07 Fakultät Konstruktions-, Produktions- und Fahrzeugtechnik
Permanent URI for this collectionhttps://elib.uni-stuttgart.de/handle/11682/8
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Item Open Access Nonlinear dynamics of the tippedisk : a holistic analysis(2023) Sailer, Simon; Leine, Remco I. (Prof. Dr. ir. habil.)This dissertation deals with the tippedisk which is a new mechanical-mathematical archetype for friction-induced instabilities and exhibits an energetically counterintuitive inversion phenomenon. In a holistic analysis, the dynamics of the tippedisk is investigated numerically in the field of multibody simulation, theoretically in the field of nonlinear dynamics, and experimentally in the focus of applied physics. Based on different nonsmooth rigid body models with set-valued force laws, the main physical mechanisms inducing the inversion behavior are identified and the governing system equations are derived. Subsequent model reduction results in a reduced system in the form of an ordinary differential equation, which is suited to be studied in the context of nonlinear dynamics. Both the local stability behavior of the non-inverted and inverted stationary spinning motions as well as the global proof of an existing heteroclinic saddle connection allow the dynamic behavior of the tippedisk to be captured analytically. The particular structure of the mathematical model reveals a singularly perturbed dynamics that evolves on multiple time scales and is characterized by slow rolling and fast sliding motions of the tippedisk. Utilizing perturbation expansions and an analysis in dimensionless quantities, the qualitative dynamics is characterized by closed-form expressions, from which a global stability map is deduced. Based on this complete stability map, three different bifurcation scenarios are identified, which correspond to different geometric and inertia properties, defining three qualitatively different types of tippedisks. Finally, the mathematical investigation is complemented by high-speed experiments on a real test specimen. Qualitative comparison of experimental measurements with simulations at different levels of abstraction completes the holistic approach to the dynamic analysis of the tippedisk.