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.
摘要
将有限元与质量集中法相结合, 建立了具有橡胶阻尼环滚动轴承支承的柔性转子的动力学模型. 在该模型中, 转子通过 Timoshenko 梁单元离散建模, 支座和轴承外圈采用质量集中法建模, 同时考虑了转子重力、 不平衡力和非线性轴承力的影响. 动力学方程采用精确积分和 Runge-Kutta 混合数值算法求解. 为了验证建模方法的正确性, 在转子-轴承试验台上进行了理论和实验分析, 发现理论与实验研究的误差率小于 10%; 此外, 还分析了橡胶阻尼环对转子-轴承耦合系统动力学特性的影响, 所得结论与实际情况相吻合. 在此基础上, 分别研究了转速和橡胶阻尼环刚度对耦合系统的分岔和混沌行为的影响. 结果表明, 随着转速的增加, 系统进入混沌状态的路径有激变、 拟周期和间歇性分岔. 然而, 随着橡胶阻尼环刚度的变化, 发现了激变、 拟周期分岔和 Hopf 分岔到混沌的途径. 此外, 轴承间隙对转子系统的动态特性也有影响, 过大的轴承间隙会使系统的周期运动变为混沌; 橡胶阻尼环的刚度对系统的运动有很大的影响.
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ZHU Hai-min, CHEN Wei-fang, and ZHU Ru-peng established the models and calculated the predicted displacement. ZHANG Li edited the draft of manuscript. GAO Jie and LIAO Mei-jun provided the measured landslides displacement data, and analyzed the measured data. All authors replied to reviewers’ comments and revised the final version.
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ZHU Hai-min, CHEN Wei-fang, ZHU Ru-peng, ZHANG Li, GAO Jie and LIAO Mei-jun declare that they have no conflict of interest.
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Foundation item: Projects(51775277, 51775265) supported by the National Natural Science Foundation of China; Project(190624DF01) supported by Nanjing University of Aeronautics and Astronautics Short Visiting Program, China
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Zhu, Hm., Chen, Wf., Zhu, Rp. et al. Dynamic analysis of a flexible rotor supported by ball bearings with damping rings based on FEM and lumped mass theory. J. Cent. South Univ. 27, 3684–3701 (2020). https://doi.org/10.1007/s11771-020-4510-z
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DOI: https://doi.org/10.1007/s11771-020-4510-z