Stress concentration at keyway for impeller with LOOSE FIT

[electricpete]

In thread407-142111 I described an impeller that is a loose fit to the shaft with no setscrew and not taper. As explained by Mike H in that thread, that is a necessary feature for this particular type of pump (gerotor).

We have been having problems with failing keys and keyways in this application. I don't want to get too deep into that except on one aspect:

Doesn't the loose fit mean that the torque will be transmitted between the impeller and shaft within a very small area of the shaft adjacent to the keyway? Won’t there be a significant stress concentration at the keyway because of this.


I know there is are standard stress concentration factor for keyways. For example Mil-hdbk-776 Figure 5 (page 12.) available for free at

http://assist.daps.dla.mil/quicksearch/basic_profile.cfm?ident_number=54093

Those standard stress concentration factors assume that the entire shaft cross section is assumed to participate in transmitting the torque. This would be the case if the torque was applied at points upstream and downstream of the keyway. This would also be pretty close if the torque is applied fairly uniformly around the outside of the shaft with a tight fit. I don't think this comes anywhere close when the torque has to be transmitted through a key and the shaft is a loose fit within the impeller.

My main question: How would one estimate a stress concentratio factor for this situation.

Data is as follows
5/8” diameter shaft
Keyway 3/32” deep by 3/16” wide by ¾” long
1.5 HP
1200RPM

[This is a duplicate of a thread posted several weeks ago in the pump forum – no response there so I’m moving it here]

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[MikeHalloran]

Just how loose are they?




Mike Halloran
Pembroke Pines, FL, USA

 

[MintJulep]

I think that the stress concentration factor would be the same. It is a function of geometry.

However, with a loose fit you are probably subjecting things to impact loading. Almost certainly at start-up, and possibly any time you have a blip in flow or pressure.

 

[MikeHalloran]

You could analyze the key as a short beam. A tight fitting key is of course only loaded in shear. If the key fits tight in both keyseats, but radial clearance exists, then the key is a short cantilever beam, one end fixed, one end guided, I think. In your case, you can assume the key is loaded at lines on four points along its length. And of course the forces are repetitive, though probably not reversed.

With that as your starting point (should be easy in a spreadsheet), then account for eccentricity between the shaft and the housing, i.e., the beam length changes, and all the pieces rub on each other.

And you might wish the check the Hertzian contact stress at the 'corners'.

Sounds like great fun.




Mike Halloran
Pembroke Pines, FL, USA

 

[electricpete]

Mike

How loose was it - I didn't measure them but I could effortlessly put the impeller on/off the shaft several times without a bit of binding.

I'll have to think about your approach.

MJulep - your response that the stress concentration is a function of key geometry only and not of the loading was the same that I got from a Mech Engineer where I work. It is a point I'd like to pursue because I don't agree at all. My reasoning: the total torque must equal the integral of shear-stress times distance from center over all area. If the shaft is loose within the impeller, the shaft material near shaft o.d. 180 opposite the key surely carries much less stress for the loose impeller than the tight impeller? Especially if I move axially to the end of the keyward towards the motor. Think some more and let me know if you still disagree. Also interested in other opinions on this.

I do have some more details in my back pocket that I am holding back (will tell you guys later). I don't want to get too far down the problem-solving path without answer a few basic questions I have first.
Thx

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[rob768]

Check the sides of the keyway (is that the correct english word) for signs of impact. This may be due to impact or torsional vibrations. Furthermore, i don;t know what is driving the pump, but if it is an E-motor, consider a soft start to avoid those impacts during start-ups. A (soft) elastic coupling in such an installation may perform wonders too.

 

[corus]

Your assumption that a keyway provides a general stress concentration in a field of stress is correct. With the loads imposed through the keyway then you'll have localised contact stresses that would have to be considered. The loose fit may add to the impact load but no arrangement could guarantee a perfect fit and you would alwasy expect some factor on your load for impact. To assess contact you'd have to assume a point or line load to be imposed at the outer surface of the keyway. You'd have to use finite elements to get an idea of the stresses at the fillet radii.

corus

 

[MintJulep]

Pete,

I think you've made my point for me. The loads are not uniformly distributed. The stress concentration factor remains a function of geometry. (I didn't say only, but I will say primarily).

Anyway, if I recall, classic key strength/stress calculations consider that the key carries 100% of the load.

 

[panduru]

I agree 100% with MintJulep when he says ...classic key strength/stress calculations consider that the key carries 100% of the load.

