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.