Vibration Analysis Of Dry Frictional Brake System Based On The Rigid-flexible Coupled Model

A rigid-flexible coupled dynamic model considering stribeck effect is established to investigate frictional flutter of disc brake system. Galerkin discretization and numerical calculation are applied to reveal the influences of coupling relationships between the vibrations of block and disc(internal resonant conditions) on the dynamic behaviors of the whole system. The influences of some parameters on system dynamic behaviors are also analyzed.Firstly, a dry-frictional and rigid-flexible coupled dynamic model is established. The frictional block is simplified as a three-DOF model. The equation of disc transverse flexible vibration is established based on thin plate theory. Stribeck effect is considered in friction modeling. Three ordinary differential equations jointed with a partial differential equation are finally established to describe the dynamic model. Then Galerkin method is applied in discretizing the partial differential equations into ordinary differential equations.Secondly, Runge-Kutta method is applied in numerical calculations. The results show that with the variation of disc annular speed, the friction block and disc keeps vibrating with small amplitude due to the sustaining variation of the contacting pressure and friction. The vibration amplitudes increase with the decreasing of the disc angular speed. Stick-slip flutter happens as the velocity is lower than a critical speed and strong movement coupling between elements of the system brings earlier occurrence of the frictional flutter. Besides, for strong movement coupling case, before the critical speed, there are intermittent speed ranges among which the amplitude is quite higher, which is due to a redistribution of friction and contacting pressure.Finally, the influences of braking pressure, friction block area and the maximum static friction coefficient on the system dynamic behaviors are analyzed by numerical simulations. The results show that the three factors affect the stabilities of block's tangential movement and disc transverse movement.