Transient gear contact simulations using a floating frame of reference approach and higher-order ansatz functions

Gear drives are crucial components for a wide range of devices such as combustion engines and wind turbines. Predictions of durability, transmission errors, and noise emission are required already during early development. To that end, deformations, velocities, stresses, and contact forces can be analyzed using numerical simulations. For this, finite element analyses (FEA) or multibody system (MBS) simulations can be used. Yet, rigid MBS can be inaccurate since contact forces must be estimated using a heuristic force-displacement law since no deformations are available. Also, the need for elaborate manual tuning of contact parameters is a drawback. FEA, on the other hand, bring about long computation times that make them inappropriate for the analysis of transient phenomena. Further, a bottleneck of FEA for gears is the expensive human labor that is necessary to generate hexahedral meshes required for contact detection. Both quadratically and linearly interpolating tetrahedral meshes can be generated quickly and reliably. Tet4 elements, however, are not a viable option due to their inferior performance. Thus, as a remedy to (i) the parametrization issues and the inaccuracy inherent while using rigid MBS descriptions, (ii) the long simulation times of FEA, and (iii) the issue of expensive manual generation of hexahedral meshes, we propose using elastic multibody systems with quadratic tetrahedral meshes for dynamic contact simulations. The novelty of this contribution is the use of quadratic ansatz functions for the description of both geometry and contact calculation in combination with a floating frame of reference formulation and model order reduction.