Rigid coupling design - friction of bolted shaft flanges

[TyVan07]

thread404-305627

So the thread above is closed and last edited 2 years ago but didn't seem to draw any conclusions. I have looked for the answer to this question before to no avail, until now! Hopefully I save someone hours of prowling the internet for this...

Shigley's Mechanical Engineering Design, 8th Ed. p.827 Eqn. 16-28 gives torque transmitted with Force, Diameter and friction coefficient as variables.

T = (F*f/3)*(D^3-d^3)/(D^2-d^2)

F = Force applied
f = Friction coefficient
D = Outer diameter
d = Inner diameter

The derivation from Eqn. 16-27 is T = 2*pi*f*p*int(r^2,r,d/2,D/2) where p is pressure. (Don't know how/if you can use math symbols on eng-tips). int = integration

Hope this helps,

Tyler

 

[electricpete]

Thanks for posting.

The derivation makes sense:
T(r) = Ftan*r = f*(Fnormal)*r = f*(p*[A])*r = f* p*[2*pi*r*dr] * r = f* * p*2*pi*r^2 dr

It strikes me that is among the most straightforward of the requirements for someone seeking to establish a torque rating without using some OEM guidance.

Some more challenging aspects could include:

1 – How to determine that normal force (p = Fnormal * area). We may know something like bolt torque. To convert that we have to account for things like thread friction, embedment, relaxation. Ok, thread factor.

2 – we probably already know the steady state torque the coupling is expected to transmit but design should be based on the peak transient torque. Would not be easy to determine.

3 – static coefficient of friction. And by the way does it change if there is misalignment or vibration?

4 – safety factor


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(2B)+(2B)' ?

 

[MikeHalloran]

Producing a repeatable (f) is a bitch.
In 1967, Ford introduced double cardan u-joints for the Thunderbird, which at the time was a fairly large car.
Part of my job was setting up the machining operations on the pinion flange, which had a plain flat face and four bolt holes, instead of the usual pair of half-bores to accept u-joint cups.
The drawing carried a _minimum_ surface roughness of 55 micro-inches for the flat face.
Our machines were too good; we had to intentionally break the cutting insert corners every time they were replaced in order to get a finish that was acceptably rough.
I hope they developed a more repeatable process for that after I left.



Mike Halloran
Pembroke Pines, FL, USA