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Fiala Wheel 2DOF

Fiala wheel 2DOF wheel with disc, drum, or mapped brake

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  • Vehicle Dynamics Blockset / Wheels and Tires

  • Fiala Wheel 2DOF block

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 SettingBrake 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.

SettingBlock 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.

SettingBlock 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:

  • Axle losses

  • Brake and drive torque

  • Tire rolling resistance

  • Ground contact through the tire-road interface

The input torque is the summation of the applied axle torque, braking torque, and moment arising from the combined tire torque.

Ti=TaTb+Td

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.

Td(s)=1|ω|ReLes+1(Fx Re+My)

To calculate the rolling resistance torque, you can specify one of these Rolling Resistance parameters.

SettingBlock 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,

My=Re{a+b|Vx|+cVx2}{Fzβpiα}tanh(4Vx)

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,

My=Re(FzCr1+Kt(TambTmeas)Fpl)tanh(ω)

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.

IfLock-Up ConditionFriction ModelDynamic Model

ω0orTS<|Ti+Tfωb|

Unlocked

Tf=Tkwhere,Tk=FcReffμktanh[4(ωd)]Ts=FcReffμsReff=2(Ro3Ri3)3(Ro2Ri2)

ω˙J=ωb+Ti+To

ω=0andTS|Ti+Tfωb|

Locked

Tf=Ts

ω=0

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.

CalculationEquation

Critical slip

κ'Critical=|μFz2Cκ|

Longitudinal force

Fx={Ck κ'                                          when |κ'|κ'Criticaltanh(4κ')(μ|Fz||(μFz)24κ'Cκ|)         when |κ'|>κ'Critical

Friction coefficient

μ=(μs(μsμk) κkα)λμ

Slip coefficient

κkα=κ'2+tan2(α')

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.

CalculationEquation

Critical slip angle

α'Critical=atan(3μ|Fz|Ca)

Lateral force

Fy={tanh(4α')μ|Fz|                           when |α'|>α'Criticaltanh(4α')μ|Fz|(1ξ3)+γCγ    when |α'|α'Criticalξ=1Ca|tan(α')|3μ|Fz|

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.

CalculationEquation

Vertical response

z¨m=Fztire+mgFz

Tire normal force

Fztire=ρzkbz˙

Vertical sidewall deflection

ρz=zgndz,z0

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.

CalculationImplementation

Overturning moment

The Fiala model does not define an overturning moment. The block implements this equation, requiring minimal parameters.

Mx=FyRecos(γ)

Aligning moment

The block implements the aligning moment as a combination of yaw rate damping and slip angle state.

Mz={ψ˙bMz                                               when |α'|>α'Criticaltanh(4α')wμ|Fz|(1ξ)ξ3+ψ˙bMz    when |α'|α'Criticalξ=1Ca|tan(α')|3μ|Fz|

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

ψ˙

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[1]

Z-Up tire and wheel coordinate systems showing wheel plane and road plane

Brakes

Disc

If 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.

Front and side view of disc brake, showing pad, disc, and caliper

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.

T={μPπBa2RmNpads4                when N0μstaticPπBa2RmNpads4         when N=0

Rm=Ro+Ri2

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

Drum

If 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.

Trshoe=(πμcr(cosθ2cosθ1)Ba22μ(2r(cosθ2cosθ1)+a(cos2θ2cos2θ1))+ar(2θ12θ2+sin2θ2sin2θ1))PTlshoe=(πμcr(cosθ2cosθ1)Ba22μ(2r(cosθ2cosθ1)+a(cos2θ2cos2θ1))+ar(2θ12θ2+sin2θ2sin2θ1))P

T={Trshoe+Tlshoe                 when N0(Trshoe+Tlshoe)μstaticμ   when N=0

Side view of drum brake

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

Mapped

If you specify the Brake Type parameter Mapped, the block uses a lookup table to determine the brake torque.

T={fbrake(P,N)                   when N0(μstaticμ)fbrake(P,N)    when N=0

The equations use these variables.

T

Brake torque

fbrake(P,N)

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, fbrake(P,N), 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.

Plot of brake torque as a function of wheel speed and applied brake pressure

Ports

Input

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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:

  • Disc

  • Drum

  • Mapped

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.

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.

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 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.

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.

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.

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.

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.

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

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Block data, returned as a bus signal containing these block values.

SignalDescriptionUnits

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

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.

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.

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.

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.

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.

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.

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

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Block Options

Use the Brake Type parameter to select the brake.

Brake Type SettingBrake 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.

SettingBlock 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

SelectingParameters

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

To calculate vertical motion, specify one of these Vertical Motion parameters.

SettingBlock 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.

SelectingEnables 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, Cκ, in N.

Lateral stiffness per slip angle, Cα, in N/rad.

Camber stiffness, Cɣ, in N/rad.

Kinematic friction, μk, dimensionless.

Static friction, μs, dimensionless.

Longitudinal relaxation length, Lrelx, in m.

Lateral relaxation length, Lrely, in m/rad.

Rolling

Rotational damping, br, in N·m·s/rad.

Rotational inertia (rolling axis), IYY, in kg·m^2.

Initial rotational velocity, in rad/s.

Unloaded radius, in m.

Pressure and Velocity

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, b, in s/m.

Dependencies

To create this parameter, select the Rolling Resistance parameter Pressure and velocity.

