Longitudinal Wheel - Disc Brake
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Page in progress. |
Longitudinal disc wheel
the brake.
blockType: SubSystem
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Path in the library: |
Description
Block Longitudinal Wheel - Disc Brake implements the longitudinal behavior of an ideal disc brake wheel. The block allows you to set the method for calculating the longitudinal force and rolling resistance, as well as the type of brake. Use this unit when modeling the transmission and longitudinal motion of a vehicle, when low-frequency forces of interaction of the tire with the road and braking forces are required to determine acceleration, braking and rolling resistance of the wheel. For example, this unit can be used to determine the torque and power required for a given driving cycle or braking event. The unit is not suitable for applications requiring combined side sliding.
The block simulates the longitudinal force as a function of wheel slip relative to the road surface. To calculate the longitudinal force, set the parameter Longitudinal Force one of the following values:
-
Magic Formula constant value— an empirical formula with constant coefficients of stiffness, shape, peak and curvature. -
Magic Formula pure longitudinal slip— an empirical formula with load-dependent coefficients according to equations 4.E9–4.E18 from [2].
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 [1]. 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 [2]. «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.
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 moment arising 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 [1]. 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 [2]. «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 , , |
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and |
Blocked |
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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;
-
— tire relaxation length;
-
— 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.
Brakes
The unit implements a disc brake. The picture shows the side and front view of the disc brake.
The disc brake converts the pressure in the brake cylinder into force and applies this force to the average 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.
Longitudinal force
To simulate the longitudinal forces of the block Longitudinal Wheel - Disc Brake An empirical formula can be used. The model provides a stationary characteristic function of the bus , that is , the longitudinal force acting on the tire, depending on the vertical load and wheel slippage .
The following variables are used in the empirical formula model:
-
— angular velocity of the wheel;
-
— wheel radius;
-
— the longitudinal speed of the wheel hub;
-
— the longitudinal speed of the tire tread;
-
— wheel slip rate;
-
— wheel slip;
-
and — vertical load and nominal vertical tire load, respectively;
-
— the longitudinal force acting on the tire at the point of contact, as well as the characteristic function tires.
The constant value of the empirical formula
If for the parameter Longitudinal Force the value is set Magic Formula constant value The block implements an empirical formula in the form of a specific form of the characteristic function of a bus with four dimensionless coefficients: , , and . These coefficients represent stiffness, shape, peak, and curvature, respectively.:
The slope of the function by equal to .
The coefficients are based on empirical tire data. Typical sets of constant coefficients of the empirical formula for common road conditions are shown in the table below.
| Surface | B | C | D | E |
|---|---|---|---|---|
Dry asphalt |
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|
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Wet asphalt |
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Snow |
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|
Ice |
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empirical formula of pure longitudinal slip
If for the parameter Longitudinal Force the value is set Magic Formula pure longitudinal slip The block implements a more general empirical formula with dimensionless coefficients, which are functions of the tire load. The block implements the longitudinal force equations from Chapter 4 of the book [2], including equations 4.E9–4.E18:
where
Values and They represent displacements of slippage and longitudinal force as a function of force versus slippage, or horizontal and vertical displacements if the function is represented as a curve. Value — coefficient of friction, depending on the longitudinal load, — a small number introduced to prevent division by zero when approaching to zero.
Vertical dynamics
If there are no vertical degrees of freedom, that is, for the parameter Vertical Motion the value is set None The block transmits the applied chassis forces directly to the rolling resistance and longitudinal force calculations.
If for the parameter Vertical Motion the value is set 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.
where
-
— normal tire force along the axis in the coordinate system associated with the wheel;
-
— the normal force of the tire, due to the stiffness of the wheel, along in the coordinate system associated with the wheel;
-
— normal tire force due to wheel damping along the axle in the coordinate system associated with the wheel;
-
— tire pressure;
-
, — the displacement and speed of the tire, respectively, along the axis in the coordinate system associated with the wheel.
This block defines vertical motion using the following differential equation:
where
-
— acceleration of the tire along the axis in the coordinate system associated with the wheel;
-
— axis mass;
-
— the normal force of the suspension or vehicle along the axis in the coordinate system associated with the wheel;
-
— acceleration of free fall.
