Formula for 'pinch bolt joint' 1

[cfinister]

Does anyone know the formula or process for relating bolt tension to the nominal internal pressure when clamping a bore to a shaft using a pinch bolt.

I have looked through text books and can't seem to get the relationship to work. There must be a way of relating the bolt tension to hoop tension and therefore stress. From which it is possible to determine the internal pressure.

Any ideas??

 

[CoryPad]

There is no easy formula. One project I was involved in had a complex FEM analysis that computed a triple integral to related pinch bolt preload to force/stress on the shaft. I recommend using a similar approach, or use a different fastening method.

 

[cfinister]

thanks CoryPad, I too have seen this method using FE. Unfortunately we don't have FE capability and I am stuck with the current fastening method.

I have divided the bolt tension by the Cross Secton area of the outer cylinder, this gives me a mean hoop stress If I assume this hoop stress is mid distance through the outer cylinder I can then determine the internal pressure maintaining equilibrium this is at the outer cylinder/shaft.

For simplicity it is reasonable to assume zero deflection of the shaft and that the fit is zero gap prior to bolt (pinch) load. I think this gives me a reasonable estimate.

Does this seem reasonable anyone??

 

[gunsmith]

I have a question unstanding the mechanism. Is there a hole in the shaft where the bolt is forced in and the pressure difference between inner and outer diameter of the shaft is parameter we are looking for?

Andreas

 

[arto]

How about ASME B&PV Code Sec VIII Div 1 Appendix 24 for clamp connections [like Graylocs or TriClover Clamps]? Might be good for a rough check.

 

[cfinister]

Gunsmith

The joint is best described as follows.

A component has a machined bore which fits over a shaft, for argument sake there is no difference between bore and shaft diameter and the shaft is solid. The component(which is cylindrical) has a slot machined through one wall in the axial direction. There are 2 lugs attached either side of the slot. A bolt is tightened through these lugs producing a reduction in bore diameter and hence producing a clamp load between bore and Shaft. The relationship I need to identify is the bolt tension vs clamp load or average contact pressure between shaft and bore.

I don't know what type of joint this is called.

 

[gunsmith]

We talk about a normal clamping device.
Let us say that a torque Mt is the outer force to withstand than we need a frictional-torque Mr which has to be produced by the clamping device (bolt). So the force pressing against the shaft has to be:

Fn > Mt/d/mu

d=diameter of the shaft
mu=friction coefficient between shaft material and component material

the Force in the bolt You need is:

Fb > Mt*l1/l2/d/mu

l1=distance between midpoint of shaft and its maximum outline point
l2=distance between midpoint of the bolt and mamximum outline point of the shaft

surface pressure has to be controlled by:

pm = Fn/d/L < pzul

pm=surface pressure
L=length of bore the shaft fits in
pzul=allowed surface pressure for the worst material in the system

I think that is all You need for the calculation.

Andreas

 

[cfinister]

Thanks Gunsmith

Can I clarify a few points

are l1 and l2 radial dimensions? and when you mention shaft outline dimension do you mean Outside Diameter?

For a given bolt load are you saying Fn=Fb*L2/L1?
In my calculations this always gives a smaller Fn than Fb, I thought pinch bolts work the other way round? You get a higher normal load for a given pinch load.


I think Fn> Mt/(d/2)/mu ?

Do you know of text where I can find this?

Chris

 

[gunsmith]

Hi Chris,

the calculation is out of &quot;Maschinenelemente&quot; from H.Roloff und W.Matek, edition 1976, page 280/281. It is a German book dealing with all kinds of machine parts and their calculation.

Fn can´t be smaller than Fb because l2 is more than 2*l1 in the example drawing here. Send me Your email and I will make a pdf-file of the two pages for You. That´s better than any explanation.

Andreas
mail@waffentechnik.com