Engee documentation

Rolling Resistance

Rolling resistance model.

blockType: Engee1DMechanical.Vehicles.Tires.RollingResistance

rolling resistance

Path in the library:

/Physical Modeling/1D Mechanical/Tires & Vehicles/Tire Subcomponents/Rolling Resistance

Description

The Rolling Resistance block represents the drag force acting on the wheel hub due to rolling resistance on the road-wheel contact surface. The block may use a constant drag coefficient, pressure and speed dependence in accordance with SAE J2452 or the empirical formula of H. Paceika. The drag force is zero when the normal force acting on the wheel-road contact surface is less than or equal to zero.

Parameterization of the constant drag coefficient

If the Resistance model parameters are set to Constant coefficient, the rolling resistance is directly proportional to the drag coefficient , where:

  • - `Rolling resistance force;

  • - normal force;

  • - rolling resistance coefficient.

The rolling resistance coefficient has a hyperbolic shape, which eliminates the discontinuity at

where

  • - is the asymptotic coefficient of rolling resistance;

  • - hub velocity;

  • - threshold speed.

Pressure and velocity dependent parameterization

If the Resistance model parameters are set to Pressure and velocity dependent (SAE J2542), the block uses the formula:

where

  • - tyre pressure;

  • - hub velocity;

  • - approximating coefficients;

  • - 1 pascal (Pa);

  • - 1 Newton (N).

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

Parameterization by Hans Paceika’s empirical formula

If the Resistance model parameters are set to Pressure and velocity dependent (Magic Formula), the block uses the empirical formula of H. Patzeki formula for calculating rolling resistance (see [1] for details) :

where

  • - is the value of the parameter Tire nominal vertical load, FNOMIN;

  • - value of parameters Scale factor of rolling resistance, LMY;

  • - elements of the Q-coefficient parameters [qsy1 qsy2 qsy3 qsy4 qsy5 qsy6 qsy7 qsy8];

  • - value of parameter Hub nominal longitudinal longitudinal speed, LONGVL;

  • - value of parameter Tire pressure;

  • - value of parameter Tire nominal pressure, NOMPRES;

  • - longitudinal speed of the wheel hub;

  • - longitudinal friction force acting on the road side;

  • - vertical load on the tyre.

The tanh expressions in this parameterization smoothly change the sign of the drag force when .

Ports

Input

# N — normal force, N
`scalar

Details

The input port associated with the normal force, in H. The positive direction of the force is downwards.

Data types

Float64.
Complex numbers support

No

# T — tread friction force, N
scalar

Details

Input port related to the road friction force on the tyre, in N. The positive direction of the force is forwards.

Dependencies

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

Data types

Float64.
Complex numbers support

No

Conserving

# H — wheel hub, m/s
`rotational mechanics

Details

The non-directional rotational port associated with the wheel hub, in m/s.

Program usage name

hub_flange

Parameters

Main

# Resistance model — rolling resistance method
Constant coefficient | Pressure and velocity dependent (SAE J2542) | Pressure and velocity dependent (Magic Formula)

Details

A method for calculating the rolling resistance of a wheel hub. Set as:

  • Constant coefficient

  • Pressure and velocity dependent (SAE J2542)

  • Pressure and velocity dependent (Magic Formula)

Values

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

Constant coefficient
Program usage name

rolling_resistance_parameterization
Evaluatable

No

# Constant coefficient — coefficient of rolling resistance of the tire

Details

The value of a constant coefficient for calculating rolling resistance.

Dependencies

To use this parameter, set the Resistance model parameter to Constant coefficient.

Default value

0.015
Program usage name

const_rolling_resistance_coefficient
Evaluatable

Yes

# Tire pressure — tire inflating pressure
Pa | uPa | hPa | kPa | MPa | GPa | kgf/m^2 | kgf/cm^2 | kgf/mm^2 | mbar | bar | kbar | atm | ksi | psi | mmHg | inHg

Details

Constant tire inflating pressure.

Dependencies

To use this parameter, set the Resistance model parameter to Pressure and velocity dependent (SAE J2542) or Pressure and velocity dependent (Magic Formula).

Units

Pa | uPa | hPa | kPa | MPa | GPa | kgf/m^2 | kgf/cm^2 | kgf/mm^2 | mbar | bar | kbar | atm | ksi | psi | mmHg | inHg
Default value

250.0e3 Pa
Program usage name

p_tire
Evaluatable

Yes

# Alpha — coefficient α

Details

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

Dependencies

To use this parameter, set the Resistance model parameter to Pressure and velocity dependent (SAE J2542).