 

[electricpete]

Can you lead me to such a classic keyway stess concentration calculation? I have not seen it. If it's out there, that's what I'm looking for.

The stress concentration shown in the MIL-Standard is based on the cross section only, not the loading pattern. Near the front of the document they talk about the "membrane analogy" for shear stress distribution. Take a flexible membrane, attach it (pinned) around the perimeter of the area (for example perimeter of the shaft). Apply a uniform pressure under the membrane and look at the bulge. The SLOPE of that membrane at any point is an indication of the value of the shear stress at that point in the shaft.

Interestingly enough, the highest shear stress than occurs at the center of the bottom of the keyway (not at the corners of the keyway).

It seems apparent from that description that this loading takes the fullest advantage of the full "remaining" (i.e. minus notch) cross section for transmitting torque. That would seem to work fine if the torque load is transmitted uniformly axially along the shaft i.e. if we applied the driving and driven torques at two different points on opposite axial sides of a long keyway. Also seems not too far off if we have a tight fit to help distribute the load around the shaft cross section. Doesn't seem to work at all with loose fit where all load is transmitted thru the key.



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[electricpete]

The discussion of the "membrane analogy" is in the MIL-HDBK-776 document on the page labeled as page 2 (page 9 of 85 of the pdf). See "base document" here:

http://assist.daps.dla.mil/quicksearch/basic_profile.cfm?ident_number=54093

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[diamondjim]

Why not try a second keyway 120 degrees
from the first? Obviously one keyway
is not working.

 

[electricpete]

Diamonjim - we'll give that some thought. Can you explain why you suggest 120 degrees instead of 180 degrees?

Back to the previous discussio - Maybe I am using the term “stress intensification” factor wrong.

The Mil-standard table 12 gives a factor f which is used to calculate
Max Shear Stress Ss = T * f / r^3
If f = 0.64, that represents the behavior of a round shaft (no key) derived as follows:

Shaft carrying torque Tq
shear strain gamma = tau/G
dtheta/dL = (Tq/J) / G
dTheta = (L * Tq) / (J * G)
tau = r * Tq / J
varies linear from 0 at center to max at outer
taumax = R * Tq / J
J = pi * r^4 / 2
Ss = R*Tq / (pi * r^4 / 2) = Tq *2 / [pi * r^3] = Tq * 16 / [pi *d^3]
Ss = Tq * (2/pi) / r^3 = 0.64 / r^3

Looking at the graph you can see if we extrapolate A/B >2.0 to the left towards B/R=0, it will intersect the axis at f=0.64.

This gives us a picture of the definition of f.... Probably stress intensification factor was not the right word for this factor. Also the text up front mentions that stress concentrations at reentrant corners are assumed relieved with generous corners and are neglected. We also have radiused corners on both keyway and key.

In summary:
It is evident that the “f” factor from the Mil-std is not what I’m looking for since it assumes uniform loading rather than load transmitted at the key. Is there another approach that assumes load transmitted at the key.


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[GregLocock]

Can you work out an effective torsional stiffness of the key/slot system?

Then you could begine to work out the actual impact force.

I rather suspect that the stress concentration factor is the least of your worries-isn't the failure more likely to occur at the outer edge of the shaft, by yielding of the shaft (or even shearing of the key), not fatigue at the radius of the bottom of the keyway?

Cheers

Greg Locock

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[desertfox]

Hi electricpete

I would like to ask whether or not the keyway of the impeller and shaft are still for within the recommended tolerance zone particulary if your saying the impellers loose on the shaft?
Don't know whether I am on the right track or not but if your keyways exceed standard tolerances I can imagine the key rocking over within the keyway so ineffect you end up with the key touching the keyway only at two diagonal corners. This I am sure would give rise high stress intensities on the edges of both key and keyay however I
have no idea how you would model this.

regards desertfox

 

[diamondjim]

Electricpete,
I read some studies awhile back that said
that 120 was the ideal for 2 keyway system.

 

[bobc]

Try an old fashioned "Gib head" key that is tapered in relation to the bore keyway. These were and still are used on large bevel gears and sprockets for roll out conveyors in steel mills. The tapered key driven in the keyway imparts a "fit" to the bore to the shaft. I would recommend both the bore keyway and the key be tapered the same. If memory serves it was 1/8" taper per foot. This allows easy assembly in the field and a reliable fit, imparted with only a hammer.
Bob Creely