Modeling And Analysis of A Jeffcott Rotor As A Continuous Cantilever Beam And An Unbalanced Disk System

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The paper presents simulations of a continuous cantilever beam and an unbalanced disk system by extending classical Jeffcott rotor approach to a model that gives the first three (or more) modes of the flexible beam. Normal modes of a constrained structure method are used to develop the equations of motion including gyroscopic effects. Centrifugal force created by the unbalanced mass of the disk is considered as a constraint for the flexible beam. The first three modes of the flexible beam having an unbalanced disk are taken intoconsideration, which cannot be found through the classical Jeffcott rotor modeling. Hence, the model computes the first three natural frequencies of the rotor, and presents a very good correspondence with the first natural frequency obtained by the Jeffcott model. The change in the natural frequencies with respect to the disk mass to shaft mass ratio and the disk diameter to shaft length ratio are computed and presented. Instability problem due to inertial effects is encountered if these two ratios are kept high; which cannot be predicted by the classical Jeffcott rotor model.
Key words: Jeffcott rotor, rotor whirl, modal vibration.


Jeffcott rotor, rotor whirl, modal vibration.

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