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Communication Dans Un Congrès Année : 2022

Nonlinear parametric analysis of geared systems: a bifurcation tracking approach

Résumé

The search for ever more efficient mechanical designs requires the influence of nonlinearities on the dynamic behaviour to be evaluated. It is well known that geared systems can exhibit a wide variety of dynamic responses such as periodic, quasi-periodic or even chaotic oscillations [1]. The type of observed dynamic regime usually depends on the values of a set of paramaters, e.g. the excitation frequency or level of nonlinearity. A small parameter variation can therefore have a significant influence on the dynamic behaviour. The harmonic balance method (HBM) coupled to a numerical continuation algorithm is commonly used to build the forced response curve (FRC) of the system, i.e, to study the evolution of the dynamic behaviour with respect to the excitation frequency. Additional parameters can be investigated by computing several FRCs although this can lead to intractable computations with large systems. A more elegant solution consists in following the evolution of bifurcation points, i.e, where changes in dynamic regime occur, with respect to an additional parameter. In this work, we propose a complex formulation of the HBM with a minimally extended system [2] to track bifurcations of a SDOF gear model similar to the one described in [1]. An original approach to model the contact between gear teeth is developed to carry out bifurcation tracking analyses with parameters that do not appear explicitly in the equations of motion.
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Dates et versions

hal-04617258 , version 1 (19-06-2024)

Identifiants

  • HAL Id : hal-04617258 , version 1

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Adrien Mélot, Emmanuel Rigaud, Joël Perret-Liaudet. Nonlinear parametric analysis of geared systems: a bifurcation tracking approach. ESMC 2022 - 11th European Solid Mechanics Conference, Jul 2022, Galway, Ireland. ⟨hal-04617258⟩
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