A \(30-\mathrm{kg}\) rotor has an eccentricity of \(1.2 \mathrm{~cm}\). It is mounted on a shaft and bearing system whose stiffness is \(2.8 \times 10^{4} \mathrm{~N} / \mathrm{m}\) and damping ratio is 0.07 . What is the amplitude of whirling when the rotor operates at \(850 \mathrm{rpm}\) ? Refer to Chapter Problem 4.32 for an explanation of whirling.

Data From Chapter Problem 4.32:
Whirling is a phenomenon that occurs in a rotating shaft when an attached rotor is unbalanced. The motion of the shaft and the eccentricity of the rotor cause an unbalanced inertia force, pulling the shaft away from its centerline, causing it to bow. Use Figure P4.32 to show that the amplitude of whirling is
\[
X=e \Lambda(r, \zeta)
\]
where \(e\) is the distance from the center of mass of the rotor to the axis of the shaft.

Transcribed Image Text:

FIGURE P4.32 C