When the vertical degree of freedom is disabled, the input normal force from the vehicle is directly transferred to the calculations of the longitudinal force and rolling resistance.:
The block uses the coordinate system associated with the wheel to resolve vertical forces.
Power accounting
To account for the power, the unit implements the equations given in the table below.
| Bus signal | Description | The equations | ||
|---|---|---|---|---|
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Traction power transmitted from the axle |
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External torque transmitted by the axle to the wheel |
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||
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Vertical force transmitted to a wheel by a vehicle or suspension |
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||
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Loss of traction power |
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Rolling resistance power |
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Braking power |
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Viscosity damping losses during rolling |
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Vertical damping power |
|
||
|
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The rate of change of vertical kinetic energy |
|
|
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The rate of change of kinetic energy of rotation |
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The rate of change of the accumulated potential energy of the sidewall |
|
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The rate of change of gravitational potential energy |
|
||
The following variables are used in power accounting equations:
-
— angular velocity of the wheel;
-
— the linear component of the velocity force;
-
— occurs at the contact point of the tire with the road due to slippage;
-
— the force of tire slip in the engagement field;
-
— normal car power;
-
— normal tire force due to wheel damping;
-
— normal tire strength due to wheel stiffness;
-
— the moment of inertia of the wheel;
-
— braking torque;
-
— rolling resistance torque;
-
— the effective radius of the tire under load and at a given pressure;
-
— the torque on the axle applied to the wheel;
-
— the longitudinal speed of the axis;
-
, , — the displacement, speed and acceleration of the tire, respectively;
-
— the vertical speed of the vehicle along the axis in the coordinate system associated with the vehicle.
Ports
Entrance
BrkPrs —
brake pressure
+
scalar
Details
Brake pressure, expressed in Pa.
| Типы данных |
|
| Support for complex numbers |
None |
AxlTrq —
the moment of rotation of the axis
+
scalar
Details
The moment of rotation of the axis relative to the axis of rotation of the wheel, expressed in nm.
| Типы данных |
|
| Support for complex numbers |
None |
Vx —
speed
+
scalar
Details
The longitudinal speed of the axis along the axis in the coordinate system associated with the vehicle, expressed in m/s.
| Типы данных |
|
| Support for complex numbers |
None |
Fz —
normal strength
+
scalar
Details
The absolute value of the normal force of the suspension or vehicle along the axis in the associated coordinate system, expressed in N.
| Типы данных |
|
| Support for complex numbers |
None |
Gnd —
surface displacement
+
scalar
Details
Surface displacement along the negative direction of the axis in the coordinate system associated with the wheel, expressed in meters.
Dependencies
To use this port, set the parameter Vertical Motion meaning Mapped stiffness and damping and in the parameter group Vertical check the box Input ground displacement.
| Типы данных |
|
| Support for complex numbers |
None |
lam_mux —
scale coefficient of friction
+
scalar
Details
Scale coefficient of longitudinal friction, dimensionless.
Dependencies
To use this port, check the box Input friction scale factor.
| Типы данных |
|
| Support for complex numbers |
None |
TirePrs —
tire pressure
+
scalar
Details
Tire pressure, expressed in Pa.
Dependencies
To use this port, install:
-
for the parameter Longitudinal Force meaning
Magic Formula pure longitudinal slip, or
-
for the parameter Vertical Motion meaning
Mapped stiffness and damping,
and in the parameter group Wheel Dynamics check the box Input tire pressure.
