Engee documentation

Fiala Wheel 2DOF

Page in progress.

A Phial wheel with two degrees of freedom and a disc the brake.

blockType: SubSystem

fiala wheel 2dof

Path in the library:

/Automotive/Wheel/Fiala Wheel 2DOF

Description

Block Fiala Wheel 2DOF implements a simplified tire model with the possibility of transverse and longitudinal slippage based on the model of E. Fiala [1]. The unit uses a translational friction model to calculate forces and moments when longitudinal and transverse slippage are combined. If you do not have the tire coefficients required for the empirical formula [4], use this block in research where extensive nonlinear joint lateral slippage or lateral motion dynamics are not required.

The unit determines the wheel’s rotation speed, vertical movement, as well as forces and torques in all six degrees of freedom based on transmission torque, brake pressure, road height, wheel camber angle, and tire pressure. The block can be used for the following types of analysis:

  • Simulation of the transmission and vehicle, where calculations of acceleration, braking and rolling resistance of the wheels require low-frequency forces of interaction of the tire with the road and braking forces with a minimum number of tire parameters.

  • The interaction of the wheel with the idealized road surface.

  • Analysis of the controllability and maneuverability of vehicles with moderate joint slippage. For such an analysis, the unit can be connected to transmission and chassis components such as differential, suspension and bodywork.

  • Yaw stability. For such an analysis, the unit can be connected to more detailed models of the braking system.

  • The interaction of tire stiffness and unsprung mass with road surface irregularities, load redistribution, or chassis movement using the vertical degree of freedom of the block.

The block combines models of wheel rotation dynamics, vertical mass, and braking. For forces and moments that depend on tire slippage, the unit implements the Fiala tire model.

You can set your own custom model parameter values or use the built-in bus model.

To calculate the rolling resistance moment, set the parameter Rolling Resistance one of the following values:

  • None — rolling resistance is not taken into account.

  • Pressure and velocity — the method defined in [2]. Rolling resistance depends on tire pressure, normal force, and speed.

  • ISO 28580 — the method defined in [3].

  • Magic Formula — the equations of the empirical formula under the number 4.E70 in [4]. «Magical» The formula is an empirical equation based on approximation coefficients.

To calculate the vertical movement, set the parameter Vertical Motion one of the following values:

  • None — the unit transmits the applied chassis forces directly to the rolling resistance and longitudinal force calculations.

  • Mapped stiffness and damping — vertical movement depends on the stiffness and damping of the wheel. Stiffness is a function of tire sidewall displacement and pressure, and damping is a function of tire sidewall velocity and pressure.

  • External deflection — The unit uses the specified sidewall deflection directly to calculate the effective radius.

Rotating wheel dynamics

The unit calculates the inertial response of the wheel, taking into account:

  • axis losses;

  • braking and driving torques;

  • rolling resistance of the tire;

  • contact with the road through the tire.

The input torque is the sum of the applied axle torque, the braking torque, and the torque resulting from the total tire torque.:

For the torque resulting from the total torque of the tire, the unit implements the traction forces of the wheel and rolling resistance with first-order dynamics. Rolling resistance has a time constant parameterized in terms of the relaxation length:

To calculate the rolling resistance moment for the parameter Rolling Resistance you can set one of the following values:

  • None — the unit sets the rolling resistance torque equal to zero.

  • Pressure and velocity — the block uses the method described in [2]. Rolling resistance is a function of tire pressure, normal force and speed, namely:

  • ISO 28580 — the block uses the method described in [3]. The method takes into account the normal load, parasitic losses and thermal corrections caused by the test conditions, namely:

  • Magic Formula — the unit calculates rolling resistance according to the equation of the empirical formula 4.E70 in [4]. «Magical» The formula is an empirical equation based on approximation coefficients.

If the brakes are on, the unit determines the braking state (locked or unlocked) based on an idealized dry clutch friction model. Depending on the state of the lock, the block uses the following friction and dynamics models.

Condition Condition The friction model The dynamic model

or

Unblocked

, where , ,

and

Blocked

The following variables are used in the equations:

  •  — angular velocity of the wheel;

  •  — a force component independent of velocity;

  •  — the linear component of the velocity force;

  •  — the quadratic component of the velocity force;

  •  — length of relaxation of the tire;

  •  — moment of inertia;

  •  — rolling resistance torque;

  •  — applied torque on the axle;

  •  — braking torque;

  •  — total tire torque;

  •  — friction torque;

  •  — net input torque;

  •  — kinetic friction torque;

  •  — net output torque;

  •  — static friction torque;

  •  — applied coupling force;

  •  — the longitudinal force that occurs at the boundary of the tire’s contact with the road surface due to slippage;

  •  — effective grip radius;

  •  — the outer radius of the annular disk;

  •  — the inner radius of the annular disk;

  •  — the effective radius of the tire under load and at a given pressure;

  •  — the longitudinal speed of the axis;

  •  — normal vehicle power;

  •  — constant rolling resistance;

  •  — ambient temperature;

  •  — measured temperature for constant rolling resistance;

  •  — the power of parasitic losses;

  •  — coefficient of thermal correction;

  •  — an indicator of the degree of tire pressure;

  •  — an indicator of the degree of normal strength;

  •  — tire pressure;

  •  — coefficient of static friction;

  •  — coefficient of kinetic friction.

