Fiala Wheel 2DOF
Fiala wheel 2DOF wheel with disc, drum, or mapped brake
Description
The Fiala Wheel 2DOF block implements a simplified tire with lateral
and longitudinal slip capability based on the E. Fiala model[1]. The block uses a translational friction model to calculate the
forces and moments during combined longitudinal and lateral slip, requiring fewer
parameters than the Combined Slip Wheel 2DOF block. If you do not have
the tire coefficients needed by the Magic Formula, consider using this block for studies
that do not involve extensive nonlinear combined lateral slip or lateral dynamics. If
your study does require nonlinear combined slip or lateral dynamics, consider using the
Combined Slip Wheel 2DOF block.
The block determines the wheel rotation rate, vertical motion, and forces and moments
in all six degrees-of-freedom (DOFs) based on the driveline torque, brake pressure, road
height, wheel camber angle, and inflation pressure. You can use this block for these
types of analyses:
Driveline and vehicle simulations that require low frequency tire-road and
braking forces for vehicle acceleration, braking, and wheel rolling
resistance calculations with minimal tire parameters.
Wheel interaction with an idealized road surface.
Ride and handling maneuvers for vehicles undergoing mild combined slip.
For this analysis, you can connect the block to driveline and chassis
components such as differentials, suspension, and vehicle body
systems.
Yaw stability. For this analyses, you can connect this block to more
detailed braking system models.
Tire stiffness and unsprung mass interactions with ground variations, load
transfer, or chassis motion using the block vertical DOF.
The block integrates rotational wheel, vertical mass, and braking dynamics models. For
the slip-dependent tire forces and moments, the block implements the Fiala tire
model.
Use the Brake Type parameter to select the
brake.
Brake Type Setting | Brake Implementation |
---|
None
| None |
Disc
| Brake that converts the brake cylinder pressure into a braking
force |
Drum
| Simplex drum brake that converts the applied force and brake
geometry into a net braking torque |
Mapped
| Lookup table that is a function of the wheel speed and applied
brake pressure |
To calculate the rolling resistance torque, specify one of these Rolling
Resistance parameters.
Setting | Block
Implementation |
---|
None
| None |
Pressure and velocity
| Method in Stepwise Coastdown Methodology for
Measuring Tire Rolling Resistance. The rolling resistance
is a function of tire pressure, normal force, and velocity. |
ISO 28580
| Method specified in ISO 28580:2018, Passenger car, truck
and bus tyre rolling resistance measurement method
— Single point test and correlation of measurement
results. |
Magic Formula
| Magic formula equations from 4.E70 in Tire
and Vehicle Dynamics. The magic formula is an empirical
equation based on fitting coefficients. |
Mapped torque
| Lookup table that is a function of the normal force and
spin axis longitudinal velocity. |
To calculate vertical
motion, specify one of these Vertical Motion
parameters.
Setting | Block Implementation |
---|
None
| Block passes the applied chassis
forces directly through to the rolling resistance
and longitudinal force
calculations. |
Mapped stiffness and
damping
| Vertical motion depends on wheel
stiffness and damping. Stiffness is a function of
tire sidewall displacement and pressure. Damping
is a function of tire sidewall velocity and
pressure. |
Rotational Wheel Dynamics
The block calculates the inertial response of the wheel subject to:
The input torque is the summation of the applied axle torque, braking torque, and
moment arising from the combined tire torque.
For the moment arising from the combined tire torque, the block implements
tractive wheel forces and rolling resistance with first-order dynamics. The rolling
resistance has a time constant parameterized in terms of a relaxation length.
To calculate the rolling resistance torque, you can specify one
of these Rolling Resistance parameters.
Setting | Block Implementation |
---|
None
| Block sets rolling resistance,
My ,
to zero. |
Pressure and velocity
| Block uses the method in SAE Stepwise Coastdown
Methodology for Measuring Tire Rolling Resistance. The
rolling resistance is a function of tire pressure, normal force, and
velocity. Specifically,
|
ISO 28580
| Block uses the method specified in ISO 28580:2018,
Passenger car, truck and bus tyre rolling resistance
measurement method — Single point test and correlation of
measurement results. The method accounts for normal
load, parasitic loss, and thermal corrections from test conditions.
Specifically,
|
Magic Formula
| Block calculates the rolling resistance,
My ,
using the Magic Formula equations from 4.E70 in Tire and
Vehicle Dynamics. The magic formula is an empirical
equation based on fitting coefficients. |
Mapped torque
| For the rolling resistance,
My ,
the block uses a lookup table that is a function of the normal force and
spin axis longitudinal velocity. |
If the brakes are enabled, the block determines the braking locked or unlocked
condition based on an idealized dry clutch friction model. Based on the lock-up
condition, the block implements these friction and dynamic models.
