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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
Name
Condition
Description
ID
-
Drive shaft rotational flange
driveshaft
Axle longitudinal flange
flange_x
Real input port for axle vertical force
f_z
Parameters
Symbol
Default
Units
Defines the tire formulation type:
Linear: linear formulation with saturation
Magic: Magic formula
tiremode
A small constant added to the denominator of the slip ratio to prevent singularity
epsilon_v
Nominal vertical load
Fz0
Traction force at nominal vertical load
Fx0
Slip ratio at peak traction force
sr0
Inertia of the two wheels and the axle
J
Wheel radius
r
Coefficients used in the Magic formula.
BCDE
Extra scaling coefficient for the Magic formula.
K
N
Residual tire force at zero slip (Use for models with fixed-step integration)
Sv
Initial Conditions
Initial tire angular velocity
w
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.
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