Longitudinal force

The block implements the longitudinal force as a function of wheel slip relative to the road surface using the following equations.

  • Critical slippage coefficient:

    where

    •  — coefficient of friction;

    •  — vertically directed force in the engagement field along the axis the coordinate system associated with the bus;

    •  — longitudinal stiffness.

  • The longitudinal force acting on the axis along the axis the coordinate system associated with the bus:

    where  — the state of slippage.

  • Coefficient of friction:

    where

    •  — coefficient of static friction;

    •  — coefficient of kinetic friction;

    •  — scale coefficient of friction.

  • Volumetric coefficient of slippage:

    where  — the state of the slip angle.

Transverse force

The block implements the lateral force as a function of the state of the wheel slip angle using the following equations.

  • Critical slip angle:

    where

    •  — coefficient of friction;

    •  — vertically directed force in the engagement field along the axis the coordinate system associated with the bus;

    •  — lateral stiffness per slip angle.

  • The transverse force acting on the axis along the axis the coordinate system associated with the bus:



    where

    •  — the state of the slip angle;

    •  — stiffness of the camber.

Vertical dynamics

The block implements vertical dynamics according to the following equations:





where

  •  — vertically directed force of the tire along the axis the coordinate system associated with the bus;

  •  — vertically directed force in the engagement field along the axis the coordinate system associated with the bus;

  •  — vertical deviation of the sidewall along the axis the coordinate system associated with the bus;

  •  — vertical stiffness of the sidewall;

  •  — vertical damping of the sidewall;

  •  — displacement of the road surface along the axis the coordinate system associated with the bus;

  •  — deflection of the tire along the axis the coordinate system associated with the bus.

Tipping, leveling, and scaling

Below are brief descriptions of the implementation of flipping, alignment, and scaling.

The throwing moment

The tipping moment is not specified in the Phial model. This block implements the following equation, requiring a minimum number of parameters:

where

  •  — the tipping moment acting on the axis relative to the axis the coordinate system associated with the bus;

  •  — the transverse force acting on the axis along the axis the coordinate system associated with the bus;

  •  — effective radial distance from the engagement field to the wheel hub;

  •  — the angle of collapse.

The moment of alignment

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



where

  •  — the moment of alignment acting on the axis relative to the axis the coordinate system associated with the bus;

  •  — the angular velocity of the tire relative to the axis coordinate system associated with the tire (yaw rate);

  •  — linear yaw velocity resistance;

  •  — the state of the slip angle;

  •  — width of the tire;

  •  — coefficient of friction;

  •  — vertically directed force in the engagement field along the axis the coordinate system associated with the bus;

  •  — lateral stiffness per slip angle.

scale coefficient of friction

To change the coefficient of friction, use the ScaleFctr input port.

Tire and wheel coordinate systems

To calculate forces and moments, the unit uses the orientation of the coordinate systems associated with the tire and wheel along the upward axis. .

  • Axes of the bus coordinate system ( ) are fixed in the reference frame connected to the bus. The origin is located at the point of contact of the tire with the road.

  • Axes of the wheel coordinate system ( ) are fixed in the frame of reference associated with the wheel. The origin is in the center of the wheel.

fiala wheel 2dof en

Brakes

The unit implements a disc brake. The picture shows the side and front view of the disc brake.

longitudinal wheel disc brake 1 en

The disc brake converts the pressure in the brake cylinder into force and applies this force to the middle radius of the brake pad.

The unit uses the following equations to calculate the braking torque for the disc brake:



where

  •  — braking torque;

  •  — applied brake pressure;

  •  — the speed of rotation of the wheel;

  •  — the number of brake pads in the disc brake assembly;

  •  — coefficient of static friction between the disc block and the rotor;

  •  — coefficient of kinetic friction between the disc block and the rotor;

  •  — diameter of the hole of the brake actuator;

  •  — the average radius of application of the brake pad force to the brake rotor;

  •  — the outer radius of the brake pad;

  •  — the inner radius of the brake pad.

Ports

Entrance

# BrkPrs — brake pressure

+ scalar | vector N by 1

Details

Brake pressure, expressed in Pa.

The vector has the size on , where  — the number of wheels. If a scalar is specified, the block assumes that the number of wheels is one.

Типы данных

Float64
Support for complex numbers

None

# AxlTrq — the moment of rotation of the axis

+ scalar | vector N by 1

Details

The moment of rotation of the axis relative to the axis of rotation of the wheel, expressed in nm.

The vector has the size on , where  — the number of wheels. If a scalar is specified, the block assumes that the number of wheels is one.

Типы данных

Float64
Support for complex numbers

None

# Vx — longitudinal velocity

+ scalar | vector N by 1

Details

Longitudinal axis speed along the axis in the coordinate system associated with the bus, expressed in m/s.

The vector has the size on , where  — the number of wheels. If a scalar is specified, the block assumes that the number of wheels is one.

Типы данных

Float64
Support for complex numbers

None

# Vy — lateral velocity

+ scalar | vector N by 1

Details

Transverse speed of the axis along the axis in the coordinate system associated with the bus, expressed in m/s.

