Rolling Resistance

R2026b

Model rolling resistance

• 

Rolling Resistance block

To add a block to a model, double-click the canvas and start typing the block name. Then, select the block from the list.

Libraries:
Simscape / Driveline / Tires & Vehicles / Tire Subcomponents

Description

The Rolling Resistance block represents 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 of the pressure and velocity dependence of the SAE J2452 standard, or the Magic Formula. 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 Parameterization

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

• 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:

• μ₀ is the asymptotic rolling resistance coefficient.

• v_hub is the hub velocity.

• v_threshold is the threshold velocity.

Pressure and Velocity Dependent Parameterization

When you set Resistance model to Pressure and velocity dependent (SAE J2542), the block uses the formula:

$$F={\left(\frac{P}{P_0}\right)}^{\alpha }{\left(\frac{N}{N_0}\right)}^{\beta }{N}_0\cdot \left(A+B\left|v_{hub}\right|+C{v}_{hub}{}^2\right)\tanh \left(\frac{4v_{hub}}{v_{threshold}}\right),$$

where:

• P is the tire pressure.

• v_hub is the hub velocity.

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

• P₀ is 1 Pascal (Pa).

• N₀ is 1 Newton (N).

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

When you set Resistance model to Pressure and velocity dependent (Magic Formula), the block uses the Magic Formula to calculate rolling resistance as

$$F=F_{Z0}{\lambda }_{My}\left(q_{sy1}+q_{sy2}\frac{F_{X,Tread}}{F_{Z0}}+q_{sy3}\left|\frac{V_H}{V_0}\right|+q_{sy4}{\left(\frac{V_H}{V_0}\right)}^4\right){\left(\frac{F_Z}{F_{Z0}}\right)}^{q_{sy7}}{\left(\frac{p_i}{p_{i0}}\right)}^{q_{sy8}}\tanh \left(\frac{4v_{hub}}{v_{threshold}}\right),$$

where:

• F_Z0 is the Tire nominal vertical load, FNOMIN parameter.

• λ_My is the Scale factor of rolling resistance, LMY parameter.

• q_sy1,...,q_sy8 are the elements of the Q-coefficient parameters [qsy1 qsy2 qsy3 qsy4 qsy5 qsy6 qsy7 qsy8] parameter.

• V₀ is the Hub nominal longitudinal speed, LONGVL parameter.

• p_i is the Tire pressure parameter.

• p_i0 is the Tire nominal pressure, NOMPRES parameter.

• V_H is the wheel hub longitudinal velocity.

• F_X,Tread is the longitudinal friction force exerted by the road on the tire tread.

• F_Z is the vertical load on the tire.

The tanh expressions in this parameterization smoothly change the sign of the resistance force when v_hub = 0.

Ports

Input

N — Normal force, N

physical signal

Physical signal input port associated with the normal force, in N. The positive force direction is down.

Programmatic Use

Port: N

T — Tread friction force, N

physical signal

Physical signal input port associated with the friction force from the road on the tire, in N. The positive force direction is forwards.

Dependencies

To enable this port, set Resistance model to Pressure and velocity dependent (Magic Formula).

Programmatic Use

Port: f_tread

Conserving

H — Wheel hub, m/s

mechanical translational

Mechanical translational conserving port associated with the wheel hub, in m/s.

Programmatic Use

Port: H

Parameters

Resistance model — Rolling resistance computational modeling method

Constant coefficient (default) | Pressure and velocity dependent (SAE J2542) | Pressure and velocity dependent (Magic Formula)

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

• Constant coefficient

• Pressure and velocity dependent (SAE J2542)

• Pressure and velocity dependent (Magic Formula)

Programmatic Use

Parameter:	model
Values:	"sdl.enum.rollingResistanceParameterization.magic" | "sdl.enum.rollingResistanceParameterization.velocity" | "sdl.enum.rollingResistanceParameterization.constant"

Constant coefficient — Resistance coefficient for rolling tire

0.015 (default) | positive scalar

Constant coefficient value to compute the rolling resistance.

Dependencies

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

Programmatic Use

Parameter: coeff

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 (SAE J2542) or Pressure and velocity dependent (Magic Formula).

Programmatic Use

Parameter: p_tire

Alpha — Approximating coefficient α

-0.003 (default) | scalar

SAE J2452 coefficient for the 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 J2542).

Programmatic Use

Parameter: alpha

Beta — Approximating coefficient β

0.97 (default) | scalar

SAE J2452 coefficient for the 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 J2542).

Programmatic Use

Parameter: beta

Coefficient A — Approximating coefficient A

84e-4 (default) | positive scalar

SAE J2452 coefficient for the 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 J2542).

Programmatic Use

Parameter: coeff_a

Coefficient B — Approximating coefficient B

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

SAE J2452 coefficient for the 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 J2542).

Programmatic Use

Parameter: coeff_b

Coefficient C — Approximating coefficient C

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

SAE J2452 coefficient for the 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 J2542).

Programmatic Use

Parameter: coeff_c

Tire nominal pressure, NOMPRES — Nominal tire pressure

240e3 Pa (default) | positive scalar

Nominal tire pressure. NOMPRES it the TIR file identifier.

Dependencies

To enable this parameter, set Resistance model to Pressure and velocity dependent (Magic Formula).

Programmatic Use

Parameter: p_tire0

Tire nominal vertical load, FNOMIN — Normal force

4000 N (default) | positive scalar

Nominal normal force, F_z0, on tire. FNOMIN is the TIR file identifier.

Dependencies

To enable this parameter, set Resistance model to Pressure and velocity dependent (Magic Formula).

Programmatic Use

Parameter: fz0

Hub nominal longitudinal velocity, LONGVL — Nominal hub longitudinal speed

16 m/s (default) | positive scalar

Nominal hub longitudinal speed. LONGVL is the TIR file identifier.

Dependencies

To enable this parameter, set Resistance model to Pressure and velocity dependent (Magic Formula).

Programmatic Use

Parameter: vH0

Q-coefficient parameters [qsy1 qsy2 qsy3 qsy4 qsy5 qsy6 qsy7 qsy8] — Magic Formula Q-coefficients

[.0082, 0, .0014, .001, 0, 0, 1.08, -.5] 1 (default) | vector of length 8

Magic Formula Q coefficients. qsy1,…, qsy8 correspond to the TIR file identifiers.

Dependencies

To enable this parameter, set Resistance model to Pressure and velocity dependent (Magic Formula).

Programmatic Use

Parameter: q_Sy

Scale factor of rolling resistance, LMY — Rolling resistance

1 (default) | positive scalar

Scale factor of the rolling resistance, λ_MY. LMY is the TIR file identifier.

Dependencies

To enable this parameter, set Resistance model to Pressure and velocity dependent (Magic Formula).

Programmatic Use

Parameter: lmy

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.

Programmatic Use

Parameter: v_thr

Extended Capabilities

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

Version History

Introduced in R2012a

R2023a: Magic Formula compatibility enhancements

The block is now compatible with the Magic Formula. You can set Resistance model to Pressure and velocity dependent (Magic Formula) to enable Magic Formula resistance parameters.