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Coupled differential algebraic equations in the simulation of flexible multibody systems with hydrodynamic force elements

The mathematical modelling of elastohydrodynamic bearings in combustion engines leads to a coupled system of (partial) differential algebraic equations, which is represented by a flexible multibody system model of the engine including crankshaft and bearing and by the Reynolds equation that describes the non‐linear effects in the fluid film. The hydrodynamic forces depend strongly on the position and the elastic deformation of crankshaft and bearing shell. We discuss the influence of the spatial discretization on accuracy and numerical effort. Since a fine spatial discretization substantially slows down the numerical solution, we propose a semi‐analytical method based on singular perturbation theory to speed‐up time integration. Numerical tests for a simplified benchmark problem illustrate the advantages of this approach. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)