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Chapter
10

Rotor Dynamics Technology

Rotor dynamics analysis began in the 1870s when efforts were made to
calculate the fundamental natural frequencies of shafts. Fifty years
later the effects of an unbalanced force on the response of a single
rotating disk were considered. For 25 more years, until 1944, analyses
were limited to simple rotors, or to graphical solutions, for the deter-
mination of fundamental frequencies. At that time, M. A. Prohl of the
General Electric Company developed a general calculation method
that could be applied to any rotor geometry for the determination of
many frequencies. This was a key breakthrough for rotor analysis and
constitutes the basis for the present-day representation of rotors.

10.1 Rotor Model
Prohl’s method enabled the analyst to represent the rotor by a mathe-
matical model that closely resembled the actual geometry. There was
no longer any need for the simplifying assumptions required in previ-
ous calculated and graphical solutions. In addition, the second and
higher mode frequencies and mode shapes could be obtained as readily
as the first.
The method divided the rotor into a series of finite elements consist-
ing of concentrated masses connected by massless springs. In current
practice, mass stations are established at virtually every rotor location
where there is a change in shaft diameter and at the wheel, thrust
collar, coupling, and bearing locations as shown in Fig. 10.1. This is a
high-speed rotor that has a total of 48 mass stations. The bearing cen-
terlines are at stations 5 and 45.
The resulting mathematical model has the same mass and stiffness
distribution as the actual rotor. Refinements are included such as the
effective stiffnesses of the shaft sections through the integral wheels
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