# Rolling Resistance

Model rolling resistance

• Library:
• Simscape / Driveline / Tires & Vehicles / Tire Subcomponents

## Description

The Rolling Resistanceblock models the resistance force that acts on the wheel hub due to the rolling resistance at the road-wheel contact surface. The block 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

When you set Resistance model to ```Constant coefficient```, the rolling resistance is directly proportional to the resistance coefficient F = Nμ, where parameters represent the following quantities:

• F is the rolling resistance force

• N is the normal Force

• μ is the rolling resistance coefficient

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

`$\mu ={\mu }_{0}\cdot \mathrm{tanh}\left(\frac{4\cdot {v}_{hub}}{{v}_{threshold}}\right),$`

where parameters represent the following quantities:

• μ0 is the asymptotic rolling resistance coefficient

• vhub is the hub velocity

• vthreshold is the threshold velocity

### Pressure and Velocity Dependent Model

When you set Resistance model to ```Pressure and velocity dependent```, the block uses the 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 is the tire pressure

• vhub is the hub velocity

• α, β, A, B, C are the approximating coefficients

• P0 is defined as 1 Pascal (Pa)

• N0 is defined as 1 Newton (N)

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

## Ports

### Input

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Physical signal input port that represents the normal force. The positive normal force is down.

### Conserving

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Mechanical translational conserving port that represents the wheel hub.

## Parameters

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Method to compute the rolling resistance on a wheel hub. The parameter has two options:

• `Constant coefficient`

• `Pressure and velocity dependent`

Constant coefficient value to compute rolling resistance.

#### Dependencies

To enable this parameter, set Resistance model to `Constant coefficient`.

Constant inflation pressure of the rolling tire.

#### Dependencies

To enable this parameter, set Resistance model to `Pressure and velocity dependent`.

SAE J2452 coefficient for pressure and velocity parameterization. You determine this value using empirical data in accordance with SAE J2452.

#### Dependencies

To enable this parameter, set Resistance model to `Pressure and velocity dependent`.

SAE J2452 coefficient for pressure and velocity parameterization. You determine this value using empirical data in accordance with SAE J2452.

#### Dependencies

To enable this parameter, set Resistance model to `Pressure and velocity dependent`.

SAE J2452 coefficient for pressure and velocity parameterization. You determine this value using empirical data in accordance with SAE J2452.

#### Dependencies

To enable this parameter, set Resistance model to `Pressure and velocity dependent`.

SAE J2452 coefficient for pressure and velocity parameterization. You determine this value using empirical data in accordance with SAE J2452.

#### Dependencies

To enable this parameter, set Resistance model to `Pressure and velocity dependent`.

SAE J2452 coefficient for pressure and velocity parameterization. You determine this value using empirical data in accordance with SAE J2452.

#### Dependencies

To enable this parameter, set Resistance model to `Pressure and velocity dependent`.

Minimum velocity that attains the maximum amount of rolling resistance.

## Version History

Introduced in R2012a