due to relative squeezing motion across the O-rings. Supporting data come from tests done in relation to O-ring supports for ball bearing races. The reaction-force model is linear but a nonlinear function of excitation frequency. The model accounts for the axial displacement doz of the O-ring from the mass center of the seal stator (FMS configuration) or seal rotor (FMR configuration), which couples the radial and pitch–yaw motion of the model's stiffness and damping matrices. Greens' coned-face-seal model is used to define the reaction moment arising across the seal faces via stiffness and damping matrices. The damping matrix does not coincide with Green's. His is constant; the matrix developed here contains terms that are harmonic at twice theprecession frequency. When averaged over one precession cycle, the new average damping matrix coincides with Green's result. When the averaged damping matrix is used, the resultant model is linear. However, because of the viscoelastic reaction-force and reaction-moment models used for the O-ring coefficients, most of the stiffness and damping matrices are strong functions of the assumed precession frequency. The new FMR model contains a skew-symmetric stiffness matrix due to the O-ring damping terms. In rotordynamics, skew symmetric stiffness matrices due to internal damping in the rotor can lead to rotordynamic instabilities.

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