Tire (Friction Parameterized)

The tire model is based on friction parameterized in terms of static and kinetic coefficients.

blockType: Engee1DMechanical.Vehicles.Tires.FrictionParameterized

Path in the library:

/Physical Modeling/1D Mechanical/Tires & Vehicles/Tire (Friction Parameterized)

Description

Block Tire (Friction Parameterized) It is a tire with friction parameterized in terms of static and kinetic coefficients. Coefficient of static friction determines the torque at which the tire loses traction and begins to slip. Kinetic coefficient of friction determines the amount of torque that the tire transmits to the road surface after the start of slipping. The tire regains traction when its relative speed over the road surface falls below the set allowable clutch speed.

To improve the accuracy of the tire model, specify properties such as tire ductility, inertia, and rolling resistance. Note that these properties increase the complexity of the bus model and may slow down the simulation. Consider ignoring the deformation and inertia of the tire when simulating the model in real time or when preparing the model for semi-natural simulation (hardware-in-the-loop, HIL).

Wheel slip

If for the parameter Slip output type the value is set Relative, then the block outputs the relative sliding velocity as a dimensionless scalar to port S. The calculation of the relative sliding speed depends on whether the ductility simulation is enabled. If the checkbox is not checked Compliance, then the S port outputs the absolute sliding speed of the wheel in the form of rotation:

where

— the longitudinal speed of the wheel hub in the port H;
— rolling radius;
— the angular velocity of the wheel axis in port A.

If the check box is selected Compliance , then the S port outputs the absolute sliding velocity of the contact point in the form of rotation:

where — the rate of change of longitudinal deformation over time, and it is equivalent to the rotational speed of the spring and damper in the recorded simulation results.

If for the parameter Slip output type the value is set Absolute, then the block uses the block friction model Fundamental Friction Clutch.

Ports

Input

# N — normal force, N
scalar

Details

The input port is connected to the normal force acting on the tire, in H. The normal force is positive if it acts on the tire in a downward direction, pressing it against the road surface.

Data types	`Float64`
Complex numbers support	No

# M — vector of friction coefficients
vector

Details

Input port associated with dimensionless coefficients of static and kinetic friction and accordingly. Provide the coefficients of friction as a two-element vector given as [ ].

Dependencies

To use this port, set the parameter Friction model meaning Physical signal friction coefficients.

Data types	`Float64`
Complex numbers support	No

Conserving

# A — the axis
rotational mechanics

Details

A mechanical rotary port connected to an axis.

Program usage name

axle_flange

# H — hub
translational mechanics

Details

A mechanical translational port connected to the wheel hub.

Program usage name

hub_flange

Output

# S — sliding speed
scalar

Details

Depending on the parameter value Slip output type outputs either a dimensionless value of the relative sliding speed (Relative), or the absolute value of the sliding velocity in rad/s (Absolute).

Data types	`Float64`
Complex numbers support	No

Parameters

# Rolling radius — tyre radius without load
m | um | mm | cm | km | in | ft | yd | mi | nmi

Details

Distance between the road surface and the centre of the tyre.

Units	`m` \| `um` \| `mm` \| `cm` \| `km` \| `in` \| `ft` \| `yd` \| `mi` \| `nmi`
Default value	`0.3 m`
Program usage name	`tire_radius`
Evaluatable	Yes

# Slip output type — option to select absolute or relative slip value
Relative | Absolute

Details

Whether the block uses relative or absolute sliding friction parameterization.

Values	`Relative` \| `Absolute`
Default value	`Relative`
Program usage name	`slip_friction_parameterization`
Evaluatable	Yes

# Friction model — friction model
Fixed kinetic friction coefficient | Table lookup kinetic friction coefficient | Physical signal friction coefficients

Details

The friction model that the block uses during simulation:

Fixed kinetic friction coefficient - the block uses constant static and kinetic coefficient of friction, which are set in the parameters Static friction coefficient and Kinetic friction coefficient.
Table lookup kinetic friction coefficient - The friction can be set using an interpolation table. The block treats the static coefficient as a constant and the kinetic coefficient as a constant or function of tyre slip. Use this setting to simulate tyre dynamics under constant road surface conditions.
Physical signal friction coefficients - block uses the M port to obtain friction coefficients [ ]. Use this setting to simulate tyre dynamics under variable pavement conditions.