Default value

-0.003
Program usage name

alpha
Evaluatable

Yes

# Beta — coefficient β

Details

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

Dependencies

To use this parameter, set the Resistance model parameter to Pressure and velocity dependent (SAE J2542).

Default value

0.97
Program usage name

beta
Evaluatable

Yes

# Coefficient A — coefficient A

Details

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

Dependencies

To use this parameter, set the Resistance model parameter to Pressure and velocity dependent (SAE J2542).

Default value

0.0084
Program usage name

coefficient_a
Evaluatable

Yes

# Coefficient B — coefficient B
s/m | s/ft

Details

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

Dependencies

To use this parameter, set the Resistance model parameter to Pressure and velocity dependent (SAE J2542).

Units

s/m | s/ft
Default value

0.00062 s/m
Program usage name

coefficient_b
Evaluatable

Yes

# Coefficient C — coefficient C
(s/m)^2 | (s/ft)^2

Details

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

Dependencies

To use this parameter, set the Resistance model parameter to Pressure and velocity dependent (SAE J2542).

Units

(s/m)^2 | (s/ft)^2
Default value

0.00016 (s/m)^2
Program usage name

coefficient_c
Evaluatable

Yes

# Tire nominal pressure, NOMPRES — nominal tire pressure
Pa | uPa | hPa | kPa | MPa | GPa | kgf/m^2 | kgf/cm^2 | kgf/mm^2 | mbar | bar | kbar | atm | ksi | psi | mmHg | inHg

Details

Nominal tire pressure. NOMPRES – ID in the TIR file.

Dependencies

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

Units

Pa | uPa | hPa | kPa | MPa | GPa | kgf/m^2 | kgf/cm^2 | kgf/mm^2 | mbar | bar | kbar | atm | ksi | psi | mmHg | inHg
Default value

240.0e3 Pa
Program usage name

p_tire_nominal
Evaluatable

Yes

# Tire nominal vertical load, FNOMIN — normal strength
N | nN | uN | mN | kN | MN | GN | dyn | lbf | kgf

Details

Rated normal power, , on the bus. FNOMIN – ID in the TIR file.

Dependencies

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

Units

N | nN | uN | mN | kN | MN | GN | dyn | lbf | kgf
Default value

4000.0 N
Program usage name

F_vertical_nominal
Evaluatable

Yes

# Hub nominal longitudinal velocity, LONGVL — nominal longitudinal rotation speed of the hub
m/s | mm/s | cm/s | km/s | m/hr | km/hr | in/s | ft/s | mi/s | ft/min | mi/hr | kn

Details

The nominal longitudinal speed of the hub. LONGVL – id of the TIR file.

Dependencies

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

Units

m/s | mm/s | cm/s | km/s | m/hr | km/hr | in/s | ft/s | mi/s | ft/min | mi/hr | kn
Default value

16.0 m/s
Program usage name

v_longitudinal_nominal
Evaluatable

Yes

# Q-coefficient parameters [qsy1 qsy2 qsy3 qsy4 qsy5 qsy6 qsy7 qsy8] — the coefficients of Q in the empirical formula

Details

Coefficients of the empirical formula Q. qsy1,…​, qsy8 match the file IDs of the TIR.

Dependencies

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

Default value

[0.0082, 0.0, 0.0014, 0.001, 0.0, 0.0, 1.08, -0.5]
Program usage name

scaling_factor_vector
Evaluatable

Yes

# Scale factor of rolling resistance, LMY — rolling resistance

Details

Scale coefficient of rolling resistance, . LMY – this is the identifier of the TIR file.

Dependencies

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

Default value

1.0
Program usage name

lambda_M_y
Evaluatable

Yes

# Velocity threshold — the speed when the entire rolling resistance force is transferred to the rolling hub
m/s | mm/s | cm/s | km/s | m/hr | km/hr | in/s | ft/s | mi/s | ft/min | mi/hr | kn

Details

The minimum speed at which maximum rolling resistance is achieved.

Units

m/s | mm/s | cm/s | km/s | m/hr | km/hr | in/s | ft/s | mi/s | ft/min | mi/hr | kn
Default value

0.001 m/s
Program usage name

v_threshold
Evaluatable

Yes

Literature

  1. Pacejka, H. B. "Tire and Vehicle Dynamics." Elsevier Science, 2005.