Estimates of the visco-elastic properties of car tyres

Traffic is a major source of green house gases. The transport field stands for 32 % of the energy consumption and 28 % of the total CO2 emissions, where road transports alone causes 84 % of these figures. The energy consumed by a car travelling at constant speed, is due to engine inefficiency, internal friction, and the energy needed to overcome resisting forces such as aerodynamic drag and rolling resistance. Rolling resistance plays a rather large role when it comes to fuel economy. An improvement in rolling resistance of 10 % can yield fuel consumption improvements ranging from 0.5 to 1.5 % for passenger cars and light trucks and 1.5 to 3 % for heavy trucks. The objective of this thesis is to estimate the power consumption in the tyres. To do this a car tyre is modelled with waveguide finite elements. A non-linear contact model is used to calculate the contact forces as the tyre is rolling on a rough road. The contact forces combined with the response of the tyre is used to estimate the input power to the tyre structure, which determines a significant part of the rolling resistance. This is the first rolling resistance model based on physical principles and design data. The elements used in the waveguide finite elements tyre model are derived and validated. The motion of the tyre belt and side wall is described with quadratic anisotropic curved deep shell elements that includes pre-stress and the motion of the tread on top of the belt by curved quadratic, Lagrange type, homogenous, isotropic two dimensional solid elements. The tyre model accounts for: the curvature, the geometry of the cross-section, the pre-stress due to inflation pressure, the anisotropic material properties and the rigid body properties of the rim and is based on data provided by Goodyear. To validate the tyre model, mobility measurements and an experimental modal analysis have been made. The model agrees very well with point mobility measurements up to roughly 250 Hz. The eigenfrequency prediction is within five percent for most of the identified modes. The estimated damping is a bit too low especially for the anti-symmetric modes. The non-proportional damping used in the model is based on an ad hoc curve fitting procedure against measured mobilities. The non-linear contact force prediction, made by the division of applied acoustics, Chalmers University of Technology takes the tyre, the road texture and the tread pattern into account. The dissipated power is calculated through the injected power and the power dissipated within each element. It is shown that a rough road leads to more dissipation than a smooth road. A demonstration on real existing motor ways, for which rolling resistance measurements also have been made, show the potential of the method. The damping is very important for the rolling resistance prediction. The damping properties of the tyremodel are therefore updated based on measurement, equivalent structure modelling and viscoelastic material models. This updated model is slightly better at the point mobility prediction and is far better at predicting the damping level of the identified modes from the experimental modal analysis.