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Research Papers

Nonsynchronous Vibration of Planar Autobalancer/Rotor System With Asymmetric Bearing Support

[+] Author and Article Information
DaeYi Jung

Assistant Professor
College of Convergence Engineering,
Kunsan National University,
558 Daehak-ro,
Gunsan-si 54150, South Korea
e-mail: dyjung@kunsan.ac.kr

Hans DeSmidt

Mechanical, Aerospace
and Biomedical Engineering,
University of Tennessee at Knoxville,
Knoxville, TN 37996
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 March 10, 2016; final manuscript received January 9, 2017; published online April 18, 2017. Assoc. Editor: Paul C.-P. Chao.

J. Vib. Acoust 139(3), 031010 (Apr 18, 2017) (24 pages) Paper No: VIB-16-1113; doi: 10.1115/1.4035814 History: Received March 10, 2016; Revised January 09, 2017

Due to inherent nonlinearity of the autobalancer, the potential for other, undesirable, nonsynchronous limit-cycle vibration exists. In such undesirable situations, the balancer masses do not reach their desired synchronous balanced steady-state positions resulting in increased rotor vibration. Such behavior has been widely studied and is well understood for rotor systems on idealized bearings with symmetric supports. However, a comprehensive study into this nonlinear behavior of an imbalanced planar-rigid rotor/autobalancing device (ABD) system mounted on a general bearing holding asymmetric damping and stiffness forces including nonconservative effects cross-coupling ones has not been fully conducted. Therefore, this research primarily focuses on the unstable nonsynchronous limit-cycle behavior and the synchronous balancing condition of system under the influence of the general bearing support. Here, solutions for rotor limit-cycle amplitudes and the corresponding whirl speeds are obtained via a harmonic balance approach. Furthermore, the limit-cycle stability is assessed via perturbation and Floquet analysis, and all the possible responses including undesirable coexistence for the bearing parameters and operating speeds have been thoroughly studied. It is found that, due to asymmetric behavior of bearing support, the multiple limit cycles are encountered in the range of supercritical speeds and more complicate coexistences are invited into the ABD–rotor system compared to the case with idealized symmetric bearing supports. The findings in this paper yield important insights for researchers wishing to utilize automatic balancing devices in more practical rotor systems mounted on a asymmetric general bearing support.

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References

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Figures

Grahic Jump Location
Fig. 1

Rigid planar rotor–ABD system supported by a generalized linear bearing holding asymmetric damping and stiffness force including cross-coupling ones

Grahic Jump Location
Fig. 4

Inaccuracy characteristics of the analytical whirl speed in (b) of Fig. 3: (a-1)–(e-1) are the time-domain simulations for (1), (2), (3), (4), and (5) in (b) of Fig. 3 and (a-2)–(e-2) are corresponding to the frequency-domain simulations of num in (a-1)–(e-1) of Fig. 4 and, (f) maxT−ta<t<Tε¯˙N(t) for three imbalance cases

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Fig. 6

Limit-cycle responses of ABD–rotor system for three different ABD ball track radius, ABD masses, and ABD viscous damping coefficients: (a-1)–(a-4) for three different track radius, (b-1)–(b-4) for three different masses, and (c-1)–(c-4) for three different viscous damping coefficients

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Fig. 7

Stability of ABD–rotor system for the primary bearing damping coefficients

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Fig. 8

Stability of ABD–rotor system for the primary bearing stiffness coefficients

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Fig. 9

Stability of asymmetric cross-coupled bearing stiffness coefficients in ABD–rotor system

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Fig. 10

Maximum rotor amplitude under the influence of asymmetric cross-coupled bearing stiffness coefficients

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Fig. 11

Rotor amplitude on the time domain corresponding to the case pointed by the arrow in Fig. 10

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Fig. 12

Whirl orbits of rotor for four different cross-coupled stiffness coefficients used in Fig. 10 at Ω¯=1.2

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Fig. 13

Maximum rotor amplitude under the influence of operating speed dependent asymmetric cross-coupled bearing stiffness coefficients

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Fig. 2

Comparison between the analytical solutions (cw and pw) and the numerical ones (num): Ω¯=1.5 for (a-1)–(a-4) and Ω¯=7.8 for (b-1)–(b-4)

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Fig. 3

Comparison between the analytical solutions (cw and pw) and the numerical ones (num): (a) nondimensional primary constant whirl speed, (b) nondimensional oscillating whirl speed of pw, (c) maximum whirling amplitude of rotor in horizontal direction, and (d) maximum whirling amplitude of rotor in vertical direction

Grahic Jump Location
Fig. 5

All the possible stable and unstable responses of ABD–rotor system: (a) cb  = 0.001 kg/s, (b) cb  = 0.0005 kg/s, and (c) cb  = 0.00025 kg/s

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