If | Lock-Up Condition | Friction Model | Dynamic Model |
---|
| Unlocked |
|
|
| Locked |
|
|
The equations use these variables.
ω | Wheel angular velocity |
a | Velocity-independent force component |
b | Linear velocity force component |
c | Quadratic velocity force component |
Le | Tire relaxation length |
J | Moment of inertia |
My | Rolling resistance torque |
Ta | Applied axle torque |
Tb | Braking torque |
Td | Combined tire torque |
Tf | Frictional torque |
Ti | Net input torque |
Tk | Kinetic frictional torque |
To | Net output torque |
Ts | Static frictional torque |
Fc | Applied clutch force |
Fx | Longitudinal force developed by the tire road interface
due to slip |
Reff | Effective clutch radius |
Ro | Annular disk outer radius |
Ri | Annular disk inner radius |
Re | Effective tire radius while under load and for a given
pressure |
Vx | Longitudinal axle velocity |
Fz | Vehicle normal force |
Cr | Rolling resistance constant |
Tamb | Ambient temperature |
Tmeas | Measured temperature for rolling resistance
constant |
Fpl | Parasitic force loss |
Kt | Thermal correction factor |
ɑ | Tire pressure exponent |
β | Normal force exponent |
pi | Tire pressure |
μs | Coefficient of static friction |
μk | Coefficient of kinetic friction |
Longitudinal Force
The block implements the longitudinal force as a function of wheel slip relative
to the road surface using these equations.
Calculation | Equation |
---|
Critical slip |
|
Longitudinal force |
|
Friction coefficient |
|
Slip coefficient |
|
The equations use these variables.
κ' | Slip state |
Fx | Longitudinal force acting on axle along tire-fixed
x-axis, |
Cκ | Longitudinal stiffness |
Fz | Vertical contact patch normal force along tire-fixed
z-axis, |
μ | Friction coefficient |
μs | Coefficient of static friction |
μk | Coefficient of kinetic friction |
κka | Comprehensive slip coefficient |
α' | Slip angle state |
λμ | Friction scaling |
Lateral Force
The block implements the lateral force as a function of wheel slip angle state
using these equations.
Calculation | Equation |
---|
Critical slip angle |
|
Lateral force |
|
The equations use these variables.
α' | Slip angle state |
Fy | Lateral force acting on axle along tire-fixed
y-axis, |
Fz | Vertical contact patch normal force along tire-fixed
z-axis |
Cɣ | Camber stiffness |
Cα | Lateral stiffness per slip angle |
μ | Friction coefficient |
Vertical Dynamics
For the vertical dynamics, the block implements these equations.
Calculation | Equation |
---|
Vertical response |
|
Tire normal force |
|
Vertical sidewall deflection |
|
The equations use these variables.
z | Tire deflection along tire-fixed
z-axis |
zgnd | Ground displacement along tire-fixed
z-axis |
Fztire | Tire normal force along tire-fixed
z-axis |
Fz | Vertical force acting on axle along tire-fixed
z-axis |
ρz | Vertical sidewall deflection along tire-fixed
z-axis |
k | Vertical sidewall stiffness |
b | Vertical sidewall damping |
Overturning, Aligning, and Scaling
This table summarizes the overturning, aligning, and scaling
implementation.
Calculation | Implementation |
---|
Overturning moment | The Fiala model does not define an overturning moment.
The block implements this equation, requiring minimal
parameters.
|
Aligning moment | The block implements the aligning moment as a
combination of yaw rate damping and slip angle state.
|
Friction scaling | To vary the coefficient of friction, use the
ScaleFctr input port. |
The equations use these variables.
Mx | Overturning moment acting on axle about tire-fixed
x-axis |
Mz | Aligning moment acting on axle about tire-fixed
z-axis |
Re | Effective contact patch to wheel carrier radial
distance |
ɣ | Camber angle |
k | Vertical sidewall stiffness |
b | Vertical sidewall damping |
| Tire angular velocity about the tire-fixed
z-axis (yaw rate) |
w | Tire width |
α' | Slip angle state |
bMz | Linear yaw rate resistance |
Fy | Lateral force acting on axle along tire-fixed
y-axis |
Cɣ | Camber stiffness |
Cα | Lateral stiffness per slip angle |
μ | Friction coefficient |
Fz | Vertical contact patch normal force along tire-fixed
z-axis |
Tire and Wheel Coordinate Systems
To resolve the forces and moments, the block uses the Z-Up orientation of the tire and wheel coordinate systems.
Tire coordinate system axes (XT, YT, ZT) are fixed in a reference frame attached to the tire. The origin is at the tire contact with the ground.
Wheel coordinate system axes (XW, YW, ZW) are fixed in a reference frame attached to the wheel. The origin is at the wheel center.
