23 rd International Conference ENGINEERING MECHANICS 2017 Svratka, Czech Republic, 15 – 18 May 2017 MATHEMATICAL MODELLING OF ROTOR SYSTEMS WITH JOURNAL BEARINGS IN LIMIT CASES P. Polach * , M. Hajžman ** , M. Byrtus *** , Š. Dyk **** , L. Smolík ***** Abstract: Dynamics of rotating systems involves behaviour and diagnostics of rotating structures. When hydrodynamic journal bearings are used to support a rotor the rotor-bearing system becomes a complex dynamic system that may exhibit serious fluid film instabilities. The understanding of the behaviour of a fluid film bearing closely before, during and after the rotor instability origin and growth is the main motivation for the complex research of local and global dynamics of a rotor-bearing system. Deep knowledge of the relations between local fluid film dynamics and dynamic response of rotating systems during instabilities can help to improve design of many modern rotating machines. Keywords: Rotor dynamics, Reynolds equation, Fluid film bearings. 1. Introduction Dynamics of rotating systems supported by journal bearings is an interesting topic of computational mechanics. When hydrodynamic journal bearings are used to support a rotor the rotor-bearing system becomes a complex dynamic system that may exhibit serious fluid film instabilities related to various limit cases, which are the main subject of this paper. The understanding of the fluid film bearing behaviour closely before, during and after the rotor instability origin and growth is the main motivation for the complex research of local and global dynamics of a rotor-bearing system. In 1925 Newkirk and Taylor discovered that a journal bearing can induce unstable vibrations of a supported rotor. This instability – commonly called oil whirl (Hori, 1959) – remains troublesome and of great concern. Lund (1962) investigated bifurcations analytically within the scope of the Hopf bifurcation theory and introduced the method of multiple scales. Later Meyers (1986) applied the bifurcation theory to oil whirl employing numerical methods. Recent development in numerical methods for nonlinear models and numerical continuation methods allowed studying the oil-induced instabilities and resulting bifurcations even deeper. Castro et al. (2008) implemented successfully nonlinear hydrodynamic forces and predicted oil whirl/whip for a real vertical power plant and a horizontal test rig. Boyaci et al. (2010) used a numerical continuation method to detect bifurcations of stationary and periodic solutions for a flexible rotor supported by two identical journal bearings. Adiletta et al. (2011) and Laha and Kakoty (2011) published the work similar to Boyaci’s. Adiletta et al. (2011) studied a rigid rotor supported by two-lobe journal bearings, whereas Laha and Kakoty (2011) studied a flexible rotor supported by porous hydrodynamic journal bearings. Mishra (2012) investigated whirl ratio for an adiabatic solution of a bearing with non-Newtonian fluid. Amamou and Chouchane (2014) discussed the stability issues including hysteresis and jump phenomena of long journal bearings utilizing nonlinear model and continuation methods. Yang et al. (2014) proposed second-order nonlinear stiffness and damping * Dr. Ing. Pavel Polach: New Technologies for the Information Society, European Centre of Excellence, University of West Bohemia, Univerzitní 8; 306 14, Pilsen; CZ, ppolach@ntis.zcu.cz ** Ing. Michal Hajžman, PhD.: New Technologies for the Information Society, European Centre of Excellence, University of West Bohemia, Univerzitní 8; 306 14, Pilsen; CZ, mhajzman@kme.zcu.cz *** Ing. Miroslav Byrtus, PhD.: New Technologies for the Information Society, European Centre of Excellence, University of West Bohemia, Univerzitní 8; 306 14, Pilsen; CZ, mbyrtus@rice.zcu.cz **** Ing. Štěpán Dyk: New Technologies for the Information Society, European Centre of Excellence, University of West Bohemia, Univerzitní 8; 306 14, Pilsen; CZ, sdyk@ntis.zcu.cz ***** Ing. Luboš Smolík: New Technologies for the Information Society, European Centre of Excellence, University of West Bohemia, Univerzitní 8; 306 14, Pilsen; CZ, carlist@ntis.zcu.cz 794