| Типы данных |
|
| 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 |
|
| 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 | ||
|---|---|---|---|---|
|
The torque on the axis associated coordinate system (SC) |
N⋅m |
||
|
Angular velocity of the wheel relative to the axis related UK |
glad/with |
||
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Angular acceleration of the wheel relative to the axis related UK |
rad/s2 |
||
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The longitudinal force acting on the vehicle along the axis related UK |
N |
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Vertical force acting on the vehicle along the axis related UK |
N |
||
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The normal force exerted on the tire due to wheel damping along the axle The SC associated with the wheel |
N |
||
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The normal force exerted on the tire due to the stiffness of the wheel along the axle The SC associated with the wheel |
N |
||
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The moment of rolling resistance relative to the axis related UK |
N⋅m |
||
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The moment of rolling resistance due to damping relative to the axis related UK |
N⋅m |
||
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The coefficient of slippage |
— |
||
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The longitudinal speed of the vehicle along the axis related UK |
m/s |
||
|
Effective radius of the wheel along the axis The SC associated with the wheel |
m |
||
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Braking torque relative to the axle related UK |
N⋅m |
||
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Brake pressure |
Pa |
||
|
Vertical deflection of the wheel along the axis The SC associated with the wheel |
m |
||
|
Vertical speed of the wheel along the axis The SC associated with the wheel |
m/s |
||
|
Vertical acceleration of the wheel along the axis The SC associated with the wheel |
m/s2 |
||
|
Displacement relative to the earth along the negative direction of the axis SK connected to the wheel (a positive input signal causes the wheel to lift) |
m |
||
|
The vertical force acting on the wheel relative to the ground along the negative direction of the axis The SC associated with the wheel |
N |
||
|
Tire pressure |
Pa |
||
|
Traction force ( taking into account relaxation effects); used to describe transients in vehicle movement |
N |
||
|
|
|
External torque transmitted by the axle to the wheel |
Tue |
|
Vertical force applied to the wheel by the vehicle or suspension |
Tue |
||
|
Loss of traction power |
Tue |
||
|
|
Rolling resistance power |
Tue |
|
|
Braking power |
Tue |
||
|
Rolling damping losses |
Tue |
||
|
Vertical damping capacity |
Tue |
||
|
The rate of change of vertical kinetic energy |
Tue |
||
|
|
The rate of change of rotational kinetic energy |
Tue |
|
|
The rate of change of the accumulated potential energy of the sidewall |
Tue |
||
|
The rate of change of gravitational potential energy |
Tue |
||
|
Traction force transmitted from the axle |
Tue |
||
| Типы данных |
|
| Support for complex numbers |
None |
# Fx —
the longitudinal force acting on the axis
+
scalar
Details
The longitudinal force acting on the axis along the axis the associated coordinate system, expressed in H. The positive force acts by moving the vehicle forward.
| Типы данных |
|
| Support for complex numbers |
None |
Omega —
angular velocity of the wheel
+
scalar
Details
Angular velocity of the wheel relative to the axis the associated coordinate system, expressed in rad/sec.
| Типы данных |
|
| Support for complex numbers |
None |
z —
vertical deflection of the wheel
+
scalar
Details
Vertical deflection of the wheel along the axis the coordinate system associated with the wheel, expressed in meters.
Dependencies
To use this port, set the parameter Vertical Motion meaning Mapped stiffness and damping.
| Типы данных |
|
| Support for complex numbers |
None |
zdot —
vertical wheel speed
+ `scalar`
Details
Vertical speed of the wheel along the axis the coordinate system associated with the wheel, expressed in m/s.
Dependencies
To use this port, set the parameter Vertical Motion meaning Mapped stiffness and damping.
| Типы данных |
|
| Support for complex numbers |
None |
Parameters
Tire Options
#
Longitudinal Force —
the method of calculating the longitudinal force
Magic Formula constant value | Magic Formula pure longitudinal slip
Details
The block simulates the longitudinal force as a function of wheel slip relative to the road surface. To calculate the longitudinal force, select one of the following values:
-
Magic Formula constant value— the block uses an empirical formula with constant coefficients of stiffness, shape, peak and curvature. -
Magic Formula pure longitudinal slip— the block uses an empirical formula with load–dependent coefficients according to equations 4.E9-4.E18 from [2].
| Values |
|
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
#
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 [1]. 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 [2]. «Magical» The formula is an empirical equation based on approximation coefficients.
| Values |
|
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
#
Vertical Motion —
vertical motion calculation method
None | Mapped stiffness and damping
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.
| Values |
|
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
# Longitudinal scaling factor lam_x — scale coefficient of friction
Details
Scale coefficient of longitudinal friction, dimensionless.
Dependencies
To use this option, uncheck the box. Input friction scale factor.
