Model order reduction by projection applied to the universal Reynolds equation

Nikolaus Euler-Rolle, Stefan Jakubek and Günter Offner

Mathematical and Computer Modelling of Dynamical Systems, 2014, vol. 20, issue 4, 374-394

Abstract: 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 the Galerkin 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.

Date: 2014
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DOI: 10.1080/13873954.2013.838587

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