The vector has the size on , where  — the number of wheels. If a scalar is specified, the block assumes that the number of wheels is one.

Типы данных

Float64
Support for complex numbers

None

# Camber — camber angle

+ scalar | vector N by 1

Details

Camber angle or the angle of inclination expressed in rad.

The vector has the size on , where  — the number of wheels. If a scalar is specified, the block assumes that the number of wheels is one.

Типы данных

Float64
Support for complex numbers

None

# YawRate — angular velocity of the tire

+ scalar | vector N by 1

Details

Angular velocity of the tire relative to the axis The coordinate system of the tire (yaw rate), expressed in rad/s.

The vector has the size on , where  — the number of wheels. If a scalar is specified, the block assumes that the number of wheels is one.

Типы данных

Float64
Support for complex numbers

None

# Prs — tire pressure

+ scalar | vector N by 1

Details

Tire pressure expressed in Pa.

The vector has the size on , where  — the number of wheels. If a scalar is specified, the block assumes that the number of wheels is one.

Типы данных

Float64
Support for complex numbers

None

# Gnd — surface displacement

+ scalar | vector N by 1

Details

Displacement of the road surface along the axis the coordinate system of the tire, expressed in meters. A positive input value raises the wheel.

The vector has the size on , where  — the number of wheels. If a scalar is specified, the block assumes that the number of wheels is one.

Типы данных

Float64
Support for complex numbers

None

# Fext is the force applied to the tire

+ scalar | vector N by 1

Details

Power applied to the tire along the axis the coordinate system associated with the vehicle, expressed in H. A positive input value compresses the tire.

The vector has the size on , where  — the number of wheels. If a scalar is specified, the block assumes that the number of wheels is one.

Dependencies

To use this port, set the parameter Vertical Motion meaning None or Mapped stiffness and damping.

Типы данных

Float64
Support for complex numbers

None

# RadialDeflct — radial deflection of the tire

+ scalar | vector N by 1

Details

Radial deflection of the tire. This value is used directly when calculating the effective radius.

The vector is the number of wheels. on . If a scalar is specified, the block assumes that the number of wheels is one.

Dependencies

To use this port, set the parameter Vertical Motion meaning External deflection.

Типы данных

Float64
Support for complex numbers

None

# ScaleFctr — scale factor

+ scalar | vector N by 1

Details

A scale factor that takes into account the change in the coefficient of friction.

The vector has the size on , where  — the number of wheels. If a scalar is specified, the block assumes that the number of wheels is one.

Типы данных

Float64
Support for complex numbers

None

# Tamb — ambient temperature

+ scalar

Details

Ambient temperature in kelvin.

Ambient temperature — this is the temperature near the tire under operating conditions, expressed in kelvins. For example, the measured ambient temperature is the ambient temperature near the tire when the vehicle is on the road.

Activate the Tamb input port to enter the measured ambient temperature.

Dependencies

To use this port, set the parameter Rolling Resistance meaning ISO 28580 and in the parameter group Rolling Resistance check the box Input ambient temperature.

Типы данных

Float64
Support for complex numbers

None

Output

# Info — information signal

+ the tire

Details

A bus containing the results of the block calculation.

The signal Description Units of measurement

AxlTrq

The torque on the axis coordinate systems (SK) of the wheel

N⋅m

Omega

Angular velocity of the wheel relative to the axis SK wheels

glad/with

Fx

The longitudinal force acting on the vehicle along the axis SK tires

N

Fy

The lateral force acting on the vehicle along the axis SK tires

N

Fz

Vertical force acting on the vehicle along the axis SK tires

N

Mx

Tipping moment relative to the axis SK tires

N⋅m

My

The moment of rolling resistance relative to the axis SK tires

N⋅m

Mz

The leveling moment relative to the axis SK tires

N⋅m

Vx

The longitudinal speed of the vehicle along the axis SK tires

m/s

Vy

The lateral speed of the vehicle along the axis SK tires

m/s

Re

Effective load radius

m

Kappa

The coefficient of longitudinal slippage

—

Alpha

Coefficient of lateral slippage

glad

a

Half the length of the engagement field

m

b

Half the width of the engagement field

m

Gamma

Camber angle

glad

psidot

Angular velocity of the tire relative to the axis Tire slope (yaw rate)

glad/with

BrkTrq

Braking torque relative to the axle SC related to the vehicle

N⋅m

BrkPrs

Brake pressure

Pa

z

Vertical deviation of the axis along the axis SK tires

m

zdot

Vertical speed of the axis along the axis SK tires

m/s

Gnd

Displacement relative to the surface along the axis SC of the tire (positive input signal causes the wheel to rise)

m

GndFz

Vertical force acting on the sidewall of the tire along the axis SK tires

N

Prs

Tire pressure

Pa

WhlTrq

Wheel torque

N⋅m

RL

Load radius

m

RadialDeflct

Radial deflection of the tire

m
Типы данных

Float64
Support for complex numbers

None

# Omega — angular velocity of the wheel

+ scalar | vector N by 1

Details

Angular velocity of the wheel relative to the axis the coordinate system of the wheel, expressed in rad/sec.

