The Rotor Dynamic Coefficients of Eccentric Mechanical Face Seals

The Reynolds equation is extended to include the effects of radial deflection in a seal with two flexibly mounted rotors. The resulting pressures are used to obtain the forces and moments introduced in the axial and angular modes by the inclusion of eccentricity in the analysis. The rotor dynamic coefficients relating the forces and moments in these modes to the axial and angular deflection are shown to be the same as those presented in the literature for the concentric case. Additional coefficients are obtained to express the dependence of these forces and moments upon the radial deflections and velocities. The axial force is shown to be decoupled from both the angular and radial modes, but the angular and radial modes are coupled to one another by the dependence of the tilting moments upon the radial deflections. The shear stresses acting upon the element faces are derived and used to obtain the radial forces acting upon the rotors. These forces are used to obtain rotor dynamic coefficients for the two radial degrees of freedom of each rotor. The additional rotor dynamic coefficients can be used to obtain the additional equations of motion necessary to include the radial degrees of freedom in the dynamic analysis. These coefficients introduce additional coupling between the angular and radial degrees of freedom, but the axial degrees of freedom remain decoupled.