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Research Papers

Rotor Balancing Via an Enhanced Automatic Dynamic Balancer With Inductively Coupled Shunt Circuit

[+] Author and Article Information
Xiaowen Su

Department of Mechanical,
Aerospace and Biomedical Engineering,
M018 Dougherty Engineering Building,
University of Tennessee,
Knoxville, TN 37996-2210
e-mail: xsu2@vols.utk.edu

Hans A. DeSmidt

Department of Mechanical,
Aerospace and Biomedical Engineering,
University of Tennessee,
234 Dougherty Engineering Building,
Knoxville, TN 37996-2210
e-mail: hdesmidt@utk.edu

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received August 24, 2018; final manuscript received November 20, 2018; published online January 22, 2019. Assoc. Editor: Izhak Bucher.

J. Vib. Acoust 141(3), 031003 (Jan 22, 2019) (14 pages) Paper No: VIB-18-1365; doi: 10.1115/1.4042200 History: Received August 24, 2018; Revised November 20, 2018

Despite the elegant nature of the automatic balancing principle for passive imbalance vibration control, the co-existence of undesired whirling limit-cycles is a major impediment to the more widespread application of automatic dynamic balancing devices also called automatic dynamic balancer (ADB) in industry. To enlarge the region of stable perfect balancing and to eliminate whirling limit-cycles, we develop an innovative enhanced ADB system. This new idea harnesses the automatic balancing principle via moving permanent magnet balancer masses which are inductively coupled to a parallel resistor–inductor–capacitor (RLC) circuit. It is found that the circuit parameters can be adjusted properly to suppress the whirling limit-cycle to enlarge the perfect balancing region. We start from a Lagrangian description of the system and get nonlinear autonomous equations-of-motion. We then solve two dominant steady-state solutions for the enhanced ADB system. One solution is for the perfect balancing equilibrium points (EPs), which can be solved analytically. While the other solution is for the whirling limit-cycle which is solved via a harmonic balance method. The stability of these solutions is then evaluated through eigenvalue analysis and Floquet theory. The newly involved electrical parameters, such as coupling coefficient, equivalent capacitance, and equivalent resistance, are designed via an arc-length continuation method to destabilize the limit-cycle solutions to then guarantee stable rotor balancing.

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References

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Figures

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Fig. 1

The planar rotor/dual mass enhanced ADB system

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Fig. 2

Stability enhancement of perfect balancing steady-state for the enhanced ADB with RLC circuit: (1) example plot, (2) ςe = 0.001, and (3) ςe = 0.01

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Fig. 3

The whirling speed solution of the ADB and the enhanced ADB when ςe = 0.001, Cn = 0.01, and Rn = 0.01: (1) full scale and (2) zoomed in

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Fig. 4

The whirling speed solution of the enhanced ADB under (1) different ςe, when Cn and Rn fixed at 0.01 and (2) different Rn when ςe = 0.001 and Cn = 0.01

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Fig. 5

Numerical verification of the solution curve for the ADB: (1) stable points and (2) unstable points

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Fig. 6

Numerical verification of the solution curve for the enhanced ADB: (1) stable points and (2) unstable points

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Fig. 7

Rotor vibration of the rotor, the ADB, and the enhanced ADB system with different rotor speeds when ςe = 0.01, Cn = 1, and Rn = 0.01 under different initials: (1) [ϕe, ϕe] for the angles of eccentric masses and zeros for other state, and (2) initials from whirl limit-cycle

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Fig. 8

Eccentric mass angles and electric charge quantity of the enhanced ADB system under (1) Rn = 0.01 and (2) Rn = 100

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Fig. 9

Eccentric mass angle of the enhanced ADB operating at Ω¯ = 0.97: (a) ΔθIc = 0.1 rad and (b) ΔθIc = 0.3 rad

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