# Stress Calculation on "D" Drive Shaft

by minger
Tags: calculation, drive, shaft, stress
 Sci Advisor P: 1,498 Hey guys, I have a problem. I need to calculate the stress on on a shaft thats driving a fan. The shaft setup is pretty simple. It's a basic circular shaft, then one side is milled to a flat, slightly resembling the letter D. So, of course I have the dimensions, and the input torque. How can I calculate a stress out of it? I have tried running a numerical analysis, but ANSYS does not like it for some reason. Anyways, I was asked to do a hand calculation and with a background in CFD, I'm kind of at a loss. Any tips? Thanks a lot,
 P: 619 You can make a conservative estimate for the shear stress using the diameter of the largest circle that will fit within the cross section (the actual diameter reduced by the amount taken off by the flat). This is fairly commonly done.
 Sci Advisor P: 1,498 I'm not concerned that the shaft cannot handle the torque. I mean, that's a simple enough $$\tau_{max} = \frac{Tr}{J}$$ What I'm concerned about is failure at the contact area because the flat is rather small. Basically, the total forces required to turn the shaft are being applied on half of the "flat" increasing in a linear manner towards the OD. Likewise, I'm concered about plastic deformation of the hub that the shaft fits into.
P: 619

## Stress Calculation on "D" Drive Shaft

You said, "...the total forces required to turn the shaft are being applied on half of the "flat" increasing in a linear manner towards the OD...." Usually where there is a shaft flat, there is a set screw applied against this flat. Is this not true in your case?

If there is a set screw, then I don't see how you can say that the force required to turn the shaft increases linearly towards the OD. Isn't the set screw a fairly concentrated load over just a small part of the flat?

Are you not also neglecting the friction torque transfer on the opposite side of the shaft when the shaft is pushed hard to the opposite side of the bore? I imagine that this is where a good bit of the torque transfer occurs, although I think it will be very difficult to quantify.

I have done quite a bit of machinery work, but I have never been asked to be concerned about this issue. Unless the part is exceptionally thin or there is some other unusual circumstance, I don't see how this could be an issue. I suppose you might do a Hertz contact stress calculation for it if you have to though.
 Sci Advisor P: 5,095 Roark's....Table 20, item 7. Also, if you can get a hold of a copy, I have been told about Isakower's book "The Shaft Book" which I found is also a reference used by Roark's. EDIT: Minger, if you want, shoot me a PM and I can help you with the reference above.
P: 1,498
 Quote by Dr.D You said, "...the total forces required to turn the shaft are being applied on half of the "flat" increasing in a linear manner towards the OD...." Usually where there is a shaft flat, there is a set screw applied against this flat. Is this not true in your case?
No, there is no set screw. The idea is that if there is a set screw then it will take the entire torque. It should be linear because of the definition of torque.

 Are you not also neglecting the friction torque transfer on the opposite side of the shaft when the shaft is pushed hard to the opposite side of the bore? I imagine that this is where a good bit of the torque transfer occurs, although I think it will be very difficult to quantify.
It's metal to metal but yes there will be some transfer due to the friction, especially being that it is a slight interference fit. However, conservatively, I would like to neglect that and assume that all the forces are transferred through the "flat".

 I have done quite a bit of machinery work, but I have never been asked to be concerned about this issue. Unless the part is exceptionally thin or there is some other unusual circumstance, I don't see how this could be an issue. I suppose you might do a Hertz contact stress calculation for it if you have to though.
We not too concerned either, but our customer has had problems with this type of shaft coupling before and they asked us to do a better analysis of it. Idealized there shouldn't be any problem. Realistically, due to the geometry of the part, it arises concerns in the corner where the shaft contacts the hub.
 P: 619 minger, since you say that there is no set screw, are you then saying that there is a D-shaped hole in the mating part? And with an interference fit? If that is the case, it would seem to me that the stress distribution around the shaft is going to be quite complicated, but that the corner of the D is going to be a hot spot, a potential crack starter because it is a stress raiser. When you say that the stress distribution should be linear across half the face of the D, you are imposing an assumed displacement field on the system, are you not? This may, or may not, be what really exists. It is one way to approach the analysis, but I don't think it can be supported as being reality. (That would assume that the other side unloads linearly until contact breaks, the interference having been overcome. There is torque associated with that side also.)
 Sci Advisor P: 1,498 Yes, both shaft and "hub" are "D" shaped. The interference is only on the curved surface, the "flat" has a loose fit. I am applying a torque to the shaft and fixing the hub. However, assuming zero friction, the "leading" edge of the shaft is moving away from the hub at any given instance. The point in the middle of the flat (at x=0), is always moving tangentially to the hub, so again, no normal forces. From there, there will be a component of the shaft moving "into" the hub. I think that I have a process which can give me some decent results. The first procedure is to assume both parts are beams. I pin the beam at what is essentially the middle of the "flat". I then draw an equivalent linearly distributed loading and solve for the loading required to counter the applied moment at the pin (the torque). From there, I just assume the system is a series of beams and solve for bending stress. That gave me decent numbers which I can believe. The next attempt is going to try and get some Hertzian stresses. I'm going to use the data that I have and try to get a "contact" area between the two parts. Then I will assume both parts are cylinders with radii that of the fillets. From there the only tricky part will determining the forces.
P: 1,498
 Quote by FredGarvin Roark's....Table 20, item 7. Also, if you can get a hold of a copy, I have been told about Isakower's book "The Shaft Book" which I found is also a reference used by Roark's. EDIT: Minger, if you want, shoot me a PM and I can help you with the reference above.

I 'just' seen your post Fred. My version of Roark (7th edition) only goes up to 17 tables, then a couple in the appendices. However, if you're referring to the torsional tables for Keyed shafts, then I don't think it will work as this shaft isn't really keyed per say.

I have found an old handbook here, the MIL-HDBK-776(AR) which is Elastic Torsional Analysis of Shafts. I'm looking through it now, if I can't find that other reference, I'll shoot you a PM.

Thanks a lot,

edit: OK, that is a really good reference by the way. However, its for the torsional stresses (as the title says). Again, what I'm really concerned about is the contact stresses developed between the two parts.
 Sci Advisor P: 5,095 The MIL handbook you mentioned is the same thing. You're all set. I have two copies of Roark's. Whatever the edition, the table item #7 should be for a milled shaft. It's another version though of the max shear stress. Since you're looking for contact stresses, it won't help.
 Sci Advisor P: 1,498 The MIL handbook, like Roark is for torsional stresses only. Basically, it's a really modified Tr/J. Anyways, I think we have a solution that we might go with, a slightly different design. Thanks for the help guys, I might be set.

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