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Pacejka

Pacejka tire model used to determine the forces and moments developed at the tire contact patch

The Pacejka 2002 tire model, unlike the analytical Fiala and Calspan models, is based on fitting experimental data to the Pacejka's Magic Formula. Complex expressions for all tire forces and moments are computed, taking into account a wide range of physical phenomena. This model requires that numerous parameters are employed.

 

Note: The hubFrame port of the Pacejka component must be connected directly to the hubFrame port of another tire body component, as shown in the diagram below.

 

 

Connections 

Name

Description

Color

hubFrame

Tire reference frame, which must be connected to a tire body component.

Gray

 

Parameters

Note: All units are assumed to be in SI unless otherwise noted.

Symbol

Default

Units

Description

ID

Fz0

5900

N

Nominal normal force

Fz0

R0

0.355

m

Unloaded radius

R0

V0

22.2

ms

Nominal (measured) forward speed

V0

LFz0

1

-

Scale factor of nominal load

LFz0

LCxy

1,1

-

Scale factor of Fx,Fy shape factor

LCxLCy

Lμxy

1,1

-

Scale factor of Fx, Fy peak friction coefficient

LmuxLmuy

LExy

1,1

-

Scale factor of Fx, Fy curvature factor

LExLEy

LKxy

1,1

-

Scale factor of Fx, Fy slip stiffness

LKxLKy

LHxy

1,1

-

Scale factor of Fx, Fy horizontal shift

LHxLHy

LVxy

1,1

-

Scale factor of Fx, Fy vertical shift

LVxLVy

Lγxyz

1,1,1

-

Scale factor of inclination for Fx, Fy, Mz

Lgammaxyz

Ltrail

1

-

Scale factor of peak pneumatic trail

Ltrail

Lres

1

-

Scale factor for offset of residual torque

Lres

LXα

1

-

Scale factor of slip-angle influence on Fx

LXalpha

LYκ

1

-

Scale factor of longslip influence on Fy

LYkappa

LVyκ

1

-

Scale factor of longslip influence on Fy vertical shift

LVykappa

LS

1

-

Scale factor of moment arm of Fx about vertical axis

LS

LMxy

1,1

-

Scale factor of overturning couple and rolling resistance torque

LMxLMy

LVMx

1

-

Scale factor of Mx vertical shift

LVMx

PCx1

1.65

-

Shape factor for longitudinal force

PCx1

PDx1...3

1,0,0

-

Longitudinal friction at Fz0, force variation with load, inclination

PDx1PDx3

PEx1...4

0,0,0,0

-

Longitudinal curvature at Fz0, variation with load, variation with load squared, factor while driving (causes asymmetry)

PEx1PEx4

PKx1...4

20,0,0

-

Longitudinal slip stiffness at Fz0, variation with load, exponent in slip stiffness with load

PKx1PKx3

PHx1...2

0,0

-

Horizontal shift of longitudinal slip at Fz0, variation with load

PHx1PHx2

PVx1...2

0,0

-

Vertical shift at Fz0, variation with load

PVx1PVx2

RBx1...2

10,6

-

Slope factor for combined slip Fx reduction, variation with load

RBx1RBx2

RCx1

1

-

Shape factor for combined slip Fx reduction

RCx1

REx1...2

0,0

-

Curvature factor for combined slip Fx reduction, variation with load

REx1REx2

RHx1

0

-

Shift factor for combined slip Fx reduction

RHx1

QSx1...3

0,0,0

-

Overturning moment coefficients

QSx1QSx3

PCy1

1.1058

-

Shape factor for pure lateral force

PCy1

PDy1...3

1.04910,0.215300,0.338480

-

Lateral peak friction, variation with load, inclination squared

PDy1PDy3

PEy1...4

0.871480,1.5278,0.0259870,0.907290

-

Lateral force curvature factor at Fz0, variation with load, sign of slip angle, inclination

PEy1PEy4

PKy1...3

23.648,2.1393,0.907290

-

Maximum value of cornering stiffness, load (Fz/Fz0) at which cornering stiffness reaches its max value, variation of with inclination

PKy1PKy3

PHy1...3

0.000178020,0.0000349800,0.0290550

-

Horizontal shift of lateral force at Fz0, variation with load, inclination

PHy1PHy3

PVy1...4

0.000453100,0.000540830,0.206230,0.155680

-

Vertical shift at Fz0, variation with load, inclination, inclination and load

PVy1PVy4

RBy1...3

16,0,0

-

Slope factor for combined slip Fy reduction, variation with slip angle, shift term for alpha in slope factor

RBy1RBy3

RCy1

1

-

Shape factor for combined slip Fy reduction

RCy1

REy1...2

0,0

-

Curvature factor for combined slip Fy reduction, variation with load

REy1REy2

RHy1...2

0,0

-

Shift factor for combined slip Fy reduction, variation with load

RHy1RHy2

RVy1...6

0,0,0,0,1.9,0

-

Longitudinal slip induced side forces at Fz0, variation with load, inclination, slip angle, longitudinal slip, and arctan of longitudinal slip

RVy1RVy6

QSy1...4

0.01,0,0,0

-

Rolling resistance coefficients

QSy1QSy4

QBz1...5

14.973,3.5918,0.72704,0.00777650,0.0081978

-

Pneumatic trail slope factor at Fz0, variation with load, load squared, inclination, absolute inclination

QBz1QBz5

QBz9...10

17.781,0

-

Slope factors for residual torque

QBz9QBz10

QCz1

1.132

-

Shape factor for pneumatic trail

QCz1

QDz1...4

0.112720,0.00267450,0.00663320,6.23800

-

Peak pneumatic trail, variation with load, inclination, load and inclination

QDz1QDz4

QDz6...9

0.00031508,0.0002961,0.081607,0.08016

-

Peak residual torque, variation with load, inclination, load and inclination

QDz6QDz9

QEz1...5

1.7447,0.58532,0,0.00292020,2.2229

-

Pneumatic trail curvature at Fz0, variation with load, load squared, sign of slip angle, sign of slip angle and inclination

QEz1QEz5

QHz1...4

0.000252220,0.0000684680,0.0192730,0.00927610

-

Pneumatic trail horizontal shift at Fz0, variation with load, inclination, load and inclination

QHz1QHz4

SSz1...4

0,0,0,0

-

Nominal value of S/R0, variation with Fy, inclination, load and inclination

SSz1SSz4

 

References

H.B. Pacejka, Tire and Vehicle Dynamics, SAE International, 2002.

 

See Also

Linear, Calspan, Fiala, User-Defined, Standard Tire

 

 


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