Nonlinear Dynamics 24: 269–283, 2001. © 2001 Kluwer Academic Publishers. Printed in the Netherlands. Stability Analysis of Sliding Whirl in a Nonlinear Jeffcott Rotor with Cross-Coupling Stiffness Coefficients JUN JIANG and HEINZ ULBRICH Institute of Mechanics, Department of Mechanical Engineering, University of Essen, 45127 Essen, Germany (Received: 26 January 2000; accepted: 30 May 2000) Abstract. An analytical study is carried out on the stability of the full annular rub solutions of an externally excited, modified Jeffcott rotor with a given rotor/stator clearance and cross-coupling influences. The obtained analytical stability conditions provide an opportunity for a better understanding of the dynamical phenomena of rotor/stator systems with rubs, such as jump phenomena and the transition between periodic and quasi-periodic full rub responses as well as between the full annular rubs and the partial rubs. A systematic study on the influence of the system parameters on these phenomena is carried out. It is found that the simultaneous presence of the coefficient of friction and the cross-coupling stiffness coefficient with a proper value may benefit the dynamics of the rotor/stator system with rubs. Keywords: Rotor/stator rub, stability analysis, rotor instability, bifurcation. Nomenclature A = amplitude of the steady-state solution c = damping of the rotor e = rotor mass eccentricity k s ,k b = stiffness of rotor shaft and stator m = mass of the rotor Q = cross-coupling stiffness r 0 = clearance between rotor and stator r = displacement of shaft geometric center,  x 2 + y 2 R 0 = non-dimensional clearance R = non-dimensional displacement of shaft center t = time x, y = horizontal and vertical displacements of shaft center X, Y = non-dimensional displacements of shaft center β = k s /k b γ = Q/k b ; µ = coefficient of friction τ = non-dimensional time ω = rotating speed of the rotor ω 2 = natural frequency of rotor system with zero clearance  = ω/ω 2  n = natural frequency of the linear Jeffcott rotor  = phase angle between mass eccentricity and displacement of shaft center ζ = damping ratio of the rotor system