Nonlinear analysis of orbital motion of a rotor subject to leakage air flow through an interlocking seal

• Published in: Journal of fluids and structures Vol. 25; no. 5; pp. 751 - 765
• Main Authors: Wang, W.Z., Liu, Y.Z., Meng, G., Jiang, P.N.
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01.07.2009; Elsevier
• Subjects: Aerodynamic forces; Applied sciences; Clearances; Drives; Exact sciences and technology; Labyrinth seal; Leakage; Locking; Machine components; Marine; Mathematical models; Mechanical engineering. Machine design; Muzynska model; Nonlinear analysis; Nonlinearity; Orbital motion; Perturbation analysis; Rotors; Seals; Seals and gaskets; Shafts, couplings, clutches, brakes; Perturbation analysis; Muzynska model; Orbital motion; Nonlinear analysis; Labyrinth seal; Motion estimation; Leak; Aerodynamics; Aerodynamic force; Mechanical clearance; Runge Kutta method; Modeling; Air flow; Perturbation method; Precession; Cavity; Gas flow; Shaft; Seal; Non linear effect; Lyapunov function
• ISSN: 0889-9746; 1095-8622
• DOI: 10.1016/j.jfluidstructs.2008.07.009

A nonlinear mathematical model for orbital motion of the rotor under the influence of leakage flow through a labyrinth seal was established in the present study. An interlocking seal was chosen for study. The rotor–seal system was modeled as a Jeffcot rotor subject to aerodynamic forcing induced by the leakage flow. Particular attention was placed on the serpentine flow path by spatially separating the aerodynamic force on the rotor surface into two parts, e.g., the seal clearance and the cavity volume. Spatio-temporal variation of the aerodynamic force on the rotor surface in the coverage of the seal clearance and the cavity volume was delineated by using the Muzynska model and perturbation analysis, respectively. The governing equation of rotor dynamics, which was incorporated with the aerodynamic force integrated over all seal clearances and cavity volumes, was solved by using the fourth-order Runge–Kutta method to obtain the orbit of the whirling rotor. Stability of the rotating rotor was inspected using the Liapunov first method. The results convincingly demonstrate that the destabilization speed of the rotor was reduced due to the aerodynamic force induced by the leakage flow through the interlocking seal. The nonlinear analysis method proposed in the present study is readily applied to dynamics of various rotor–seal systems with labyrinth seals.