1. Two-Axle Vehicle Model
A simple two-axle longitudinal vehicle model is shown in Figure 1. Notice that the body-fixed axis is placed at the center of gravity of the vehicle with y-axis pointing out of the page. We can understand all the various forces acting on the vehicle by drawing the free-body diagram.
Fig 1. Two-Axle Longitudinal Model
Fig 2. Free-Body Diagram of the Vehicle
Table 1. Vehicle Parameters
2. Equations of Motion
Let us assume that for a passenger car,ha ≈ hd ≈ h and the vehicle does not leave the ground with only motion along the longitudinal axis.
From Euler's Equations for a rigid body
with the following assumptions
steady state: maximum traction
3. Vehicle Dynamics Simulation
Given the traction forces above, we can implement the dynamics model in LabVIEW MathScript RT module and simulate the dynamics using the LabVIEW Control Design and Simulation Module. The overall model is shown in Figure 3.
Fig 3. Block Diagram of Longitudinal Vehicle Model
We can simulate the vehicle response for various road grades and drive configuration. As shown in Figure 4, the front panel provides vehicle responses for two difference road grades.
Fig 4. Vehicle Dynamics Simulation for grade 0% (Left) 25%(Right)
This article briefly introduces the concepts of basic vehicle dynamics. The kinematic equations are implemented using LabVIEW Control Design and Simulation Module and LabVIEW MathScript RT Module.
You can download an evaluation copy of the modules here
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5. Related Links
ME 390: Vehicle Dynamics and Controls (Spring 2011)
Prof. Raul. G. Longoria, ME, University of Texas, Austin