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 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.
Ports
Input
N — Normal force
physical 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 coefficients
physical signal | vector | [μs,
μk]
Physical signal input port associated with the static (μs) and kinetic (μk) friction coefficients. Provide the friction coefficients as a two-element vector, specified in the order [μs, μk].
Dependencies
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.
Output
S — Slip
physical signal
Physical signal output port associated with the relative slip between the tire and road.
Conserving
A — Axle
mechanical rotational
Mechanical rotational port associated with the axle that the tire sits on.
H — Hub
mechanical translational
Mechanical translational port associated with the wheel hub that transmits the thrust generated by the tire to the remainder of the vehicle.
Parameters
Main
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 (μs) and kinetic (μk) friction coefficients to the block as an array of two elements in the order [μs, μk]. |
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 scalar
Distance 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
(μs) and kinetic
(μk) friction
coefficients to the block as an array of two elements in the order
[μs,
μk].
Dependencies
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 scalar
Ratio of the allowable longitudinal force to the normal force allowed before the tire begins to slip (μs). The parameter must be greater than either the kinetic friction coefficient or the largest value in the kinetic friction coefficient vector.
Dependencies
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 scalar
Ratio of the transmitted longitudinal force to the normal force allowed during tire slip (μk). The ratio must be greater than zero.
Dependencies
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) | vector
Vector 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.
Dependencies
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) | vector
Vector 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.
Dependencies
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.
Dependencies
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.
Dependencies
This parameter is visible when the Friction
model parameter is set to Table lookup
kinetic friction coefficient. For more
information, see Main Parameter Dependencies.
Dynamics
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.
Dependencies
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 scalar
Tire longitudinal stiffness CFx.
Dependencies
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 scalar
Tire longitudinal damping bFx.
Dependencies
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.
Dependencies
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 scalar
Rotational inertia Iw of the wheel-tire assembly.
Dependencies
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) | scalar
Initial angular velocity, Ω(0), of the tire.
Dependencies
Selecting Specify inertia and initial
velocity for the Inertia
parameter, exposes this parameter. For more information, see Dynamics Parameter Dependencies Table.
Rolling Resistance
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.
Dependencies
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.
Dependencies
Each Resistance model option exposes related parameters. For more information, see Rolling Resistance Parameter Dependencies Table.
Constant coefficient — Proportionality constant
0.015 (default) | positive scalar
Coefficient that sets the proportionality between the normal force and the rolling resistance force. The parameter must be greater than zero.
Dependencies
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 scalar
Inflation pressure of the tire. The parameter must be greater than zero.
Dependencies
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) | scalar
Exponent of the tire pressure in the model equation. See Rolling Resistance Parameter Dependencies Table.
Dependencies
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) | scalar
Exponent of the normal force model equation. See Rolling Resistance Parameter Dependencies Table.
Dependencies
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 A
84e-4 (default)
Velocity-independent force component in the model equation. The parameter must be greater than zero. See Pressure and Velocity Dependent Model.
Dependencies
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 B — Velocity-dependent force component B
6.2e-4
s/m (default) | positive scalar
Velocity-dependent force component in the model equation. The parameter must be greater than zero. See Pressure and Velocity Dependent Model.
Dependencies
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 C — Velocity-dependent force component C
1.6e-4
s^2/m^2 (default) | positive scalar
Force component that depends on the square of the velocity term in the model equation. The parameter must be greater than zero. See Pressure and Velocity Dependent Model.
Dependencies
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.
Velocity threshold — Wheel hub velocity threshold for mathematical slip model
0.001
m/s (default) | positive scalar
Velocity 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.
Dependencies
Selecting On for the Rolling
resistance parameter exposes this parameter. For more
information, see Rolling Resistance Parameter Dependencies.
Advanced
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 scalar
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 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 scalar
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.
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.
More About
Real-Time and Hardware-in-the-Loop Simulation
For optimal simulation performance, set the Dynamics > Compliance parameter to No compliance - Suitable for HIL
simulation.
Extended Capabilities
C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.
See Also
Fundamental Friction Clutch | Tire (Magic Formula) | Tire (Simple) | Tire-Road Interaction (Magic Formula)