Z-Up Orientation
Brakes
DiscIf you specify the Brake Type parameter Disc
,
the block implements a disc brake. This figure shows the side and front views of a disc brake.
A disc brake converts brake cylinder pressure from the brake cylinder into force. The disc brake applies the force at the brake pad mean radius.
The block uses these equations to calculate brake torque for the disc brake.
The equations use these variables.
T | Brake torque |
P | Applied brake pressure |
N | Wheel speed |
Npads | Number of brake pads in disc brake assembly |
μstatic | Disc pad-rotor coefficient of static friction |
μ | Disc pad-rotor coefficient of kinetic friction |
Ba | Brake actuator bore diameter |
Rm | Mean radius of brake pad force application on brake rotor |
Ro | Outer radius of brake pad |
Ri | Inner radius of brake pad |
DrumIf you specify the Brake Type parameter Drum
,
the block implements a static (steady-state) simplex drum brake. A simplex drum brake
consists of a single two-sided hydraulic actuator and two brake shoes. The brake shoes
do not share a common hinge pin.
The simplex drum brake model uses the applied force and brake geometry to calculate a net torque for each brake shoe. The drum model assumes that the actuators and shoe geometry are symmetrical for both sides, allowing a single set of geometry and friction parameters to be used for both shoes.
The block implements equations that are derived from these equations in
Fundamentals of Machine Elements.
The equations use these variables.
T | Brake torque |
P | Applied brake pressure |
N | Wheel speed |
μstatic | Disc pad-rotor coefficient of static
friction |
μ | Disc pad-rotor coefficient of kinetic
friction |
Trshoe | Right shoe brake torque |
Tlshoe | Left shoe brake torque |
a | Distance from drum center to shoe hinge pin
center |
c | Distance from shoe hinge pin center to brake actuator
connection on brake shoe |
r | Drum internal radius |
Ba | Brake actuator bore diameter |
Θ1 | Angle from shoe hinge pin center to start of brake pad
material on shoe |
Θ2 | Angle from shoe hinge pin center to end of brake pad
material on shoe |
MappedIf you specify the Brake Type parameter
Mapped
, the block uses a lookup table to determine the brake
torque.
The equations use these variables.
T | Brake torque |
| Brake torque lookup table |
P | Applied brake pressure |
N | Wheel speed |
μstatic | Friction coefficient of drum pad-face interface under static conditions |
μ | Friction coefficient of disc pad-rotor interface |
The lookup table for the brake torque, , is a function of applied brake pressure and wheel speed, where:
T is brake torque, in N·m.
P is applied brake pressure, in bar.
N is wheel speed, in rpm.
Ports
Input
expand all
BrkPrs
— Brake pressure
scalar
| N
-by-1
vector
Brake pressure, in Pa.
Vector is the number of wheels, N,
by 1
. If you provide a scalar value, the block assumes that number of
wheels is one.
Dependencies
To enable this port, for the Brake Type parameter, specify
one of these types:
AxlTrq
— Axle torque
scalar
| N
-by-1
vector
Axle torque, Ta, about wheel spin axis, in N·m.
Vector is the number of wheels, N,
by 1
. If you provide a scalar value, the block assumes that number of
wheels is one.
Vx
— Longitudinal velocity
scalar
| N
-by-1
vector
Axle longitudinal velocity, Vx, along
tire-fixed x-axis, in m/s.
Vector is the number of wheels, N,
by 1
. If you provide a scalar value, the block assumes that number of
wheels is one.
Vy
— Lateral velocity
scalar
| N
-by-1
vector
Axle lateral velocity, Vy, along tire-fixed
y-axis, in m/s.
Vector is the number of wheels, N,
by 1
. If you provide a scalar value, the block assumes that number of
wheels is one.
Camber
— Camber angle
scalar
| N
-by-1
vector
Camber angle, ɣ, in rad.
Vector is the number of wheels, N,
by 1
. If you provide a scalar value, the block assumes that number of
wheels is one.
YawRate
— Tire angular velocity
scalar
| N
-by-1
vector
Tire angular velocity, r, about the tire-fixed
z-axis (yaw rate), in rad/s.
Vector is the number of wheels, N,
by 1
. If you provide a scalar value, the block assumes that number of
wheels is one.
Prs
— Tire inflation pressure
scalar
| N
-by-1
vector
Tire inflation pressure, pi, in Pa.
Vector is the number of wheels, N,
by 1
. If you provide a scalar value, the block assumes that number of
wheels is one.
Gnd
— Ground displacement
scalar
| N
-by-1
vector
Ground displacement along tire-fixed z-axis, in m. Positive input
produces wheel lift.
