Vehicle Dynamics

INSTITUTIONAL AFFILIATION
ADVANCED DYNAMICS WITH APPLIED COMPUTER
MODELLING
2018/2019
ASSIGNMENT 2
VEHICLE DYNAMICS
STUDENT NAME
STUDENT REGISTRATION NUMBER
DATE OF SUBMISSION
2019

Vehicle Dynamics
INTRODUCTION
A half-car model is a 2D vehicle model used to model the vehicle’s response when driving over
various road surfaces. The model consists of the body of the vehicle, the unsprung mass at the
front, and the unsprung mass at the rear [1]. The tire stiffness in this design is modelled using the
spring and damper while the body accounts for the mass.
ASSUMPTIONS
(i) Car is tested on a test-rig and not on an actual road.
(ii) Road displacement are enforced when the vertical displacements are applied on the
lower end of the spring representing the tire.
(iii) The angular displacement of the car body may cause a change in the horizontal
distance between the attachment points.
The vehicle parameters for a medium-sized car are based on a 50/50 front-rear weight
distribution based on the use of similar spring and damper values at the front and rear are as
shown in the table below [2],
These parameters are measured for the entire car body. The suspension values and the unsprung
mass values are measured at the corner of the vehicle and hence are not an aggregate value of the
entire vehicle system.

Vehicle Dynamics
SYSTEM MODELLING
The linear suspension for the half car suspension model is obtained by applying Newton’s
second law of motion formulating linear differential equations to describe the dynamics of the
passive half car suspension [3],
Using the free body diagram for the half car model,
The rear tire and the front tire are considered rather stiff and when the tire hits a different road
profile, an upward force is transmitted to the wheels in a vertical acceleration of the wheels [4].
The suspension elements tend to dampen the vertical force for the transmission of the car body.
Representing the equations in matrix form, we obtain,