Vibration of a rotating shaft with nonlinear spring characteristics during acceleration through a critical speed. 2nd report. A critical speed of a 1/2-order subharmonic oscillation.

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This paper deals with a nonstationary vibration of a flexible rotating shaft with nonlinear spring characteristics. Especially, we investigate a phenomenon during constant acceleration and deceleration passing through a critical speed of a 1/2-order subharmonic oscillation of forward precession. In numerical simulation, we examined the influence of the angular acceleration λ and the initial angular position ψ0 of a rotor unbalance on the maximum amplitude of the subharmonic oscillation. As a result, the followings are clarified : (1) in order to always pass through this critical speed with a finite amplitude during acceleration, an angular acceleration greater than a certain value λ0 is necessary, (2) the maximum amplitude depends on ψ0 markedly, and (3) whether the shaft can pass through this critical speed or not depends on ψ0 when 0 < λ < λ0. We ascertained the validity of these theoretical results by experiments.