Vector is the number of wheels, N,
by 1
. If you provide a scalar value, the block assumes that number of
wheels is one.
Fext
— Axle force applied to tire
scalar
| N
-by-1
vector
Axle force applied to tire, Fext, along
vehicle-fixed z-axis (positive input compresses the tire), in
N·m.
Vector is the number of wheels, N,
by 1
. If you provide a scalar value, the block assumes that number of
wheels is one.
ScaleFctrs
— Scale factor
scalar
| N
-by-1
vector
Scale factor to account for variations in the coefficient of
friction.
Vector is the number of wheels,
N, by 1
. If you provide a
scalar value, the block assumes that number of wheels is one.
Output
expand all
Info
— Block data
bus
Block data, returned as a bus signal containing these block
values.
Signal | Description | Units |
---|
AxlTrq
| Axle torque about wheel-fixed
y-axis | N·m |
Omega
| Wheel angular velocity about wheel-fixed
y-axis | rad/s |
Fx
| Longitudinal vehicle force along tire-fixed
x-axis | N |
Fy
| Lateral vehicle force along tire-fixed
y-axis | N |
Fz
| Vertical vehicle force along tire-fixed
z-axis | N |
Mx
| Overturning moment about tire-fixed
x-axis | N·m |
My
| Rolling resistance torque about tire-fixed
y-axis | N·m |
Mz
| Aligning moment about tire-fixed
z-axis | N·m |
Vx
| Vehicle longitudinal velocity along
tire-fixed
x-axis | m/s |
Vy
| Vehicle lateral velocity along tire-fixed
y-axis | m/s |
Re
| Loaded effective radius | m |
Kappa
| Longitudinal slip ratio | NA |
Alpha
| Side slip angle | rad |
a
| Contact patch half length | m |
b
| Contact patch half width | m |
Gamma
| Camber angle | rad |
psidot
| Tire angular velocity about the tire-fixed
z-axis (yaw
rate) | rad/s |
BrkTrq
| Brake torque about the vehicle-fixed
y-axis | N·m |
BrkPrs
| Brake pressure | Pa |
z
| Axle vertical displacement along tire-fixed
z-axis | m |
zdot
| Axle vertical velocity along tire-fixed
z-axis | m/s |
Gnd
| Ground displacement along tire-fixed
z-axis (positive input
produces wheel lift) | m |
GndFz
| Vertical sidewall force on ground along
tire-fixed
z-axis | N |
Prs
| Tire inflation pressure | Pa |
Omega
— Wheel angular velocity
scalar
| N
-by-1
vector
Wheel angular velocity, ω, about wheel-fixed y-axis, in rad/s.
Vector is the number of wheels, N,
by 1
. If you provide a scalar value, the block assumes that number of
wheels is one.
Fx
— Longitudinal axle force
scalar
| N
-by-1
vector
Longitudinal force acting on axle, Fx, along
tire-fixed x-axis, in N. Positive force acts to move the vehicle
forward.
Vector is the number of wheels, N,
by 1
. If you provide a scalar value, the block assumes that number of
wheels is one.
Fy
— Lateral axle force
scalar
| N
-by-1
vector
Lateral force acting on axle, Fy, along
tire-fixed y-axis, in N.
Vector is the number of wheels, N,
by 1
. If you provide a scalar value, the block assumes that number of
wheels is one.
Fz
— Vertical axle force
scalar
| N
-by-1
vector
Vertical force acting on axle, Fz, along
tire-fixed z-axis, in N.
Vector is the number of wheels, N,
by 1
. If you provide a scalar value, the block assumes that number of
wheels is one.
Mx
— Overturning moment
scalar
| N
-by-1
vector
Longitudinal moment acting on axle, Mx,
about tire-fixed x-axis, in N·m.
Vector is the number of wheels, N,
by 1
. If you provide a scalar value, the block assumes that number of
wheels is one.
My
— Rolling resistive moment
scalar
| N
-by-1
vector
Lateral moment acting on axle, My, about
tire-fixed y-axis, in N·m.
Vector is the number of wheels, N,
by 1
. If you provide a scalar value, the block assumes that number of
wheels is one.
Mz
— Aligning moment
scalar
| N
-by-1
vector
Vertical moment acting on axle, Mz, about
tire-fixed z-axis, in N·m.
Vector is the number of wheels, N,
by 1
. If you provide a scalar value, the block assumes that number of
wheels is one.
Parameters
expand all
Block Options
Brake Type
— Select type
None
| Disc
| Drum
| Mapped
Use the Brake Type parameter to select the
brake.
