Arch Appl Mech (2014) 84:519–541 DOI 10.1007/s00419-013-0815-9 ORIGINAL Hui Ma · Hui Li · Heqiang Niu · Rongze Song · Bangchun Wen Numerical and experimental analysis of the first- and second-mode instability in a rotor-bearing system Received: 29 July 2013 / Accepted: 10 December 2013 / Published online: 28 December 2013 © Springer-Verlag Berlin Heidelberg 2013 Abstract Aiming at the oil film instability of the sliding bearing at high speeds, a rotor test rig is built to study the non-linear dynamic behaviours caused by the first- and second-mode instability. A lumped mass model (LMM) of the rotor system considering the gyroscopic effect is established, in which the graphite self- lubricating bearing and the sliding bearing are simulated by a spring–damping model and a nonlinear oil film force model based on the assumption of short bearings, respectively. Moreover, a finite element model is also established to verify the validity of the LMM. The researches focus on the effects of two loading conditions (the first- and second-mode imbalance excitation) on the onset of instability and nonlinear responses of the rotor-bearing system by using the amplitude–frequency response, spectrum cascade, vibration waveform, orbit, and Poincaré map. Finally, experiments are carried out on the test rig. Simulation and experiment all show that oil film instability can excite complicated combination frequency components about the rotating frequency and the first-/second-mode whirl/whip frequency. Keywords Oil film instability · Rotor system · Dynamic behaviours · Combination frequency · The first-/second-mode whirl/whip List of symbols C Damping matrix of the global system C 1 Rayleigh damping matrix C 2 Bearing damping matrix c Bearing clearance c blx , c bly Dampings of the left bearing in x and y directions D Bearing diameter E Young’s modulus F b Oil film force vector of the right bearing F bx 5 , F by5 Oil film forces of the right bearing in x and y directions F e Unbalanced force vector of the rotor system f bx 5, f by5 Dimensionless oil film forces of the right bearing in x and y directions f n1 , f n2 The first- and second-mode whirl/whip frequencies f r Rotating frequency G Gyroscopic matrix g Acceleration of gravity I Moment of inertia J di (i = 1, 2, 3, 4, 5) Diametral moment of inertia about any axis perpendicular to the rotor axis H. Ma (B ) · H. Li · H. Niu · R. Song · B. Wen School of Mechanical Engineering and Automation, Northeastern University, Shenyang, Liaoning 110819, People’s Republic of China Tel: +86-24-83684491 Fax: +86-24-83684491 E-mail: mahui_2007@163.com