Rolling Resistance

Model rolling resistance

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

$μ = μ_{0} \cdot \tanh (\frac{4 \cdot v_{h u b}}{v_{t h r e s h o l d}}),$

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:

$F = {(\frac{P}{P_{0}})}^{α} {(\frac{N}{N_{0}})}^{β} N_{0} \cdot (A + B | v_{h u b} | + C v_{h u b}^{2}) \tanh (\frac{4 v_{h u b}}{v_{t h r e s h o l d}}),$

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

$F = F_{Z 0} λ_{M y} (q_{s y 1} + q_{s y 2} \frac{F_{X, T r e a d}}{F_{Z 0}} + q_{s y 3} | \frac{V_{H}}{V_{0}} | + q_{s y 4} {(\frac{V_{H}}{V_{0}})}^{4}) {(\frac{F_{Z}}{F_{Z 0}})}^{q_{s y 7}} {(\frac{p_{i}}{p_{i 0}})}^{q_{s y 8}} \tanh (\frac{4 v_{h u b}}{v_{t h r e s h o l d}}),$

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

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N — Normal force, N
physical signal

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

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).

Conserving

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H — Wheel hub, m/s
mechanical translational

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

Parameters

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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)

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.

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).