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RE: Radius of Gyration

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Liaquat Ally Akhand wrote:



The physical interpretation :


If a rotating fan is pushed to right, the fan will rotate downward as well as righ.


The downward movement is about an axis having a radius. The radius is

known as Radius of Gyration.

<end quote>



I assume fan has horizontal axis and rotating clockwise. An important point to note is reference to “an axis”: not necessarily the centre of the fan drive shaft.


Ideally, can locate the mass of the fan blade and the mass of the drive shaft, at a distance equal to their radius of gyration from their centres of mass. Hopefully their centres of rotation match.


Since fan unlikely to be perfectly symmetrical from material of uniform density, unlikely in practice to have centre of mass where assume it is. The assumed symmetry and uniformity discarded and each fan blade treated separately. The whole system dynamically balanced, by adding mass or drilling holes, to remove excessive wobble and chatter of the system. Or so as I recollect the theory.


As for strength of materials the mass moment of inertia is replaced by second moment of area: in essence the mass is located in a flat plate of uniform thickness and density.


Moments of area have other uses, such as finding mean value from statistical distributions. And another balancing act is the lever rule for liquidus curves, like the iron-carbon equilibrium diagram.


To conclude: locate centre of mass, and determine radius of gyration. If mass concentrated at distance of radius of gyration from centre of mass and rotates about axis through centre of mass, then have stability. If rotates about any other axis have instability.


As for the mathematics Christopher Wright covered that.



Conrad Harrison

B.Tech (mfg & mech), MIIE, gradTIEAust



South Australia