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Research Papers

Imbalance Vibration Suppression of a Supercritical Shaft via an Automatic Balancing Device

[+] Author and Article Information
H. A. DeSmidt

Assistant Professor of Aerospace Engineering, 606 Dougherty Engineering Building, University of Tennessee, Knoxville, TN 37996-2210; Department of Mechanical, Aerospace and Biomedical Engineering, University of Tennessee, Knoxville, TN 37996-2210hdesmidt@utk.edu

J. Vib. Acoust 131(4), 041001 (May 28, 2009) (13 pages) doi:10.1115/1.3025834 History: Received November 02, 2007; Revised October 06, 2008; Published May 28, 2009

This research explores the use of automatic balancing (AB) devices or “autobalancers” for imbalance vibration suppression of flexible shafts operating at supercritical speeds. Essentially, an autobalancer is a passive device consisting of several freely moving eccentric masses or balancer balls free to roll within a circular track mounted on a rotor that is to be balanced. At certain speeds, the stable equilibrium positions of the balls are such that they reduce or cancel the rotor imbalance. This “automatic balancing” phenomenon occurs as a result of the nonlinear dynamic interactions between the balancer balls and the rotor transverse vibration. Thus, autobalancer devices can passively compensate for unknown imbalance without the need for a control system and are able to naturally adjust for changing imbalance conditions. Autobalancers are currently utilized for imbalance correction in some single plane rotor applications such as computer hard-disk drives, CD-ROM drives, machine tools and energy storage flywheels. While autobalancers can effectively compensate for imbalance of planar, disk-type, rigid rotors, the use of autobalancing devices for nonplanar and flexible shafts with multiple modes of vibration has not been fully considered. This study explores the dynamics and stability of an imbalanced flexible shaft-disk system equipped with a dual-ball automatic balancing device. The system is analyzed by solving a coupled set of nonlinear equations to determine the fixed-point equilibrium conditions in rotating coordinates, and stability is assessed via eigenvalue analysis of the perturbed system about each equilibrium configuration. It is determined that regions of stable automatic balancing occur at supercritical shaft speeds between each flexible mode. Additionally, the effects of bearing support stiffness, axial mounting offset between the imbalance and autobalancer planes, and ball/track viscous damping are explored. This investigation develops a new, efficient, analysis method for calculating the fixed-point equilibrium configurations of the flexible shaft-AB system. Finally, a new effective force ratio parameter is identified, which governs the equilibrium behavior of flexible shaft/AB systems with noncollocated autobalancer and imbalance planes. This analysis yields valuable insights for balancing of flexible rotor systems operating at supercritical speeds.

Copyright © 2009 by American Society of Mechanical Engineers
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References

Figures

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Figure 11

Disk-plane steady-state vibration; τ=100, cb=1×10−6, lb=0.45, and ld=0.35

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Figure 12

Effective imbalance force ratio versus speed: (a) τ=10 and (b) τ=100, cb=1×10−6, lb=0.45, and ld=0.35

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Figure 1

Imbalanced shaft-disk with autobalancer

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Figure 2

Flexible rotor with dual-ball autobalancer

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Figure 3

Iterative solution for balanced equilibrium

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Figure 4

Iterative solution for merged and opposed equilibrium conditions

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Figure 5

ND natural frequencies versus bearing stiffness

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Figure 6

Fixed-point autobalancer equilibrium angles: (a) merged equilibrium and (b) balanced equilibrium; τ=10, cb=1×10−6, lb=0.45, and ld=0.35

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Figure 7

AB-plane steady-state vibration; τ=10, cb=1×10−6, lb=0.45, and ld=0.35

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Figure 8

Disk-plane steady-state vibration; τ=10, cb=1×10−6, lb=0.45, and ld=0.35

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Figure 9

Fixed-point autobalancer equilibrium angles: (a) merged equilibrium and (b) balanced equilibrium; τ=100, cb=1×10−6, lb=0.45, and ld=0.35

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Figure 10

AB-plane steady-state vibration; τ=100, cb=1×10−6, lb=0.45, and ld=0.35

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Figure 13

Autobalancer ball equilibrium angles for several values of ball damping: (a) cb=1×10−4, (b) cb=1×10−5, (c) cb=1×10−6; τ=10, lb=0.45, and ld=0.35

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Figure 14

Disk lateral vibration parameter, χd, versus AB location, lb, and shaft speed, Ω; τ=10, cb=1×10−6, and ld=0.35

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Figure 15

Disk out-of-plane tilting parameter, ψd, versus AB location, lb, and shaft speed, Ω; τ=10, cb=1×10−6, and ld=0.35

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Figure 16

Regions of overall disk vibration suppression versus AB location, lb, and shaft speed, Ω; τ=10, cb=1×10−6, and ld=0.35

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Figure 17

AB-shaft-disk system operating conditions: (a) ND shaft speed and (b) imbalance mass ratio; (c) imbalance phase angle (case 1)

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Figure 18

Disk vibration amplitude during spinup from Ω=[0–2.5] followed by sudden imbalance change; τ=100, cb=1×10−6, lb=0.45, and ld=0.35 (case 1)

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Figure 19

AB ball angles during spinup from Ω=[0–2.5] followed by sudden imbalance change; τ=100, cb=1×10−6, lb=0.45, and ld=0.35 (case 1)

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Figure 20

AB-shaft-disk system operating conditions: (a) N.D. shaft speed and (b) imbalance mass ratio; (c) imbalance phase angle (case 2)

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Figure 21

Disk vibration amplitude; Ω=[0–0.75], τ=100, cb=1×10−6, lb=0.45, and ld=0.35 (case 2)

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Figure 22

ND shaft speed and AB ball speeds; τ=100, cb=1×10−6, lb=0.45, and ld=0.35 (case 2)

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