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
# Input friction scale factor — activating the lam_mux port
Details
Check the box Input friction scale factor to activate the input port lam_mux for the scale coefficient of longitudinal friction and disable the parameter Longitudinal scaling factor lam_x.
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
Wheel Dynamics
# Axle viscous damping coefficient br, N*m*s/rad — dampening
Details
Ratio viscous damping of the axis, expressed in nm/rad.
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
# Wheel inertia Iyy, Kg*m^2 — inertia
Details
The moment of inertia of the wheel, expressed in kg⋅m2.
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
# Wheel initial angular velocity omegao, rad/s — wheel speed
Details
The initial angular velocity of the wheel along the axis the associated coordinate system, expressed in rad/sec.
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
# Relaxation length Lrel, m — Relaxation length
Details
The relaxation length of the wheel, expressed in meters.
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
# Loaded radius Re, m — radius under load
Details
Wheel radius under load, expressed in meters.
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
# Unloaded radius UNLOADED_RADIUS, m — radius without load
Details
The radius of the wheel without load, expressed in meters.
Dependencies
To use this parameter, set for the parameter Rolling Resistance meaning Pressure and velocity or Magic Formula.
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
# Nominal longitudinal speed LONGVL, m/s — speed
Details
Nominal longitudinal speed along the axis the associated coordinate system, expressed in m/s.
Dependencies
To use this parameter, set for the parameter Longitudinal Force meaning Magic Formula pure longitudinal slip.
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
# Nominal camber angle gamma, rad — collapse
Details
Nominal camber angle, expressed in rad.
Dependencies
To use this parameter, set:
-
for the parameter Longitudinal Force meaning
Magic Formula pure longitudinal slip, or -
for the parameter Rolling Resistance meaning
Magic Formula.
| Default value |
|
| Program usage name |
|
| 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 Longitudinal Force meaning
Magic Formula pure longitudinal slip, or -
for the parameter Rolling Resistance meaning
Magic Formula.
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
# Pressure press, Pa — pressure
Details
Tire pressure, expressed in Pa.
Dependencies
To use this parameter, set:
-
for the parameter Longitudinal Force meaning
Magic Formula pure longitudinal slip, or -
for the parameter Vertical Motion meaning
Mapped stiffness and damping,
and in the parameter group Wheel Dynamics uncheck the box Input tire pressure.
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
# Input tire pressure — activating the TirePrs port
Details
Check the box Input tire pressure to activate the TirePrs input port for setting tire pressure and disable the parameter Pressure press, Pa.
Dependencies
To use this parameter, set:
-
for the parameter Longitudinal Force meaning
Magic Formula pure longitudinal slip, or -
for the parameter Vertical Motion meaning
Mapped stiffness and damping.
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
Longitudinal
# Pure longitudinal peak factor Dx — ratio
Details
Coefficient of the net longitudinal peak, dimensionless.
The coefficients are based on empirical tire data and correspond to typical sets of constant coefficients of the empirical formula for common road conditions.
| Surface | B | C | D | E |
|---|---|---|---|---|
Dry asphalt |
|
|
|
|
Wet asphalt |
|
|
|
|
Snow |
|
|
|
|
Ice |
|
|
|
|
Dependencies
To use this parameter, set for the parameter Longitudinal Force meaning Magic Formula constant value.
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
# Pure longitudinal shape factor Cx — ratio
Details
Coefficient of pure longitudinal shape, dimensionless.
The coefficients are based on empirical tire data and correspond to typical sets of constant coefficients of the empirical formula for common road conditions.
| Surface | B | C | D | E |
|---|---|---|---|---|
Dry asphalt |
|
|
|
|
Wet asphalt |
|
|
|
|
Snow |
|
|
|
|
Ice |
|
|
|
|
Dependencies
To use this parameter, set for the parameter Longitudinal Force meaning Magic Formula constant value.
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
# Pure longitudinal shape factor Bx — ratio
Details
Coefficient of net longitudinal stiffness, dimensionless.
The coefficients are based on empirical tire data and correspond to typical sets of constant coefficients of the empirical formula for common road conditions.
| Surface | B | C | D | E |
|---|---|---|---|---|
Dry asphalt |
|
|
|
|
Wet asphalt |
|
|
|
|
Snow |
|
|
|
|
Ice |
|
|
|
|
Dependencies
To use this parameter, set for the parameter Longitudinal Force meaning Magic Formula constant value.
