EngOpt 2008 - International Conference on Engineering Optimization Rio de Janeiro, Brazil, 01 - 05 June 2008. Parameters Identification of a Rotor on Lubricated Journal Bearings Vincenzo D’Agostino, Domenico Guida, Alessandro Ruggiero Department of Mechanical Engineering, University of Salerno,Italy, guida@unisa.it 1. Abstract The idea of system identification is to recover the system properties through investigations of ex- perimental data records. The choice of appropriate methods for system identification depends on both types of experimental records and the objectives of the identification. There are various identification tools well documented in literature concerning linear and non-linear systems. The last item is very important because the presence of non-linearity essentially complicates the identification problem since the linear superposition principle becomes inapplicable. In this paper we propose a direct method for the identification of the parameters for one general class of non-linear systems. The only requirement is that the system must be modeled by analytic or sufficiently smooth functions. The approach is based on the Lie operator representations and the corresponding Lie series solutions. This kind of solutions can be obtained for a general class of non-linear systems in the form of analytical power series. The applica- tion that we propose concerns a method for the identification of the parameters of a mechanical system composed of rotor on two lubricated journal bearings. In this application we have used a set of numerical results obtained by integrating the motion equations, then, developed a numerical procedure in order to minimize the difference between numerical and approximating solution, last, obtained by using Lie series. 2. Keywords: Journal Bearings, Stiffness Coefficients, Damping Coefficients, Parameters Identifi- cation, Lie Series 3. Introduction Hydrodynamic journal bearings are commonly used for supporting rotating shafts subjected to high radial loads. Applications can be seen in a wide variety of machines where satisfactory performance is vital for proper functioning, such as pumps, turbines, compressors, etc. The steadily increasing demands on the performance of these high speed machinery have led to considerable interest in the use of well designed rotor/shaft systems. It is well known that the problem of instability for fluid-film journal bearings supported rotors is of primary importance. This instability occurs when the speed exceeds a certain value, and appears as a self-excited orbital motion induced by the action of fluid dynamic forces. This vibratory motion can cause considerable mechanical problems, like rubbing between journal and bearing, blades and stator in turbo-machines, or more generally vibrations of the whole rotating machinery. Since (Newkirk and Taylor, 1925) first demonstrated that the oil whirl is caused by the dynamic oil film forces in the bearings, numerous theoretical and experimental investigations were devoted to the study of dynamic characteristic problems of journal bearings (Hori, 1959; Holmes, 1960; Reddi and Trumpler, 1962; Lund and Saibel, 1967; Badgley and Booker, 1969; Akers et al., 1971; Kirk and Gunter, 1976 a,b; Grosby, 1982; Akkok and Ettles, 1984). Stability of rotors in bearings is generally analyzed using two different approaches. One approach consists to perform a time-transient integration method for the complete set of equation of motion. Therefore, even for relatively simple systems this becomes a formidable task since the Reynolds’ equation for the bearings has to be evaluated at each time step. The other approach is characterized by the linearization of the fluid forces acting on the bearings in the neighborhood of a well-determined stationary equilibrium position so that asymptotic stability conditions can be determined. In the latter case, it is necessary to know the stiffness and damping coefficients to linearize the hydrodynamic forces. It is evident that the first approach can provide more information to study the rotor dynamic behavior, for example the possibility to compute minimum fluid film thickness; moreover, this method is not affected by the consequences of linearization. However, it is worth noting that the resulting numerical code can be complex. Therefore, if determination of the system stability is the only goal, it is undoubtedly more convenient to use dynamic coefficients. 1