Tire (Friction Parameterized)

Tire with friction parameterized in terms of static and kinetic coefficients

• Library:

• Simscape / Driveline / Tires & Vehicles

• 

Description

The Tire (Friction Parameterized) block models a tire with friction parameterized in terms of static and kinetic coefficients. The static friction coefficient determines the applied torque at which the tire loses traction and begins to slip. The kinetic friction coefficient determines the amount of torque that the tire transmits to the pavement once it begins to slip. The tire regains traction once its relative velocity over the pavement falls below the traction velocity tolerance specified.

To increase the fidelity of the tire model, the block enables you to specify properties such as tire compliance, inertia, and rolling resistance. However, these properties increase the complexity of the tire model and can slow down simulation. Consider ignoring tire compliance and inertia if simulating the model in real time or if preparing the model for hardware-in-the-loop (HIL) simulation.

The traction state model of this block is based on the traction state model of the Fundamental Friction Clutch block. For more information on the state model, see Clutch States.

Ports

Input

N — Normal force

physical signal

Physical signal input port associated with the normal force acting on the tire. The normal force is positive if it acts downward on the tire, pressing it against the pavement.

M — Friction coefficients

physical signal | vector | [μ_s, μ_k]

Physical signal input port associated with the static (μ_s) and kinetic (μ_k) friction coefficients. Provide the friction coefficients as a two-element vector, specified in the order [μ_s, μ_k].

Dependencies

Port M is exposed only if the Main > Friction model parameter is set to Physical signal friction coefficients. For more information, see Main Parameter Dependencies.

Output

S — Slip

physical signal

Physical signal output port associated with the relative slip between the tire and road.

Conserving

A — Axle

mechanical rotational

Mechanical rotational port associated with the axle that the tire sits on.

H — Hub

mechanical translational

Mechanical translational port associated with the wheel hub that transmits the thrust generated by the tire to the remainder of the vehicle.

Parameters

Main

Specify characteristics of the tire, such as the rolling radius or static friction coefficient. The table shows how the visibility of some Main parameters depends on the options that you choose for other parameters. To learn how to read the table, see Parameter Dependencies.

Main Parameter Dependencies

Main
Rolling radius
Friction model — Choose Fixed kinetic friction coefficient, Table lookup kinetic friction coefficient, or Physical signal friction coefficients
Fixed kinetic friction coefficient	Table lookup kinetic friction coefficient	Physical signal friction coefficients — Exposes physical signal input port M for providing the static (μs) and kinetic (μk) friction coefficients to the block as an array of two elements in the order [μs, μk].
Static friction coefficient
Kinetic friction coefficient	Tire slip vector
	Kinetic friction coefficient vector
	Interpolation method
	Extrapolation method

Rolling radius — Unloaded tire-wheel radius

0.3 m (default) | positive scalar

Distance between the pavement and the center of the tire.

Friction model — Friction model

Fixed kinetic friction coefficient (default) | Table lookup kinetic friction coefficient | Physical signal friction coefficients

The block provides three friction models. The default model, Fixed kinetic friction coefficient, uses constant static and kinetic friction coefficients that you specify.

To specify friction using table lookup, set the Friction model parameter to Table lookup kinetic friction coefficient. While this model treats the static coefficient as a constant, it treats the kinetic coefficient as a constant or function of tire slip. Use this model to model tire dynamics under constant pavement conditions.

To model tire dynamics under variable pavement conditions, set the Friction model parameter to Physical signal friction coefficients. Selecting this model exposes physical signal inport M. Use the M port to provide the static (μ_s) and kinetic (μ_k) friction coefficients to the block as an array of two elements in the order [μ_s, μ_k].

Dependencies

Each friction model option exposes related parameters and hides unrelated parameters. Selecting Physical signal friction coefficients exposes physical signal input port M. For more information, see Main Parameter Dependencies.

Static friction coefficient — Static friction coefficient

0.90 (default) | positive scalar

Ratio of the allowable longitudinal force to the normal force allowed before the tire begins to slip (μ_s). The parameter must be greater than either the kinetic friction coefficient or the largest value in the kinetic friction coefficient vector.

Dependencies

This parameter is visible when the Friction model parameter is set to Fixed kinetic friction coefficient or Table lookup kinetic friction coefficient. For more information, see Main Parameter Dependencies.

Kinetic friction coefficient — Kinetic friction coefficient

0.70 (default) | positive scalar

Ratio of the transmitted longitudinal force to the normal force allowed during tire slip (μ_k). The ratio must be greater than zero.

Dependencies

This parameter is visible when the Friction model parameter is set to Fixed kinetic friction coefficient. For more information, see Main Parameter Dependencies.

Tire slip vector — Tire slip vector

[0, .02, .06, .15, .6, 1] rad/s (default) | vector

Vector of tire slip values that correspond to the kinetic friction coefficients in the Kinetic friction coefficient vector parameter. The vectors must be the same size. If the Tire slip vector parameter contains only nonnegative values, the slip versus friction function is assumed to be symmetric about the slip axis.