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
# Pure longitudinal shape factor Ex — ratio
Details
Coefficient of net longitudinal curvature, dimensionless.
The coefficients are based on empirical tire data and correspond to typical sets of constant coefficients of the empirical formula for common road conditions.
| Surface | B | C | D | E |
|---|---|---|---|---|
Dry asphalt |
|
|
|
|
Wet asphalt |
|
|
|
|
Snow |
|
|
|
|
Ice |
|
|
|
|
Dependencies
To use this parameter, set for the parameter Longitudinal Force meaning Magic Formula constant value.
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
# Cfx shape factor PCX1 — ratio
Details
Cfx shape coefficient, dimensionless.
Dependencies
To use this parameter, set for the parameter Longitudinal Force meaning Magic Formula pure longitudinal slip.
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
# Longitudinal friction at nominal normal load PDX1 — ratio
Details
Coefficient of longitudinal friction at nominal normal load, dimensionless.
Dependencies
To use this parameter, set for the parameter Longitudinal Force meaning Magic Formula pure longitudinal slip.
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
# Frictional variation with load PDX2 — ratio
Details
The change in the coefficient of friction depending on the load is a dimensionless value.
Dependencies
To use this parameter, set for the parameter Longitudinal Force meaning Magic Formula pure longitudinal slip.
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
# Frictional variation with camber PDX3, 1/rad^2 — ratio
Details
The change in the coefficient of friction depending on the camber of the wheels, 1/ rad ^ 2 ^.
Dependencies
To use this parameter, set for the parameter Longitudinal Force meaning Magic Formula pure longitudinal slip.
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
# Longitudinal curvature at nominal normal load PEX1 — ratio
Details
Coefficient of longitudinal curvature at nominal normal load, dimensionless.
Dependencies
To use this parameter, set for the parameter Longitudinal Force meaning Magic Formula pure longitudinal slip.
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
# Variation of curvature factor with load PEX2 — ratio
Details
The change in the coefficient of curvature depending on the load is a dimensionless value.
Dependencies
To use this parameter, set for the parameter Longitudinal Force meaning Magic Formula pure longitudinal slip.
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
# Variation of curvature factor with square of load PEX3 — ratio
Details
The change in the coefficient of curvature depending on the square of the load, a dimensionless value.
Dependencies
To use this parameter, set for the parameter Longitudinal Force meaning Magic Formula pure longitudinal slip.
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
# Longitudinal curvature factor with slip PEX4 — ratio
Details
Coefficient of longitudinal curvature with slip, dimensionless.
Dependencies
To use this parameter, set for the parameter Longitudinal Force meaning Magic Formula pure longitudinal slip.
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
# Longitudinal slip stiffness at nominal normal load PKX1 — ratio
Details
Coefficient of longitudinal slip stiffness at nominal normal load, dimensionless.
Dependencies
To use this parameter, set for the parameter Longitudinal Force meaning Magic Formula pure longitudinal slip.
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
# Variation of slip stiffness with load PKX2 — ratio
Details
The change in the coefficient of slip stiffness depending on the load is a dimensionless value.
Dependencies
To use this parameter, set for the parameter Longitudinal Force meaning Magic Formula pure longitudinal slip.
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
# Slip stiffness exponent factor PKX3 — ratio
Details
An indicator of the degree of slip stiffness, dimensionless.
Dependencies
To use this parameter, set for the parameter Longitudinal Force meaning Magic Formula pure longitudinal slip.
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
# Horizontal shift in slip ratio at nominal normal load PHX1 — ratio
Details
Horizontal displacement of the slip coefficient at nominal normal load, dimensionless value.
Dependencies
To use this parameter, set for the parameter Longitudinal Force meaning Magic Formula pure longitudinal slip.
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
# Variation of horizontal slip ratio with load PHX2 — ratio
Details
The change in the coefficient of horizontal slippage depending on the load is a dimensionless value.
Dependencies
To use this parameter, set for the parameter Longitudinal Force meaning Magic Formula pure longitudinal slip.