Brake Type Setting | Brake Implementation |
---|
None
| None |
Disc
| Brake that converts the brake cylinder pressure into a braking
force |
Drum
| Simplex drum brake that converts the applied force and brake
geometry into a net braking torque |
Mapped
| Lookup table that is a function of the wheel speed and applied
brake pressure |
Rolling Resistance
— Select type
None
(default) | Pressure and velocity
| ISO 28580
| Magic Formula
| Mapped torque
To calculate the rolling resistance torque, specify one of these Rolling
Resistance parameters.
Setting | Block
Implementation |
---|
None
| None |
Pressure and velocity
| Method in Stepwise Coastdown Methodology for
Measuring Tire Rolling Resistance. The rolling resistance
is a function of tire pressure, normal force, and velocity. |
ISO 28580
| Method specified in ISO 28580:2018, Passenger car, truck
and bus tyre rolling resistance measurement method
— Single point test and correlation of measurement
results. |
Magic Formula
| Magic formula equations from 4.E70 in Tire
and Vehicle Dynamics. The magic formula is an empirical
equation based on fitting coefficients. |
Mapped torque
| Lookup table that is a function of the normal force and
spin axis longitudinal velocity. |
Dependencies
Selecting | Parameters |
---|
Pressure and
velocity
| Velocity independent force coefficient,
aMy Linear velocity force
component, bMy Quadratic
velocity force component,
cMy Tire pressure exponent,
alphaMy Normal force
exponent, betaMy |
ISO 28580
| Parasitic losses force,
Fpl Rolling resistance
constant, Cr Thermal
correction factor,
Kt Measured temperature,
Tmeas Parasitic losses
force, Fpl Ambient
temperature, Tamb |
Magic Formula
| Rolling resistance torque coefficient,
QSY Longitudinal force
rolling resistance coefficient,
QSY2 Linear rotational
speed rolling resistance coefficient,
QSY3 Quartic rotational
speed rolling resistance coefficient,
QSY4 Camber squared rolling
resistance torque,
QSY5 Load based camber
squared rolling resistance torque,
QSY6 Normal load rolling
resistance coefficient,
QSY7 Pressure load rolling
resistance coefficient,
QSY8 Rolling resistance
scaling factor, lam_My |
Mapped torque
| Spin axis velocity breakpoints,
VxMy Normal force breakpoints,
FzMy Rolling resistance
torque map, MyMap |
Vertical Motion
— Select type
None
(default) | Mapped stiffness and damping
To calculate vertical
motion, specify one of these Vertical Motion
parameters.
Setting | Block Implementation |
---|
None
| Block passes the applied chassis
forces directly through to the rolling resistance
and longitudinal force
calculations. |
Mapped stiffness and
damping
| Vertical motion depends on wheel
stiffness and damping. Stiffness is a function of
tire sidewall displacement and pressure. Damping
is a function of tire sidewall velocity and
pressure. |
Selecting | Enables These Parameters |
---|
Mapped stiffness and
damping
| Wheel mass,
MASS Initial tire
deflection,
zo Initial
velocity,
zdoto Initial
wheel vertical velocity (wheel fixed frame),
zdoto Vertical
deflection breakpoints,
zFz Pressure
breakpoints,
pFz Force due to
deflection,
Fzz Vertical
velocity breakpoints,
zdotFz Force due
to velocity, Fzzdot |
Longitudinal and Lateral
Longitudinal stiffness, Ckappa
— Longitudinal stiffness
1e7
(default) | scalar
Longitudinal stiffness, Cκ,
in N.
Lateral stiffness per slip angle, Calpha
— Lateral stiffness
4.5e4
(default) | scalar
Lateral stiffness per slip angle,
Cα, in N/rad.
Camber stiffness, Cgamma
— Camber stiffness
1e3
(default) | scalar
Camber stiffness, Cɣ, in
N/rad.
Kinematic friction, muMin
— Friction
.8
(default) | scalar
Kinematic friction, μk,
dimensionless.
Static friction, muMax
— Friction
1
(default) | scalar
Static friction, μs,
dimensionless.
Longitudinal relaxation length, Lrelx
— Length
.05
(default) | scalar
Longitudinal relaxation length,
Lrelx, in m.
Lateral relaxation length, Lrely
— Length
.15
(default) | scalar
Lateral relaxation length,
Lrely, in m/rad.
Rolling
Rotational damping, br
— Damping
1e-3
(default) | scalar
Rotational damping, br, in N·m·s/rad.
Rotational inertia (rolling axis), IYY
— Inertia
0.74
(default) | scalar
Rotational inertia (rolling axis), IYY, in kg·m^2.
Initial rotational velocity, omegao
— Velocity
0
(default) | scalar
Initial rotational velocity, in rad/s.
Unloaded radius, UNLOADED_RADIUS
— Radius
0.309384029954441
(default) | scalar
Pressure and Velocity
Velocity independent force coefficient, aMy
— Force coefficient
8e-4
(default) | scalar
Velocity-independent force coefficient, a, in s/m.
