Force resulting from misalignment of a coaxial rotating system

I have a rotating ring that is coaxial to a rotating disk and each one rotates at a different velocity to create sliding between them. They have flat sliding surfaces and there is a load pushing them together creating a distribution of friction forces between them. The velocities and the load remain constant. If one axis is displaced a small amount, will this create a force that tries to separate the rotating system?

I’m performing a test a Southwest Research Institute to verify a theoretical friction force equation that is required to obtain equilibrium when two sliding bodies are observed from a third moving body.