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 v_hub = 0:

$$\mu ={\mu }_0\cdot \tanh \left(\frac{4\cdot v_{hub}}{v_{threshold}}\right),$$

where parameters represent the following quantities:

• μ₀ is the asymptotic rolling resistance coefficient

• v_hub is the hub velocity

• v_threshold is the threshold velocity

Pressure and Velocity Dependent Model

When you set Resistance model to Pressure and velocity dependent, the block uses the formula:

$$F={\left(\frac{P}{P_0}\right)}^{\alpha }{\left(\frac{N}{N_0}\right)}^{\beta }{N}_0\cdot \left(A+B\left|v_{hub}\right|+C{v}_{hub}{}^2\right),$$

where parameters represent the following quantities:

• P is the tire pressure

• v_hub 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

N — Normal force, N

physical signal

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

Conserving

H — Wheel hub, m/s

mechanical translational

Mechanical translational conserving port that represents the wheel hub.

Parameters

Resistance model — Rolling resistance computational modeling method

Constant coefficient (default) | Pressure and velocity dependent

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

• Constant coefficient

• Pressure and velocity dependent

Constant coefficient — Resistance coefficient for rolling tire

0.015 (default) | positive scalar

Constant coefficient value to compute rolling resistance.

Dependencies

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

Tire pressure — Inflation pressure of rolling tire

250e3 Pa (default) | positive scalar

Constant inflation pressure of the rolling tire.

Dependencies

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

Alpha — Approximating coefficient α

-0.003 (default) | scalar

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.

Beta — Approximating coefficient β

0.97 (default) | scalar

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.

Coefficient A — Approximating coefficient A

84e-4 (default) | positive scalar

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.

Coefficient B — Approximating coefficient B

6.2e-4 s/m (default) | nonnegative scalar

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.

Coefficient C — Approximating coefficient C

1.6e-4 s^2/m^2 (default) | nonnegative scalar

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.

Velocity threshold — Velocity when full rolling resistance force is transmitted to rolling hub

0.001 m/s (default) | positive scalar

Minimum velocity that attains the maximum amount of rolling resistance.

Extended Capabilities

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

Version History

Introduced in R2012a