Tire

Linear and Magic Formula tire model component

Note:  This component is used with the Longitudinal Vehicle Dynamics component.

The Tire component models the longitudinal dynamics of a two tires together with the wheels and axle. The tire longitudinal forces are modeled either by a linear formulation (with saturation) or by the Magic formula. Wheel/axle inertia is included but no compliance is considered.

Equations

The tire translation and rotation velocities are given as

 =

 =  ,     =

Where    is the tire translation along the road and   is the tire rotation.

The equation of motion is

Where    is the tire inertia,   is the axle torque,    is the traction/brake force, and   is the tire radius.    

The slip ratio is approximated by

Where    is a small positive number added to avoid singularity.

The tire contact force, f, is calculated as

where parameters  and  are added to the standard Magic formula to adjust the tire force and facilitate fixed step integration, respectively. Also,

Connections 

Parameters

Initial Conditions

See Also

MapleSim Driveline Library Overview

MapleSim Library Overview

1-D Mechanical Overview

Longitudinal Vehicle Dynamics

Tire Component Library

Vehicle and Tire

Vehicle

References

Pacejka, Hans B. Tire and Vehicle Dynamics. Second Edition. SAE International and Elsevier, 2005.