The vector has the size on , where  — the number of wheels. If a scalar is specified, the block assumes that the number of wheels is one.

Типы данных

Float64
Support for complex numbers

None

# Fx is the longitudinal force acting on the axis

+ scalar | vector N by 1

Details

Longitudinal force acting on the axis along the axis the coordinate system of the tire, expressed in H. The positive force acts by moving the vehicle forward.

The vector has the size on , where  — the number of wheels. If a scalar is specified, the block assumes that the number of wheels is one.

Типы данных

Float64
Support for complex numbers

None

# Fy is the transverse force acting on the axis

+ scalar | vector N by 1

Details

Transverse force acting on the axis along the axis the coordinate system of the bus, expressed in N.

The vector has the size on , where  — the number of wheels. If a scalar is specified, the block assumes that the number of wheels is one.

Типы данных

Float64
Support for complex numbers

None

# Fz is the vertical force acting on the axis

+ scalar | vector N by 1

Details

Vertical force acting on the axis along the axis the coordinate system of the bus, expressed in N.

The vector has the size on , where  — the number of wheels. If a scalar is specified, the block assumes that the number of wheels is one.

Типы данных

Float64
Support for complex numbers

None

# Mx — tipping moment

+ scalar | vector N by 1

Details

Longitudinal moment acting on the axis relative to the axis The coordinate system of the bus, expressed in NM.

The vector has the size on , where  — the number of wheels. If a scalar is specified, the block assumes that the number of wheels is one.

Типы данных

Float64
Support for complex numbers

None

# My — moment of rolling resistance

+ scalar | vector N by 1

Details

Transverse moment acting on the axis relative to the axis The coordinate system of the bus, expressed in NM.

The vector has the size on , where  — the number of wheels. If a scalar is specified, the block assumes that the number of wheels is one.

Типы данных

Float64
Support for complex numbers

None

# Mz — equalizing moment

+ scalar | vector N by 1

Details

Vertical moment acting on the axis relative to the axis The coordinate system of the bus, expressed in NM.

The vector has the size on , where  — the number of wheels. If a scalar is specified, the block assumes that the number of wheels is one.

Типы данных

Float64
Support for complex numbers

None

Parameters

TIre Options

# Rolling Resistance — moment of rolling resistance
None | Pressure and velocity | ISO 28580 | Magic Formula

Details

To calculate the rolling resistance moment, select one of the following values:

  • None — rolling resistance is not taken into account.

  • Pressure and velocity — the method defined in [2]. Rolling resistance depends on tire pressure, normal force, and speed.

  • ISO 28580 — the method defined in [3].

  • Magic Formula — the equations of the empirical formula under the number 4.E70 in [4]. «Magical» The formula is an empirical equation based on approximation coefficients.

Values

None | Pressure and velocity | ISO 28580 | Magic Formula
Default value

Pressure and velocity
Program usage name

rolling_dropdown
Tunable

No
Evaluatable

Yes

# Vertical Motion — vertical motion calculation method
None | Mapped stiffness and damping | External deflection

Details

To calculate vertical movement, select one of the following values:

  • None — the unit transmits the applied chassis forces directly to the rolling resistance and longitudinal force calculations.

  • Mapped stiffness and damping — vertical movement depends on the stiffness and damping of the wheel. Stiffness is a function of tire sidewall displacement and pressure, and damping is a function of tire sidewall velocity and pressure.

  • External deflection — The unit uses the specified sidewall deflection directly to calculate the effective radius.

Values

None | Mapped stiffness and damping | External deflection
Default value

None
Program usage name

vertical_dropdown
Tunable

No
Evaluatable

Yes

Longitudinal and Lateral

# Longitudinal stiffness Ckappa, N — longitudinal stiffness

Details

Longitudinal stiffness , defined as a scalar or vector on expressed in H. If a scalar is specified, the block uses this value for all wheels. If a vector is specified, the remaining longitudinal and transverse parameters must also be set as vectors.

 — the number of wheels; it must match the dimensions of the input signals.

Default value

1.0e4
Program usage name

Ckappa
Tunable

No
Evaluatable

Yes

# Lateral stiffness per slip angle Calpha, N/rad — transverse stiffness

Details

Transverse stiffness per slip angle, set as a scalar or vector on expressed in N/rad. If a scalar is specified, the block uses this value for all wheels. If a vector is specified, the remaining longitudinal and transverse parameters must also be set as vectors.

 — the number of wheels; it must match the dimensions of the input signals.

Default value

1.0e4
Program usage name

Calpha
Tunable

No
Evaluatable

Yes

# Camber stiffness Cgamma, N/rad — camber stiffness

Details

Camber stiffness , defined as a scalar or vector on expressed in N/rad. If a scalar is specified, the block uses this value for all wheels. If a vector is specified, the remaining longitudinal and transverse parameters must also be set as vectors.

 — the number of wheels; it must match the dimensions of the input signals.

Default value

1.0e3
Program usage name

Cgamma
Tunable

No
Evaluatable

Yes

# Kinematic friction muMin — kinetic friction

Details

Coefficient of kinetic friction , defined as a dimensionless scalar or vector on . If a scalar is specified, the block uses this value for all wheels. If a vector is specified, the remaining longitudinal and transverse parameters must also be set as vectors.