Values	`Fixed kinetic friction coefficient` \| `Table lookup kinetic friction coefficient` \| `Physical signal friction coefficients`
Default value	`Fixed kinetic friction coefficient`
Program usage name	`friction_model`
Evaluatable	Yes

# Static friction coefficient — static friction coefficient

Details

The ratio of the allowable longitudinal force to the allowable normal force before the tyre starts to slip, . The value of this parameter must be greater than Kinetic friction coefficient or greater than the highest value in the parameter Kinetic friction coefficient vector.

Dependencies

To use this parameter, set the parameters Friction model to the value of Fixed kinetic friction coefficient or Table lookup kinetic friction coefficient.

Default value	`0.9`
Program usage name	`static_friction_coefficient`
Evaluatable	Yes

# Kinetic friction coefficient — kinetic friction coefficient

Details

The ratio of the longitudinal force transmitted to the road to the allowable normal force during slip, . The coefficient must be greater than zero.

Dependencies

To use this parameter, set the parameter Friction model to the value of Fixed kinetic friction coefficient.

Default value	`0.7`
Program usage name	`kinetic_friction_coefficient`
Evaluatable	Yes

Details

Tyre slip values. The elements of this vector correspond to the elements of the vector Kinetic friction coefficient vector. If the parameter Tire slip vector contains only non-negative values, the block assumes that the slip friction function is symmetrical about the slip axis.

Dependencies

To use this parameter, set the Friction model parameters to the value of Table lookup kinetic friction coefficient.

Units	`rad/s` \| `deg/s` \| `rad/min` \| `deg/min` \| `rpm` \| `rps`
Default value	`[0.0, 0.02, 0.06, 0.15, 0.6, 1.0] rad/s`
Program usage name	`slip_vector`
Evaluatable	Yes

# Kinetic friction coefficient vector — kinetic friction coefficients

Details

Kinetic friction coefficients for given tyre slip values. The elements of this vector correspond to the elements of the vector Tire slip vector. The vectors must be of the same size.

Dependencies

To use this parameter, set the Friction model parameters to Table lookup kinetic friction coefficient.

Default value	`[0.89, 0.88, 0.8, 0.75, 0.7, 0.7]`
Program usage name	`kinetic_friction_coefficient_vector`
Evaluatable	Yes

# Interpolation method — interpolation method
Linear | Smooth

Details

Interpolation method to process the dependence of tyre slip on kinetic friction. To prioritise performance, select Linear. To obtain a continuous curve with continuous first order derivatives, select Smooth.

Dependencies

To use this parameter, set the Friction model parameters to . Table lookup kinetic friction coefficient.

Values	`Linear` \| `Smooth`
Default value	`Linear`
Program usage name	`friction_interpolation_method`
Evaluatable	Yes

# Extrapolation method — extrapolation method
Linear | Nearest | Error

Details

An extrapolation method for treating the dependence of tyre slip on kinetic friction:

Linear - select this option to obtain a curve with continuous first-order derivatives in the extrapolation region and at the boundary with the interpolation region.
Nearest - select this option to obtain an extrapolation that does not rise above the highest point in the data or below the lowest point in the data.
Error - select this option to get an extrapolation that does not go into extrapolation mode and that the data is within the range of the table. If the input signal is outside the table range, the simulation stops and displays an error.

Dependencies

To use this option, set the Friction model parameters to Table lookup kinetic friction coefficient.

Values	`Linear` \| `Nearest` \| `Error`
Default value	`Linear`
Program usage name	`friction_extrapolation_method`
Evaluatable	Yes

Dynamics

# Compliance — consideration of tyre pliability

Details

Whether tyre pliability consideration should be included:

if the check box Compliance is not selected, the unit neglects dynamic deformation.
if the check box Compliance is selected, the unit treats the tyre as a spring-damped system under load.

Default value	`false (switched off)`
Program usage name	`enable_compliance`
Evaluatable	Yes

# Inertia — inertia model

Details

Select this check box to take the tyre inertia into account.

Dependencies

To use this parameter, select the check box Compliance.

