Vehicle

Longitudinal vehicle dynamics component

Note:  This component is used with the Tire component.

The Vehicle component models the longitudinal dynamics of a vehicle. The model has only one degree of freedom (longitudinal motion). Lateral and vertical motions as well as roll, pitch, and yaw are neglected. The Vehicle component is intended for use with two Tire components. The front and rear axles connections are modeled using a real output port for vertical force and a 1-D mechanical translation flange to transfer longitudinal force and motion between the vehicle and the axle.

Equations

The Vehicle equations are given by

${v}_{x}$ =

${a}_{x}$ =

Where s  is the longitudinal DOF of the vehicle, l  is the vehicle wheel base, and  a  is the distance from the front axle to the projection point of the vehicle CG onto the line connecting front and rear axles

The equation of longitudinal motion is

Where  ${F}_{l}$   is the external force on the vehicle and  ${F}_{x}$  is the traction force and is defined by

Also, ${F}_{d}$   is calculated as

The weight distribution for front and rear axles is calculated by the following equations:

where h is distance from the CG to the ground.

Connections

 Name Condition Description ID ${\mathrm{flange}}_{a}$ - Front axle longitudinal flange flange_xf ${\mathrm{flange}}_{b}$ - Rear axle longitudinal flange flange_xr ${f}_{\mathrm{zf}}$ - Real output port for front axle vertical force f_zf ${f}_{\mathrm{zf}}$ - Real output port for real axle vertical force f_zf ${v}_{x}$ - Real output port for vehicle forward velocity (km/h) speed ${F}_{l}$ use external load = true Conditional real input port for the externally applied longitudinal force Fl

Parameters

 Symbol Default Units Description ID $\mathbf{false}$ - Enables/Disables external load: true - external load (force) port is enabled false - external load (force) port is disabled useExternalLoad $g$ $9.81$ $\frac{m}{{s}^{2}}$ Gravitational acceleration g $\mathrm{α}$ $0$ $\mathrm{rad}$ Ground inclination alpha $h$ $0.5$ $m$ Distance from CG to the ground h $l$ $3$ $m$ Wheel base l $a$ $1.5$ $m$ Distance from front axle to the normal projection point of CG onto the ground a $m$ $1500$ $\mathrm{kg}$ Vehicle mass m $A$ $1$ ${m}^{2}$ Vehicle effective cross-section A ${C}_{d}$ $0.3$ $-$ Coefficient of drag Cd $\mathrm{ρ}$ $1.2$ $\frac{\mathrm{kg}}{{m}^{3}}$ Mass density of air rho ${v}_{w}$ $0$ $\frac{m}{s}$ Wind speed vw

Initial Conditions

 Symbol Condition Default Units Description ID ${V}_{x\mathrm{0}}$ $-$  $\frac{m}{s}$ Initial forward velocity vx

References

Pacejka, Hans B. Tire and Vehicle Dynamics. Second Edition. SAE International and Elsevier, 2005.