Friends,
I am trying to understand how the natural frequencies evolves with the speed of rotation. I tried plotting Campbell diagram for a flat circular disc. I found that forward whirls increased the natural frequency whereas the backward whirls reduced the natural frequency with an increasing speed of rotation. Why does this happen? I found form the online sources that the change in natural frequency takes places because of gyroscopic couples and changing damping coefficients. In the simulation I had carried out, I had assumed very small damping ratio so the effect must be purely because of gyrosciopic couple. I that is so, then, I reason that since gyroscopic couple only stabilizes the axis of rotation, it would manifest inform of an increase in stiffness. This may explain the increase in frequency in forward whirls but how does the added stiffness reduce the natural frequency in backward whirls. Can anyone answer this?
I am completely new to this topic. Hope to learn from you.
Hi friends. I have found answer to this question. The answer came with the realization that gyroscopic couple does not always stabilize the axis of rotation. Depending on the direction of the precessional motion, it can even destabilize the system. During forward whirls the precessional motion causes the system to become stiffer where as in the backward whirls, the gyroscopic couple is negative and tends to increase the deflection or lower the stiffness. Thus in forward whirls the natural frequency increases and in backward whirls, it decreases with speed of rotation.
I found the following paper useful:
https://www.google.co.in/url?sa=t&source=web&rct=j&url=http://sandv.com/downloads/0505swan.pdf&ved=2ahUKEwiy9vm4iYLdAhUHs48KHeowAIoQFjAWegQIBhAB&usg=AOvVaw3ajC2XLfv6T3ERkiXB4P_t
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