How to determine deflection of beam

[oreocrumble]

Homework Statement

At work I am currently confronted with the following problem.
How to theoretically calculate the deflection at the tip of a rotating beam with torque loading?


y= unknown deflection at tip
L= rod length
E= Young's Modulus
I= Moment Inertia

Homework Equations

Ideally, if the beam is rotating along its longitudinal axis, there should be no deflection along its length. However, in the real world, due to runout, straightness and other factors not being perfect, the higher the torque applied by a motor at the fixed end, the more deflection occurs at the free end.

The Attempt at a Solution

Could I use the cantilever beam loading equation to solve this somehow?

y = (-F*L^3)/ (3*E*I)

Maybe if I can calculate the load at the tip with an accelerometer?

 

[AlephZero]

No, the cantilever beam equation ignores the most important part of the problem, namely that the beam is rotatiing!

When the beam starts to bend, the centripetal forces on it increase as it becomes more unbalanced, which increases the bending further. Also, the rotating beam acts like a gyroscope and this affects its deflected shape.

The only "hand calc formulas" that I know of for rotordynamics are for rotors with a light (assumed massless) flexible shaft with rigid heavy disks attached to it - similar to a steam turbine rotor, etc. They don't seem to be relevant to your structure. What you need is some software that can do rotordynamic analysis. Many finite element analysis systems can do this as a standard procedure. There are also specialist software packages that only do rotordynamics, but they would probably have far more options than you need.