Sliding bifurcations and chaos induced by dry friction in a braking system

Abstract In this paper, non-smooth bifurcations and chaotic dynamics are investigated for a braking system. A three-degree-of-freedom model is considered to capture the complicated nonlinear characteristics, in particular, non-smooth bifurcations in the braking system. The stick–slip transition is analyzed for the braking system. From the results of numerical simulation, it is observed that there also exist the grazing–sliding bifurcation and stick–slip chaos in the braking system.

[1]  Mariusz M Holicke,et al.  MELNIKOV'S METHOD AND STICK–SLIP CHAOTIC OSCILLATIONS IN VERY WEAKLY FORCED MECHANICAL SYSTEMS , 1999 .

[2]  Jan Awrejcewicz,et al.  How to predict stick-slip chaos in R4 , 2004 .

[3]  Stephen John Hogan,et al.  Local Analysis of C-bifurcations in n-dimensional piecewise smooth dynamical systems , 1999 .

[4]  Karl Henrik Johansson,et al.  Self-oscillations and sliding in Relay Feedback Systems: Symmetry and bifurcations , 2001, Int. J. Bifurc. Chaos.

[5]  C J Budd,et al.  Grazing and border-collision in piecewise-smooth systems: a unified analytical framework. , 2001, Physical review letters.

[6]  Panayiotis Papadopoulos,et al.  On the transient dynamics of a multi-degree-of-freedom friction oscillator: a new mechanism for disc brake noise , 2005 .

[7]  Ugo Galvanetto Some Discontinuous Bifurcations in a Two-Block STICK-SLIP System , 2001 .

[8]  Ugo Galvanetto,et al.  Sliding bifurcations in the dynamics of mechanical systems with dry friction—remarks for engineers and applied scientists , 2004 .

[9]  Ugo Galvanetto,et al.  Events Maps in a Stick-Slip System , 1997 .

[10]  M. I. Feigin,et al.  On the structure of C-bifurcation boundaries of piecewise-continuous systems , 1978 .

[11]  Karl Henrik Johansson,et al.  Self-Oscillations in Relay Feedback Systems ; Symmetry and Bifurcations , 2000 .

[12]  Mario di Bernardo,et al.  C-bifurcations and period-adding in one-dimensional piecewise-smooth maps , 2003 .

[13]  Mario di Bernardo,et al.  On a Novel Class of Bifurcations in Hybrid Dynamical Systems , 2001, HSCC.

[14]  Mario di Bernardo,et al.  On the existence of stable asymmetric limit cycles and chaos in unforced symmetric relay feedback systems , 2001, 2001 European Control Conference (ECC).

[15]  Oliver M. O’Reilly,et al.  Automotive disc brake squeal , 2003 .

[16]  Vadim I. Utkin,et al.  Sliding Modes in Control and Optimization , 1992, Communications and Control Engineering Series.

[17]  David J. Wagg,et al.  Rising phenomena and the multi-sliding bifurcation in a two-degree of freedom impact oscillator , 2004 .

[18]  J. Awrejcewicz,et al.  Stick-slip chaos detection in coupled oscillators with friction , 2005 .

[19]  Arne Nordmark,et al.  Non-periodic motion caused by grazing incidence in an impact oscillator , 1991 .

[20]  Y. Wang,et al.  FRICTION-INDUCED NOISE AND VIBRATION OF DISC BRAKES , 1989 .

[21]  John E. Mottershead,et al.  Dynamic instabilities in a simple model of a car disc brake , 1999 .

[22]  M. di Bernardo,et al.  Bifurcations of dynamical systems with sliding: derivation of normal-form mappings , 2002 .

[23]  Alan R. Champneys,et al.  Unified Framework for the analysis of grazing and border-collisions in piecewise-smooth systems , 2001 .