Shaft Clamp Torque Capacity 1

[LL631]

Is this derivation correct for the torque capacity of a 2-piece shaft collar clamp?

The axial force formula is from Shigleys for a 1-piece clamp, but the derivation is not given.

 

[Tmoose]

"These results should be used as a guide only "

https://www.staffordmfg.com/torsional-holding-power.html

How did you do ?

 

[LL631]

Was out by a factor of 2 but I understand my mistake now, 2 screws does not create twice the clamping pressure. In practice the 2-screw split design can give more clamping pressure but only due to the fact that less force is going into bending the clamp.

 

[electricpete]

Good derivation (good simplifications for thin wall).
I'm going to save that one.

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(2B)+(2B)' ?

 

[dvd]

It is hard to differentiate between the radius of the shaft and radius of the collar. It seems to me that differences due to i.d. and o.d. tolerances will be important in this derivation.

 

[LL631]

Yes, in reality this will play a role but for simplification it is assumed they are the same, the equation already uses friction in 2 places so is probably only good for ballpark work anyway.

In reality the clamp ID is typically 0.005" larger than the shaft OD to ensure a fit. The clamp is split so there is a (1mm) gap between the two halves, as the screws are tightened the clamp is "pulled in" around the shaft, the gap stops the two halves bottoming out.

The assumption is that all the screw tension translates into uniform tension around the clamp / uniform pressure onto the shaft. For a true thin-wall condition D/t > 20 (a hose clamp) you can see this assumption is pretty accurate. But in reality the clamp is thick-walled so some of the screw tension is being used to pull the clamp in around the shaft, this will result in a pressure distribution around the shaft relative to the angle (maximum parallel to the screws and minimum perpendicular to them) but is also going to be relative to the stiffness of the clamp and geometry, probably one for FEA if better accuracy was needed.

 

[electricpete]

In reality the clamp ID is typically 0.005" larger than the shaft OD to ensure a fit. The clamp is split so there is a (1mm) gap between the two halves, as the screws are tightened the clamp is "pulled in" around the shaft, the gap stops the two halves bottoming out.

...But in reality the clamp is thick-walled, so...

We can still make an easy bounding-low estimate of torque capability for thick wall scenario.

On that third figure on the right, assume all the force transmitted from clamp to shaft is distributed over a narrow band of unknown widith DX at 12:00 position, instead of uniformly distributed as in the thin shell.

The total force on in that narrow band is approximately the screw tension. All of the force at that location acts in the normal direction creating friction, it doesn't care over what area it is distributed.

Ffriction = 2 * mu * [Fscrew] = 2*mu*[Tt/(k*d)]
(the factor of 2 accounts for the fact that we have reaction force to screw tension both at top and at bottom)

T = Friction * r = 2*mu*r*[Tt/(k*d)]

It is a factor of Pi lower than the thin wall result. So without doing the thick wall math, at least we can still give an estimate to within a factor of ~ 3.


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(2B)+(2B)' ?

 

[electricpete]

I was a factor of 2 off. The normal force at 12:00 position should be twice the screw tension (assuming gaps were maintained at both 3:00 and 9:00), and that same force is applied both at 12:00 and at 6:00. So my factor of 2 above should become a factor of 4.

Ffriction = 4 * mu * [Fscrew] = 4*mu*[Tt/(k*d)]

T = Friction * r = 4*mu*r*[Tt/(k*d)

So it is only a factor of Pi/2 (~1.6) difference between the thin wall and conservative thick wall solution. The real solution lies somewhere between the two solutions (within the assumptions of the model).






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(2B)+(2B)' ?