Shaft Flexure Calculation

[djm883]

Is there a way to determine shaft flexure?

The application of the shaft is for a centrifugal fan that is supported by 2 spherical roller bearings. The fan is belt driven from an 8 groove sheave that is mounted to the shaft extending from one of the bearings.

We calculated the deflections at the sheave load and impeller load and the slope of the shaft at the 2 bearings.

The shaft slope was calculated to be .106 degrees for the bearing between the sheave load and impeller and thought to be negligible. Is this calculation determining shaft flexure? Is there a limit at which the slope becomes excessive?

Any help will be appreciated.

Thanks,
Don

 

[dvd]

If your belts won't stay on; if you have exceeded the bearing allowable angular deflection; if the impeller runs into the inlet cone you may have excess angular deflection.

I guess the more important question is: are you in the fan business? If not, you really ought to contact the fan manufacturer if you are having problems, or modifying their equipment.

 

[desertfox]

Hi djm883

You have calculated the slope of the beam, the maximum deflection of the beam occurs where the slope goes to zero
between the supports.
Have a look at this site:-

http://www.roymech.co.uk/Useful_Tables/Beams/Beam_theory.html

regards

desertfox

 

[djm883]

Thanks for the replies.

My company does not work on fans. Since we have a contract with a client that is in charge of the fan maintenance, they have asked us to look at a fan having problems.

We inspected the fan while it was running then we removed the bearing caps to inspect the internal rollers and components.

The fan was hitting the inlet cone slightly during operation, but when we were manually turning the impeller it did not contact the inlet cone. We also noted an abnormal noise in the fixed bearing (the bearing in between the sheave and impeller).

Long story short, when we removed the fixed bearing, the bearing was not firmly mounted to the shaft. We measured the shaft to be slightly undersized by .004". The Contractor keeps mentioning that the cause for the bearing to loosen was the shaft flexure, but we want to eliminate this option and think it is the undersized shaft preventing the lock nut from securing the bearing properly. The result of the bearing moving while operating caused a gouge in the shaft from the lock washer.

As for contacting the fan designer, the fans were designed 25 years ago and from getting little response from contacting them in the past, I don't think they will be much help.

For the shaft deflection, we calculated the shaft deflection at the centerline of the impeller and the sheave load to make sure they weren't excessive (largest deflection was .057").

Sorry for the long response.

 

[desertfox]

Hi djm883

Was the shaft recently replaced?
Was the calculated deflection based on the shaft being 0.004" under size.
I thought you were the contractor to your client, this contractor then is a third party who recently machined the shaft on your behalf?
We need more info if you require further help like dimensions of shaft, speed rotation, materials etc.

regards

desertfox

 

[desertfox]

Hi Again

Another thought what is the clearence the normal clearence
between fan and inlet cone?
If thats less than 0.057" then the shaft is deflecting to much assuming that where the fan hits the inlet duct is were
maximum deflection of the shaft occurs.

regards

desertfox

 

[djm883]

The shaft was not recently replaced, but an analysis of the shaft shows it is coming close to reaching the theoretical fatigue life.

We are preparing a new design of the shaft to eliminate the stress concentration causing the shaft to have a finite life (which happens to be at the fixed bearing location). Increasing the shaft strength and eliminating this detail will give the shaft a theoretical fatigue life, but we want to make sure the shaft isn't flexing (meaning we aren't planning on increasing the shaft diameter). The Contractor will be remachining the shaft and installing it in place.

The shaft diameter at the bearings is 5.4375". At the impeller, the shaft diameter is 9.778". The plans have a gap of .250" between the impeller and inlet cone. The shaft material is AISI 1045. The deflection calculation was based on shaft sizes in tolerance.

 

[desertfox]

Hi djm883

How are you increasing shaft strength?
Why don't you calculate the deflection with the under size shaft and compare the difference although it probably won't be significant.
Fatigue is dependant on the cyclic stress the shaft see's
so how are you reducing this stress?

regards

desertfox

 

[djm883]

The new material we are planning on using is 4340 with a yield strength of 69 ksi. The current plans specify the minimum yield for the shaft material is 30 ksi.

Also, the bearing was mounted using a withdraw sleeve so there were threads and a keyway cut at the same location causing a high stress concentration. We will be using an adapter sleeve for mounting the bearing which will eliminate the threads and keyway.

Thanks for the help.

 

[electricpete]

Shigley's Standard Handbook of Machine Design 2nd ed states

"The tight constraint in shaft design is usually a distortion at a particular
location. For example, shaft slope at a bearing centerline should typically be less
than 0.001 rad for cylindrical and tapered roller bearings, 0.004 rad for deep-groove
ball bearings, and 0.0087 rad for spherical ball bearings (typically)."

Your 0.1 degrees is down around 0.0018 rad, could be a problem for cylindrical roller bearings but should not be a problem for spherical roller bearings based on these "typical" numbers. (I assume a bearing manufacturer could give you a better number)

One wonders whether dynamic effects may play a role. Probably not if machine is operating far below first resonance, but could be important if operating near a flexible rotor resonance. As you probably know, a coastdown test while monitoring vibration magnitude/phase can be useful to help identify where the machine is operating in relation to resonances.


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[djm883]

Thanks for that quote. I have been searching for something like that.

The bearing is a spherical roller bearing. The fan runs at 114 rpm with a critical speed at 631 rpm. We measured vibration measurement during operation and all of them were in the normal range except for the transverse which was in the satisfactory range.

 

[Tmoose]

What stress concentration factor are you using for a threaded, keyed shaft? Does magnaflux or dye penettrant inspection show any crack indications?

Bearings loosening on shafts is often an installation problem. But the variable direction (relative to the shaft) loading inherent with belt drives (power plus installed belt tension) requires moderate shaft>bearing-ID interference or tapered adapters that create the equivalent to an interference.

Minimizing shaft overhang by keeping the drive sheave close to the bearing does wonders sometimes.

The inner race of taper bore bearings WILL be installed slightly skewed on the shaft, creating a dynamically misaligned running condition, generating some extra heat and some high frequency vibration. How much depends on how skewed the bearing is. Referencing the side of the inner race while drawing the bearing up the taper may help reduce the problem.

 

[dvd]

First off, has your original question been answered? Are you still interested in conversation on this problem?

25 year old fan may have weld failures. If you suspect that the shaft undersize problem may not be the whole story a thorough inspection may be warranted to determine if welds have fatigued with frame and/or housing moving under load. Is this a unitary base fan with the motor mounted to the fan base? Also from your description I assume this is a double-width/double-inlet fan with the impeller supported by bearings on both sides, not a cantilevered impeller. Does the impeller rub coincide with the transverse direction from your vibration analysis? Has the foundation been disturbed? Is this a hot-air fan, have ductwork changes been made which cause thermal expansion to impose a load on the inlet box or inlet ductwork?