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Research Papers

Sliding Mode Control of Flexible Rotor Based on Estimated Model of Magnetorheological Squeeze Film Damper

[+] Author and Article Information
Abdolreza Ohadi

e-mail: a_r_ohadi@aut.ac.ir
Acoustics Research Laboratory,
Department of Mechanical Engineering,
Amirkabir University of Technology,
Hafez Avenue, 424,
Tehran 15916-34311, Iran

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received June 14, 2012; final manuscript received April 19, 2013; published online June 18, 2013. Assoc. Editor: Ranjan Mukherjee.

J. Vib. Acoust 135(5), 051023 (Jun 18, 2013) (11 pages) Paper No: VIB-12-1180; doi: 10.1115/1.4024609 History: Received June 14, 2012; Revised April 19, 2013

By using magnetorheological (MR) fluid as the lubricating oil in a traditional squeeze film damper (SFD), one can build a variable-damping SFD, thereby controlling the vibration of a rotor by controlling the magnetic field. This study aims to control the vibration of a flexible rotor system using a magnetorheological squeeze film damper (MR-SFD). In order to evaluate the performance of the damper, the Bingham plastic model is used for the MR fluid and the hydrodynamic equation of MR-SFD is presented. Usually, the numerical methods are necessary for solving this equation. These methods are too costly and time consuming, especially in the simulation of complex rotors and the implementation of model-based controllers. To fix this issue, an innovative estimated equation for pressure distribution in MR-SFD is presented in this paper. By integration of this explicit expression, the hydrodynamic forces of MR-SFD are easily calculated as an algebraic equation. It is shown that the pressure and forces, which are calculated from the introduced expression, are consistent with the corresponding results of the original equations. Furthermore, considering the structural and parametric uncertainties of the system, proportional-integral-furthermore controller (PID) and sliding mode controllers are chosen for reducing the vibration level of the flexible rotor system, which is modeled by the finite element method. The time and frequency responses of a flexible rotor in the presence of these controllers show a good performance in reducing vibration of the shaft's midpoint, although near the rotor's critical speed the results of the sliding mode controller (SMC) are better than the corresponding results of the PID controller. The last part of this article is devoted to an analysis of the system's uncertainties. The results of the open loop system indicate that changes in the stiffness coefficient of the elastic foundation and the temperature of the MR fluid (two uncertainties of the system) strongly affects the outputs while using the controllers well increases the robustness of the system. The obtained results indicate that both the PID and sliding mode controllers have good performance against the uncertainty of the stiffness coefficient, but for changes in the MR fluid's temperature, the SMC presents better outputs compared to the PID controller, especially for high rotational speeds.

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References

Figures

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Fig. 1

Schematic view of the squeeze film damper [18]

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Fig. 2

Variation of the Bingham correction factor versus the (a) eccentricity ratio, (b) electrical current, and (c) rotational speed (for each parameter; the other two parameters are fixed)

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Fig. 3

Variation of the pressure distribution for different values of the rotational speed, eccentricity ratio, and electrical current (num.: numerical solution of Eq. (2); est.: estimated model based on Eq. (4))

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Fig. 4

Radial and tangential force variation for different values of rotational speed and electric current (num.: numerical solution of Eq. (2); est.: estimated model based on Eq. (4))

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Fig. 5

Schematic of the rotor bearing system assembled on the MR damper [18]

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Fig. 6

Time domain analysis for ω = 995rpm: (a) displacement of the disk center (w: displacement in the x direction, v: displacement in the y direction), (b) eccentricity ratio of the damper, and (c) the electrical current

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Fig. 7

Frequency response of the system for the SMC, the PID controller, and no control (I = 0(A)) conditions

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Fig. 8

Frequency response of the rotor in the presence of uncertainty in the stiffness of the foundation (the SMC compared to the no control (I = 0(A)) condition)

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Fig. 9

Frequency response of the rotor in the presence of uncertainty in the MR fluid temperature (the SMC compared to the no control (I = 0(A)) condition)

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Fig. 10

Frequency response of the rotor in the presence of uncertainty in the stiffness of the foundation (the SMC in comparison with the PID controller)

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Fig. 11

Frequency response of the rotor in the presence of uncertainty in the MR fluid temperature (the SMC in comparison with the PID controller)

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