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TECHNICAL PAPERS

# Dynamic Behavior of an AMB/Supported Rotor Subject to Parametric Excitation

[+] Author and Article Information
Y. A. Amer, A. S. Sabbah

Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, Egypt

M. H. Eissa

Department of Engineering Mathematics, Faculty of Electronic Engineering, Menouf 32952, Egypt

U. H. Hegazy1

Department of Mathematics, Faculty of Science, Al-Azhar University, Gaza, Palestineuhijazy@yahoo.com

1

Corresponding author. Present address: Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, Egypt.

J. Vib. Acoust 128(5), 646-652 (Feb 14, 2006) (7 pages) doi:10.1115/1.2202163 History: Received April 01, 2005; Revised February 14, 2006

## Abstract

The dynamical behavior of a parametrically excited simple rigid disk-rotor supported by active magnetic bearings (AMB) is investigated, without gyroscopic effects. The principal parametric resonance case is considered and studied. The motion of the rotor is modeled by a coupled second-order nonlinear ordinary differential equations. Their approximate solutions are sought applying the method of multiple scales. A reduced system of four first-order ordinary differential equations are determined to describe the time variation of the amplitudes and phases of the vibration in the horizontal and vertical directions. The steady-state response and the stability of the solutions for various parameters are studied numerically, using the frequency response function method. The numerical results show that the system behavior includes multiple solutions, jump phenomenon, and sensitive dependence on initial conditions. It is also shown that the system parameters have different effects on the nonlinear response of the rotor. Results are compared to previously published work.

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## Figures

Figure 5

Principal parametric resonance solution

Figure 7

Numerical solution under various values of the system parameters

Figure 6

The system is sensitive to initial conditions

Figure 1

Model of a rigid rotor with active magnetic bearings (A,B) and sensors (C,D)

Figure 2

Schematic for modeling magnetic forces acting on the rotor

Figure 3

The response solution (physical coefficients are: Ω=6.0, ω=3.0, μ=0.02, f=0.5, αi, i=1,2,…7 are −0.9, 0.05, −0.011, −0.016, 0.00002, 0.0001, and −0.018, respectively)

Figure 4

Nonresonant time response solution (physical coefficients are: Ω=2.5, ω=3.0, μ=0.02, f=0.5, αi, i=1,2,…,7 are −0.9, 0.05, −0.011,−0.016, 0.00002, 0.0001, and −0.018, respectively)

## Errata

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