# Rolling Resistance

Model rolling resistance

## Library

Tires & Vehicles/Tire Subcomponents

## Description

The block models the resistance force that acts on the wheel hub due to the rolling resistance at the road-wheel contact surface. The model can use a constant resistance coefficient or the pressure and velocity dependence of the SAE J2452 standard. The resistance force is zero when the normal force acting at the wheel-road surface is less than or equal to zero.

### Constant Resistance Coefficient Model

In the constant coefficient model, the rolling resistance is directly proportional to the resistance coefficient:

F=Nμ

where parameters represent the following quantities:

• F — Rolling resistance force

• N — Normal Force

• μ — Rolling resistance coefficient

The rolling resistance coefficient has a hyperbolic form that eliminates discontinuity at vhub=0:

μ=μ0tanh(4vhub/vthreshold)

where parameters represent the following quantities:

• μ0 — Asymptotic rolling resistance coefficient

• vhub — Hub velocity

• vthreshold — Threshold velocity

### Pressure and Velocity Dependent Model

The pressure- and velocity-dependent model uses the following formula:

$F={\left(\frac{P}{{P}_{0}}\right)}^{\alpha }{\left(\frac{N}{{N}_{0}}\right)}^{\beta }{N}_{0}\cdot \left(A+B|{v}_{hub}|+C{v}_{hub}{}^{2}\right)$

where parameters represent the following quantities:

• P — Tire pressure

• vhub — Hub velocity

• α, β, A, B, C — Approximating coefficients

• P0 — 1 Pascal (Pa)

• N0 — 1 Newton (N)

In the previous equation, parameters P0 and N0 remove the physical units from each exponential expression base.

Connection H is a mechanical translational conserving port that represents the hub of the tire. Connection N is a physical signal input port that represents the normal force acting on the tire. Normal force is positive if it points downward.

## Dialog Box and Parameters

### Resistance Model

Select the model used to compute the rolling resistance on a wheel hub. The parameter provides two options:

• `Constant coefficient`

• `Pressure and velocity dependent`

The default value is `Constant coefficient`.

### Constant Coefficient

Selecting the `Constant coefficient` option exposes two model parameters: Constant coefficient and Velocity threshold.

Constant Coefficient

Coefficient that sets the proportionality between the normal force and the rolling resistance force. The parameter must be greater than zero. The default value is `255`.

Velocity Threshold

Velocity at which the full rolling resistance force is transmitted to the rolling hub. The parameter ensures the force remains continuous during velocity direction changes, which increases the numerical stability of the simulation. The parameter must be greater than zero. The default value is `0.001 m/s`.

### Pressure and Velocity Dependent

Tire pressure

Inflation pressure of the tire. The parameter must be greater than zero. The default value is `250e+3 Pa`.

Alpha

Exponent of the tire pressure in the model equation. See Pressure and Velocity Dependent Model. The default value is `-0.003`.

Beta

Exponent of the normal force model equation. The default value is `0.97`.

Coefficient A

Velocity independent force component in the model equation. The parameter must be greater than zero. The default value is `84e-4`.

Coefficient B

Velocity dependent force component in the model equation. The parameter must be greater than zero. The default value is ```6.2e-4 s/m```.

Coefficient C

Force component that depends on the square of the velocity term in the model equation. The parameter must be greater than zero. The default value is `1.6e-4 s^2/m^2`.

Velocity Threshold

Velocity at which the full rolling resistance force is transmitted to the rolling hub. The parameter ensures the force remains continuous during velocity direction changes, which increases the numerical stability of the simulation. The parameter must be greater than zero. The default value is `1e-3 m/s`.

## Ports

PortDescription

N

Physical signal input port that represents the normal force

H

Conserving translational port that represents the wheel hub