Tire with friction parameterized in terms of static and kinetic coefficients

Tires & Vehicles

This 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.

Port A represents the axle on which the tire sits. Port H represents the wheel hub that transmits the thrust generated by the tire to the remainder of the vehicle. Port N accepts a physical signal input of the normal force acting on the tire. The normal force is positive if it acts downward on the tire, pressing it against the pavement. Port S outputs a physical signal with the tire slip measured during simulation.

The block provides two friction variants. The default variant, ```
Fixed
friction coefficients
```

, accepts the static and kinetic
friction coefficients as block parameters. This variant treats the
static coefficient as a constant. It treats the kinetic coefficient
as a constant or function of tire slip. Use this variant to model
tire dynamics under constant pavement conditions.

The alternative variant, `Variable friction coefficients`

,
accepts the static and kinetic friction coefficients as a physical
signal input. Use this variant to model tire dynamics under variable
pavement conditions. Selecting this variant exposes physical signal
port M. Use this port to provide the static and kinetic friction coefficients
as a two-element vector, specified in this order.

To change block variants:

Right-click the tire block.

In the context-sensitive menu, select

**Simscape**>**Block choice**.Select the desired block variant.

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-Loop (HIL) simulation.

The traction state model of this block is based on that of the Fundamental Friction Clutch block. For more information on the state model, see Clutch State, Transition, and Variable Summary.

Use the **Tire Parameters** pane to specify
characteristics of the tire, such as the rolling radius or static
friction coefficient.

**Rolling radius**Distance between the pavement and the center of the tire. This distance must be positive. The default value is

`0.30 m`

.**Static friction coefficient**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. The default is`0.9`

.This parameter is visible when the block variant is set to

`Fixed friction coefficients`

. For more information about the block variants, see the block description.**Friction model**Parameterization through which to specify the kinetic friction coefficient. Options include:

`Fixed kinetic friction coefficient`

— (Default) Uses a constant kinetic function coefficient. Exposes**Kinetic friction coefficient**parameter.`Table lookup kinetic friction coefficient`

— Uses a function of slip. Exposes**Tire slip vector**and**Kinetic friction coefficient vector**parameters.

This parameter is visible when the block variant is set to

`Fixed friction coefficients`

. For more information about the block variants, see the block description.**Kinetic friction coefficient**Ratio of the transmitted longitudinal force to the normal force allowed during tire slip (

*μ*_{k}). The ratio must be greater than zero. Default`0.7`

.This parameter is visible when the tire variant is set to

`Fixed friction coefficients`

and the**Friction model**parameter is set to`Fixed kinetic friction coefficient`

. For more information about the block variants, see the block description.**Tire slip vector**Vector that contains values of tire slip 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. Default vector is`[0 0.02 0.06 0.15 0.6 1]`

.This parameter is visible when the tire variant is set to

`Fixed friction coefficients`

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

. For more information about the block variants, see the block description.**Kinetic friction coefficient vector**Vector that contains kinetic friction coefficients that correspond to the tire slip values specified in the

**Tire slip vector**parameter. The vectors must be the same size. Default vector is`[0.89 0.88 0.8 0.75 0.7 0.7]`

.This parameter is visible when the tire variant is set to

`Fixed friction coefficients`

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

. For more information about the block variants, see the block description.**Interpolation method**Interpolation method for the lookup table to use for processing the tire slip-kinetic friction coefficient characteristic. Interpolation options include:

`Linear`

— Select this option to get the best performance.`Smooth`

— Select this option to produce a continuous curve with continuous first-order derivatives.

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

This parameter is visible when the tire variant is set to

`Fixed friction coefficients`

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

. For more information about the block variants, see the block description.**Extrapolation method**Extrapolation method for the lookup table to use for processing the tire slip-kinetic friction coefficient characteristic.

`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.

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

`Fixed friction coefficients`

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

. For more information about the block variants, see the block description.

**Compliance**Specifies whether the model includes longitudinal stiffness and damping.

`No compliance - Suitable for HIL simulation`

— (Default) Does not include longitudinal stiffness and damping.`Specify stiffness and damping`

— Includes longitudinal stiffness and damping. Exposes the**Longitudinal stiffness**and**Longitudinal damping**parameters.

**Longitudinal stiffness**The longitudinal stiffness of the tire. The parameter must be greater than zero. Default is

`1e+6 N/m`

.The

**Longitudinal stiffness**parameter appears if the**Compliance**parameter is`Specify stiffness and damping`

.**Longitudinal damping**The longitudinal damping of the tire. The parameter must be greater than zero. Default is

`1000 N/(m/s)`

.The

**Longitudinal damping**parameter appears if the**Compliance**parameter is`Specify stiffness and damping`

.**Inertia**Specifies whether the model the model includes tire inertia.

`No inertia`

— (Default) Does not include tire inertia.`Specify inertia and initial velocity`

— Includes tire inertia and initial velocity. Exposes the**Tire inertia**and**Initial velocity**parameters.

**Tire inertia**The rotational inertia of the tire. The parameter must be greater than zero. Default is

`1 kg*m^2`

.The

**Tire inertia**parameter appears if the**Inertia**parameter is`Specify inertia and initial velocity`

.**Initial velocity**The initial rotational velocity of the tire. Default is

`0 rad/s`

.The

**Initial velocity**parameter appears if the**Inertia**parameter is`Specify inertia and initial velocity`

.

**Rolling resistance**Option to turn on and off rolling resistance modeling in the tire. Settings you can select include:

`No rolling resistance`

— Ignore the effects of rolling resistance.`Specify rolling resistance`

— Model the effects of rolling resistance using the selected parameterization. Selecting this setting causes the block to expose the**Resistance model**parameter.

**Resistance model**Parameterization with which to model rolling resistance in the tire. Options include

`Constant coefficient`

and`Pressure and velocity dependent`

. The default setting is`Constant coefficient`

.

Pressure and velocity dependent

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

**Traction velocity tolerance**The 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 to suddenly change velocity when the tire gains traction, and can result in an unstable simulation. The parameter must be greater than zero. Default is

`0.01 m/s`

.**Engagement threshold force**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. Default is`10 N`

.**Initial traction state**Specifies whether the tire is initially in traction or slipping.

`Tire is initially slipping`

— (Default)`Tire is initially in traction`

Port | Description |
---|---|

A | Conserving mechanical rotational port associated with the axle of the tire |

H | Conserving mechanical translational port associated with the hub of the tire |

N | Physical signal input port associated with the normal force on the tire |

M | Physical signal input associated with the static and kinetic friction coefficients of the tire |

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

The sdl_4wd_dynamics example model shows the use of the Tire (Friction Parameterized) block.

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