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 — radius of the tire without load
m | um | mm | cm | km | in | ft | yd | mi | nmi

Details

The distance between the road surface and the center of the tire.

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 an absolute or relative slip value
Relative | Absolute

Details

Whether the block uses relative or absolute parameterization of sliding friction.

Values	`Relative` \| `Absolute`
Default value	`Relative`
Program usage name	`slip_friction_parameterization`
Evaluatable	No

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

Details

The friction model that the unit uses during the simulation:

Fixed kinetic friction coefficient — the unit uses constant static and kinetic coefficients 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 unit considers the static coefficient as a constant, and the kinetic coefficient as a constant or a function of tire slippage. Use this setting to simulate tire dynamics in conditions of constant road surface.
Physical signal friction coefficients — the unit uses the M port to obtain the coefficients of friction [ ]. Use this setting to simulate tire dynamics in variable road 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	No

# Static friction coefficient — coefficient of static friction

Details

The ratio of the permissible longitudinal force to the permissible normal force before the tire starts to slip, . The value of this parameter should be higher. Kinetic friction coefficient or more than the largest value in the parameter Kinetic friction coefficient vector.

Dependencies

To use this parameter, set for the parameter Friction model meaning 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 — coefficient of kinetic friction

Details

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

Dependencies

To use this parameter, set for the parameter Friction model meaning Fixed kinetic friction coefficient.

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

Details

Tire slip values. The elements of this vector correspond to the elements of the vector Kinetic friction coefficient vector. If the parameter Tire slip vector If it contains only non-negative values, then the block assumes that the function of sliding versus friction is symmetric relative to the sliding axis.

Dependencies

To use this parameter, set for the parameter Friction model meaning 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 the specified tire slip values. The elements of this vector correspond to the elements of the vector Tire slip vector. The vectors must be the same size.

Dependencies

To use this parameter, set for the parameter Friction model meaning 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 — the interpolation method
Linear | Smooth

Details

An interpolation method for processing the dependence of tire slip on kinetic friction. To prioritize performance, select Linear. To get a continuous curve with continuous first-order derivatives, select Smooth.

Dependencies

To use this parameter, set for the parameter Friction model meaning Table lookup kinetic friction coefficient.

Values	`Linear` \| `Smooth`
Default value	`Linear`
Program usage name	`friction_interpolation_type`
Evaluatable	No

# Extrapolation method — the extrapolation method
Linear | Nearest | Error

Details

An extrapolation method for processing the dependence of tire slip on kinetic friction:

Linear — select this option to get a curve with continuous first-order derivatives in the extrapolation domain and on the boundary with the interpolation domain.
Nearest — Select this option to get 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 avoid going into extrapolation mode and to keep the data within the range of the table. If the input signal is outside the range of the table, the simulation stops and outputs an error.

Dependencies

To use this parameter, set for the parameter Friction model meaning Table lookup kinetic friction coefficient.

Values	`Linear` \| `Nearest` \| `Error`
Default value	`Linear`
Program usage name	`friction_extrapolation_type`
Evaluatable	No

Dynamics

# Compliance — accounting for tire compliance

Details

Do I need to include tire compliance accounting?:

if the check box Compliance if not installed, the unit ignores dynamic deformation.
if the check box Compliance If installed, the unit treats the tire as a spring-damping system under load.

Default value	`false (switched off)`
Program usage name	`enable_compliance`
Evaluatable	No

# Inertia — the inertia model

Details

Check this box to account for the inertia of the bus.

Dependencies

To use this option, check the box Compliance.

Default value	`false (switched off)`
Program usage name	`enable_inertia`
Evaluatable	No

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

Details

The longitudinal stiffness of the tire.

Dependencies

To use this option, check the 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 tire.

Dependencies

To use this option, check the 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

The moment of inertia of the wheel and tire.

Dependencies

To use this option, check the 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 tire .

Dependencies

To use this option, check the 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 — consider rolling resistance

Details

Check this box to take rolling resistance into account.

Default value	`false (switched off)`
Program usage name	`enable_resistance`
Evaluatable	No

# 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 using a constant coefficient.
Pressure and velocity dependent (SAE J2452) — 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	No

# Constant coefficient — the constant of proportionality

Details

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

Dependencies

To use this option, check the box Rolling resistance, and for the parameter Resistance model set the value 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 force of rolling resistance is transmitted to the wheel hub. This parameter ensures that the force remains continuous when changing the direction of velocity, which increases the numerical stability of the simulation. The parameter must be greater than zero.

Dependencies

To use this option, check the box 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 — tire 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

Tire inflating pressure. The parameter must be greater than zero.

Dependencies