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

Abstract

This paper deals with the nonstationary oscillations of a flexible rotating shaft with nonlinear spring characteristics. In particular, 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 simulations, 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 following points are clarified: (1) the maximum amplitude depends markedly on λ and ψ0; (2) in order to always pass through this critical speed with finite amplitude during acceleration, an angular acceleration greater than a certain value λ0 is necessary; and (3) when the angular acceleration is less than this critical value λ0 (0<λ<λ0), the shaft's ability to pass through this critical speed depends on ψ0. We ascertained the validity of these theoretical results by experiments.