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Research Papers

Chaotic Vibration Analysis of a Coaxial Rotor System in Active Magnetic Bearings and Contact With Auxiliary Bearings

[+] Author and Article Information
Reza Ebrahimi

Department of Mechanical Engineering,
Isfahan University of Technology,
Isfahan 84156-83111, Iran
e-mail: r.ebrahimi1988@gmail.com

Mostafa Ghayour

Professor
Department of Mechanical Engineering,
Isfahan University of Technology,
Isfahan 84156-83111, Iran
e-mail: ghayour@cc.iut.ac.ir

Heshmatallah Mohammad Khanlo

Assistant Professor
Department of Aerospace Engineering,
Aeronautical University of
Science and Technology,
Tehran 13846-73411, Iran
e-mail: khanloh47@yahoo.com

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received May 26, 2016; final manuscript received August 17, 2016; published online December 5, 2016. Assoc. Editor: Ahmet S. Yigit.

J. Comput. Nonlinear Dynam 12(3), 031012 (Dec 05, 2016) (11 pages) Paper No: CND-16-1249; doi: 10.1115/1.4034869 History: Received May 26, 2016; Revised August 17, 2016

In many cases of rotating systems, such as jet engines, two or more coaxial shafts are used for power transmission between a high/low-pressure turbine and a compressor. The major purpose of this study is to predict the nonlinear dynamic behavior of a coaxial rotor system supported by two active magnetic bearings (AMBs) and contact with two auxiliary bearings. The model of the system is formulated by ten degrees-of-freedom in two different planes. This model includes gyroscopic moments of disks and geometric coupling of the magnetic actuators. The nonlinear equations of motion are developed by the Lagrange's equations and solved using the Runge–Kutta method. The effects of speed parameter, speed ratio of shafts, and gravity parameter on the dynamic behavior of the coaxial rotor–AMB system are investigated by the dynamic trajectories, power spectra analysis, Poincaré maps, bifurcation diagrams, and the maximum Lyapunov exponent. Also, the contact forces between the inner shaft and auxiliary bearings are studied. The results indicate that the speed parameter, speed ratio of shafts, and gravity parameter have significant effects on the dynamic responses and can be used as effective control parameters for the coaxial rotor–AMB system. Also, the results of analysis reveal a variety of nonlinear dynamical behaviors such as periodic, quasi-periodic, period-4, and chaotic vibrations, as well as jump phenomena. The obtained results of this research can give some insight to engineers and researchers in designing and studying the coaxial rotor–AMB systems or some turbomachinery in the future.

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References

Figures

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Fig. 1

Model of a coaxial rotor supported by two AMBs and two auxiliary bearings

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Fig. 2

A cross section diagram of AMB placed at point A

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Fig. 3

Schematic diagram of the contact between the inner shaft and the auxiliary bearing A

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Fig. 4

Bifurcation diagrams of x2(nT) and x4(nT) versus speed parameter S for counter-rotating shafts with neglecting the influence of weight

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Fig. 5

Trajectories of disk d1, power spectrum of x2, and Poincaré maps of disk d1 at S = 0.23, 2, and 3.02 for counter-rotating shafts with neglecting the influence of weight

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Fig. 6

Bifurcation diagrams of x2(nT) and x4(nT) versus speed parameter S for corotating shafts with neglecting the influence of weight

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Fig. 7

The radial component of the contact force between the inner shaft and the auxiliary bearing A for counter-rotating and corotating shafts

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Fig. 8

Bifurcation diagrams of x2(nT) and x4(nT) versus speed parameter S for counter-rotating shafts with considering the influence of weight

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Fig. 9

Trajectories of disk d1, power spectrum of x2, and Poincaré maps of disk d1 at S = 0.36 and 1.25 for counter-rotating shafts with considering the influence of weight

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Fig. 10

The maximum Lyapunov exponent at S = 0.23 with (left side) and without (right side) considering the influence of weight

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