A LuGre tire friction model with exact aggregate dynamics

The LuGre dynamic point contact friction model for the two-dimensional translation of a body on a surface has been used to derive a model for the friction forces and moments at the contact patch of a tire. The resulting tire friction model is distributed, i.e., is described by a set of partial differential equations. Several approximations have been used in the literature to approximate this distributed model using a set of ordinary differential equations, making the model more appropriate for control design and on-line estimation. In this paper, the method of moments is used to derive a set of ordinary differential equations to describe the exact average dynamics of the distributed model. Three cases of normal load distribution are considered and compared with each other: uniform, trapezoidal and quartic load distribution. Simulations are also presented to compare with existing approximate lumped models.