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Research Papers

Model-Based Switching-Crack Identification in a Jeffcott Rotor With an Offset Disk Integrated With an Active Magnetic Bearing

[+] Author and Article Information
Sandeep Singh

Assistant Professor
Department of Mechanical Engineering,
Indian Institute of Technology Guwahati,
Guwahati 781039, Assam, India

Rajiv Tiwari

Professor
Department of Mechanical Engineering,
Indian Institute of Technology, Guwahati,
Guwahati 781039, Assam, India
e-mail: rtiwari@iitg.ernet.in

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received March 28, 2015; final manuscript received November 24, 2015; published online January 12, 2016. Assoc. Editor: Fu-Cheng Wang.

J. Dyn. Sys., Meas., Control 138(3), 031006 (Jan 12, 2016) (11 pages) Paper No: DS-15-1135; doi: 10.1115/1.4032292 History: Received March 28, 2015; Revised November 24, 2015

Vibration characteristics of a cracked Jeffcott rotor with an offset disk under the action of an active magnetic bearing (AMB), implemented to improve the radial positioning of the rotor, has been studied. Presence of the AMB suppresses the vibration induced due to the crack and unbalance; identification of the crack could be made by utilizing the vibration signal in conjunction with the controller current of the AMB. A four degrees-of-freedom (DOF) cracked rotor is modeled considering the gyroscopic effect due to the offset disk and a switching crack excitation function (SCEF) to introduce the breathing of crack. The dynamic condensation is applied to eliminate rotational displacements, which would pose practical difficulty in accurate measurement, from the system equations of motion (EOM) to develop an identification algorithm. Frequency domain transformation of the EOM is made with the help of the full spectrum analysis. An algorithm developed with the purpose of crack identification in the form of additive crack stiffness estimates the viscous damping, disk unbalance, and AMB constants as well. The algorithm has been tested for the measurement noise (in the displacement and the current) and bias errors in system parameters, and found to be robust.

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Figures

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Fig. 1

Cracked rotor with offset disk and AMB support

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Fig. 2

(a) Rotating and inertial frame of reference and (b) Relative position of crack and unbalance

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Fig. 3

A rotor element showing various loads at the crack section

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Fig. 5

Generated response: (a) x-displacement and (b) angular displacement about x-axis

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Fig. 7

(a) X-displacement response during ramp up and (b) envelope of x-displacement response during ramp up

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Fig. 4

The simulinkTM model used for response generation

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Fig. 6

Full spectrum plots: (a) amplitude of quadrature linear displacement, (b) amplitude of quadrature current, (c) phase of quadrature displacement, and (d) phase of quadrature current

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