Model order reduction by projection applied to the universal Reynolds equation |
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Authors: | Nikolaus Euler-Rolle Stefan Jakubek |
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Institution: | Christian Doppler Laboratory for Model Based Calibration Methodologies at the Institute of Mechanics and Mechatronics, Vienna University of Technology, 1040 Vienna, Austria |
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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. |
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Keywords: | Reynolds equation model order reduction Galerkin projection Jacobian matrix |
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