Disc brake squeal is a manifestation of friction(induced, self(excited instability in disc brake systems. This paper investigates the non( smooth bifurcations and chaotic dynamics associated with braking systems. In most situations, decreasing squealing is a means to sup( press chaotic disturbances, which would otherwise compromise the comfort of passengers. The proposed method begins with an estima( tion of the largest Lyapunov exponent using synchronization to differentiate between periodic and chaotic motions. We then observe complex nonlinear behaviors associated with a range of parameters and plot them in a bifurcation diagram. Rich dynamics of disc brake systems are examined using the bifurcation diagram, phase portraits, Poincaré maps, frequency spectra, and Lyapunov exponents. Finally, state feedback control is used to overcome chaotic behaviors and prevent squealing from occurring during braking. Finally, the effective( ness of the proposed control method is examined through numerical simulations.
' ": Disc brake; Chaotic; Squealing; Synchronization; Lyapunov exponent; State feedback Nonlinear mechanical systems can be described as smooth dynamic systems; however, numerous practical engineering systems do not comply with this description. Dry friction, clearance, and impact factors can produce sudden changes in vector fields. Mechanical systems that exhibit impacts, which are referred to as impact oscillators, are strongly nonlinear or piecewise linear because of sudden changes in velocities of vibrating bodies at the instant of impact. Impact oscillators arise when the components of a vibrating system collide with rigid obstacles or with each other. Such systems with impacts exist in a wide variety of engineering applications, particularly in mechanisms and machines with clearances or gaps. As the physical process during impact is strongly nonlinear and dis( continuous, the impact system can exhibit rich and compli( cated dynamic behaviors [1]. Owing to their considerable advantages, gear mechanisms have extensive applications in modern power transmission systems. In the presence of gear backlash, which is either introduced intentionally at the design stages or caused by manufacturing errors and wear, the equa( tion of motion of such systems becomes strongly nonlinear. Hence, instability, vibration, and noise are the essential prob( lems of the gear transmission system. In general, the nonlinear dynamic behaviors of gear transmission are conditioned by the time(varying stiffness, static transmission error, backlash, and sliding friction. Considerable research effort has been devoted to the study of the nonlinear dynamics of gear transmission systems with backlash [2]. Such systems are referred to as non(smooth dynamic systems. Dry friction is a typical non( smooth factor, which plays an important role in numerous engineering applications. Dry friction is a source of self( sustained undulations referred to as stick(slip oscillations, which can have undesirable effects, such as squeaking noise produced by...