Dependencies
To create this parameter, select the Rolling Resistance parameter
Pressure and velocity
.
Linear velocity force component, bMy
— Force component
.001
(default) | scalar
Linear velocity force component, b, in s/m.
Dependencies
To create this parameter, select the Rolling Resistance parameter
Pressure and velocity
.
Quadratic velocity force component, cMy
— Force component
1.6e-4
(default) | scalar
Quadratic velocity force component, c, in s^2/m^2.
Dependencies
To create this parameter, select the Rolling Resistance parameter
Pressure and velocity
.
Tire pressure exponent, alphaMy
— Pressure exponent
-0.003
(default) | scalar
Tire pressure exponent, ɑ, dimensionless.
Dependencies
To create this parameter, select the Rolling Resistance parameter
Pressure and velocity
.
Normal force exponent, betaMy
— Force exponent
0.97
(default) | scalar
Normal force exponent, β, dimensionless.
Dependencies
To create this parameter, select the Rolling Resistance parameter
Pressure and velocity
.
ISO 28580
Parasitic losses force, Fpl
— Force loss
10
(default) | scalar
Parasitic force loss,
Fpl, in
N.
Dependencies
To create this parameter, select the Rolling Resistance parameter
ISO 28580
.
Rolling resistance constant, Cr
— Constant
1e-3
(default) | scalar
Rolling resistance constant,
Cr, in
N/kN. ISO 28580 specifies the rolling resistance
unit as one newton of tractive resistance for
every kilonewtons of normal load.
Dependencies
To create this parameter, select the Rolling Resistance parameter
ISO 28580
.
Thermal correction factor, Kt
— Correction factor
.008
(default) | scalar
Thermal correction factor,
Kt, in
1/degC.
Dependencies
To create this parameter, select the Rolling Resistance parameter
ISO 28580
.
Measured temperature, Tmeas
— Temperature
298.15
(default) | scalar
Measured temperature,
Tmeas,
in K.
Dependencies
To create this parameter, select the Rolling Resistance parameter
ISO 28580
.
Ambient temperature, Tamb
— Temperature
298.15
(default) | scalar
Measured temperature,
Tamb, in
K.
Dependencies
To create this parameter, select the Rolling Resistance parameter
ISO 28580
.
Input ambient temperature
— Selection
off
(default) | on
Select to create input port
Tamb
.
Dependencies
To create this parameter, select the Rolling Resistance parameter
ISO 28580
.
Magic Formula
Rolling resistance torque coefficient, QSY1
— Torque coefficient
0.007
(default) | scalar
Rolling resistance torque coefficient, dimensionless.
Dependencies
To create this parameter, select the Rolling Resistance parameter Magic
Formula
.
Longitudinal force rolling resistance coefficient, QSY2
— Force resistance coefficient
0
(default) | scalar
Longitudinal force rolling resistance coefficient, dimensionless.
Dependencies
To create this parameter, select the Rolling Resistance parameter Magic
Formula
.
Linear rotational speed rolling resistance coefficient, QSY3
— Linear speed coefficient
0.0015
(default) | scalar
Linear rotational speed rolling resistance coefficient, dimensionless.
Dependencies
To create this parameter, select the Rolling Resistance parameter Magic
Formula
.
Quartic rotational speed rolling resistance coefficient, QSY4
— Quartic speed coefficient
8.5e-05
(default) | scalar
Quartic rotational speed rolling resistance coefficient, dimensionless.
Dependencies
To create this parameter, select the Rolling Resistance parameter Magic
Formula
.
Camber squared rolling resistance torque, QSY5
— Camber resistance torque
0
(default) | scalar
Camber squared rolling resistance torque, in 1/rad^2.
Dependencies
To create this parameter, select the Rolling Resistance parameter Magic
Formula
.
Load based camber squared rolling resistance torque, QSY6
— Load resistance torque
0
(default) | scalar
Load based camber squared rolling resistance torque, in 1/rad^2.
Dependencies
To create this parameter, select the Rolling Resistance parameter Magic
Formula
.
Normal load rolling resistance coefficient, QSY7
— Normal resistance coefficient
0.9
(default) | scalar
Normal load rolling resistance coefficient, dimensionless.
Dependencies
To create this parameter, select the Rolling Resistance parameter Magic
Formula
.
Pressure load rolling resistance coefficient, QSY8
— Pressure resistance coefficient
-0.4
(default) | scalar
Pressure load rolling resistance coefficient, dimensionless.
Dependencies
To create this parameter, select the Rolling Resistance parameter Magic
Formula
.
Rolling resistance scaling factor, lam_My
— Scale
1
(default) | scalar
Rolling resistance scaling factor, dimensionless.
