Tire (Friction Parameterized)
Tire with friction parameterized in terms of static and kinetic coefficients
Libraries:
Simscape /
Driveline /
Tires & Vehicles
Description
The Tire (Friction Parameterized) block represents a tire with friction parameterized in terms of static and kinetic coefficients. The static friction coefficient, μs, determines the applied torque at which the tire loses traction and begins to slip. The kinetic friction coefficient, μk, determines the amount of torque that the tire transmits to the pavement once it begins to slip. The tire regains traction when its relative velocity over the pavement falls below the specified traction velocity tolerance.
To increase the fidelity of the tire model, specify properties such as tire compliance, inertia, and rolling resistance. Note that 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 when preparing the model for hardware-in-the-loop (HIL) simulation.
Wheel Slip
When you set Slip output type to Relative
,
the block outputs the relative slip velocity as a unitless physical signal at port
S, such that
where:
Vx is the wheel hub longitudinal velocity at port H.
rw is the rolling radius.
Ω is the wheel axle angular velocity at port A.
When you set Slip output type to
Absolute
, port S outputs the
absolute contact point slip velocity in a rotational form such that
where u is the time-rate of change in longitudinal deformation and u/rw is equivalent to the rotational velocity of the spring and damper in the logged simulation results.
When you set Slip output type to Absolute
,
the block uses the friction model of the Fundamental Friction Clutch block. The figure demonstrates how the
block implements slip:
When you set Compliance to No
compliance - Suitable for HIL simulation
, the block sets .
Examples
Vehicle with Four-Wheel Drive
A four-wheel drive vehicle starting from rest and ascending a 15 degree incline. Initially the vehicle rolls backwards until the engine develops sufficient torque to counter the slope. The tire compliance dynamics can be seen as the vehicle starts to accelerate. The model variant chosen for all of the tires can be set to the Simple, Friction Parameterized, or Magic Formula tire model using the hyperlinks in the model.
Ports
Input
N — Normal force, N
physical signal
Physical signal input port associated with the normal force acting on the tire, in N. The normal force is positive if it acts downward on the tire, pressing it against the pavement.
M — Friction coefficients, unitless
physical signal | two-element vector
Physical signal input port associated with the unitless static and kinetic friction coefficients, μs and μk, respectively. Provide the friction coefficients as a two-element vector, specified in the order [μs, μk].
Dependencies
To enable this port, set Friction model to
Physical signal friction
coefficients
.
Output
S — Slip, unitless or in rad/s
physical signal
Physical signal output port associated with the slip between the tire and road, unitless or in rad/s. When you set Output type to:
Relative
, the port outputs unitless, relative slip.Absolute
, the port outputs absolute slip in rad/s.
Conserving
A — Axle
mechanical rotational
Mechanical rotational conserving port associated with the axle.
H — Hub
mechanical translational
Mechanical translational conserving port associated with the wheel hub.
Parameters
Main
Rolling radius — Unloaded tire-wheel radius
0.3
m
(default) | positive scalar
Distance between the pavement and the center of the tire.
Slip output type — Relative or absolute switch option
Relative
(default) | Absolute
Whether the block uses a relative or absolute slip friction parameterization.
Friction model — Friction model
Fixed kinetic friction
coefficient
(default) | Table lookup kinetic friction
coefficient
| Physical signal friction
coefficients
Friction model the block uses during the simulation. When you select:
Fixed kinetic friction coefficient
, the block uses the constant static and kinetic friction coefficients that you specify.Table lookup kinetic friction coefficient
, you can specify friction using a table lookup. The block treats the static coefficient as a constant and treats the kinetic coefficient as a constant or function of tire slip. Use this setting to simulate tire dynamics under constant pavement conditions.Physical signal friction coefficients
, the block enables port M for you to provide [μs, μk]. Use this setting to simulate tire dynamics under variable pavement conditions.
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 value of this parameter must be greater than either the Kinetic friction coefficient parameter or the largest value in the Kinetic friction coefficient vector parameter.
Dependencies
To enable this parameter, set Friction model to Fixed
kinetic friction coefficient
or Table
lookup kinetic friction coefficient
.
Kinetic friction coefficient — Kinetic friction coefficient
0.70
(default) | positive scalar
Ratio of the longitudinal force transferred to the road to the normal force allowed during tire slip, μk. The ratio must be greater than zero.
Dependencies
To enable this parameter, set Friction model
to Fixed kinetic friction
coefficient
.
Tire slip vector — Tire slip
[0, .02, .06, .15, .6, 1]
rad/s
(default) | vector
Reference tire slip. The elements in this vector correspond one-to-one with the Kinetic friction coefficient vector parameter. If the Tire slip vector parameter contains only nonnegative values, the block assumes the slip-versus-friction function to be symmetric about the slip axis.
Dependencies
To enable this parameter, set Friction model
to Table lookup kinetic friction
coefficient
.
Kinetic friction coefficient vector — Kinetic friction coefficient
[.89, .88, .8, .75, .7, .7]
(default) | vector
Kinetic friction coefficient for a given tire slip. The elements in this vector correspond one-to-one with the Tire slip vector parameter. The vectors must be the same size.
Dependencies
To enable this parameter, set Friction model
to Table lookup kinetic friction
coefficient
.