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, ɑ, dimensionless.

Dependencies

To create this parameter, select the Rolling Resistance parameter Pressure and velocity.

Normal force exponent, β, dimensionless.

Dependencies

To create this parameter, select the Rolling Resistance parameter Pressure and velocity.

ISO 28580

Parasitic force loss, Fpl, in N.

Dependencies

To create this parameter, select the Rolling Resistance parameter ISO 28580.

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, in 1/degC.

Dependencies

To create this parameter, select the Rolling Resistance parameter ISO 28580.

Measured temperature, Tmeas, in K.

Dependencies

To create this parameter, select the Rolling Resistance parameter ISO 28580.

Measured temperature, Tamb, in K.

Dependencies

To create this parameter, select the Rolling Resistance parameter ISO 28580.

Select to create input port Tamb.

Dependencies

To create this parameter, select the Rolling Resistance parameter ISO 28580.

Magic Formula

Rolling resistance torque coefficient, dimensionless.

Dependencies

To create this parameter, select the Rolling Resistance parameter Magic Formula.

Longitudinal force rolling resistance coefficient, dimensionless.

Dependencies

To create this parameter, select the Rolling Resistance parameter Magic Formula.

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, dimensionless.

Dependencies

To create this parameter, select the Rolling Resistance parameter Magic Formula.

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, in 1/rad^2.

Dependencies

To create this parameter, select the Rolling Resistance parameter Magic Formula.

Normal load rolling resistance coefficient, dimensionless.

Dependencies

To create this parameter, select the Rolling Resistance parameter Magic Formula.

Pressure load rolling resistance coefficient, dimensionless.

Dependencies

To create this parameter, select the Rolling Resistance parameter Magic Formula.

Rolling resistance scaling factor, dimensionless.

Dependencies

To create this parameter, select the Rolling Resistance parameter Magic Formula.

Mapped

Spin axis velocity breakpoints, in m/s.

Dependencies

To create this parameter, select the Rolling Resistance parameter Mapped torque.

Normal force breakpoints, in N.

Dependencies

To create this parameter, select the Rolling Resistance parameter Mapped torque.

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, in m.

Linear yaw rate resistance, bMz, in N·m·s/rad.

Brake

Static friction coefficient, dimensionless.

Dependencies

To enable this parameter, for the Brake Type parameter, specify one of these types:

  • Disc

  • Drum

  • Mapped

Kinematic friction coefficient, dimensionless.

Dependencies

To enable this parameter, for the Brake Type parameter, specify one of these types:

  • Disc

  • Drum

  • Mapped

Disc

Disc brake actuator bore, in m.

Dependencies

To enable the disc brake parameters, select Disc for the Brake Type parameter.

Brake pad mean radius, in m.

Dependencies

To enable the disc brake parameters, select Disc for the Brake Type parameter.

Number of brake pads.

Dependencies

To enable the disc brake parameters, select Disc for the Brake Type parameter.

Drum

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, in m.

Dependencies

To enable the drum brake parameters, select Drum for the Brake Type parameter.

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, in m.

Dependencies

To enable the drum brake parameters, select Drum for the Brake Type parameter.

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, in deg.

Dependencies

To enable the drum brake parameters, select Drum for the Brake Type parameter.

Mapped

Brake actuator pressure breakpoints, in bar.

Dependencies

To enable the mapped brake parameters, select Mapped for the Brake Type parameter.

Wheel speed breakpoints, in rpm.

Dependencies

To enable the mapped brake parameters, select Mapped for the Brake Type parameter.

The lookup table for the brake torque, fbrake(P,N), 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.

Plot showing brake torque as a function of wheel speed and applied brake pressure

Dependencies

To enable the mapped brake parameters, select Mapped for the Brake Type parameter.

Vertical

Wheel mass, in kg. Used in the vertical motion calculations.

Dependencies

To enable this parameter, set Vertical Motion to Mapped stiffness and damping.

Initial axle displacement along wheel-fixed z-axis, in m.

Dependencies

To enable this parameter, set Vertical Motion to Mapped stiffness and damping.

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, in m/s^2.

Dependencies

To enable this parameter, set Vertical Motion to Mapped stiffness and damping.

Mapped Stiffness and Damping

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.

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 sidewall deflection and pressure along wheel-fixed z-axis, in N.

Dependencies

To enable this parameter, set Vertical Motion to Mapped stiffness and damping.

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 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, in N. Used with all vertical force calculations.

Minimum normal force, in N. Used with all vertical force calculations.

Maximum pressure, PRESMAX, in Pa.

Minimum pressure, PRESMIN, in Pa.

Max allowable slip ratio (absolute), KPUMAX, dimensionless.

Minimum allowable slip ratio (absolute), KPUMIN, dimensionless.

Max allowable slip angle (absolute), ALPMAX, in rad.

Minimum allowable slip angle (absolute), ALPMIN, in rad.

Maximum allowable camber angle CAMMAX, in rad.

Minimum allowable camber angle, CAMMIN, in rad.

Minimum ambient temperature, TMIN, in K.

Dependencies

To create this parameter, select the Rolling Resistance parameter ISO 28580.

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.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Introduced in R2019a

[1] Reprinted with permission Copyright © 2008 SAE International. Further distribution of this material is not permitted without prior permission from SAE.