Longitudinal Vehicle Dynamics

Longitudinal vehicle dynamics component

Note:  This component is used with the Tire component.

The Longitudinal Vehicle Dynamics 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

$s_{\mathrm{xr}} \= s- l \+ a$ 

$s_{\mathrm{xf}} \= s \+ a$ 

$v_x$ = $\frac{\ⅆ}{\ⅆ t}s$

$a_x$ = $\frac{\ⅆ}{\ⅆ t}v$

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

$m · a_x \= F_x - F_d - m · g · \sin \left(\mathrm{\α}\right) - F_l$

Where  $F_l$  is the external force on the vehicle and  $F_x$  is the traction force and is defined by

$F_x \= f_{\mathrm{xr}} \+ f_{\mathrm{xf}}$

Also, $F_d$  is calculated as

$F_d \= \frac{1}{2}{C}_d · \mathrm{\ρ} · A · ∣v_x - v_w∣ · \left(v_x - v_w\right)$

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

$l · f_{\mathrm{zf}} \= -h · \left(m · a_x\+ F_d \+ m · g · \sin \left(\mathrm{\α}\right) - F_l\right) \+ m · g · \cos \left(\mathrm{\α}\right) · \left(l - a\right)$

$l · f_{\mathrm{zr}} \= -h · \left(m · a_x\+ F_d \+ m · g · \sin \left(\mathrm{\α}\right) - F_l\right) \+ m · g · \cos \left(\mathrm{\α}\right) · a$

where h is distance from the CG to the ground.

Connections 

Parameters

Initial Conditions

See Also

Driveline Library Overview

MapleSim Library Overview

1-D Mechanical Overview

Tire Component Library

Vehicle and Tire

Tire

References

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