Default value	`false (switched off)`
Program usage name	`enable_inertia`
Evaluatable	Yes

# Longitudinal stiffness — longitudinal rigidity
N/m | mN/m | kN/m | MN/m | GN/m | kgf/m | lbf/ft | lbf/in

Details

Longitudinal stiffness of the tyre.

Dependencies

To use this parameter, select the check box Compliance.

Units	`N/m` \| `mN/m` \| `kN/m` \| `MN/m` \| `GN/m` \| `kgf/m` \| `lbf/ft` \| `lbf/in`
Default value	`1.0e6 N/m`
Program usage name	`k_longitudinal`
Evaluatable	Yes

# Longitudinal damping — Longitudinal damping
N*s/m | kgf*s/m | lbf*s/ft | lbf*s/in

Details

Longitudinal damping of the tyre.

Dependencies

To use this parameter, select the check box Compliance.

Units	`Ns/m` \| `kgfs/m` \| `lbfs/ft` \| `lbfs/in`
Default value	`1000.0 N*s/m`
Program usage name	`C_longitudinal`
Evaluatable	Yes

Details

Moment of inertia of wheel and tyre.

Dependencies

To use this parameter, select the check box Inertia.

Units	`kgm^2` \| `gm^2` \| `kgcm^2` \| `gcm^2` \| `lbmin^2` \| `lbmft^2` \| `slugin^2` \| `slugft^2`
Default value	`1.0 kg*m^2`
Program usage name	`I_tire`
Evaluatable	Yes

Details

Initial angular velocity of the tyre .

Dependencies

To use this parameter, select the check box Inertia.

Units	`rad/s` \| `deg/s` \| `rad/min` \| `deg/min` \| `rpm` \| `rps`
Default value	`0.0 rad/s`
Program usage name	`w_start`
Evaluatable	Yes

Rolling Resistance

# Rolling resistance — roll resistance

Details

Select this check box to take rolling resistance into account.

Default value	`false (switched off)`
Program usage name	`enable_resistance`
Evaluatable	Yes

# Resistance model — rolling resistance model
Constant coefficient | Pressure and velocity dependent (SAE J2452)

Details

A model for calculating rolling resistance:

Constant coefficient - Rolling resistance is taken into account by means of a constant coefficient.
Pressure and velocity dependent (SAE J2452) - The rolling resistance is determined in accordance with SAE J2452.

Values	`Constant coefficient` \| `Pressure and velocity dependent (SAE J2452)`
Default value	`Constant coefficient`
Program usage name	`rolling_resistance_parameterization`
Evaluatable	Yes

# Constant coefficient — proportionality constant

Details

A coefficient that establishes the proportionality between the normal force and the rolling resistance force. The parameters must be greater than zero.

Dependencies

To use this parameter, select the check box Rolling resistance, and set the parameters Resistance model to Constant coefficient.

Default value	`0.015`
Program usage name	`const_rolling_resistance_coefficient`
Evaluatable	Yes

# Velocity threshold — threshold speed for rolling resistance
m/s | mm/s | cm/s | km/s | m/hr | km/hr | in/s | ft/s | mi/s | ft/min | mi/hr | kn

Details

The speed at which the full rolling resistance force is transferred to the wheel hub. This parameter ensures that the force remains continuous as the direction of speed changes, which increases the numerical stability of the simulation. The parameters must be greater than zero.

Dependencies

To use this parameter, select the checkbox Rolling resistance.

Units	`m/s` \| `mm/s` \| `cm/s` \| `km/s` \| `m/hr` \| `km/hr` \| `in/s` \| `ft/s` \| `mi/s` \| `ft/min` \| `mi/hr` \| `kn`
Default value	`0.001 m/s`
Program usage name	`v_threshold`
Evaluatable	Yes

# Tire pressure — tyre pressure
Pa | uPa | hPa | kPa | MPa | GPa | kgf/m^2 | kgf/cm^2 | kgf/mm^2 | mbar | bar | kbar | atm | ksi | psi | mmHg | inHg

Details

Tyre inflation pressure. The parameters must be greater than zero.

Dependencies

To use this parameter, select the check box Rolling resistance, and set the parameters Resistance model to the value of Pressure and velocity dependent (SAE J2452).

