Nonstationary Vibration of a Rotating Shaft with Nonlinear Spring Characteristics during Acceleration through a Critical Speed : A Critical Speed of a 1/3-Order Subharmonic Oscillation

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Nonstationary vibration characteristics during acceleration through a critical speed of a 1/3-order subharmonic oscillation of forward precession are investigated in a rotating shaft system. The following results are obtained : (1) A resonance curve is separated from a zero-amplitude resonance curve (a trivial solution) which is stable at any rotating speed ω. If there exists an initial disturbance at the start of acceleration, the solution jumps to the resonance curve and a subharmonic oscillation occurs. (2) The maximum amplitude during acceleration depends not only on the angular acceleration λ but also on the initial disturbance ⊿P, the initial rotating speed ω_s, and the initial angular posion Ψ_o of the unbalance. (3) For the initial angular position Ψ_o, the maximum amplitude varies periodically. (4) The amplitude grows infinitely for some values of Ψ_o when the angular acceleration λ takes a value between two critical values λ_1 and λ_2. If the angular acceleration is outside of this range, the rotor can always pass the critical speed with a finite maximum amplitude. In addition, characteristics of some other subharmonic oscillations of backward precession are discussed briefly. Finally, nonstationary vibration characteristics at various critical speeds, such as a major critical speed, a summed-and-differential harmonic resonance and subharmonic resonances, are compared.
一般社団法人日本機械学会の論文
1992-09-15