Wedge Problem

When I started looking into this problem I thought it would be rather easy. As I got into it further I found it getting more difficult. I will explain the image first. These components are circular, but I have unwrapped them for simplification. The block on the top is a complete ring. Force F1 is a force due to torque. The lower section can be considered ground. The wedge has a small preload that is applied toward the top portion(the ring). What I am trying to solve for is the angle of the wedge. When a force(due to torque) is applied to the top portion(the ring), what angle will keep any component from sliding when F1 is applied?

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Do you mean for F1 to be normal to the view, as in a pulley or gear clamp?

F1 is just the force due to torque. It is tangent to the ring, or normal to the view.

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OK. So, there is no simple answer. For a given combination of wedge angle, preload, and materials, there will be a maximum torque. Vary any one and the answer varies. Are you familiar with the products like Ringfeder keyless shaft locks?

No I have not heard of Ringfeder?
Do you know of anywhere I can find help with this.

After I had a look at the Ringfeder, I have found it to be different. The Ringfeder wedge is axial, my problem has a radial wedge. As far as materials having an effect on maximum torque, I have came to the conclusion that material doesn't matter. If I apply the same torque to two different material and expand an extremely hard material 0.1mm radially and a not so hard material 0.25mm, would they not both contain the same amount of energy when expanded.

OK, I misunderstood your problem since I thought you were using axial wedging. Your wedges are radial, something like a Bendix? Are you specifying anything about the coefficients of friction?