Bifurcation analysis of a preloaded Jeffcott rotor Evgueni V. Karpenko, Ekaterina E. Pavlovskaia, Marian Wiercigroch * Centre for Applied Dynamics Research, Department of Engineering, University of Aberdeen, Aberdeen AB24 3UE, UK Accepted 16 May 2002 Abstract A model of two-degrees-of-freedom Jeffcott rotor system with bearing clearance subjected of an out-of-balance excitation is considered. The influence of preloading and viscous damping of the snubber ring is introduced in the mathematicaldescription.Aprogrammeofnumericalsimulationsisconductedtoshowhowthepreloadingandviscous damping change the dynamics of the rotor system. Bifurcation diagrams and Lyapunov exponents are constructed to explore stability. It is shown that dynamics of the rotor system can be effectively controlled by varying the preloading andthedampingbothoftherotorandthesnubberring.Inthemostconsideredcasespreloadingstabilisesthedynamic responses. Ó 2002 Elsevier Science Ltd. All rights reserved. 1. Introduction In general the analysis of rotor systems can be based on a simple model like the Jeffcott rotor [1–3,5–8,12,13], or more complicated multidimensional systems, such as presented in [4,9–11]. Many papers have been devoted to two- degrees-of-freedom models with clearance, e.g. [1–3,5–8]. In particular, Choy and Padovan [2], Muszynska and Goldman [3], Al-Bedoor [4] and Childs [5] paid attention to the rub interactions in rotating machinery. Ehrich [6] investigated spontaneous sidebanding, where Ganesan [7] looked at the stability analysis. Tiwari et al. [11] examined morecomplicatedatwo-degrees-of-freedommodeloftherigidrotorsupportedbyadeepgrooveballbearing.Neilson andBarr[9]consideredafour-degrees-of-freedomrotorsystemwithradialclearance.Afiniteelementschemebasedon the Timoshenko theory was used by Abduljabbar et al. [10]. In this study an active control strategy was comprised of twostages:atfirsttocontrolthefreevibrationsoftherotorandatsecondtosupresstheperiodicexcitations.Gonsalves et al. [8] designed an experimental rig similar to the Jeffcott model and made a comparative analysis between the ex- perimental and numerical results. Further numerical investigations on the same model by Karpenko et al. [13] have shown an existence of multiple attractors and fractal basins of attraction. Despiteofsignificanttheoreticalandexperimentaleffortsontwo-degrees-of-freedommodels,theeffectofpreloading of the snubber ring has not been yet properly addressed. Therefore, in this paper the dynamics of a preloaded Jeffcott rotorisdiscussed,whereweconsidertheinfluenceofviscousdamping,stiffness,preloading,andout-of-balancemasson the steady-state response of the system. This is a continuation of our previous work [12,13], where the unpreloaded model of the rotor was analysed. The current and previous studies were undertaken to simulate the behaviour of our laboratory experimental rig shown in Fig. 1. The rig essentially consists of two main parts: a rigid rotor (1) elastically supported by four flexural rods (2) and excited by an out-of-balance (3), and a snubber ring (4) also elastically sup- portedandpreloadedbyfourcompressionsprings(5).Therotorassemblyiscomprisedofamildsteelrotor,runningin two angular contact bearings. A pair of dampers (6) is attached to the rotor, one in horizontal and one in vertical * Corresponding author. E-mail address: m.wiercigroch@eng.abdn.ac.uk (M. Wiercigroch). 0960-0779/03/$ - see front matter Ó 2002 Elsevier Science Ltd. All rights reserved. PII:S0960-0779(02)00107-8 Chaos, Solitons and Fractals 15 (2003) 407–416 www.elsevier.com/locate/chaos ARTICLE IN PRESS