IntroductionFor a rotating shaft there is a speed at which, for any small initial
deflection, the centripetral force is equal to the elastic restoring force. At this
point the deflection increases greatly and the shaft is said to "whirl". Below and above this speed
this effect is very much reduced. This critical (whirling speed) is dependent on
the shaft dimensions, the shaft material and the shaft loads . The critical speed is
the same as the frequency of traverse vibrations.
Where m = the mass of the shaft assumed concentrated at single point . For a horizontal shaft this can be expressed as Where y = the static deflection at the location of the concentrated mass Symbols
Theory Consider a rotating horizontal shaft with a central mass (m) which has a centre of gravity (G)slightly away from the geometric centroid(O) The centrifugal force on the shaft = m ω When the denominator = 0 ,that is [ KEI / m ω For a simply supported beam with a central mass K = 48 .. See examples below Substituting ω This is plotted below.. This curve shows the deflection of the shaft (from the static deflection position) at any speed ω in terms of the critical speed. Cantilever rotating massMass of shaft neglected Central rotating mass- Long BearingsMass of shaft neglected Central rotating mass - Short BearingsMass of shaft neglected Non-Central rotating mass - Short BearingsMass of shaft neglected Cantilevered Shaftm = mass /unit length Shaft Between short bearingsm = mass /unit length Shaft Between long bearingsm = mass /unit length Combined loading This is known as Dunkerley's method an is based on the theory of superposition.... |

- Mitcalc-Shafts ..Notes associated with spreadsheet calculator - very useful on their own
- Critical speeds - Distributed Loads ..Useful Webpage from~EngnieersEdge
- Critical speeds - Wikipedia ..Detailed notes