Global bifurcations and chaos for a rotor-active magnetic bearing system with time-varying stiffness

2020

Shock and Vibration

Self Cite

The asymptotic perturbation method is used to analyze the nonlinear vibrations and chaotic dynamics of a rotor-active magnetic bearing (AMB) system with 16-pole legs and the time-varying stiffness. Based on the expressions of the electromagnetic force resultants, the influences of some parameters, such as the cross-sectional area Aα of one electromagnet and the number N of windings in each electromagnet coil, on the electromagnetic force resultants are considered for the rotor-AMB system with 16-pole legs. Based on the Newton law, the governing equation of motion for the rotor-AMB system with 16-pole legs is obtained and expressed as a two-degree-of-freedom system with the parametric excitation and the quadratic and cubic nonlinearities. According to the asymptotic perturbation method, the four-dimensional averaged equation of the rotor-AMB system is derived under the case of 1 : 1 internal resonance and 1 : 2 subharmonic resonances. Then, the frequency-response curves are employed to study the steady-state solutions of the modal amplitudes. From the analysis of the frequency responses, both the hardening-type nonlinearity and the softening-type nonlinearity are observed in the rotor-AMB system. Based on the numerical solutions of the averaged equation, the changed procedure of the nonlinear dynamic behaviors of the rotor-AMB system with the control parameter is described by the bifurcation diagram. From the numerical simulations, the periodic, quasiperiodic, and chaotic motions are observed in the rotor-active magnetic bearing (AMB) system with 16-pole legs, the time-varying stiffness, and the quadratic and cubic nonlinearities.

Section: Introductionmentioning

confidence: 99%

Nonlinear Vibrations of a Rotor-Active Magnetic Bearing System with 16-Pole Legs and Two Degrees of Freedom

2020

Shock and Vibration

Self Cite

“…Chasalevris and Papadopoulos [22] developed a semi-analytical simulation of a rotor-bearing system consisting of a journal bearing with finite length and a multi-segment continuous rotor and evaluated the nonlinear dynamic characteristics of this system in three different cases. Zhang [23,24] studied the transient and steady-state nonlinear dynamics in a rotor-active magnetic bearing (AMB) system with the time-varying stiffness. The global bifurcations and chaotic motion obtained from the system implied that stiffness had a major impact on the rotor dynamics and the nonlinear parameters should be considered in the calculation of the rotor system.…”

Section: Introductionmentioning

confidence: 99%

Research on Steady-State Characteristics of Centrifugal Pump Rotor System with Weak Nonlinear Stiffness

Zhou

Qiu

et al. 2018

TFAMENA

Steady-state vibration response characteristics of a motion model of a centrifugal pump rotor system with weak nonlinear stiffness have been calculated by using the multiple scale method (MSM). The theoretical results were in good agreement with the numerical results. Based on the MSM and the numerical method, the effects of detuning parameter, nonlinear stiffness parameter and natural frequency on steady-state amplitude were also investigated. Finally, Lyapunov's theorem on stability in the first approximation was applied for the determination of the system's stable and unstable solution regions. The calculated results imply that the centrifugal pump rotor system with weak nonlinear stiffness exhibits typical nonlinear vibration characteristics. The variation of detuning parameter, nonlinear stiffness parameter and natural frequency can result in a jump phenomenon, and their corresponding curves present 'hard spring', 'soft spring' and 'S'-shaped amplitude characteristic, respectively. Smaller detuning parameter and natural frequency or greater nonlinear stiffness parameter are beneficial to decreasing the steady-state response amplitude. The results can provide reference for an investigation into nonlinear vibration characteristics of a centrifugal pump rotor system.

“…It determines conditions under which Shilnikov-type homoclinic orbits may be present in a perturbed system. Employing this technique, the global bifurcations and chaos of several mechanic models are investigated [14][15][16]. Subsequently, Camassa et al [17] proposed an extended Melnikov method to study the multi-pulse jumping of homoclinic and heteroclinic orbits in a class of perturbed Hamiltonian systems.…”

Section: Introductionmentioning

confidence: 99%

Global bifurcations and single‐pulse homoclinic orbits of a plate subjected to the transverse and in‐plane excitations

Math Methods in App Sciences

Chen

2017

Communicated by T. WannerThe Shilnikov-type single-pulse homoclinic orbits and chaotic dynamics of a simply supported truss core sandwich plate subjected to the transverse and the in-plane excitations are investigated in detail. The resonant case considered here is principal parametric resonance and 1:2 internal resonance. Based on the normal form theory, the desired form for the global perturbation method is obtained. By using the global perturbation method developed by Kovacic and Wiggins, explicit sufficient conditions for the existence of a Shilnikov-type homoclinic orbit are obtained, which implies that chaotic motions may occur for this class of truss core sandwich plate in the sense of Smale horseshoes. Numerical results obtained by using the fourth-order Runge-Kutta method agree with theoretical analysis at least qualitatively.It is not difficult to show that, when the condition 3 2ˇ2 4 fI r cos c > 0 is satisfied, the fixed point p 0 is a center, and when the condition 3 2ˇ2 4 fI r cos s < 0 is satisfied, the fixed point q 0 is a saddle, which is connected to itself by a homoclinic orbit. The phase portrait of system (37) is given in Figure 3(a). Following the analysis presented by Kovacic and Wiggins, it is found that for sufficiently small , the