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# coefficient of friction - cylindrical interference - torsional vs axial loading

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## coefficient of friction - cylindrical interference - torsional vs axial loading

(OP)
My question is - Is it well known or commonly assumed that friction in a hub shaft interface is different in various directions?

A co-worker has made an analysis spreadsheet to "calaculate" the interference fit required for a for a 3.5" thick hub installed on a nominal Ø12.5" steel shaft.
His spreadsheet uses a coefficeint of friction of .19 for the axial loading, and .26 for the torsional loading.
When I asked him about the different values, he said "because they are different."

My opinion is coefficient of friction values are assumptions at the very best, but the choice of different values intrigued me.

I looked up one or two machine design text book calculations, and an API Standard, and did not find differences listed.
IN fact API 671 said to use 0.15, although that might be specifically for hydraulically fitted couplings, which presumably are "lubricated" , if only for the first few hours of service.

thanks,

Dan T

### RE: coefficient of friction - cylindrical interference - torsional vs axial loading

Tmoose:
I suspect the/any difference has a lot to do with whether the friction is having to be overcome in the design or process; or whether the friction is being counted on to help you or to help carry a load. Then, you want to be conservative in setting your friction coefficients so your design works with the actual friction, either hurting or helping you. In your example the longitudinal press fit might be fairly clean so it presses on fairly easily. But, that process also scores the faying surfaces and kinda welds the two parts together, galling, scoring, mechanical/geometric interferences, etc., such that the torsional interference (friction?) now has a greater value, greater coef, of friction. I would want to see some testing to confirm these different coef’s. of friction, not just something pulled out of thin air.

### RE: coefficient of friction - cylindrical interference - torsional vs axial loading

I'd be very skeptical, unless he has some test results (which in my experience is a great idea). I don't see how two parallel plates with a normal load and some form of lubricant film between them can tell which direction they are moving in. Which is what is happening in detail at each bit of the contact area. Of course it may be a units thing.

Cheers

Greg Locock

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### RE: coefficient of friction - cylindrical interference - torsional vs axial loading

(OP)
In service the vertical hub load would be on the order of 300,000 lbs.
If it were not for a stout plate bolted to the hub with six 2" bolts that bears on the end of the shaft.
I believe the hub is installed by heating it, with the above mentioned plate in place to set the shaft position. The provisions for pullers appear limited (again by the above mentioned plate), but I would want a powerful angry puller/pusher ready and waiting to seat the shaft at the first sign of "sticking."

The transmitted torque is on the order of 100,000 lb•ft, requiring only about 1/2 the contact pressure of the axial load.
If it were not for two substantial ( but dimensions unknown today) "dutchmen" pins Somewhat wishfully fitted axially in the shaft/hub interface at assembly.

So the ratios of the loading used in my co-worker's analysis show the axial load is far greater than the torsional, in this case.

### RE: coefficient of friction - cylindrical interference - torsional vs axial loading

I don't understand your setup (and I'm pretty sure you can analyse it way better than me anyway). But I did have one thought on your original post question - maybe a diffeence in expected coefficients of friction in these two directions would arise from shaft vibration/bending effects.

"Machine Elements Life and Design" by CRC Press, section 5.2.1.2 describes a modification (reduction) to the static coefficient of friction to account for the presence of an alternating bending moment on the shaft. The formula for the reduction takes into account the values for length, diameter, and surface pressure of the cylindrical interface, the alternating bending moment, and an experimentally determined factor beta.

My intuition says this particular reduction is more relevant to coefficient of friction for relative axial movement than for circumferential relative movement. However, as far as I can tell the formula doesn't distinguish the axial vs circumferential. But then they make an odd statement about this effect as if it follows from the formula: “In contrast to the transmission of axial forces, the torque transmitting capacity never decreases to zero, but it may be as little as 15% or less of the static load capacity”. I don’t understand why they make that statement, because again the formula does not distinguish circumferential vs axial that I can see.

They also make another statement: "In addition, if the bending stress on one side of the connection is larger than on the other side, there arises an axial force aimed to press the shaft out of the hub toward the larger bending stress" This statement makes sense to me, and maybe is the reason my intuition thinks these effects are more relevant in the axial direction, even though this particular sentence is related to generation of a new force rather than change of coeffient of friction. The axial force effect seems distinct from the reduction in coefficient of friction since there is a predicted reduction in coefficient of friction even when bending on both sides is the same and there is no axial force created by the bending moment.

The associated reference is Grechistchev, E.S. and Iliashenko, A.A., Interference Fit Connections, Machinostroenie, Moscow, 1981 (in Russian).

=====================================
(2B)+(2B)' ?

### RE: coefficient of friction - cylindrical interference - torsional vs axial loading

The only difference in the application of the friction factor i know of is due to the asssembly of interference fits.
Press fitting (axial assembly) allows less applicable friction than shrink fitting (called @ hereabouts to be the radial or transversal fit connection).
The mechanics of that are described above.
Maybe there's a point to check those numbers in your colleagues calcs, as per my tables they seem rather high. Max. applicable f.f. for St-St and shrink fit is 0,12.
Concluding from that, maybe the stout plate & the dutchman pins are there for some (historical) reason.

Regards

Roland Heilmann

### RE: coefficient of friction - cylindrical interference - torsional vs axial loading

Hi Tmoose

I often have to do interference fits on rotating shafts with couplings etc, we always use the same coefficient of friction both for the axial assembly and then checking at what torque the interference fit can take safely without slip, if I increased the coeff of friction for the torsional loading I would not be on the right side of caution.

“Do not worry about your problems with mathematics, I assure you mine are far greater.” Albert Einstein

### RE: coefficient of friction - cylindrical interference - torsional vs axial loading

(OP)
Thanks everyone.

It is not my project, and he just asked me to look over and comment on his analysis spreadsheet, so I'm trying to get the best understanding I can.
We are "reverse engineering" a very mature product, but one not without reliability issues,

Dan T.

===========

EPete, overall what do you think of that reference "Machine Elements Life and Design" by CRC Press ?

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