Bifurcation and stability analyses for a pad-on-disc frictional system

摘要

Friction-induced vibration of a pad-on-disc frictional system is analyzed in this paper. Equations of motion are established considering the moving load simulation and using the Stribeck-type friction model. The partial differential equation of the disc vibration is reduced to the 1st-order mode by the Galerkin method, then the obtained frictional coupled ODE equations are solved by the Runge–Kutta method. The system stability is investigated by the complex eigenvalue analysis, which shows that the relative-equilibrium of the braking pad loses its stability through super-critical Hopf bifurcation in tangential direction, no matter where the contact position is. Simulations show that the pure-slip limit cycle is resulted at the initial stage of the friction-induced instability. When the rotating speed decreases to a turning point, the pure-slip vibration turns to be stick–slip one as the amplitude increases to a certain level. Then the amplitude of stick–slip type limit cycle vibration decreases with the further decreasing speed. The Hopf point and turning point are influenced by the contacting stiffness. Three types of limit-cycle vibrations are analyzed both in time- and frequency-domains, which shows the critical speeds (Hopf points) under 1:2 and 1:4 internal resonances are much higher than that under non-internal resonance The higher the critical speed is, the earlier the instability occurs. That is to say the strong dynamical coupling between the moving elements of a structure brings earlier occurrence of the frictional instability during braking procedure. As a counterpart of the pad, the disc vibrates also with large amplitude transversely. Influences of the braking initial displacement and the normal pressure between the pad and disc on the instability are also discussed.