Abstract The dynamic performance of a vehicle is mainly determined by the interaction of its tires and road. A vehicle can only move and maneuver by the force systems generated under the tires. In this chapter, we introduce the required coordinate frames to determine the location and orientation of tires in the vehicle body coordinate frame; the mathematical equation to calculate longitudinal and lateral forces; and individual equations needed to develop dynamic equations of vehicles in the following chapters. The resultant force system that a tire receives from the ground is at the center of the tireprint and can be decomposed along x t, y t, and z t axes of the tire coordinate frame T. The interaction of a tire with road generates a three-dimensional (3D) force system including three forces and three moments. The force system at the tireprint of a loaded, rolling, steered, cambered tire includes: forward force F x, lateral force F y, vertical force F z, aligning moment M z, roll moment M x, and pitch moment M y. The forward force F x and lateral force F y are the most significant forces in vehicle maneuvering. To accelerate or brake a vehicle, a longitudinal force must be developed between the tire and the ground. When a torque T is applied to the spin axis of a tire, longitudinal slip ratio s occurs and a longitudinal force F x is generated at the tireprint proportional to s. The tire lateral force F y is a function of two angles of the tire: sideslip angle α and camber angle γ. The F x and F y take the tire load F z, sideslip α, longitudinal slip s, and the camber angle γ as input. We adopt the proportional-saturation model for longitudinal and lateral slips of tire. When α = 0, a small longitudinal slip s < s s generates the longitudinal force F x∕F z = C s s, and when s = 0, a small sideslip angle α < α s generates a lateral force of F y∕F z = −C α α. When there exists a longitudinal slip s < s s and then we also introduce a sideslip α < α s, the longitudinal force will reduce. Similarly, when there exists a longitudinal slip s < s s, the lateral force will drop. The elliptic mathematical model introduces the analytical expression of the interaction F x∕F z and F y∕F z. Because the longitudinal and lateral forces are affected by the vertical force F z on the tire, there must be a model to calculate the weight transfer during forward and lateral acceleration. Such equations are calculated in this chapter.
Tire Dynamics
Advanced Vehicle Dynamics ; 1-113
2019-01-01
113 pages
Aufsatz/Kapitel (Buch)
Elektronische Ressource
Englisch
Springer Verlag | 2017
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