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Forced oscillations of a rotating shaft with nonlinear spring characteristics and internal damping (1/2 order subharmonic oscillations and entrainment)

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Abstract

Nonlinear forced oscillations of a rotating shaft with nonlinear spring characteristics and internal damping are studied. In particular, entrainment phenomena at the critical speeds of 1/2 order subharmonic oscillations of forward and backward whirling modes are investigated. A self-excited oscillation appears in the wide range above the major critical speed. The amplitude of this oscillation reaches a limit value and then a self-sustained oscillation occurs. In the vicinity of a 1/2 order subharmonic oscillation of a forward whirling mode, a self-excited oscillation is entrained by a subharmonic oscillation. In the vicinity of a 1/2 order subharmonic oscillation of a backward whirling mode, either a self-excited oscillation or a subharmonic oscillation occurs.

Experiments were made by an elastic rotating shaft with a disc. Nonlinearity in its restoring force was due to an angular clearance of a bearing and internal damping was due to friction between the shaft and an inner ring of the bearing. A self-excited oscillation was observed in the range above the major critical speed and this self-excited oscillation was entrained by a 1/2 order subharmonic oscillation of a forward whirling mode.

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Abbreviations

O−xyz :

rectangular coordinate system

θ, θx, θy :

inclination angle of a shaft and its projections on the xz- and yz-planes

θ′x, θ′y :

inclination angles in rotating coordinates

θ, ϕ:

polar coordinates

I p :

polar moment of inertia of a rotor

I :

diametral moment of inertia of a rotor

i p :

ratio of I p to I

τ:

dynamic unbalance of a rotor

ω:

rotating speed (angular velocity)

F :

magnitude of a dynamic unbalance force, F = (1 − i p )τω2

c :

external damping coefficient

h :

internal damping coefficient

t :

time

D θx , D θy :

internal damping terms in stationary coordinates

D θx , D θy :

internal damping terms in rotating coordinates

N θx , N θy :

nonlinear terms in restoring forces

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Authors and Affiliations

  1. School of Engineering, Nagoya University, Furo-cho, Chikusa-ku, 464-01, Nagoya, Japan

    Yukio Ishida

  2. Department of Science and Technology, Meijo University, Shiogamaguchi, Tenpaku-ku, 468, Nagoya, Japan

    Toshio Yamamoto

Authors
  1. Yukio Ishida
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  2. Toshio Yamamoto
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Ishida, Y., Yamamoto, T. Forced oscillations of a rotating shaft with nonlinear spring characteristics and internal damping (1/2 order subharmonic oscillations and entrainment). Nonlinear Dyn 4, 413–431 (1993). https://doi.org/10.1007/BF00053689

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  • DOI: https://doi.org/10.1007/BF00053689

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