Dependencies

This parameter is visible when the Friction model parameter is set to Table lookup kinetic friction coefficient. For more information, see Main Parameter Dependencies.

Kinetic friction coefficient vector — Kinetic friction coefficient

[.89, .88, .8, .75, .7, .7] (default) | vector

Vector of kinetic friction coefficients that correspond to the tire slip values specified in the Tire slip vector parameter. The vectors must be the same size.

Dependencies

This parameter is visible when the Friction model parameter is set to Table lookup kinetic friction coefficient. For more information, see Main Parameter Dependencies.

Interpolation method — Interpolation method

Linear (default) | Smooth

Interpolation method for the lookup table to use for processing the tire slip-kinetic friction coefficient characteristic. To prioritize performance, select Linear. To produce a continuous curve with continuous first-order derivatives, select Smooth.

For more information on interpolation algorithms, see the PS Lookup Table (1D) block reference page.

Dependencies

This parameter is visible when the Friction model parameter is set to Table lookup kinetic friction coefficient. For more information, see Main Parameter Dependencies.

Extrapolation method — Extrapolation method

Linear (default) | Nearest | Error

Extrapolation method for the lookup table to use for processing the tire slip-kinetic friction coefficient characteristic. To produce:

• A curve with continuous first-order derivatives in the extrapolation region and at the boundary with the interpolation region, select Linear.

• An extrapolation that does not go above the highest point in the data or below the lowest point in the data, select Nearest.

• An error if the input signal is outside the range of the table, select Error. This option ensures that simulation occurs only if your data is within the table range.

For more information on extrapolation algorithms, see the PS Lookup Table (1D) block reference page.

Dependencies

This parameter is visible when the Friction model parameter is set to Table lookup kinetic friction coefficient. For more information, see Main Parameter Dependencies.

Dynamics

The table shows how the visibility of some parameters depends on the options that you choose for other parameters. To learn how to read the table, see Parameter Dependencies.

Dynamics Parameter Dependencies Table

Dynamics
Compliance — Choose No compliance - Suitable for HIL simulation or Specify stiffness and damping
No compliance - Suitable for HIL simulation	Specify stiffness and damping
	Longitudinal stiffness
	Longitudinal damping
Inertia — Choose No Inertia or Specify inertia and initial velocity
No Inertia	Specify inertia and initial velocity
	Tire inertia
	Initial velocity

Compliance — Dynamical compliance model

No compliance - Suitable for HIL simulation (default) | Specify stiffness and damping

Model for the dynamical compliance of the tire.

• No compliance - Suitable for HIL simulation — Tire is modeled with no dynamical compliance.

• Specify stiffness and damping — Tire is modeled as a stiff, dampened spring and deforms under load.

Dependencies

Selecting the Specify stiffness and damping parameterization method, exposes stiffness and damping parameters. For more information, see Dynamics Parameter Dependencies Table.

Longitudinal stiffness — Longitudinal stiffness

1e6 N/m (default) | positive scalar

Tire longitudinal stiffness C_Fx.

Dependencies

Selecting Specify stiffness and damping for the Compliance parameter, exposes this parameter. For more information, see Dynamics Parameter Dependencies Table.

Longitudinal damping — Longitudinal damping

1000 N/(m/s) (default) | positive scalar

Tire longitudinal damping b_Fx.

Dependencies

Selecting Specify stiffness and damping for the Compliance parameter, exposes this parameter. For more information, see Dynamics Parameter Dependencies Table.

Inertia — Inertia model

No inertia (default) | Specify inertia and initial velocity

Model for the rotational inertia of the tire.

• No inertia — Tire is modeled with no dynamical compliance.

• Specify inertia and initial velocity — Tire is modeled as a stiff, dampened spring and deforms under load.

Dependencies

Selecting the Specify inertia and initial velocity parameterization method, exposes inertia and velocity parameters. For more information, see Dynamics Parameter Dependencies Table.

Tire inertia — Rotational inertia

1 kg*m^2 (default) | positive scalar

Rotational inertia I_w of the wheel-tire assembly.

Dependencies

Selecting Specify inertia and initial velocity for the Inertia parameter, exposes this parameter. For more information, see Dynamics Parameter Dependencies Table.

Initial velocity — Initial rotational velocity

0 rad/s (default) | scalar

Initial angular velocity, Ω(0), of the tire.

Dependencies

Selecting Specify inertia and initial velocity for the Inertia parameter, exposes this parameter. For more information, see Dynamics Parameter Dependencies Table.

Rolling Resistance

The table shows how the visibility of some Rolling Resistance parameters depends on the options that you choose for other parameters. To learn how to read the table, see Parameter Dependencies.

Rolling Resistance Parameter Dependencies Table

Rolling Resistance
Rolling resistance — Choose Off or On
Off	On
	Resistance model — Choose Constant coefficient or Pressure and velocity dependent
	Constant coefficient	Pressure and velocity dependent
	Constant coefficient	Tire pressure
		Alpha
		Beta
		Coefficient A
		Coefficient B
		Coefficient C
	Velocity threshold

Rolling resistance — Rolling resistance option

Off (default) | On

Options for modeling rolling resistance are:

• Off — Neglect rolling resistance.

