Research On Nonlinear Dynamic Of Vibro-Impact System With Dry Friction

The mechanical components with friction and clearances exist in almost all-mechanical system. The non-smooth factor with friction and clearances belongs to the category of nonlinear dynamics. Owing to the existence of the factor, the dynamic behavior of the vibration system becomes complex. It even changes the topology structure of the mechanical dynamic system and reduces the precision of the system. Induced vibration and braking noise are becoming the hot problem of the nonlinear dynamics in the current times. Theoretical analysis and numerical simulation methods are used to investigate the nonlinear dynamics behavior of vibro-impact system affected by dry friction. The main contents of this dissertation are as following:1. Some recent achievements, developments and unsolved problems of vibro-impact systems are surveyed. The model of friction is considered in engineering, In order to capture accurately dividing points, the theoretical method about the points which separates slip phases form stick phases is expounded, the dynamic responses of a two-degree-freedom vibration system with dry friction and the routs from periodic motion to chaos are analyzed by numerical simulation. Lyapunov exponent is used to investigate the stability of the dry friction system.2. Based on investigation and simulation of nonlinear dynamic behavior of vibrate system affected by dry friction, the one-degree-freedom vibro-impact dynamic system with dry friction and clearance is considered. Slip, stick, and impact of system motions are analyzed and their engaging conditions are put forward respectively. Based on the explicit solutions corresponding to different phases, the complicated nonlinear dynamic behaviors are investigated by numerical simulations. Periodic motion, quasi-periodic motion, bifurcation, chaos behavior and stick-slip-vibration induced by dry friction are investigated by numerical simulations. The routes from fixed points of Poincare map to chaos are reported.3. The dynamical model of the two-degree-of-freedom dry friction oscillators with symmetric clearance is established. Theoretical and numerical simulation methods are used to resolve the response of the system; the results indicate that there exists pitchfork bifurcation, by which symmetrical periodic motion is transformed to a pair of anti-symmetrical periodic motions, further leading to chaos via Hopf bifurcation or period-doubling bifurcation. As the parameters change largely, there exist rich symmetrical periodic motion, anti-symmetrical periodic motion, stick-slip-impact motion, quasi-periodic motion, chaos and co-existing attractors determined by initial conditions. The influences of the global bifurcation behaviors affected by dry friction are discussed. 4. Base on the theory of tribology, dynamics theory, theory of stick-slip and negative slope characteristic of friction force-velocity curve, it establishes a dynamics model of the brake system, the affect braking force and braking velocity to braking noise are investigated by numerical simulation. It will contribute to the controlling of braking noise. At the end of this dissertation, the main investigation results are summarized.