Documentation

# 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

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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.

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

#### 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

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

### Conserving

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

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

## Parameters

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### 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

Friction model — Choose ```Fixed kinetic friction coefficient```, ```Table lookup kinetic friction coefficient```, or ```Physical signal friction coefficients```

Fixed kinetic friction coefficientTable lookup kinetic friction coefficientPhysical 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

Distance between the pavement and the center of the tire.

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 (μs) and kinetic (μk) friction coefficients to the block as an array of two elements in the order [μs, μk].

#### 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.

Ratio of the allowable longitudinal force to the normal force allowed before the tire begins to slip (μs). 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.

Ratio of the transmitted longitudinal force to the normal force allowed during tire slip (μk). 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.

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.

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 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 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 simulationSpecify stiffness and damping

Longitudinal stiffness

Longitudinal damping

Inertia — Choose ```No Inertia``` or ```Specify inertia and initial velocity```

No InertiaSpecify inertia and initial velocity

Tire inertia

Initial velocity

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.

Tire longitudinal stiffness CFx.

#### Dependencies

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

Tire longitudinal damping bFx.

#### Dependencies

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

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.

Rotational inertia Iw 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 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`

OffOn

Resistance model — Choose `Constant coefficient` or ```Pressure and velocity dependent```

Constant coefficientPressure and velocity dependent

Constant coefficient

Tire pressure

Alpha

Beta

Coefficient A

Coefficient B

Coefficient C

Velocity threshold

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.

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.

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.

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.

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.

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.

Velocity-independent force component in the model equation. The parameter must be greater than zero. See Pressure and Velocity Dependent Model.

#### 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-dependent force component in the model equation. The parameter must be greater than zero. See Pressure and Velocity Dependent Model.

#### 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.

Force component that depends on the square of the velocity term in the model equation. The parameter must be greater than zero. See Pressure and Velocity Dependent Model.

#### 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 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.

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

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.

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.

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

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## Extended Capabilities

### C/C++ Code GenerationGenerate C and C++ code using Simulink® Coder™. 