Nonlinear dynamics and motion bifurcations of 12-pole variable stiffness rotor active magnetic bearings system under complex resonance

IF 2.8 3区工程技术 Q2 MECHANICS International Journal of Non-Linear Mechanics Pub Date : 2024-11-17 DOI:10.1016/j.ijnonlinmec.2024.104958

W.S. Ma , F.H. Liu , S.F. Lu , X.J. Song , S. Huang , Y.K. Zhu , X. Jiang

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Abstract

In this study, we analyze the nonlinear dynamic characteristics of a 12-pole variable stiffness rotor active magnetic bearings (rotor-AMBs) under intricate resonance conditions. Using the principles of electromagnetic bearings, a model for the 12-pole variable stiffness rotor-AMBs system is developed. Next, the dynamic equations for a two-degree-of-freedom 12-pole variable stiffness rotor-AMBs system are derived, incorporating both quadratic and cubic nonlinearities, through Newton's second law. Considering the primary parametric resonance, 1:1 internal resonance, and 1/2 subharmonic resonance, the multiple time scale perturbation method is applied to derive the average equation of the system. Based on these averaged equations, the characteristics and complex dynamics of the system are analyzed. Finally, MATLAB software is employed for numerical simulations of the 12-pole variable stiffness rotor-AMBs system. The simulation results indicate that the nonlinear control parameters can modify the system's softening and hardening spring behaviors. Varying the parametric excitation amplitude leads to diverse dynamic behaviors, including single-periodic motion, double-periodic motion, and chaotic vibrations.

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复杂共振下 12 极变刚度转子主动磁轴承系统的非线性动力学和运动分岔

在本研究中，我们分析了 12 极可变刚度转子有源磁轴承（转子-AMB）在错综复杂的共振条件下的非线性动态特性。利用电磁轴承的原理，建立了 12 极可变刚度转子-AMB 系统的模型。接着，通过牛顿第二定律，结合二次方和三次方非线性，推导出了两自由度 12 极可变刚度转子-AMB 系统的动态方程。考虑到主要参数共振、1:1 内部共振和 1/2 次谐波共振，应用多时标扰动法推导出系统的平均方程。根据这些平均方程，对系统的特性和复杂动力学进行分析。最后，采用 MATLAB 软件对 12 极变刚度转子-AMB 系统进行数值模拟。仿真结果表明，非线性控制参数可以改变系统的软化和硬化弹簧行为。改变参数激励振幅会导致多种动态行为，包括单周期运动、双周期运动和混沌振动。

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来源期刊

International Journal of Non-Linear Mechanics 物理-力学

CiteScore

5.50

自引率

9.40%

发文量

192

审稿时长

67 days

期刊介绍： The International Journal of Non-Linear Mechanics provides a specific medium for dissemination of high-quality research results in the various areas of theoretical, applied, and experimental mechanics of solids, fluids, structures, and systems where the phenomena are inherently non-linear. The journal brings together original results in non-linear problems in elasticity, plasticity, dynamics, vibrations, wave-propagation, rheology, fluid-structure interaction systems, stability, biomechanics, micro- and nano-structures, materials, metamaterials, and in other diverse areas. Papers may be analytical, computational or experimental in nature. Treatments of non-linear differential equations wherein solutions and properties of solutions are emphasized but physical aspects are not adequately relevant, will not be considered for possible publication. Both deterministic and stochastic approaches are fostered. Contributions pertaining to both established and emerging fields are encouraged.