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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.
The effective rolling radius of the tire. The rolling radius must be greater than zero. Default is 0.30 m.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.