An Analytical Model of a Tire's Interaction on Snow

Abstract

Snow covered roads are a common problem during the winter months in the Northern Hemisphere. The roads become slippery due to the accumulation of snow on the surfaces and hence signi cantly changes the coefficient of friction, resulting in accidents. It is with this motivation the traction of a tire needs to be maximized. Unlike a tire on an asphalt surface, the tire is subjected to a complex interaction on snow. Various phenomena that contribute to the force generation on a snow surface are studied with a physical motivation in this report. By understanding the net force generation of a tire, a physical approach is used to develop a vehicle dynamics model that can be used for e.g handling simulations. The plausible phenomena contributing to the net force generation of a tire are the rubber-snow interaction, snow-snow interaction, snow braking force, bulldozing resistance and the digging force. The rubber-snow and the snow-snow interaction are the major source of traction on snow. The other plausible forces have comparatively less contribution but are important to be established for further understanding the tire traction on snow. Accurate models are necessary to obtain reliable results. And with simulations being the heart of today's automotive industry, the models need to be simple enough so that it can be used with low processing power. Thus from an engineer's point of view, an analytically derived model is important for vehicle dynamics simulations. Also by adding more phenomena to our models, we can thus potentially understand more while keeping it as simple as possible. In this thesis, we extend the common brush model to study the snow interaction and its effect on the net force generation. Further, by analytically deriving the quantities it was possible to connect tire design to vehicle performance, which can be essential for a tire manufacturer. From the results obtained we see that the net effect of the derived tire model shows a good match to available measurement data. The model which includes the material properties can be thus potentially used on other loose surfaces with veri cation from test data.