Dependencies
To create this parameter, select the Rolling Resistance parameter Magic
Formula
.
Mapped
Spin axis velocity breakpoints, VxMy
— Breakpoints
-20:1:20
(default) | vector
Spin axis velocity breakpoints, in m/s.
Dependencies
To create this parameter, select the Rolling Resistance parameter
Mapped torque
.
Normal force breakpoints, FzMy
— Breakpoints
0:200:1e4
(default) | vector
Normal force breakpoints, in N.
Dependencies
To create this parameter, select the Rolling Resistance parameter
Mapped torque
.
Rolling resistance torque map, MyMap
— Lookup table
array
Rolling resistance torque versus axle speed and normal force, in N·m.
Dependencies
To create this parameter, select the Rolling Resistance parameter
Mapped torque
.
Aligning
Wheel width, WIDTH
— Width
0.209
(default) | scalar
Wheel width, WIDTH, in m.
Linear yaw rate resistance, bMz
— Resistance
0 | scalar
Linear yaw rate resistance,
bMz, in N·m·s/rad.
Brake
Static friction coefficient, mu_static
— Static friction
.3
(default) | scalar
Static friction coefficient, dimensionless.
Dependencies
To enable this parameter, for the Brake Type parameter, specify one of
these types:
Kinetic friction coefficient, mu_kinetic
— Kinetic friction
.2
(default) | scalar
Kinematic friction coefficient, dimensionless.
Dependencies
To enable this parameter, for the Brake Type parameter, specify one of
these types:
Disc
Disc brake actuator bore, disc_abore
— Bore distance
.05
(default) | scalar
Disc brake actuator bore, in m.
Dependencies
To enable the disc brake parameters, select Disc
for
the Brake Type parameter.
Brake pad mean radius, Rm
— Radius
.177
(default) | scalar
Brake pad mean radius, in m.
Dependencies
To enable the disc brake parameters, select Disc
for
the Brake Type parameter.
Number of brake pads, num_pads
— Count
2
(default) | scalar
Number of brake pads.
Dependencies
To enable the disc brake parameters, select Disc
for
the Brake Type parameter.
Drum
Drum brake actuator bore, disc_abore
— Bore distance
0.0508
(default) | scalar
Drum brake actuator bore, in m.
Dependencies
To enable the drum brake parameters, select Drum
for
the Brake Type parameter.
Shoe pin to drum center distance, drum_a
— Distance
0.123
(default) | scalar
Shoe pin to drum center distance, in m.
Dependencies
To enable the drum brake parameters, select Drum
for
the Brake Type parameter.
Shoe pin center to force application point distance, drum_c
— Distance
0.212
(default) | scalar
Shoe pin center to force application point distance, in m.
Dependencies
To enable the drum brake parameters, select Drum
for
the Brake Type parameter.
Drum internal radius, drum_r
— Radius
0.15
(default) | scalar
Drum internal radius, in m.
Dependencies
To enable the drum brake parameters, select Drum
for
the Brake Type parameter.
Shoe pin to pad start angle, drum_theta1
— Angle
0
(default) | scalar
Shoe pin to pad start angle, in deg.
Dependencies
To enable the drum brake parameters, select Drum
for
the Brake Type parameter.
Shoe pin to pad end angle, drum_theta2
— Angle
126
(default) | scalar
Shoe pin to pad end angle, in deg.
Dependencies
To enable the drum brake parameters, select Drum
for
the Brake Type parameter.
Mapped
Brake actuator pressure breakpoints, brake_p_bpt
— Breakpoints
vector
Brake actuator pressure breakpoints, in bar.
Dependencies
To enable the mapped brake parameters, select Mapped
for
the Brake Type parameter.
Wheel speed breakpoints, brake_n_bpt
— Breakpoints
vector
Wheel speed breakpoints, in rpm.
Dependencies
To enable the mapped brake parameters, select Mapped
for
the Brake Type parameter.
Brake torque map, f_brake_t
— Lookup table
array
The lookup table for the brake
torque, , is a function of applied brake pressure and wheel speed, where:
T is brake torque, in N·m.
P is applied brake pressure, in bar.
N is wheel speed, in rpm.
Dependencies
To enable the mapped brake parameters, select Mapped
for
the Brake Type parameter.
Vertical
Wheel mass, m
— Mass
9.46491996974568
(default) | scalar
Wheel mass, in kg. Used in the vertical motion calculations.
Dependencies
To enable this parameter, set Vertical Motion to Mapped
stiffness and damping
.
Initial tire deflection, zo
— Deflection
0
(default) | scalar
Initial axle displacement along wheel-fixed
z-axis, in m.
Dependencies
To enable this parameter, set Vertical Motion to Mapped
stiffness and damping
.