Interpolation method — Interpolation method
Linear
(default) | Smooth
Interpolation method for the lookup table to process 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
To enable this parameter, set Friction model to Table
lookup kinetic friction coefficient
.
Extrapolation method — Extrapolation method
Linear
(default) | Nearest
| Error
Extrapolation method for the lookup table to process the tire slip-kinetic friction coefficient characteristic. To produce:
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.Error
— Select this option to avoid going into the extrapolation mode when you want your data to be within the table range. If the input signal is outside the range of the table, the simulation stops and generates an error.
For more information on extrapolation algorithms, see the PS Lookup Table (1D) block reference page.
Dependencies
To enable this parameter, set Friction model to Table
lookup kinetic friction coefficient
.
Dynamics
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
— The block ignores dynamical compliance.Specify stiffness and damping
— The block treats the tire as a stiff, dampened spring that deforms under load.
Longitudinal stiffness — Longitudinal stiffness
1e6
N/m
(default) | positive scalar
Tire longitudinal stiffness, CFx.
Dependencies
To enable this parameter, set Compliance to
Specify stiffness and damping
.
Longitudinal damping — Longitudinal damping
1000
N/(m/s)
(default) | positive scalar
Tire longitudinal damping, bFx.
Dependencies
To enable this parameter, set Compliance to
Specify stiffness and damping
.
Inertia — Inertia option
No inertia
(default) | Specify inertia and initial
velocity
Whether to simulate tire rotational inertia. When you select
No inertia
— The block ignores inertia.Specify inertia and initial velocity
— The block treats the tire as a stiff, dampened spring that deforms under load.
Dependencies
To enable this parameter, set Inertia to
Specify inertia and initial
velocity
.
Tire inertia — Tire rotational inertia
1
kg*m^2
(default) | positive scalar
Rotational inertia, Iw, of the wheel-tire assembly.
Dependencies
To enable this parameter, set Inertia to
Specify inertia and initial
velocity
.
Initial velocity — Initial rotational velocity
0
rad/s
(default) | scalar
Initial angular velocity, Ω(0), of the tire.
Dependencies
To enable this parameter, set Inertia to Specify
inertia and initial velocity
.
Rolling Resistance
Rolling resistance — Rolling resistance option
Off
(default) | On
Whether to simulate rolling resistance. When you select
Off
, the block ignores rolling resistanceOn
the block includes rolling resistance in the simulation.
Resistance model — Rolling resistance option
Constant
coefficient
(default) | Pressure and velocity dependent
Whether to simulate the rolling resistance of the tire. When you select
Constant coefficient
— The block ignores rolling resistance.Pressure and velocity dependent
— Include rolling resistance.
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
To enable this parameter, set Rolling resistance to
On
and Resistance
model to Constant
coefficient
.
Tire pressure — Tire pressure
250e3
Pa
(default) | positive scalar
Inflation pressure of the tire. The parameter must be greater than zero.
Dependencies
To enable this parameter, set Rolling
resistance to On
and
Resistance model to Pressure
and velocity dependent
.
Alpha — Tire pressure equation exponent
-0.003
(default) | scalar
Exponent of the tire pressure in the model equation.
Dependencies
To enable this parameter, set Rolling
resistance to On
and
Resistance model to Pressure
and velocity dependent
.
Beta — Normal force equation exponent
0.97
(default) | scalar
Exponent of the normal force model equation.
Dependencies
To enable this parameter, set Rolling
resistance to On
and
Resistance model to Pressure
and velocity dependent
.
Coefficient A — Velocity-independent force component A
84e-4
(default) | positive scalar
Velocity-independent force component in the model equation. The parameter must be greater than zero.
Dependencies
To enable this parameter, set Rolling
resistance to On
and
Resistance model to Pressure
and velocity dependent
.
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.
Dependencies
To enable this parameter, set Rolling
resistance to On
and
Resistance model to Pressure
and velocity dependent
.
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.
Dependencies
To enable this parameter, set Rolling
resistance to On
and
Resistance model to Pressure
and velocity dependent
.
Velocity threshold — Wheel hub velocity threshold for mathematical slip model
0.001
m/s
(default) | positive scalar
Velocity at which the block applies the full rolling resistance. This 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
To enable this parameter, set Rolling resistance to
On
.
Advanced
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. If this value is too low, the tire does not gain traction. If this value is too high, the tire velocity changes suddenly when the tire gains traction, which can result in an unstable simulation. The parameter must be greater than zero.
Engagement threshold force — Engagement threshold force
10
N
(default) | positive scalar
Threshold force at which block applies the normal force to the tire. If this value is too low, the tire gains and loses traction rapidly. If this value is too high, the block produces 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™.
Version History
Introduced in R2012aR2024b: Improve compliance and inertia
The block locations of the inertias and compliance to be more accurate during acceleration. The block uses new definitions of absolute and relative slip to more closely reflect the Tire (Magic Formula) block. Models that contain the Tire (Friction Parameterized) block generate different outputs in R2024b than in previous releases.
R2022b: Select slip output type
You can now model relative tire slip, which is consistent with the Tire
(Magic Formula) block. To select between relative and absolute
slip, set Output type to Relative
or
Absolute
. The output at port S is now
multiplied by -1
compared to versions prior to R2024b.
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