 — the number of wheels; it must match the dimensions of the input signals.

Default value

0.8
Program usage name

muMin
Tunable

No
Evaluatable

Yes

# Static friction muMax — static friction

Details

Coefficient of static friction , defined as a dimensionless scalar or vector on . If a scalar is specified, the block uses this value for all wheels. If a vector is specified, the remaining longitudinal and transverse parameters must also be set as vectors.

 — the number of wheels; it must match the dimensions of the input signals.

Default value

0.9
Program usage name

muMax
Tunable

No
Evaluatable

Yes

# Longitudinal relaxation length Lrelx, m — the longitudinal length of relaxation

Details

The longitudinal length of relaxation , defined as a scalar or vector on expressed in meters. If a scalar is specified, the block uses this value for all wheels. If a vector is specified, the remaining longitudinal and transverse parameters must also be set as vectors.

 — the number of wheels; it must match the dimensions of the input signals.

Default value

0.1
Program usage name

Lrelx
Tunable

No
Evaluatable

Yes

# Lateral relaxation length Lrely, m/rad — transverse length of relaxation

Details

Transverse length of relaxation , specified as a scalar or vector on expressed in m/rad. If a scalar is specified, the block uses this value for all wheels. If a vector is specified, the remaining longitudinal and transverse parameters must also be set as vectors.

 — the number of wheels; it must match the dimensions of the input signals.

Default value

0.1
Program usage name

Lrely
Tunable

No
Evaluatable

Yes

Rolling Resistance

# Velocity independent force coefficient aMy — coefficient of force independent of velocity

Details

Ratio force independent of velocity, dimensionless.

Dependencies

To use this parameter, set for the parameter Rolling Resistance meaning Pressure and velocity.

Default value

0.0008
Program usage name

aMy
Tunable

No
Evaluatable

Yes

# Linear velocity force component bMy, s/m — the linear component of the force of velocity

Details

The linear component of the force of velocity expressed in s/m .

Dependencies

To use this parameter, set for the parameter Rolling Resistance meaning Pressure and velocity.

Default value

0.001
Program usage name

bMy
Tunable

No
Evaluatable

Yes

# Quadratic velocity force component cMy, s^2/m^2 — the quadratic component of the force of velocity

Details

The quadratic component of the force of velocity , in c2/m2.

Dependencies

To use this parameter, set for the parameter Rolling Resistance meaning Pressure and velocity.

Default value

0.00016
Program usage name

cMy
Tunable

No
Evaluatable

Yes

# Tire pressure exponent alphaMy — the indicator of the degree of tire pressure

Details

The indicator of the degree of tire pressure , dimensionless.

Dependencies

To use this parameter, set for the parameter Rolling Resistance meaning Pressure and velocity.

Default value

-0.003
Program usage name

alphaMy
Tunable

No
Evaluatable

Yes

# Normal force exponent betaMy — an indicator of the degree of normal strength

Details

An indicator of the degree of normal strength , dimensionless.

Dependencies

To use this parameter, set for the parameter Rolling Resistance meaning Pressure and velocity.

Default value

0.97
Program usage name

betaMy
Tunable

No
Evaluatable

Yes

# Parasitic losses force Fpl, N — parasitic power losses

Details

Parasitic power losses expressed in N.

Dependencies

To use this parameter, set for the parameter Rolling Resistance meaning ISO 28580.

Default value

10.0
Program usage name

Fpl
Tunable

No
Evaluatable

Yes

# Rolling resistance constant Cr, N/kN — coefficient of rolling resistance

Details

Rolling resistance constant expressed in N/kN. In the ISO 28580 standard, the unit of measurement of rolling resistance is defined as one newton of traction resistance for each kilonewton of normal load.

Dependencies

To use this parameter, set for the parameter Rolling Resistance meaning ISO 28580.

Default value

0.001
Program usage name

Cr
Tunable

No
Evaluatable

Yes

# Thermal correction factor Kt, 1/degC — coefficient of thermal correction

Details

Coefficient of thermal correction expressed in 1/degree (on the Celsius scale).

Dependencies

To use this parameter, set for the parameter Rolling Resistance meaning ISO 28580.

Default value

0.008
Program usage name

Kt
Tunable

No
Evaluatable

Yes

# Measured temperature Tmeas, K — Temperature during testing

Details

The measured ambient temperature near the tire during testing, expressed in kelvins.

Dependencies

To use this parameter, set for the parameter Rolling Resistance meaning ISO 28580.

Default value

298.15
Program usage name

Tmeas
Tunable

No
Evaluatable

Yes

# Ambient temperature Tamb, K — Operating temperature

Details

The measured ambient temperature near the tire under operating conditions, expressed in kelvins. For example, the measured ambient temperature is the ambient temperature near the tire when the vehicle is on the road.

Dependencies

To use this parameter, set for the parameter Rolling Resistance meaning ISO 28580.

Default value

298.15
Program usage name

Tamb
Tunable

No
Evaluatable

Yes

# Input ambient temperature — ambient temperature input option

Details

Select this option to activate the Tamb input port to set the measured ambient temperature.

