| Such an unbalance could be normally caused due to manufacturing limitations. For a turbo-machinery bladed disc assembly, there could be as many as 50-100 blades around the disc. Even small fluctuations in the masses of individual blades attached around the periphery of the disk could cause eccentricity of the effective center of mass. Similarly uneven windings in an armature could lead to eccentricity.
For steady state rotation (whirling), from the equilibrium of forces we have,
 (2.1.1)
where,
“k” stands for the equivalent stiffness offered by the shaft to deflection at the location of the disc; If the shaft were simply supported in its bearings at either end and the disc were centrally located, the stiffness of the shaft “k” would be given by
 .
“r” is the deflection of the shaft's geometric center at the location of the disc;
“m” is the mass of the disc;
“  ” is the speed of rotation;
“e” is the eccentricity i.e., constant distance between the geometric center (S) and center of mass (G). |
