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Technical Briefs

Extension of Campbell's Major Resonance With Experimental Demonstration

[+] Author and Article Information
Robert P. Czachor

Chief Consulting Engineer, Structures
GE Aircraft Engines,
1 Neumann Way,
Cincinnati, OH 45215
e-mail: robert.p.czachor@aol.com

For a disk, λ = ∞, and for a free-free cylinder, λ = 0, so that the behavior of any geometry can then be bracketed between the limiting possible values of λ.

Contributed by the Design Engineering Division of ASME for publication in the Journal of Vibration and Acoustics. Manuscript received February 13, 2012; final manuscript received March 19, 2013; published online June 18, 2013. Assoc. Editor: Alan Palazzolo.

J. Vib. Acoust 135(5), 054501 (Jun 18, 2013) (5 pages) Paper No: VIB-12-1039; doi: 10.1115/1.4024209 History: Received February 13, 2012; Revised March 19, 2013

The interaction of vibratory traveling waves in rotating and stationary axisymmetric components is examined. In the most general case, a resonance can occur when the wave propagation speed in a first structure is equal in magnitude and direction to the rotational velocity of an adjacent structure. When a backward wave in a rotor appears stationary, a major resonance, as discussed in Wilfred Campbell's classic paper (Campbell, W., 1924, “The Protection of Steam Turbine Disc Wheels from Axial Vibrations,” Trans ASME, 46, pp. 31–160), results. A related resonance has been observed when the wave propagation speed in the stator is equal to the physical speed of the adjacent rotor. A third mechanism is derived for resonance between a wave in rotor 1 and a co- or counter-rotating rotor 2. Description of a component test which demonstrated this final phenomenon is provided.

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References

Figures

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Fig. 1

Campbell major resonance from [1]

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Fig. 2

Campbell [1] major resonance in terms of wave propagation speed with revised sign convention

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Fig. 3

Campbell stator resonance; wave propagation speed wrt stationary observer

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Fig. 4

Campbell stator resonance; frequency wrt stationary observer

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Fig. 5

Campbell counter-rotating resonance; wave propagation speed wrt stationary observer

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Fig. 6

Campbell counter-rotating resonance; frequency wrt stationary observer

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Fig. 7

Campbell counter-rotating resonance; frequency wrt rotor 1

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Fig. 8

Rub test hardware and test facility

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Fig. 9

Rub test cross section details

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Fig. 10

Rub test outer rotor frequency data for ω1 = 36.17 rps

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Fig. 11

Rub test Campbell diagram; wave propagation speed wrt stationary observer

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Fig. 12

Rub test Campbell diagram; frequency wrt rotor 1

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Fig. 13

Rub test outer rotor frequency response from rotor 1/ rotor 2 rub event

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Fig. 14

Frequency nomenclature

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