The measured ambient temperature — this is the temperature near the tire under operating conditions, expressed in kelvins. For example, the measured ambient temperature is the ambient temperature near the tire when the vehicle is on the road.

Dependencies

To use this parameter, set for the parameter Rolling Resistance meaning ISO 28580.

Default value

false (switched off)
Program usage name

Tamb_checkbox
Tunable

No
Evaluatable

Yes

# Nominal inflation pressure NOMPRES, Pa — pressure

Details

Nominal pressure, expressed in Pa.

Dependencies

To use this parameter, set for the parameter Rolling Resistance meaning Magic Formula.

Default value

220000.0
Program usage name

NOMPRES
Tunable

No
Evaluatable

Yes

# Rolling resistance torque coefficient QSY1 — torque ratio

Details

Rolling resistance torque coefficient, dimensionless.

Dependencies

To use this parameter, set for the parameter Rolling Resistance meaning Magic Formula.

Default value

0.007
Program usage name

QSY1
Tunable

No
Evaluatable

Yes

# Longitudinal force rolling resistance coefficient QSY2 — coefficient of force resistance

Details

Coefficient of rolling resistance of longitudinal force, dimensionless.

Dependencies

To use this parameter, set for the parameter Rolling Resistance meaning Magic Formula.

Default value

0.0
Program usage name

QSY2
Tunable

No
Evaluatable

Yes

# Linear rotational speed rolling resistance coefficient QSY3 — linear velocity coefficient

Details

Coefficient of rolling resistance of linear rotation speed, dimensionless.

Dependencies

To use this parameter, set for the parameter Rolling Resistance meaning Magic Formula.

Default value

0.0015
Program usage name

QSY3
Tunable

No
Evaluatable

Yes

# Quartic rotational speed rolling resistance coefficient QSY4 — the coefficient of the fourth degree of speed

Details

Coefficient of rolling resistance of the fourth degree of rotation speed, dimensionless.

Dependencies

To use this parameter, set for the parameter Rolling Resistance meaning Magic Formula.

Default value

8.5e-5
Program usage name

QSY4
Tunable

No
Evaluatable

Yes

# Camber squared rolling resistance torque QSY5, 1/rad^2 — the moment of resistance to collapse

Details

The square of the rolling resistance moment of the camber, expressed in 1/rad ^2 ^.

Dependencies

To use this parameter, set for the parameter Rolling Resistance meaning Magic Formula.

Default value

0.0
Program usage name

QSY5
Tunable

No
Evaluatable

Yes

# Load based camber squared rolling resistance torque QSY6, 1/rad^2 — moment of load resistance

Details

The square of the rolling resistance moment of the camber, taking into account the load, expressed in 1/rad ^2 ^.

Dependencies

To use this parameter, set for the parameter Rolling Resistance meaning Magic Formula.

Default value

0.0
Program usage name

QSY6
Tunable

No
Evaluatable

Yes

# Normal load rolling resistance coefficient QSY7 — the coefficient of normal resistance

Details

Coefficient of rolling resistance of normal load, dimensionless.

Dependencies

To use this parameter, set for the parameter Rolling Resistance meaning Magic Formula.

Default value

0.9
Program usage name

QSY7
Tunable

No
Evaluatable

Yes

# Pressure load rolling resistance coefficient QSY8 — pressure resistance coefficient

Details

Coefficient of pressure rolling resistance, dimensionless.

Dependencies

To use this parameter, set for the parameter Rolling Resistance meaning Magic Formula.

Default value

-0.4
Program usage name

QSY8
Tunable

No
Evaluatable

Yes

# Nominal normal force FNOMIN, N — power

Details

Nominal design load on the wheel along the axis the coordinate system associated with the wheel, expressed in H.

Dependencies

To use this parameter, set for the parameter Vertical Motion meaning Mapped stiffness and damping and for the parameter Rolling Resistance meaning Magic Formula.

Default value

4000.0
Program usage name

FNOMIN
Tunable

No
Evaluatable

Yes

# Rolling resistance scaling factor lam_My — scale factor

Details

Scale coefficient of rolling resistance, dimensionless.

Dependencies

To use this parameter, set for the parameter Rolling Resistance meaning Magic Formula.

Default value

1.0
Program usage name

lam_My
Tunable

No
Evaluatable

Yes

Aligning

# Tire nominal section width WIDTH, m — nominal width of the tire profile

Details

The nominal width of the tire profile, expressed in meters.

Default value

0.209045013245853
Program usage name

WIDTH
Tunable

No
Evaluatable

Yes

# Linear yaw rate resistance bMz, N*m*s/rad — linear yaw velocity resistance

Details

Linear yaw velocity resistance expressed in N⋅m⋅s/rad.

Default value

0.0
Program usage name

bMz
Tunable

No
Evaluatable

Yes

Brake

# Static friction coefficient mu_static — static friction

Details

The coefficient of static friction, defined as a dimensionless scalar or vector on . If a scalar is specified, the block uses this value for all wheels. If a vector is specified, the other brake parameters must also be set as vectors.

 — the number of wheels; it must match the dimensions of the input signals.

