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.

Extended Capabilities

C/C++ Code GenerationGenerate C and C++ code using Simulink® Coder™.

Introduced in R2012a

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