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Model a tire using kinetic and static friction coefficients

The block represents a model of a tire that is parameterized with static and dynamic friction coefficients. When the static friction limit is exceeded, the tire loses traction and begins to slip. The kinetic friction coefficient determines the ability of the tire to transmit torque when slipping. The kinetic friction coefficient is either fixed or is a function of the current slip. The tire can regain traction when the magnitude of the relative velocity between the tire and ground is less than the traction velocity tolerance parameter.

Connection A is a mechanical rotational conserving port associated with the axle of the tire. Connection H is a mechanical translational conserving port associated with the hub of the tire. The physical signal input N is the normal force acting on the wheel. A force pushing the tire into the ground is considered positive. Output physical signal port S gives the current slip.

By default, the tire does not have inertia, stiffness, or damping.
You can specify these additional dynamics using the **Dynamics **tab.
These dynamics require additional computation and might make the model
less suitable for real-time simulation.

The **Advanced** tab contains parameters that
the state machine uses to determine the mode of the tire. The parameter
defaults are reasonable in many simulations. Adjust the parameters
If the model is not switching from the traction state to the slipping
state (or vice-versa) at appropriate times in the simulation, adjust
the parameters.

The traction or slip state model for the Tire (Friction Parameterized) block is based on that of the Fundamental Friction Clutch block. For more information on the state machine, see Clutch State, Transition, and Variable Summary.

The kinetic friction coefficient can vary only as a function of slip during simulation. Therefore, you cannot drive over multiple different surfaces during one simulation.

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

**Rolling radius**The effective rolling radius of the tire. The rolling radius must be greater than zero. Default is

`0.30 m`.**Static friction coefficient**The 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. Default is`0.9`.**Friction model**Specifies whether the kinetic friction coefficient is constant or a function of slip. The choices are:

`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.

**Kinetic friction coefficient**The ratio of the transmitted longitudinal force to the normal force allowed while the tire is slipping (

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

**Kinetic friction coefficient**parameter appears if the**Friction model**parameter is`Fixed kinetic friction coefficient`.**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 non-only negative 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]`.The

**Tire slip vector**parameter appears if you set the**Friction model**parameter to`Table lookup kinetic friction coefficient`.**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]`.The

**Kinetic friction coefficient vector**parameter appears if the**Friction model**parameter is`Table lookup kinetic friction coefficient`.**Interpolation method**The interpolation method for the lookup table to use for processing the tire slip-kinetic friction coefficient characteristic. The interpolation method choices are:

`Linear`(default)`Cubic``Spline`

The interpolation uses the PS Lookup Table (1-D).Simscape™ block.

The

**Interpolation method**parameter appears if the**Friction model**parameter is`Table lookup kinetic friction coefficient`.**Extrapolation method**The extrapolation method for the lookup table to use for processing the tire slip-kinetic friction coefficient characteristic.

`From last 2 points`— (Default) Performs extrapolation with linear method, regardless of the specified interpolation method.`From last point`— Preserves last value if an argument falls outside of the specified range.

The

**Extrapolation method**parameter appears if you set the**Friction model**parameter to`Table lookup kinetic friction coefficient`.

**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**Method used to specify the rolling resistance acting on a rotating wheel hub. The default value is

`Specify rolling resistance`.

Select this option to ignore the effect of rolling resistance on a model.

Select between two rolling resistance models: `Constant
coefficient` and `Pressure and velocity dependent`.

The default value is `Pressure and velocity dependent`.

Pressure and velocity dependent

Use the **Advanced** tab to specify parameters
that the state machine uses to determine the mode 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 |

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

The sdl_4wd_dynamicssdl_4wd_dynamics example model shows the use of the Tire (Friction Parameterized) block.

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

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