Torque capacity of D-shaft (shaft with a milled flat)

[cumfy]

There are numerous references to the basic equation for the torque capacity of a keyed shaft, but I can find absolutely nothing for a simple D-shaped shaft (ie a plain shaft with a single, plain, parallel flat milled on it) with a D-shaped hub. No set screw.

It seems so simple but there's nothing, the nearest reference I could find was on this forum 5 years back https://www.physicsforums.com/showthread.php?t=293700, in which no one could give a solution.

Anyone know of a definitive treatment/reference ?

 

[DScheuf]

I believe there was a solution in the forum 5 years back where a user referenced Roark's Handbook. I've used the following equation from Roark's on a past project for what appears to be similar to your application. At the time, I didn't have access to FEA software to check against.

Tau_max = Torque/(B*r^3) where B = 0.6366+1.7598*h/r - 5.4897*(h/r)^2 +14.062*(h/r)^3 - 14.510*(h/r)^4 + 6.434*(h/r)^5 where h = the radius of the shaft minus the radius of the flat side of shaft (assuming you draw a circle tangent to the flat side line).