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Tire with friction parameterized in terms of static and kinetic coefficients

**Library:**Simscape / Driveline / Tires & Vehicles

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.

`N`

— Normal forcephysical 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 coefficientsphysical signal | vector | [

Physical signal input port associated with the static
(*μ _{s}*) and kinetic
(

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.

`S`

— Slipphysical signal

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

`A`

— Axlemechanical rotational

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

`H`

— Hubmechanical translational

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

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 | Physical signal friction
coefficients — Exposes physical signal
input port M for providing the static
(μ) and
kinetic (_{s}μ) friction
coefficients to the block as an array of two elements in the
order [_{k}μ,
_{s}μ]._{k} |

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 scalarDistance 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 (

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 scalarRatio 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.

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 scalarRatio of the transmitted longitudinal force to the normal force
allowed during tire slip (*μ _{k}*).
The ratio must be greater than zero.

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) | vectorVector 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.

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) | vectorVector 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.

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.

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.

**Friction
model** parameter is set to ```
Table lookup
kinetic friction coefficient
```

. For more
information, see Main Parameter Dependencies.

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 | Specify stiffness and
damping |

Longitudinal stiffness | |

Longitudinal damping | |

Inertia — Choose | |

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.

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 scalarTire longitudinal stiffness
*C _{Fx}*.

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 scalarTire longitudinal damping
*b _{Fx}*.

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.

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 scalarRotational inertia *I _{w}* of the
wheel-tire assembly.

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) | scalarInitial angular velocity, *Ω*(0), of the tire.

Selecting ```
Specify inertia and initial
velocity
```

for the **Inertia**
parameter, exposes this parameter. For more information, see Dynamics Parameter Dependencies Table.

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 | On | |

Resistance model — Choose
| ||

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.

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.

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

`Constant coefficient`

— Proportionality constant`0.015`

(default) | positive scalarCoefficient that sets the proportionality between the normal force and the rolling resistance force. The parameter must be greater than zero.

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

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) | scalarExponent of the tire pressure in the model equation. See Rolling Resistance Parameter Dependencies Table.

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) | scalarExponent of the normal force model equation. See Rolling Resistance Parameter Dependencies Table.

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 `84e-4`

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

`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 `6.2e-4`

`s/m`

(default) | positive scalarVelocity-dependent force component in the model equation. The parameter must be greater than zero.

`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 `1.6e-4`

`s^2/m^2`

(default) | positive scalarForce component that depends on the square of the velocity term in the model equation. The parameter must be greater than zero.

`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 scalarVelocity 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.

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.

`Traction velocity tolerance`

— Traction velocity tolerance`0.01`

`m/s`

(default) | positive scalarMagnitude 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 scalarNormal 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.

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

.

Generate C and C++ code using Simulink® Coder™.

Fundamental Friction Clutch | Tire (Simple) | Tire (Magic Formula) | Tire-Road Interaction (Magic Formula)

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