USE AND LIMITATIONS OF THE HARMONIC BALANCE METHOD FOR RUB-IMPACT PHENOMENA IN ROTOR-STATOR DYNAMICS

In the present paper, a Harmonic Balance Method (HBM) coupled with a pseudo-arc length continuation algorithm is pre- sented for the prediction of the steady state behaviour of a rotor- stator contact problem. The ability of the HBM to reproduce the four most common phenomena encountered during rotor to sta- tor contact situations (i.e. 'no-rub', 'full annular rub', 'partial rub' and 'backward whirl/whip') is investigated. A modified Jef- fcott rotor model is used and results of the proposed algorithm are compared with traditional time marching solutions and ana- lytical predictions. The advantages and limitations of the HBM for this kind of problem are analyzed. It is shown that the HBM is orders of magnitude faster than transient simulations, and pro- vides very accurate results. However, in its current form it is unable to predict quasi-periodic behaviour. Detailed analysis of the transient solutions yields valuable information for the future extension of the HBM to efficient quasi-periodic simulations.

[1]  Jun Jiang,et al.  Determination of the global responses characteristics of a piecewise smooth dynamical system with contact , 2009 .

[2]  Y. Cheung,et al.  A Variable Parameter Incrementation Method for Dynamic Instability of Linear and Nonlinear Elastic Systems , 1982 .

[3]  Eric Jones,et al.  SciPy: Open Source Scientific Tools for Python , 2001 .

[4]  D. J. Ewins,et al.  Analytical Formulation of Friction Interface Elements for Analysis of Nonlinear Multi-Harmonic Vibrations of Bladed Disks , 2003 .

[5]  Dara W. Childs,et al.  Prediction of Dry-Friction Whirl and Whip Between a Rotor and a Stator , 2006 .

[6]  Jun Jiang,et al.  Stability Analysis of Sliding Whirl in a Nonlinear Jeffcott Rotor with Cross-Coupling Stiffness Coefficients , 2001 .

[7]  Arthur W. Lees,et al.  THE INFLUENCE OF TORSION ON ROTOR/STATOR CONTACT IN ROTATING MACHINERY , 1999 .

[8]  Christophe Pierre,et al.  n-dimensional Harmonic Balance Method extended to non-explicit nonlinearities , 2006 .

[9]  Horst Ecker,et al.  Nonlinear dynamics of a rotor contacting an elastically suspended stator , 2007 .

[10]  Chaoshun Li,et al.  Dynamic response of a rub-impact rotor system under axial thrust , 2009 .

[11]  J. Griffin,et al.  An Alternating Frequency/Time Domain Method for Calculating the Steady-State Response of Nonlinear Dynamic Systems , 1989 .

[12]  Soon-Yi Wu,et al.  Incremental harmonic balance method with multiple time scales for aperiodic vibration of nonlinear systems , 1983 .

[13]  Donald E. Bently,et al.  Full Annular RUB in Mechanical Seals, Part II: Analytical Study , 2002 .

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

[15]  D. Ewins,et al.  Analytical Formulation of Friction Interface Elements for Analysis of Nonlinear Multi-Harmonic Vibrations of Bladed Discs , 2002 .

[16]  Bangchun Wen,et al.  Periodic motions of a dual-disc rotor system with rub-impact at fixed limiter , 2008 .

[17]  Z. C. Feng,et al.  Rubbing phenomena in rotor–stator contact , 2002 .

[18]  J. Andersons,et al.  Overcritical high-speed rotor systems, full annular rub and accident , 2006 .

[19]  P. Sundararajan,et al.  An algorithm for response and stability of large order non-linear systems : Application to rotor systems , 1998 .