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1 Machine Dynamics Problems

1 2003

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Gyroscopic Effect in the Stability Problem of a Slender Rotating Shaft with Follower Load

Kurnik W., Przybyłowicz P. M., Weronko J., Wiatr P.

Machine Dynamics Problems

2003

Vol. 27, No. 2

55-70

The paper is concerned with stability analysis of a flexible rotating shaft supported as a cantilever beam and subjected to tip-concentrated follower load. Such systems exhibit two mechanisms of instability of flutter type, different in physical nature and, what is most important, interacting to produce complicated stability regions in the space of rotation speed and follower load. In such systems even for high-speed working conditions, the rotary inertia as well as the gyroscopic effect is usually neglected like in slender beams. However, in some regions of parameters, especially in slightly internally dissipative shafts the gyroscopic effect can considerably change the boundaries of the stability domain. Moreover, an interesting phenomenon can be observed when two pairs of eigenvalues with different speeds at the same time intersect the imaginary axis of the complex plane. This leads to bifurcation with four critical eigenvalues similar to that studied by Iooss in the Navier-Stokes equations.