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Unbalance force

A rotating mass that is not centered on the rotation axis (unbalance) produces a rotating centripetal force that grows with the square of the angular velocity. This is a common source of vibration in motors, fans and other rotating equipment, and quickly becomes a major problem at high speeds.

F = me\omega^2

unbalance force

Symbols

$F$	unbalance force (amplitude)	N
$m$	unbalance mass	kg
$e$	eccentricity	m
$\omega$	angular velocity	rad/s

Example

$m = 0.05$ kg, $e = 5$ mm, $n = 3000$ rpm ( $\omega \approx 314$ rad/s):

$F = 0.05\cdot 0.005\cdot 314^2 \approx 24.7$ N.

Because

F \propto \omega^2

, doubling the speed gives four times the unbalance force.

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