Default value

0.3
Program usage name

mu_static
Tunable

No
Evaluatable

Yes

# Kinetic friction coefficient mu_kinetic — kinetic friction

Details

Kinetic friction coefficient, defined as a dimensionless scalar or vector on . If a scalar is specified, the block uses this value for all wheels. If a vector is specified, the other brake parameters must also be set as vectors.

 — the number of wheels; it must match the dimensions of the input signals.

Default value

0.2
Program usage name

mu_kinetic
Tunable

No
Evaluatable

Yes

# Disc brake actuator bore disk_abore, m — the distance between the holes

Details

Diameter of the disc brake drive hole, specified as a scalar or vector on in meters. If a scalar is specified, the block uses this value for all wheels. If a vector is specified, the other brake parameters must also be set as vectors.

 — the number of wheels; it must match the dimensions of the input signals.

Default value

0.05
Program usage name

disk_abore
Tunable

No
Evaluatable

Yes

# Brake pad mean radius Rm, m — radius

Details

The average radius of the brake pad, set as a scalar or vector on in meters. If a scalar is specified, the block uses this value for all wheels. If a vector is specified, the other brake parameters must also be set as vectors.

 — the number of wheels; it must match the dimensions of the input signals.

Default value

0.177
Program usage name

Rm
Tunable

No
Evaluatable

Yes

# Number of brake pads, num_pads — number of pads

Details

The number of brake pads, specified as a dimensionless scalar or vector on . If a scalar is specified, the block uses this value for all wheels. If a vector is specified, the other brake parameters must also be set as vectors.

 — the number of wheels; it must match the dimensions of the input signals.

Default value

2.0
Program usage name

num_pads
Tunable

No
Evaluatable

Yes

Vertical

# Tire mass MASS, kg — tire weight

Details

The mass of the tire, given as a scalar or vector on in kg. If a scalar is specified, the block uses this value for all wheels. If a vector is specified, the other vertical parameters must also be set as vectors.

 — the number of wheels; it must match the dimensions of the input signals.

Dependencies

To use this parameter, set for the parameter Vertical Motion meaning Mapped stiffness and damping.

Default value

9.46491996974568
Program usage name

MASS
Tunable

No
Evaluatable

Yes

# Initial tire displacement zo, m — initial tire displacement

Details

The initial bus offset, specified as a scalar or vector on in meters. If a scalar is specified, the block uses this value for all wheels. If a vector is specified, the other vertical parameters must also be set as vectors.

 — the number of wheels; it must match the dimensions of the input signals.

Dependencies

To use this parameter, set for the parameter Vertical Motion meaning Mapped stiffness and damping.

Default value

0.0
Program usage name

zo
Tunable

No
Evaluatable

Yes

# Initial wheel vertical velocity (wheel fixed frame) zdoto, m/s — initial speed of the wheel

Details

The initial vertical speed of the wheel, set as a scalar or vector on in m/s. If a scalar is specified, the block uses this value for all wheels. If a vector is specified, the other vertical parameters must also be set as vectors.

 — the number of wheels; it must match the dimensions of the input signals.

Dependencies

To use this parameter, set for the parameter Vertical Motion meaning Mapped stiffness and damping.

Default value

0.0
Program usage name

zdoto
Tunable

No
Evaluatable

Yes

# Gravity GRAVITY, m/s^2 — acceleration of free fall

Details

Acceleration of gravity, in m/s 2.

Dependencies

To use this parameter, set for the parameter Vertical Motion meaning Mapped stiffness and damping.

Default value

-9.81
Program usage name

GRAVITY
Tunable

No
Evaluatable

Yes

# Vertical deflection breakpoints [zFz], m — inflection points

Details

The vector of the inflection points of the sidewall deflection corresponding to the force table, expressed in meters.

Dependencies

To use this parameter, set for the parameter Vertical Motion meaning Mapped stiffness and damping.

Default value

[0.0 0.01 0.1]
Program usage name

zFz
Tunable

No
Evaluatable

Yes

# Pressure breakpoints [pFz], Pa — inflection points

Details

A vector of pressure data points corresponding to the force table, expressed in Pa.

Dependencies

To use this parameter, set for the parameter Vertical Motion meaning Mapped stiffness and damping.

Default value

[10000.0 1.0e6]
Program usage name

pFz
Tunable

No
Evaluatable

Yes

# Force due to deflection [Fzz], N — power

Details

The force resulting from the deflection of the sidewall and the pressure along the axis the coordinate system associated with the wheel, expressed in H.

Dependencies

To use this parameter, set for the parameter Vertical Motion meaning Mapped stiffness and damping.

Default value

[0.0 1000.0 10000.0; 0.0 10000.0 100000.0]
Program usage name

Fzz
Tunable

No
Evaluatable

Yes

# Vertical velocity breakpoints [zdotFz], m/s — inflection points

Details

The vector of inflection points of the sidewall velocity corresponding to the force in the velocity table, expressed in m/s.

Dependencies

To use this parameter, set for the parameter Vertical Motion meaning Mapped stiffness and damping.

Default value

[-20.0 0.0 20.0]
Program usage name

zdotFz
Tunable

No
Evaluatable

Yes

# Force due to velocity [Fzzdot], N — power

Details

The force due to the velocity and pressure of the sidewall and the pressure along the axis the coordinate system associated with the wheel, expressed in H.

