On the radial dynamics of friction disks

An analytical and numerical study of the radial dynamics of friction disks is presented. Of particular interest are two types of motion which are characteristic for the considered systems: self-centering of the friction disk at the low rotation speeds and the instability of this equilibrium at high speeds. It is shown that the last one leads to a limit cycle with large radial displacements and intensive slip between the disks. The amplitude of the limit cycle is limited by damping in the simplest case of linear springs. In reality the amplitude can be limited by different kinds of nonlinearity both in radial or in normal directions. These two types of motion exist alongside with pure sticking already in the simplest pin-on-disk apparatus which is a standard experimental setup for investigations of the friction coefficient. The strong coupling between the torsion and radial modes appears as an additional effect in a system of two rotating disks with the frictionally transmitted torque. It is shown that this coupling can destabilize the limit cycle and create a new one with slowly modulated amplitude. All analytical results are compared with numerical simulations.