A wave model of a circular tyre. Part 2: side-wall and force transmission modelling

A dynamic model of a curved side-wall of a pressurised tyre is presented. The model uses a previously derived wave equation. The side-wall is assumed to have a uniform thickness over the whole distance between the belt and the hub. A vertical or a horizontal displacement is input at the connection with the belt and the forces input and those transmitted to the hub are calculated and described in terms of dynamic stiffness. The effect of various parameters such as pressure, geometry, belt wavelength and material properties are investigated. The side-wall model is applied to a belt model to give a full tyre model. An integral around the belt circumference is performed to give the forces transmitted to the hub. The effect of the air within the cavity is calculated from the uncoupled carcass vibration. Finally, some experiments were made on a tyre and the model was fitted, thereby giving an estimate of the tyre material properties and validating the model for both belt vibration prediction and force transmission to the hub.