Dependencies

To use this parameter, set for the parameter Vertical Motion meaning Mapped stiffness and damping.

Default value

[500.0 0.0 -500.0; 250.0 0.0 -250.0]
Program usage name

Fzzdot
Tunable

No
Evaluatable

Yes

Wheel

# Tire unloaded radius UNLOADED_RADIUS, m — radius without load

Details

The radius of the tire without load, expressed in meters.

Default value

0.309384029954441
Program usage name

UNLOADED_RADIUS
Tunable

No
Evaluatable

Yes

# Initial wheel rotational velocity omegao, rad/s — initial angular velocity of the wheel

Details

The initial angular velocity of the wheel, given as a scalar or vector on in rad/s. If a scalar is specified, the block uses this value for all wheels. If a vector is specified, the rest of the rotation parameters must also be set as vectors.

 — the number of wheels; it must match the dimensions of the input signals.

Default value

0.0
Program usage name

omegao
Tunable

No
Evaluatable

Yes

# Tire rotational inertia (rolling axis) IYY, kg*m^2 — moment of inertia of the tire

Details

The moment of inertia of the tire (axis of rotation), set as a scalar or vector on in kg⋅m2. If a scalar is specified, the block uses this value for all wheels. If a vector is specified, the rest of the rotation parameters must also be set as vectors.

 — the number of wheels; it must match the dimensions of the input signals.

Default value

0.740633832792491
Program usage name

IYY
Tunable

No
Evaluatable

Yes

# Rotational damping br, N*m*s/rad — rotation damping

Details

Rotational damping, specified as a scalar or vector on In N⋅m⋅s/glad. If a scalar is specified, the block uses this value for all wheels. If a vector is specified, the rest of the rotation parameters must also be set as vectors.

 — the number of wheels; it must match the dimensions of the input signals.

Default value

0.001
Program usage name

br
Tunable

No
Evaluatable

Yes

Simulation setup

# Maximum normal force FZMAX, N — maximum normal force

Details

The maximum normal force expressed in N. Is used in all calculations of vertical force.

Default value

10000.0
Program usage name

FZMAX
Tunable

No
Evaluatable

Yes

# Minimum normal force FZMIN, N — minimum normal force

Details

The minimum normal force, expressed in N. Is used in all calculations of vertical force.

Default value

100.0
Program usage name

FZMIN
Tunable

No
Evaluatable

Yes

# Maximum pressure PRESMAX, Pa — maximum pressure

Details

The maximum pressure expressed in Pa.

Default value

1003118.65547859
Program usage name

PRESMAX
Tunable

No
Evaluatable

Yes

# Minimum pressure PRESMIN, Pa — minimum pressure

Details

Minimum pressure, expressed in Pa.

Default value

9982.11955979412
Program usage name

PRESMIN
Tunable

No
Evaluatable

Yes

# Max allowable slip ratio (absolute) KPUMAX — maximum allowable coefficient of slippage

Details

The maximum allowable coefficient of slippage in absolute value, dimensionless.

Default value

1.48764378595932
Program usage name

KPUMAX
Tunable

No
Evaluatable

Yes

# Minimum allowable slip ratio (absolute) KPUMIN — minimum allowable coefficient of slippage

Details

The minimum allowable coefficient of slippage in absolute value, dimensionless.

Default value

-1.48007456759542
Program usage name

KPUMIN
Tunable

No
Evaluatable

Yes

# Max allowable slip angle (absolute) ALPMAX, rad — maximum allowable slip angle

Details

The maximum allowable absolute slip angle, expressed in rad.

Default value

1.47424202250808
Program usage name

ALPMAX
Tunable

No
Evaluatable

Yes

# Minimum allowable slip angle (absolute) ALPMIN, rad — minimum allowable slip angle

Details

The minimum allowable absolute slip angle, expressed in rad.

Default value

-1.50806269049027
Program usage name

ALPMIN
Tunable

No
Evaluatable

Yes

# Max allowable camber angle (absolute) CAMMAX, rad — maximum allowable camber angle

Details

The maximum allowable angle of collapse in absolute terms, expressed in rad.

Default value

0.173142086627737
Program usage name

CAMMAX
Tunable

No
Evaluatable

Yes

# Minimum allowable camber angle (absolute) CAMMIN, rad — minimum allowable camber angle

Details

The minimum allowable angle of collapse in absolute terms, expressed in rad.

Default value

-0.173348165334087
Program usage name

CAMMIN
Tunable

No
Evaluatable

Yes

# TMIN — minimum ambient temperature

Details

Minimum ambient temperature expressed in kelvin.

Dependencies

To use this parameter, set for the parameter Rolling Resistance meaning ISO 28580.

Default value

0.0
Program usage name

TMIN
Tunable

No
Evaluatable

Yes

# TMAX — maximum ambient temperature

Details

Maximum ambient temperature expressed in kelvin.

Dependencies

To use this parameter, set for the parameter Rolling Resistance meaning ISO 28580.

Default value

400.0
Program usage name

TMAX
Tunable

No
Evaluatable

Yes

Literature

  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.