Modeling Combined Braking and Steering Tire Forces

Abstract

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.

Importance of Vertical Dynamics for Accurate Modelling, Friction Estimation and Vehicle Motion Control

“…Once again, several papers consider only the longitudinal velocity of the vehicle's CoG, and calculate the lateral velocity at the non-steered tire frame [20], [21]. Even the most rigorous calculations that take into account the steered tire frame do not take into account vertical dynamics in the side-slip calculation [14].…”

Modelling the tyre forces for a simulation analysis of a vehicle accident reconstruction

“…F x ( s ) and F y ( α ) were set using the modified bilinear model as described; then the NC 6 model of the combined tyre forces F x ( α, s ) and F y ( α, s ), taking into account the effects of both the slip ratio and slip angle, and the MNC model 5 were constructed and compared. The NC combined tyre forces and the MNC combined tyre forces are given by…”

“…2 This tyre force is generally accepted to be well expressed by the Bakker–Nyborg–Pacejka 3,4 equation (the ‘magic formula’), but some coefficients must be determined through appropriate experiments. Brach and Brach 5 proposed the combined tyre forces F x ( α, s ) and F y ( α, s ) (the modified Nicolas–Comstock model (MNC)), which considered the effects of both the slip ratio and the slip angle on the longitudinal tyre force F x ( α, s ) and the lateral tyre force F y ( α, s ) estimated as a single function for the slip ratio or the slip angle based on the experimental magic formula. When this method is used, the deficiencies of the Nicolas–Comstock (NC) 6 combined-tyre-force model were resolved.…”

The Relationship Between Tire Mark Striations and Tire Forces

“…This deceleration can then be used to investigate vehicle speed during an accident. Brach proposed a method for using the lateral and longitudinal plots together in the combined braking and yawing scenario [13]. Figure 6 depicts a tire in the midst of a yaw while braking.…”