Quarter Car Modelling Assignment

UNIVERSITYOF HERTFORDSHIRE
School of Engineering and Technology
7AAD0054 - Automotive dynamics and safety
Quarter Car Modelling
Assignment
Student Name
Student Registration Number
Date of submission
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UNIVERSITYOF HERTFORDSHIRE
School of Engineering and Technology
Tasks
The quarter car model has been used by the automotive researchers to study the dynamics of a vehicle
during the design phase. The model examines the dynamics of the vehicle focusing on one wheel
section over different road surfaces during transmission. The software used in the simulation of
Newton’s second law of motion is MATLAB R2018b software. The simulation discusses the
suspension based on different damping coefficients as determined in the system payload as well as the
car speed.
Task 1 (3 marks)
Perform free body diagram (FBD) for the system to satisfy the Newton’s 2nd low. Please develop your
own assumptions and provide/plot a clear evaluation on applied forces to the identified masses.
SOLUTION
The quarter car model is a combination of a single wheel with two degree of freedom. The following
is a physical model of the quarter car model,
The free body diagram alongside the physical vehicle wheel representation is as illustrated below,
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UNIVERSITYOF HERTFORDSHIRE
School of Engineering and Technology
Assumptions:
(i) The quarter car model is a representation of the entire vehicle in the analysis of the active
suspension and system dynamics.
(ii) The damper has two or more opted damping rates that require a high force at low
velocities and a low force at high velocities and can move quite swiftly among the two.
Task 2 (3 marks)
Find the equation of motions and response of the system to oscillations. You may use your own
assumptions as used in the FBD of the system. Please make sure to address loading scenarios applied
to masses, springs and damping elements. Please consider any external forces applied to the system.
SOLUTION
ms ̈Z s=−bs ( ̇Zs − ̇Zu ) −ks ( Zs−Zu ) +f a
mu ̈Zu=bs ( ̇Z s− ̇Zu ) + ks ( Z s−Zu ) −f a +bt ( ̇Zr− ̇Zu ) +k t ( Zt −Zu )
Task 3 (3 marks)
Please consider both free and forced vibration and compare the results. The assumption made in
previous tasks can be used here. However, your defined assumptions should be based on clear and
specific metrics which you may use to assess these solutions.
To obtain the undamped natural frequencies of the unperturbed system, the damper parameters and
forces are equated to zero such that,
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