Dynamic analysis of a flexible rotor supported by ball bearings with damping rings based on FEM and lumped mass theory
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Dynamic analysis of a flexible rotor supported by ball bearings with damping rings based on FEM and lumped mass theory ZHU Hai-min(朱海民)1, CHEN Wei-fang(陈蔚芳)1, ZHU Ru-peng(朱如鹏)1, ZHANG Li(张丽)2, GAO Jie(高洁)3, LIAO Mei-jun(廖梅军)3 1. National Key Laboratory of Science and Technology on Helicopter Transmission, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China; 2. Faculty of Engineering and Environment, Northumbria University, Newcastle NE17RU, UK; 3. AECC Hunan Aviation Powerplant Research Institute, Zhuzhou 412000, China © Central South University Press and Springer-Verlag GmbH Germany, part of Springer Nature 2020 Abstract: A dynamic model of a flexible rotor supported by ball bearings with rubber damping rings was proposed by combining the finite element and the mass-centralized method. In the proposed model, the rotor was built with the Timoshenko beam element, while the supports and bearing outer rings were modelled by the mass-centralized method. Meanwhile, the influences of the rotor’s gravity, unbalanced force and nonlinear bearing force were considered. The governing equations were solved by precise integration and the Runge-Kutta hybrid numerical algorithm. To verify the correctness of the modelling method, theoretical and experimental analysis is carried out by a rotor-bearing test platform, where the error rate between the theoretical and experimental studies is less than 10%. Besides that, the influence of the rubber damping ring on the dynamic properties of the rotor-bearing coupling system is also analyzed. The conclusions obtained are in agreement with the real-world deployment. On this basis, the bifurcation and chaos behaviors of the coupling system were carried out with rotational speed and rubber damping ring’s stiffness. The results reveal that as rotational speed increases, the system enters into chaos by routes of crisis, quasi-periodic and intermittent bifurcation. However, the paths of crisis, quasi-periodic bifurcation, and Hopf bifurcation to chaos were detected under the parameter of rubber damping ring’s stiffness. Additionally, the bearing gap affects the rotor system’s dynamic characteristics. Moreover, the excessive bearing gap will make the system’s periodic motion change into chaos, and the rubber damping ring’s stiffness has a substantial impact on the system motion. Key words: finite element method; Timoshenko beam; rubber damping ring; bifurcation; chaos Cite this article as: ZHU Hai-min, CHEN Wei-fang, ZHU Ru-peng, ZHANG Li, GAO Jie, LIAO Mei-jun. Dynamic analysis of a flexible rotor supported by ball bearings with damping rings based on FEM and lumped mass theory [J]. Journal of Central South University, 2020, 27. DOI: https://doi.org/10.1007/s11771-020-4510-z.
1 Introduction The rotor of the helicopter tail transmission system is often made into a thin-walled structure, which is installed on bearing supports through ball bearings. To improve the vibration and adjust the
natural frequency of the rotor-bearing system, rubber damping rings are often installe
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