Dynamic stability of rotating shaft with concentrated load at free end

[SriMat]

Dear friends,

I have this practical problem with maintaining the dynamic stability of a rotating (about vertical axis) hollow cylindrical shaft which has a concentrated load connected (rigid) to its 'free end'. The shaft is screwed on to a motor capable of rotating at various speeds.

Specifications are: Hollow shaft - Length: 80cm
Weight: 70 gms
ID - 0.5cm, OD - 0.8cm

Concentrated load - Length: 5cm
Weight: 70 gms
Cylinder OD: 1.6cm

Rotational speeds : 1rpm - 250 rpm


Whats making matters worse is that this 'free end' is actually immersed in liquids of different viscosities and densities. As you might know, the application I am talking about is for measuring viscosities of liquids.

I don't know how to determine the damping effect offered by the liquid, the downward axial force acting due to the weight of the (shaft+load) itself (and any corrections due to buoyancy effects) and their effects on the torsional load due to rotation in the liquid at various speeds.

The shaft starts making larger and larger circles when rotating at higher speeds (especially with low viscosity liquids), which I believe, is what is introducing a lot of errors into my measurements.

Sorry about the long post. Thanks a lot for reading on. I would be eagerly waiting to hear from you folks soon..

Cheers,
SriMat.

P.S: here is one paper I found - but not quite sufficient to help me -

http://www.sciencedirect.com/scienc...7c42680803f95e113753777bc62&ie=/sdarticle.pdf

 

[electricpete]

First s.w.a.g. would be simple resonance. You didn't give us the material type (E) so can't even attempt a calculation. How about trying to shift the resonant frequency higher by:
stiffening the shaft
or
shortening the shaft
or
decreasing the weight on the end of the shaft?

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[GregLocock]

I think you might have a forced response, in this case there is an instability because of Bernouilli. If the cylinder is slightly eccentric then its most eccentric side will have a reduced pressure on it, so the cylinder will experience a net force making it run even more eccentrically.

This would be easy to check - the amplitude of the orbit would /increase/ with fluid density.

Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[SriMat]

Thanks a lot - electricpete and Greglocock.

electricpete: Material type - The hollow cylinder is made of Alumina (Al2O3) which has an E of 300 GPa and the concentrated load is made of Molybdenum, which has a E of ~325 GPa. These have been considered due to the nature of the application - which is at high temperatures (upto 1600 degrees C), which also dictates the length requirements. I will be attempting a lighter concentrated load trial using aluminium instead of molybdenum, but only at room temperature conditions.

Greglocock: True - I too have observed such behaviour doing trials with low density (1 g/cc) and higher density liquids (3.5 g/cc)..I believe that this eccentric rotation is the reason for errors in my measurements, but have to understand it fully and would like to prove it mathematically.

"Please see FAQ731-376 for tips on how to make the best use of Eng-Tips" - was this intended specifically for my post? If yes, I would like to correct myself I have gone wrong somewhere..Thanks for that.

 

[GregLocock]

No that's just my sig.

Work out the effective stiffness at the tip. Then work out the pressure differential due to the speed difference across the spindle, for the inside and outside points, for a given eccentricity. Then compare the force generated for that eccentricity with the restoring stiffness force.

Hmm, a quick look says that the pressure differential is proportional to the eccentricity. How odd.

Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[SriMat]

Dear Greg,

Thanks a lot for that, Greg.

As a last-ditch experimental effort, I am trying to see the effect of the long shaft by cutting down on the length of the shaft and doing similar measuremnts at room temperature - this to make sure that the length is what is causing all the trouble (as I have always thought). If it is proven experimentally, this correction term I'm working on will need to be used.. I'll keep the forum posted about any progress..

Thank you very much.
Cheers,
SriMat.