Research On Dry-frictional Dynamics Of Disc Brake System

The brake system is the main device that slows down the vehicle to stop,which plays an important role in keeping the vehicle stable and reliable.The disc brake unit is the most widely used in the brake system,including the rotating brake disc and the symmetrical friction pads bound by the clamp.The working principle is to provide the normal pressure and friction force between pads and disc.Disc brake system is a typical dry friction system,and the irrationality in the design can lead to problems such as instability and noise.Therefore,it enhances great engineering value and practical significance to study the dynamic characteristics of disc brake system and propose methods for optimizing system parameters.This paper proposes theoretical analysis,analytical and numerical simulation and experimental exploration to study the dynamic characteristics of the disc brake system,and the main content are shown below.1.Equations of motion of the disc-pad and annular beam-pad coupling brake system considering the Stribeck-type friction force are established.A simulation procedure is adopted using the finite difference method,Galerkin method and averaging method to deal with the moving interactions.Accordingly,numerical procedure consists of the order reduction method and the augment by non-smooth basis function with linear spring.Then the PDE of lateral vibration the disc is reduced to a group of ODEs.2.Focusing on the transverse vibration at the outer edge area of disc,an annular beam with flexible and continuous boundary conditions is adopted.Simulation procedure is proposed to deal with the moving interactions and calculation is carried out by using the finite difference method,which shows that only the first-order mode vibration of the beam can be induced.Results show that as the rotating speed is decreased below the critical speeds,the relative equilibrium of the pad on the disc loses its stability and stick-slip type limit cycle vibrations.The period of stick-slip vibration with large amplitude will be shortened with higher moving deceleration.The prominent part and discontinuity appear in the mode shape and the shear force distribution,respectively,at the acting position of moving force.3.The PDE of the disc vibration is reduced to the 1st-order mode by the Galerkin method,then the obtained frictional coupled ODEs 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,and then the amplitude of stick-slip type limit cycle vibration decreases with the further decreasing speed.Dynamical responses of these typical flutters are discussed by the time-domain and frequency-domain analyses.4.Influences of the system parameters containing the normal pressure and contact stiffness are analyzed.Results show that the critical speeds(Hopf points)under 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.Larger contact stiffness and normal pressure inspire earlier occurrence of the frictional instability and larger limit cycle amplitude and turning points are influenced by the contact stiffnesses.5.Considering the stochastic variation of frictional coefficient and normal pressure,probability distribution can be depicted.Results show that the area of the stable state is affected by the rotating speed and the variance of the input values,meanwhile the higher initial displacement of preload or friction coefficient can bring occurrence of more probably instability in uncertain state.6.Partial results are verified by the experiment and finite element analysis.Disc’s modes with different pitch circles and pitch diameters are proposed.The orthogonal bending modes and torsional modes are proposed.Frequencies of the pad-on-disc coupled system are tested and reponses are attained by dynamic experiments.