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
# Vertical shift in load at nominal normal load PVX1 — ratio
Details
Vertical displacement of the load at nominal normal load, dimensionless value.
Dependencies
To use this parameter, set for the parameter Longitudinal Force meaning Magic Formula pure longitudinal slip.
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
# Variation of vertical shift with load PVX2 — ratio
Details
The change in vertical displacement depending on the load is a dimensionless value.
Dependencies
To use this parameter, set for the parameter Longitudinal Force meaning Magic Formula pure longitudinal slip.
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
# Linear variation of longitudinal slip stiffness with tire pressure PPX1 — ratio
Details
Linear change in the coefficient of longitudinal slip stiffness as a function of tire pressure, dimensionless value.
Dependencies
To use this parameter, set for the parameter Longitudinal Force meaning Magic Formula pure longitudinal slip.
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
# Quadratic variation of longitudinal slip stiffness with tire pressure PPX2 — ratio
Details
The quadratic change in the coefficient of longitudinal slip stiffness as a function of tire pressure, a dimensionless value.
Dependencies
To use this parameter, set for the parameter Longitudinal Force meaning Magic Formula pure longitudinal slip.
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
# Linear variation of peak longitudinal friction with tire pressure PPX3 — ratio
Details
Linear change in the coefficient of peak longitudinal friction as a function of tire pressure, dimensionless value.
Dependencies
To use this parameter, set for the parameter Longitudinal Force meaning Magic Formula pure longitudinal slip.
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
# Quadratic variation of peak longitudinal friction with tire pressure PPX4 — ratio
Details
The quadratic change in the coefficient of peak longitudinal friction as a function of tire pressure, a dimensionless value.
Dependencies
To use this parameter, set for the parameter Longitudinal Force meaning Magic Formula pure longitudinal slip.
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
# Slip speed decay function scaling factor lam_muV — ratio
Details
Scale factor of the slip rate attenuation function, dimensionless.
Dependencies
To use this parameter, set for the parameter Longitudinal Force meaning Magic Formula pure longitudinal slip.
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
# Brake slip stiffness scaling factor lam_Kxkappa — ratio
Details
Scale coefficient of brake slip stiffness, dimensionless.
Dependencies
To use this parameter, set for the parameter Longitudinal Force meaning Magic Formula pure longitudinal slip.
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
# Longitudinal shape scaling factor lam_Cx — ratio
Details
The scale factor of the longitudinal shape, dimensionless.
Dependencies
To use this parameter, set for the parameter Longitudinal Force meaning Magic Formula pure longitudinal slip.
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
# Longitudinal curvature scaling factor lam_Ex — ratio
Details
Scale factor of longitudinal curvature, dimensionless.
Dependencies
To use this parameter, set for the parameter Longitudinal Force meaning Magic Formula pure longitudinal slip.
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
# Longitudinal horizontal shift scaling factor lam_Hx — ratio
Details
The scale factor of the longitudinal horizontal displacement, dimensionless.
Dependencies
To use this parameter, set for the parameter Longitudinal Force meaning Magic Formula pure longitudinal slip.
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
# Longitudinal vertical shift scaling factor lam_Vx — ratio
Details
The scale factor of the longitudinal vertical displacement, dimensionless.
Dependencies
To use this parameter, set for the parameter Longitudinal Force meaning Magic Formula pure longitudinal slip.
| Default value |
|
| Program usage name |
|
| 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 |
|
| Program usage name |
|
| 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 |
|
| Program usage name |
|
| 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 expressed in c2/m2.
Dependencies
To use this parameter, set for the parameter Rolling Resistance meaning Pressure and velocity.
| Default value |
|
| Program usage name |
|
| 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 |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
# Normal force exponent betaMy — the indicator of normal strength
Details
The indicator of normal strength , dimensionless.
