Two-dimensional FrBD friction models for rolling contact: extension to linear viscoelasticity
This work addresses friction modeling for rolling contact in engineering applications, but it is incremental as it extends an existing framework to viscoelasticity.
The paper tackled extending the FrBD friction model to linear viscoelasticity for rolling contact, resulting in a system of hyperbolic PDEs that capture complex relaxation phenomena and demonstrate well-posedness and passivity for any physically meaningful parameters.
This paper extends the distributed rolling contact FrBD framework to linear viscoelasticity by considering classic derivative Generalised Maxwell and Kelvin-Voigt rheological representations of the bristle element. With this modelling approach, the dynamics of the bristle, generated friction forces, and internal deformation states are described by a system of 2(n+1) hyperbolic partial differential equations (PDEs), which can capture complex relaxation phenomena originating from viscoelastic behaviours. By appropriately specifying the analytical expressions for the transport and rigid relative velocity, three distributed formulations of increasing complexity are introduced, which account for different levels of spin excitation. For the linear variants, well-posedness and passivity are analysed rigorously, showing that these properties hold for any physically meaningful parametrisation. Numerical experiments complement the theoretical results by illustrating steady-state characteristics and transient relaxation effects. The findings of this paper substantially advance the FrBD paradigm by enabling a unified and systematic treatment of linear viscoelasticity.