Initial wheel vertical velocity (wheel fixed frame), zdoto
— Velocity
0
(default) | scalar
Initial axle velocity along wheel-fixed z-axis,
in m.
Dependencies
To enable this parameter, set Vertical Motion to Mapped
stiffness and damping
.
Gravitational acceleration, GRAVITY
— Gravity
-9.81
(default) | scalar
Gravitational acceleration, in m/s^2.
Dependencies
To enable this parameter, set Vertical Motion to Mapped
stiffness and damping
.
Mapped Stiffness and Damping
Vertical deflection breakpoints, zFz
— Breakpoints
[0 .01 .1]
(default) | vector
Vector of sidewall deflection breakpoints corresponding to the force
table, in m.
Dependencies
To enable this parameter, set Vertical Motion to Mapped
stiffness and damping
.
Pressure breakpoints, pFz
— Breakpoints
[10000 1000000]
(default) | vector
Vector of pressure data points corresponding to the force table, in
Pa.
Dependencies
To enable this parameter, set Vertical Motion to Mapped
stiffness and damping
.
Force due to deflection, Fzz
— Force
[0 1e3 1e4; 0 1e4 1e5]
(default) | vector
Force due to sidewall deflection and pressure along wheel-fixed
z-axis, in N.
Dependencies
To enable this parameter, set Vertical Motion to Mapped
stiffness and damping
.
Vertical velocity breakpoints, zdotFz
— Breakpoints
[-20 0 20]
(default) | scalar
Vector of sidewall velocity breakpoints corresponding to the force due
to velocity table, in m.
Dependencies
To enable this parameter, set Vertical Motion to Mapped
stiffness and damping
.
Force due to velocity, Fzzdot
— Force
[500 0 -500;250 0 -250]
(default) | array
Force due to sidewall velocity and pressure along wheel-fixed
z-axis, in N.
Dependencies
To enable this parameter, set Vertical Motion to Mapped
stiffness and damping
.
Simulation
Maximum normal force, FZMAX
— Force
10000
(default) | scalar
Maximum normal force, in N. Used with all vertical force calculations.
Minimum normal force, FZMIN
— Force
0
(default) | scalar
Minimum normal force, in N. Used with all vertical force calculations.
Maximum pressure, PRESMAX
— Pressure
1003118
(default) | scalar
Maximum pressure, PRESMAX, in Pa.
Minimum pressure, PRESMIN
— Pressure
9982
(default) | scalar
Minimum pressure, PRESMIN, in Pa.
Max allowable slip ratio (absolute), KPUMAX
— Ratio
1.5
(default) | scalar
Max allowable slip ratio (absolute), KPUMAX, dimensionless.
Minimum allowable slip ratio (absolute), KPUMIN
— Ratio
-1.5
(default) | scalar
Minimum allowable slip ratio (absolute), KPUMIN,
dimensionless.
Max allowable slip angle (absolute), ALPMAX
— Angle
1.5708
(default) | scalar
Max allowable slip angle (absolute), ALPMAX, in rad.
Minimum allowable slip angle (absolute), ALPMIN
— Angle
-1.5708
(default) | scalar
Minimum allowable slip angle (absolute), ALPMIN, in rad.
Maximum allowable camber angle, CAMMAX
— Angle
0.173
(default) | scalar
Maximum allowable camber angle CAMMAX, in rad.
Minimum allowable camber angle, CAMMIN
— Angle
-0.173
(default) | scalar
Minimum allowable camber angle, CAMMIN, in rad.
Minimum ambient temperature, TMIN
— Tmin
0
(default) | scalar
Minimum ambient temperature, TMIN, in
K.
Dependencies
To create this parameter, select the Rolling Resistance parameter
ISO 28580
.
Maximum ambient temperature, TMAX
— Tmax
400
(default) | scalar
Maximum ambient temperature, TMAX, in
K.
Dependencies
To create this parameter, select the Rolling Resistance
parameter ISO 28580
.
References
[1] Fiala, E. "Seitenkrafte am Rollenden
Luftreifen." VDI Zeitschrift, V.D.I.. Vol 96, 1954.
[2] Highway Tire Committee.
Stepwise Coastdown Methodology for Measuring Tire Rolling
Resistance. Standard J2452_199906. Warrendale, PA: SAE International,
June 1999.
[3] ISO 28580:2018.
Passenger car, truck and bus tyre rolling resistance measurement method —
Single point test and correlation of measurement results. ISO
(International Organization for Standardization), 2018.
[4] Pacejka, H. B. Tire
and Vehicle Dynamics. 3rd ed. Oxford, UK: SAE and Butterworth-Heinemann,
2012.
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[1] Reprinted with permission Copyright © 2008 SAE International. Further distribution of this material is not permitted without prior permission from SAE.