Dependencies
To use this parameter, set for the parameter Rolling Resistance meaning Pressure and velocity.
| Default value |
|
| Program usage name |
|
| 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 |
|
| Program usage name |
|
| 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 |
|
| Program usage name |
|
| 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 |
|
| Program usage name |
|
| 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 |
|
| Program usage name |
|
| 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 |
|
| Program usage name |
|
| 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 |
|
| Program usage name |
|
| 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 |
|
| Program usage name |
|
| 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 |
|
| Program usage name |
|
| 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 |
|
| Program usage name |
|
| 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 |
|
| Program usage name |
|
| 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 |
|
| Program usage name |
|
| 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 |
|
| Program usage name |
|
| 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 |
|
| Program usage name |
|
| 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 |
|
| Program usage name |
|
| 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 |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
Brake
# Static friction coefficient mu_static — static friction
Details
The coefficient of static friction, defined as a dimensionless scalar.
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
# Kinetic friction coefficient mu_kinetic — kinetic friction
Details
The coefficient of kinetic friction, defined as a dimensionless scalar.
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
# Disc brake actuator bore disk_abore, m — the distance between the holes
Details
The diameter of the disc brake drive hole, set as a scalar in meters.
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
# Brake pad mean radius Rm, m — radius
Details
The average radius of the brake pad, set as a scalar in meters.
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
# Number of brake pads num_pads — number of pads
Details
The number of brake pads, set as a dimensionless scalar.
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
Vertical
# 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 install:
-
for the parameter Longitudinal Force meaning
Magic Formula pure longitudinal slip, or -
for the parameter Rolling Resistance meaning
Magic Formula.
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
# Nominal rated load scaling factor lam_Fzo — ratio
Details
Scale factor of the nominal design load, dimensionless. It is used to scale the normal load in specific operating conditions.
Dependencies
To use this parameter, set for the parameter Vertical Motion meaning Mapped stiffness and damping and for the parameter Longitudinal Force meaning Magic Formula pure longitudinal slip.
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
# Wheel and unsprung mass m, kg — weight
Details
Wheel weight and unsprung weight, expressed in kg. It is used in calculations of vertical motion.
Dependencies
To use this parameter, set for the parameter Vertical Motion meaning Mapped stiffness and damping.
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
# Initial deflection zo, m — deviation
Details
The initial displacement of the axis along the axis the coordinate system associated with the wheel, expressed in meters.
Dependencies
To use this parameter, set for the parameter Vertical Motion meaning Mapped stiffness and damping.
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
# Initial velocity zdoto, m/s — speed
Details
The initial velocity of the axis along the axis the coordinate system associated with the wheel, expressed in m/s.
Dependencies
To use this parameter, set for the parameter Vertical Motion meaning Mapped stiffness and damping.
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
# Gravitational acceleration g, m/s^2 — acceleration of free fall
Details
Acceleration of gravity, expressed in m/s 2.
Dependencies
To use this parameter, set for the parameter Vertical Motion meaning Mapped stiffness and damping.
| Default value |
|
| Program usage name |
|
| 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 |
|
| Program usage name |
|
| 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 |
|
| Program usage name |
|
| 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 |
|
| Program usage name |
|
| 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 |
|
| Program usage name |
|
| 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 |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
# Ground displacement Gndz, m — offset
Details
Surface displacement along the negative direction of the axis in the coordinate system associated with the wheel, expressed in meters.
Dependencies
To use this parameter, set for the parameter Vertical Motion meaning Mapped stiffness and damping.
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
# Input ground displacement — activating the Gnd port
Details
Check the box Input ground displacement to activate the Gnd input port to set the surface offset and disable the parameter Ground displacement Gndz, m.
Dependencies
To use this parameter, set for the parameter Vertical Motion meaning Mapped stiffness and damping.
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
Simulation Setup
# 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 |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
# 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 |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
# Max allowable slip ratio (absolute) kappamax — ratio
Details
The maximum allowable absolute slip coefficient, dimensionless.
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
# Velocity tolerance used to handle low velocity situations VXLOW, m/s — allowance
Details
The speed tolerance used to handle low-speed situations, expressed in m/s.
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
Literature
-
Highway Tire Committee. Stepwise Coastdown Methodology for Measuring Tire Rolling Resistance. Standard J2452_199906. Warrendale, PA: SAE International, June 1999.
-
Pacejka, H. B. Tire and Vehicle Dynamics. 3rd ed. Oxford, United Kingdom: SAE and Butterworth-Heinemann, 2012.
-
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.