Units	`Pa` \| `uPa` \| `hPa` \| `kPa` \| `MPa` \| `GPa` \| `kgf/m^2` \| `kgf/cm^2` \| `kgf/mm^2` \| `mbar` \| `bar` \| `kbar` \| `atm` \| `ksi` \| `psi` \| `mmHg` \| `inHg`
Default value	`250000.0 Pa`
Program usage name	`p_tire`
Evaluatable	Yes

# Alpha — exponent in the equation for tyre pressure

Details

The exponent in the equation for tyre pressure.

Dependencies

To use this parameter, tick the checkbox Rolling resistance, and set the parameters Resistance model to Pressure and velocity dependent (SAE J2452).

Default value	`-0.003`
Program usage name	`alpha`
Evaluatable	Yes

# Beta — exponent in the equation for the normal force

Details

The exponent in the equation for normal force.

Dependencies

To use this parameter, select the checkbox Rolling resistance, and set the parameters Resistance model to Pressure and velocity dependent (SAE J2452).

Default value	`0.97`
Program usage name	`beta`
Evaluatable	Yes

# Coefficient A — velocity-independent force component, A

Details

The velocity-independent force component in the model equation. The parameters must be greater than zero.

Dependencies

To use this parameter, select the checkbox Rolling resistance, and set the Resistance model parameters to Pressure and velocity dependent (SAE J2452).

Default value	`0.0084`
Program usage name	`coefficient_a`
Evaluatable	Yes

# Coefficient B — velocity-dependent force component, B
s/m | s/ft

Details

The velocity-dependent force component of the model equation. The parameters must be greater than zero.

Dependencies

To use this parameter, select the Rolling resistance checkbox and set the Resistance model parameters to Pressure and velocity dependent (SAE J2452).

Units	`s/m` \| `s/ft`
Default value	`0.00062 s/m`
Program usage name	`coefficient_b`
Evaluatable	Yes

# Coefficient C — velocity-dependent force component C
(s/m)^2 | (s/ft)^2

Details

A force component that depends on the square of the velocity term in the model equation. The parameters must be greater than zero.

Dependencies

To use this parameter, select the checkbox Rolling resistance, and set the parameter Resistance model to Pressure and velocity dependent (SAE J2452).

Units	`(s/m)^2` \| `(s/ft)^2`
Default value	`0.00016 (s/m)^2`
Program usage name	`coefficient_c`
Evaluatable	Yes

Advanced

# Traction velocity tolerance — permissible value of the clutch recovery rate
m/s | mm/s | cm/s | km/s | m/hr | km/hr | in/s | ft/s | mi/s | ft/min | mi/hr | kn

Details

The value of the relative speed between tyre and ground at which the tyre regains traction. If this value is too low, there is no grip. If this value is too high, the speed of the tyre changes suddenly when it gains traction, which can lead to an unstable simulation. The parameters must be greater than zero.

Units	`m/s` \| `mm/s` \| `cm/s` \| `km/s` \| `m/hr` \| `km/hr` \| `in/s` \| `ft/s` \| `mi/s` \| `ft/min` \| `mi/hr` \| `kn`
Default value	`0.01 m/s`
Program usage name	`v_traction_threshold`
Evaluatable	Yes

# Engagement threshold force — threshold bonding force
N | nN | uN | mN | kN | MN | GN | dyn | lbf | kgf

Details

The threshold force at which the block applies normal force to the tyre. If this value is too low, the tyre gains and loses traction quickly. If this value is too high, the block generates unrealistically low static and dynamic friction forces. The parameters should be greater than zero.

Units	`N` \| `nN` \| `uN` \| `mN` \| `kN` \| `MN` \| `GN` \| `dyn` \| `lbf` \| `kgf`
Default value	`10.0 N`
Program usage name	`F_vertical_threshold`
Evaluatable	Yes

# Initial traction state — initial state of coupling
Tire is initially slipping | Tire is initially in traction

Details

Select which state the tyre will be in at the beginning of the simulation:

Tire is initially in traction - in clutch;
Tire is initially slipping - in sliding.

Values	`Tire is initially slipping` \| `Tire is initially in traction`
Default value	`Tire is initially slipping`
Program usage name	`initial_traction_state`
Evaluatable	Yes