Nonlinear analysis of orbital motion of a rotor subject to leakage air flow through an interlocking seal |
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| Authors: | WZ Wang YZ Liu G Meng PN Jiang |
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| Institution: | 1. Key Lab of Education Ministry for Power Machinery and Engineering, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, China;2. State Key Lab of Mechanical System and Vibration, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, China;3. Department of R&D, Shanghai Turbine Company, 333 Jiang Chuan Road, Shanghai 200240, China;1. D. Guggenheim School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA 30332, United States;2. Department of Continuum Mechanics and Structural Analysis, University Carlos III of Madrid, Avda. de la Universidad, 30. 28911 Leganés, Madrid, Spain;1. Kamioka Observatory, Institute for Cosmic Ray Research, The University of Tokyo, Higashi-Mozumi, Kamioka, Hida, Gifu 506-1205, Japan;2. Information and Multimedia Center, Gifu University, Gifu 501-1193, Japan;3. Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo, Kashiwa, Chiba 277-8582, Japan;4. Kobayashi-Maskawa Institute for the Origin of Particles and the Universe, Nagoya University, Furo-cho, Chikusa-ku, Nagoya, Aichi 464-8602, Japan;5. Department of Physics, Kobe University, Kobe, Hyogo 657-8501, Japan;6. Korea Research Institute of Standards and Science, Daejeon 305-340, South Korea;7. Department of Physics, Miyagi University of Education, Sendai, Miyagi 980-0845, Japan;8. Solar Terrestrial Environment Laboratory, Nagoya University, Nagoya, Aichi 464-8602, Japan;9. Department of Physics, Sejong University, Seoul 143-747, South Korea;10. Department of Physics, Tokai University, Hiratsuka, Kanagawa 259-1292, Japan;11. School of Science and Technology, Tokai University, Hiratsuka, Kanagawa 259-1292, Japan;12. Department of Physics, Faculty of Engineering, Yokohama National University, Yokohama, Kanagawa 240-8501, Japan |
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| Abstract: | 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. |
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