• On — Include rolling resistance.

Dependencies

Selecting On exposes rolling resistance parameters. For more information, see Rolling Resistance Parameter Dependencies Table.

Resistance model — Rolling resistance model

Constant coefficient (default) | Pressure and velocity dependent

Model for the rolling resistance of the tire.

• Constant coefficient — Neglect rolling resistance.

• Pressure and velocity dependent — Include rolling resistance.

Dependencies

Each Resistance model option exposes related parameters. For more information, see Rolling Resistance Parameter Dependencies Table.

Constant coefficient — Proportionality constant

0.015 (default) | positive scalar

Coefficient that sets the proportionality between the normal force and the rolling resistance force. The parameter must be greater than zero.

Dependencies

Selecting On for the Rolling resistance parameter and Constant coefficient for the Resistance model parameter exposes this parameter. For more information, see Rolling Resistance Parameter Dependencies Table.

Tire pressure — Tire pressure

250e3 Pa (default) | positive scalar

Inflation pressure of the tire. The parameter must be greater than zero.

Dependencies

Selecting On for the Rolling resistance parameter and Pressure and velocity dependent for the Resistance model parameter exposes this parameter. For more information, see Rolling Resistance Parameter Dependencies Table.

Alpha — Tire pressure equation exponent

-0.003 (default) | scalar

Exponent of the tire pressure in the model equation. See Rolling Resistance Parameter Dependencies Table.

Dependencies

Selecting On for the Rolling resistance parameter and Pressure and velocity dependent for the Resistance model parameter exposes this parameter. For more information, see Rolling Resistance Parameter Dependencies Table.

Beta — Normal force equation exponent

0.97 (default) | scalar

Exponent of the normal force model equation. See Rolling Resistance Parameter Dependencies Table.

Dependencies

Selecting On for the Rolling resistance parameter and Pressure and velocity dependent for the Resistance model parameter exposes this parameter. For more information, see Rolling Resistance Parameter Dependencies Table.

Coefficient A — Velocity-independent force component A

84e-4 (default)

Velocity-independent force component in the model equation. The parameter must be greater than zero.

Dependencies

Selecting On for the Rolling resistance parameter and Pressure and velocity dependent for the Resistance model parameter exposes this parameter. For more information, see Rolling Resistance Parameter Dependencies Table.

Coefficient B — Velocity-dependent force component B

6.2e-4 s/m (default) | positive scalar

Velocity-dependent force component in the model equation. The parameter must be greater than zero.

Dependencies

Selecting On for the Rolling resistance parameter and Pressure and velocity dependent for the Resistance model parameter exposes this parameter. For more information, see Rolling Resistance Parameter Dependencies Table.

Coefficient C — Velocity-dependent force component C

1.6e-4 s^2/m^2 (default) | positive scalar

Force component that depends on the square of the velocity term in the model equation. The parameter must be greater than zero.

Dependencies

Selecting On for the Rolling resistance parameter and Pressure and velocity dependent for the Resistance model parameter exposes this parameter. For more information, see Rolling Resistance Parameter Dependencies Table.

Velocity threshold — Wheel hub velocity threshold for mathematical slip model

0.001 m/s (default) | positive scalar

Velocity at which the full rolling resistance force is transmitted to the rolling hub. The parameter ensures that the force remains continuous during velocity direction changes, which increases the numerical stability of the simulation. The parameter must be greater than zero.

Dependencies

Selecting On for the Rolling resistance parameter exposes this parameter. For more information, see Rolling Resistance Parameter Dependencies.

Advanced

Use the Advanced tab to specify parameters that the state machine uses to determine the model of the tire.

Traction velocity tolerance — Traction velocity tolerance

0.01 m/s (default) | positive scalar

Magnitude of the relative velocity between the tire and ground at which the tire regains traction. Setting this value too low prevents the tire from entering a state where it has traction. Setting it too high can cause the tire velocity to change suddenly when the tire gains traction, and can result in an unstable simulation. The parameter must be greater than zero.

Engagement threshold force — Engagement threshold force

10 N (default) | positive scalar

Normal force values below the Engagement threshold force are not applied to the tire. Setting this value too low can cause the tire to gain and lose traction rapidly. Setting this value too high can give unrealistically low static and dynamic friction forces. The parameter must be greater than zero.

Initial traction state — Initial traction state

Tire is initially slipping (default) | Tire is initially in traction

Option to have the tire in traction or slipping at the start of simulation.

Model Examples

Vehicle with Four-Wheel Drive

A four-wheel drive vehicle starting from rest and ascending a 15 degree incline. Initially the vehicle rolls backwards until the engine develops sufficient torque to counter the slope. The tire compliance dynamics can be seen as the vehicle starts to accelerate. The model variant chosen for all of the tires can be set to the Simple, Friction Parameterized, or Magic Formula tire model using the hyperlinks in the model.

More About

Real-Time and Hardware-in-the-Loop Simulation

For optimal simulation performance, set the Dynamics > Compliance parameter to No compliance - Suitable for HIL simulation.

Extended Capabilities

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