Sommerfeld and Mass Parameter Identification of Lubricated Journal Bearings

Abstract: In this paper we propose a method for identification of two parameters that define the structure of lubricated journal bearings. In rotordynamics literature these parameters are named Sommerfeld number and Mass Number, respectively. The system analyzed belongs to the class of systems that are described by n non-linear second order differential equations. We have obtained the analytical solutions of these equations using Lie series expansion. This method can be applied to a vast class of dynamical systems, provided that they are described by smooth equations. Lie series expansion is a mathematical tool that allows us to obtain the system response in recursive way using symbolic PC-codes. Besides, this procedure involves only a few experimental data and makes the identification process very quick. It is worth noting that the application that we propose does not take into account neither the issue connected to experimental data noise nor the unavoidable disturbances that occurs in measurement process. Actually, in applied system identification one must always pay attention to the signal noise and to the robustness of the solution with respect to disturbances, but these issues are over the goal of this paper. Key–Words: Nonlinear System Identification, Parameter Identification, Lubricated Journal Bearings