The LuGre dynamic point contact friction model for the two-dimensional translation of a body on a surface has been used in the past to derive a model for the friction forces and moments at the contact patch of a tire. The resulting tire friction model is distributed, 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 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: uniform, trapezoidal and cubic load distribution. Simulations are also presented to compare with existing approximate steady-state lumped models. I.
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Tsiotras et al. (2004) studied this question.