Modeling Combined Braking and Steering Tire Forces

The force distributed over the contact patch between a tire and a road surface is typically modeled in component form for dynamic simulations. The two components in the plane of the contact patch are the braking, or traction force, and the steering, or side or cornering force. A third force distributed over the contacts patch is the normal force, perpendicular to the road surface. The two tangential components in the plane of the road are usually modeled separately since they depend primarily on independent parameters, wheel slip and sideslip. Mathematical expressions found in the literature for each component include exponential functions, piecewise linear functions and the Bakker-Nyborg-Pacejka equations, among others. Because braking and steering frequently occur simultaneously and their resultant tangential force is limited by friction, the two components must be properly combined for a full range of the wheel slip and sideslip parameters. This paper examines the way in which these two components are combined for an existing approach known as the Nicolas-Comstock model. First, performance criteria for tire modeling are proposed. Then the Nicolas-Comstock model is examined relative to the criteria. As originally proposed, this model falls short of meeting the criteria over the full range of transverse and longitudinal wheel slip values and sideslip angles. A modified version of the Nicolas-Comstock model is presented that satisfies these performance criteria. Finally, comparisons are made of the Modified Nicolas-Comstock model to other combined tire force models and to existing tire force measurements.