# 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 represents a tire with friction parameterized in terms of static and kinetic coefficients. The static friction coefficient, μs, determines the applied torque at which the tire loses traction and begins to slip. The kinetic friction coefficient, μk, determines the amount of torque that the tire transmits to the pavement once it begins to slip. The tire regains traction when its relative velocity over the pavement falls below the specified traction velocity tolerance.

To increase the fidelity of the tire model, specify properties such as tire compliance, inertia, and rolling resistance. Note that 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 when preparing the model for hardware-in-the-loop (HIL) simulation.

### Wheel Slip

When you set Slip output type to `Relative`, the block outputs the relative slip velocity as a unitless physical signal at port S. The relative slip output calculation depends on whether you simulate compliance. When you set Compliance to `No compliance - Suitable for HIL simulation`, port S outputs the absolute wheel slip velocity in rotational form as

`$S=\frac{{V}_{x}}{{r}_{w}}-\Omega ,$`

where:

• Vx is the wheel hub longitudinal velocity at port H.

• rw is the rolling radius.

• Ω is the wheel axle angular velocity at port A.

When you set Compliance to ```Specify stiffness and damping```, port S outputs the absolute contact point slip velocity in a rotational form such that

`$S=\frac{{V}_{x}}{{r}_{w}}+\frac{u}{{r}_{w}}-\Omega ,$`

where u is the time-rate of change in longitudinal deformation and u/rw is equivalent to the rotational velocity of the spring and damper in the logged simulation results.

When you set Slip output type to `Absolute`, the block uses the friction model of the Fundamental Friction Clutch block.

## Ports

### Input

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

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

#### Dependencies

To enable this port, set Friction model to ```Physical signal friction coefficients```.

### Output

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Physical signal output port associated with the slip between the tire and road, unitless or in rad/s. When you set Output type to:

• `Relative`, the port outputs unitless, relative slip.

• `Absolute`, the port outputs absolute slip in rad/s.

### Conserving

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Mechanical rotational conserving port associated with the axle.

Mechanical translational conserving port associated with the wheel hub.

## Parameters

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### Main

Distance between the pavement and the center of the tire.

Whether the block uses a relative or absolute slip friction parameterization.

Friction model the block uses during the simulation. When you select:

• ```Fixed kinetic friction coefficient```, the block uses the constant static and kinetic friction coefficients that you specify.

• ```Table lookup kinetic friction coefficient```, you can specify friction using a table lookup. The block treats the static coefficient as a constant and treats the kinetic coefficient as a constant or function of tire slip. Use this setting to simulate tire dynamics under constant pavement conditions.

• ```Physical signal friction coefficients```, the block enables port M for you to provide [μs, μk]. Use this setting to simulate tire dynamics under variable pavement conditions.

Ratio of the allowable longitudinal force to the normal force allowed before the tire begins to slip, μs. The value of this parameter must be greater than either the Kinetic friction coefficient parameter or the largest value in the Kinetic friction coefficient vector parameter.

#### Dependencies

To enable this parameter, set Friction model to ```Fixed kinetic friction coefficient``` or ```Table lookup kinetic friction coefficient```.

Ratio of the longitudinal force transferred to the road to the normal force allowed during tire slip, μk. The ratio must be greater than zero.

#### Dependencies

To enable this parameter, set Friction model to ```Fixed kinetic friction coefficient```.

Reference tire slip. The elements in this vector correspond one-to-one with the Kinetic friction coefficient vector parameter. If the Tire slip vector parameter contains only nonnegative values, the block assumes the slip-versus-friction function to be symmetric about the slip axis.

#### Dependencies

To enable this parameter, set Friction model to ```Table lookup kinetic friction coefficient```.

Kinetic friction coefficient for a given tire slip. The elements in this vector correspond one-to-one with the Tire slip vector parameter. The vectors must be the same size.

#### Dependencies

To enable this parameter, set Friction model to ```Table lookup kinetic friction coefficient```.

Interpolation method for the lookup table to process 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

To enable this parameter, set Friction model to ```Table lookup kinetic friction coefficient```.

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

• `Linear` — Select this option to produce a curve with continuous first-order derivatives in the extrapolation region and at the boundary with the interpolation region.

• `Nearest` — Select this option to produce an extrapolation that does not go above the highest point in the data or below the lowest point in the data.

• `Error` — Select this option to avoid going into the extrapolation mode when you want your data to be within the table range. If the input signal is outside the range of the table, the simulation stops and generates an error.

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

#### Dependencies

To enable this parameter, set Friction model to ```Table lookup kinetic friction coefficient```.

### Dynamics

Model for the dynamical compliance of the tire.

• ```No compliance - Suitable for HIL simulation``` — The block ignores dynamical compliance.

• `Specify stiffness and damping` — The block treats the tire as a stiff, dampened spring that deforms under load.

Tire longitudinal stiffness, CFx.

#### Dependencies

To enable this parameter, set Compliance to `Specify stiffness and damping`.

Tire longitudinal damping, bFx.

#### Dependencies

To enable this parameter, set Compliance to `Specify stiffness and damping`.

Whether to simulate tire rotational inertia. When you select

• `No inertia` — The block ignores inertia.

• ```Specify inertia and initial velocity``` — The block treats the tire as a stiff, dampened spring that deforms under load.

#### Dependencies

To enable this parameter, set Inertia to ```Specify inertia and initial velocity```.

Rotational inertia, Iw, of the wheel-tire assembly.

#### Dependencies

To enable this parameter, set Inertia to ```Specify inertia and initial velocity```.

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

#### Dependencies

To enable this parameter, set Inertia to ```Specify inertia and initial velocity```.

### Rolling Resistance

Whether to simulate rolling resistance. When you select

• `Off`, the block ignores rolling resistance

• `On` the block includes rolling resistance in the simulation.

Whether to simulate the rolling resistance of the tire. When you select

• `Constant coefficient` — The block ignores rolling resistance.

• `Pressure and velocity dependent` — Include rolling resistance.

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

#### Dependencies

To enable this parameter, set Rolling resistance to `On` and Resistance model to ```Constant coefficient```.

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

#### Dependencies

To enable this parameter, set Rolling resistance to `On` and Resistance model to ```Pressure and velocity dependent```.

Exponent of the tire pressure in the model equation.

#### Dependencies

To enable this parameter, set Rolling resistance to `On` and Resistance model to ```Pressure and velocity dependent```.

Exponent of the normal force model equation.

#### Dependencies

To enable this parameter, set Rolling resistance to `On` and Resistance model to ```Pressure and velocity dependent```.

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

#### Dependencies

To enable this parameter, set Rolling resistance to `On` and Resistance model to ```Pressure and velocity dependent```.

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

#### Dependencies

To enable this parameter, set Rolling resistance to `On` and Resistance model to ```Pressure and velocity dependent```.

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

#### Dependencies

To enable this parameter, set Rolling resistance to `On` and Resistance model to ```Pressure and velocity dependent```.

Velocity at which the block applies the full rolling resistance. This 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

To enable this parameter, set Rolling resistance to `On`.

Magnitude of the relative velocity between the tire and ground at which the tire regains traction. If this value is too low, the tire does not gain traction. If this value is too high, the tire velocity changes suddenly when the tire gains traction, which can result in an unstable simulation. The parameter must be greater than zero.

Threshold force at which block applies the normal force to the tire. If this value is too low, the tire gains and loses traction rapidly. If this value is too high, the block produces 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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## Version History

Introduced in R2012a

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