How to find required clamping force of bolts to prevent flange faces from twising due to torque?

Question

I have a gearbox adapter that bolts onto a flange and I need to work out how much clamping force is needed to prevent the faces from slipping and keep the bolts in tension rather than shear when torque is applied. However I can't use the straightforward friction equation here $(F_f =\mu \cdot F_n)$ because I don't know how to work out how the force from the applied torque is distributed.

For context, the torque being applied to the flange is $9123N \cdot m$ and the flange has an inside diameter of $185 mm$ and and outside diameter of $275 mm$. There are $12$ x $16 mm$ bolt holes at a diameter of $196 mm$. The two faces bolted together are made of $1020$ mild steel.

I figured that while friction doesn't have anything to do with surface area, in this case it would be better to have the flange face diameters as wide as possible because it would require less frictional force to resist the torque at a wider radius. However this has just confused me as I don't know what/where the forces are acting on the faces.

How can I find to force from torque that is distributed over a surface such as this?

Answer 1

The simplest way by far is to select a prospective bolt, calculate the clamping force this creates when it is torqued to rated torque, and use the bolt circle as an approximation of the moment arm. Compare this against the rated torque spec and duty type for the gearbox. Grade 5 bolts are ordinarily adequate for industrial uses. Some fussier machines or harsh environments may need grade 8. Most fussy ones would have the receiving flange tapped for a particular bolt.

The real problem here is for shock load tolerance, torque pulses from diesels, vibration tolerance, brake and clutch engagement torques, etc.

Since many of these issues are balled into load factor coefficients, and can be as high as 300% or 400% in severe cases, getting the effective flange pressure radius right to within 5% isn't very important to the big picture. Repeatability with new and to-spec hardware using a calibrated torque wrench is only 10%. Five years from now, some mechanic is going to replace a bolt with one pulled from a coffee can and tighten it with pliers. That's what you need to design for in most cases, and is why typical flanges are more than adequate.