A hybrid tyre model for in-plane dynamics

A ring model for pneumatic and non-pneumatic tyres is presented. In this model, the tread is discretised by means of lumped masses, interconnected by curved Timoshenko beams, ideally assumed massless and unloaded, and linked to the rim by spring-damper elements taking into account the sidewall properties. The equations of motion are derived via Hamilton's variational principle. The hybrid continuous-discrete approach allows to overcome the need of employing expensive methods to solve the governing equations of the systems, since they are split in two different sets. As a result, a closed-form solution for the displacement field of each beams can be provided. A qualitative analysis is carried out for different values of the elastic modulus of the tread. Results for both the normal and the tangential interactions are coherent with the physical behaviour of the real tyre. Finally, the model is validated and compared to already existing ones, showing the best overall agreement with experimental data.