Nonlinear response and nonsmooth bifurcations of an unbalanced machine-tool spindle-bearing system

In this effort, a six-degree-of-freedom (DOF) model is presented for the study of a machine-tool spindle-bearing system. The dynamics of machine-tool spindle system supported by ball bearings can be described by a set of second order nonlinear differential equations with piecewise stiffness and damping due to the bearing clearance. To investigate the effect of bearing clearance, bifurcations and routes to chaos of this nonsmooth system, numerical simulation is carried out. Numerical results show when the inner race touches the bearing ball with a low speed, grazing bifurcation occurs. The solutions of this system evolve from quasi-periodic to chaotic orbit, from period doubled orbit to periodic orbit, and from periodic orbit to quasi-periodic orbit through grazing bifurcations. In addition, the tori doubling process to chaos which usually occurs in the impact system is also observed in this spindle-bearing system.

[1]  F. Chu,et al.  BIFURCATION AND CHAOS IN A RUB-IMPACT JEFFCOTT ROTOR SYSTEM , 1998 .

[2]  Guanrong Chen,et al.  Nonlinear responses of a rub-impact overhung rotor , 2004 .

[3]  Erwin Krämer,et al.  Dynamics of Rotors and Foundations , 1993 .

[4]  Aki Mikkola,et al.  Dynamic model of a deep-groove ball bearing including localized and distributed defects. Part 1: Theory , 2003 .

[5]  Ioannis Antoniadis,et al.  Effect of rotational speed fluctuations on the dynamic behaviour of rolling element bearings with radial clearances , 2006 .

[6]  Johannes Brändlein,et al.  Ball and roller bearings: Theory, design, and application , 1985 .

[7]  G. Luo,et al.  Period-doubling bifurcations and routes to chaos of the vibratory systems contacting stops , 2004 .

[8]  Daniel Nelias,et al.  A unified and simplified treatment of the non-linear equilibrium problem of double-row rolling bearings. Part 1: Rolling bearing model , 2003 .

[9]  Weiyang Qin,et al.  Grazing bifurcation and chaos in response of rubbing rotor , 2008 .

[10]  Albert C. J. Luo,et al.  A periodically forced, piecewise linear system, Part II: The fragmentation mechanism of strange attractors and grazing , 2007 .

[11]  Balakumar Balachandran,et al.  Grazing bifurcations in an elastic structure excited by harmonic impactor motions , 2008 .

[12]  Qihan Li,et al.  The existence of periodic motions in rub-impact rotor systems , 2003 .

[13]  Michael Peter Kennedy,et al.  Nonsmooth bifurcations in a piecewise linear model of the Colpitts Oscillator , 2000 .

[14]  Celso Grebogi,et al.  Universal behavior of impact oscillators near grazing incidence , 1995 .

[15]  Guanrong Chen,et al.  Grazing Bifurcation in the Response of Cracked Jeffcott Rotor , 2004 .

[16]  G. Luo,et al.  Dynamics of an impact-forming machine , 2006 .

[17]  Harry Dankowicz,et al.  Local analysis of co-dimension-one and co-dimension-two grazing bifurcations in impact microactuators , 2005 .

[18]  R. I. Zadoks,et al.  A NUMERICAL STUDY OF AN IMPACT OSCILLATOR WITH THE ADDITION OF DRY FRICTION , 1995 .

[19]  Kent Robertson Van Horn,et al.  Design and application , 1967 .

[20]  O. Prakash,et al.  DYNAMIC RESPONSE OF AN UNBALANCED ROTOR SUPPORTED ON BALL BEARINGS , 2000 .

[21]  Aki Mikkola,et al.  Dynamic model of a deep-groove ball bearing including localized and distributed defects. Part 2: Implementation and results , 2003 .

[22]  Ravi Prakash,et al.  The effect of speed of balanced rotor on nonlinear vibrations associated with ball bearings , 2003 .

[23]  Ekaterina Pavlovskaia,et al.  Low-dimensional maps for piecewise smooth oscillators , 2007 .