Achieving high-precision transient local contact behavior without introducing unphysical dynamics

Abstract

When coupling reduced bodies often so-called correction modes for the reduction of stiffness and mass matrix are added, with each correction mode contributing a dynamic component. These correction modes are typically unphysical vibration modes with very high associated frequencies, impeding explicit time integration schemes. This paper introduces a novel approach for treating contact with high precision between reduced elastic bodies in Elastic Multibody Systems to accurately capture local deformation without introducing unphysical dynamical components. Instead of using correction mode shapes, we propose shifting the transfer function of the reduced elastic body such that the static response is corrected by a constant term called feedthrough.The benefits of this approach are manifold. First, no unphysical correction modes with stiff dynamics are needed, allowing for larger time steps. Second, by capturing precisely the local contact deformation in a static sense, the model is made robust against high numerical contact penalties, relieving the engineer of a trial-and-error approach for defining a proper contact penalty. Moreover, stress results are accurate even in the contact area. Applied to a fully linearly-elastic gearing example, the presented method allows for efficient simulations with accurate results.