Vertical shaft deflection

[Latexman]

I'm out of my area and I need some guidance please.

I have an agitator that bolts to the center nozzle on the top head of a tank. The 316 SS, 114" long, 2.5" diameter shaft is solid and hangs vertically down into the tank. It has a 5 hp motor. The impeller turns at 100 RPM.

The agitator disperses a powder into water until it dissolves. The powder is added from 50 # bags by hand, one at a time. The powder will clump, but not in 50 # chunks.

I'm trying to get a conservative value of the maximum deflection at the bottom of the shaft so I know how much room I have to put in a steam sparger. The only nozzle I have available is at the same level as the bottom impeller.

What value of hydraulic force service factor would be recommended to account for dynamic operation in this service?

What is the modulus of elasticity (E) of 316 SS?

Is the second area of momentum (I) for a vertical, solid shaft with a horizontal force through it's center
I = pi.radius⁴/4?

Is deflection = Dynamic Force.Length³/(3.E.I)

Thanks!


Good luck,
Latexman

 

[MikeHalloran]

S.F. ? don't know
E = about 28 million psi
I = pi * d^4 / 64, so, Yes.
Yes.
I had to drag out my Machinery's Handbook to check. You should get one.

But the deflection of an unbalanced impeller also includes angular deformation of the tank head. I have seen them flex enough to notice from a distance, even on glass lined tanks.

I think you need to ask the tank manufacturer for help.





Mike Halloran
Pembroke Pines, FL, USA

 

[unclesyd]

You might want to checkout the literature at this site.

http://www.lightnin-mixers.com/sites/lightnin/

 

[electricpete]

deflection = Dynamic Force.Length3/(3.E.I)

Since you have the word "dynamic" in there, I'll be picky and point out that the deflection thus calculated is a static deflection from a static force.

With a mass on the bottom of the shaft, and a possible force varying with time, the dynamic stiffness at frequency of force variation would be needed to determine the deflection.

Also, the equation would apply to a cantilevered shaft, which would be only an approximation of the real system supported at two or more bearings and coupled above.

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[electricpete]

static stiffness may be good enough if the frequency of the force is far below first resonance.

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[Latexman]

When I observe the operation, the top head and nozzle are very stable.

The classic equation is Static Force.Length³/(3.E.I), but I included the "fudge factor":

Dynamic Force = hydraulic force service factor x Static Force

The RPM is < 70% of first critical.

Any idea of a conservative hydraulic force service factor for this application? I was thinking of using 4.

Good luck,
Latexman

 

[electricpete]

http://www.pump-zone.com/article_pdf.php?id=22

Here is an article addressing shaft deflection. Formula for force on the first page. Formula for deflection at top of second page (graphic)...I'm not sure what all those terms are.


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