Max torque on a couple to cause slip

[CaptainofIron]

So I've been spinning my wheels (I guess I should say slipping, haha) on this problem we've been having

We have a coupling intended to transfer torque:

One side of the coupling is a smaller insert that slides inside of a larger nut. The insert has male threads on one side and the nut has female threads on the other side.

The insert has 2 friction surfaces that will carry the torque, 1 is a flat ring, the other is a conical section inclined at 37 degrees

I need to calculate the maximum torque the joint will carry until the insert will slip inside of the nut.

Here is a sketch of both friction surfaces
Case 1:

Case 2:

So I solved the first one, the flat ring, hoping that it would provide enough frictional resistance so that we could properly torque the male threads on the insert, but its close. Now I am looking at the conical section in case 2 trying to figure that out, but its been a WHILE since I have done this.

for case 1 I got T=(2*μ*(F/(Ro^2-Ri^2))*((Ro^3-Ri^3)/3)


Thanks

 

[Navin A S]

in advance for any help you can provide! For case 2, you'll need to take into account the angle of inclination which will affect the co-efficients of friction. The formula you have provided is for a flat surface; however, you can use this formula to approximate the maximum torque that can be transmitted through the conical section. To do this, you'll need to calculate the normal force acting on the conical section, which can be determined using the formula: F=μ*N, where μ is the coefficient of friction and N is the normal force. Once you have the normal force, you can then calculate the maximum torque that can be transmitted through the conical section using the formula T=(μ*F)*((Ro^3-Ri^3)/3).