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N. Euler-Rolle, S. Jakubek, G. Offner:
"Model order reduction by projection applied to the universal Reynolds' equation";
Mathematical and Computer Modelling of Dynamical Systems, 20 (2014), 4; S. 374 - 394.

The approach presented in this paper yields a reduced order solution to the universal Reynolds´ equation for incompressible fluids, which is valid in lubrication as well as in cavitation regions, applied to oil-film lubricated journal bearings in internal combustion engines. The extent of cavitation region poses a free boundary condition to the problem and is determined by an iterative spatial evaluation of a superposed modal solution. Using a Condensed Galerkin and Petrov-Galerkin method, the number of degrees of freedom of the original grid is reduced to obtain a fast but still accurate short-term prediction of the solution. Based on the assumption that a detailed solution of a previous combustion cycle is available, a basis and an optimal test space for Galerkin´s method is generated. The resulting reduced order model is efficiently exploited in a time-saving evaluation of the Jacobian matrix describing the elastohydrodynamic coupling in a multi-body dynamics simulation using flexible components. Finally, numerical results are presented for a single crankshaft main bearing of typical dimensions.

Reynolds' equation, model order reduction, Galerkin projection, Jacobian matrix

http://dx.doi.org/10.1080/13873954.2013.838587