In order to avoid contact between the vibrating rotor and the stator, annular seals are designed with a relatively large radial clearance (∼100 μm) and, therefore, have an important leakage. The floating ring annular seal is able to reduce the leakage flow rate by using a much lower clearance. The seal is designed as a ring floating on the rotor in order to accommodate its vibrations. The pressure difference between the upstream and the downstream chambers is pressing the nose of the floating ring (secondary seal) against the stator. The forces acting on the floating ring are the resultant of the hydrodynamic pressure field inside the primary seal, the friction forces in the secondary seal, and the inertia forces resulting from the non-negligible mass of the ring. For proper working conditions, the ring of the annular seal must be able to follow the vibration of the rotor without any damage. Under the effect of the unsteady hydrodynamic pressure field (engendered by the vibration of the rotor), of the friction force, and of the inertia force, the ring will describe a periodic, a quasi-periodic, or a chaotic motion. Damage can come from heating due to friction in the secondary seal or from repeated impacts between the rotor and the ring. The present work presents an analytic model able to take into account only the synchronous periodic whirl motion of the floating ring.

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