Automotive Dynamics and Safety | Quarter Car Modelling

This assignment aims to enhance students’ knowledge on applied computer simulation and practical methods to analyze vehicles dynamics and vibration. The successful student will be able to apply analysis techniques to load an active suspension example, use commercial packages to model a quarter car model, understand the impact of modeling choices, and more.

UNIVERSITYOF HERTFORDSHIRE
School of Engineering and Technology
COURSEWORK ASSIGNMENT
Module Title: Automotive dynamics
and safety Module Code: 7AAD0054
Assignment Title: Quarter car
modelling Individual Assignment
Tutor: Mahmoud Chizari Internal Moderator: Marzio
Grasso
Student ID Number ONLY: Year Code:
Marks Awarded %:
This assignment is worth 15% of
the overall assessment for the
coursework.
Marks Awarded after Lateness Penalty
applied %:
Penalties for Late Submissions
 Late submission of any item of coursework will be capped at a minimum
pass mark if received up to one week late. Any submission received more
than one week late will be awarded a mark of zero.
 Late submission of referred coursework will automatically be awarded a
mark of zero.
 Note: The School operates a strict policy on late submission.
StudyNet marks all work submitted late, even by one second, as
Late, in which case the above late penalties will be applied.
Where genuine serious adverse circumstances apply, you may
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extension is requested a reasonable period in advance of the
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issues will not be considered as admissible circumstances. For
this reason, you are advised to submit at least one hour before
the deadline.
Please refer to your student handbook for details about the grading schemes
used by the School when assessing your work. Guidance on assessment will
also be given in the Module Guide.
Guidance on avoiding academic assessment offences such as plagiarism and
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ASSIGNMENT BRIEF
Students, you should delete this section before submitting your
work.
This Assignment assesses the following module Learning Outcomes
(Take these from the module DMD):
This assignment aims to enhance students’ knowledge on applied computer
simulation and practical methods to analyse vehicles dynamics and vibration.
The successful student will be able to;
 Apply analysis techniques to load an active suspension example
 Use commercial packages to model quarter car model with an aim to
understand;
 A method of characterizing the Newton laws for modelling oscillating
behaviour
 A theoretical approach to establish calculation of a 2 degree of freedom
system
 the impact of the modelling choices to the accuracy of results under
different loading conditions
 understands subtle different approaches to model a vibrating system
 how these findings can be used to improve the actual suspension
system
 The assignment will reinforce a student to;
 analyse an oscillating structural event such as frequencies and shape
modes.
 understand the fundamental differences to structural behaviour under
different modal assumptions (boundary conditions, load combinations)
 understand how loads can develop through an assembly. The chosen
vehicle part should belong to this simple assembly
 compare theoretical outputs to the computer models
 appreciate how a fundamental approach to simulation can be used to
derive structural performance.
Assignment Brief:
For the purposes of this assignment you have been tasked with simulating
a simplified model of a quarter car active suspension. You are encouraged
to consider the identified loading scenarios and complete the tasks of this
assignment. You may develop your own assumptions under your identified
loading/displacement scenarios and provide a clear evaluation on the
oscillating system when experiencing road conditions. Your defined
assumptions should be based on a clear loading and boundary condition
you may use to assess these solutions. These should lead you to develop
your own Simulink model. In final stage a comparison should be made on
the theoretical and Simulink models.
Please provide a report with your assumptions, calculations, solutions and
observations as follows;
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UNIVERSITYOF HERTFORDSHIRE
School of Engineering and Technology
• Your assumptions in terms of design, requirements and measurables
• State clearly your requirements and their limits
• Justify your model choices and calculate their influence on its
performance
• Compare theoretical and simulation findings for differences and
similarities
• Highlight design recommendations which can improve the function of
the design.
Important notes:
All students must submit their individual report through Canvas.
The mark will be awarded to individual within the Canvas.
Submission Requirements:
 Students must run the computer model and compare the finding with
theoretical method.
 The report must be submitted using provided template.
Please see brief below in this document for upload information.
This assignment is worth 15% of the overall assessment for this module.
Marks awarded for:
The assignment contains 5 tasks to be answered by all students.
Each task worth an equal 3 marks of total 15 marks for this assignment.
Please see blow document for detail of the tasks.
A note to the Students:
1. For undergraduate modules, a score above 40% represent a pass
performance at honours level.
2. For postgraduate modules, a score of 50% or above represents a pass
mark.
3. Modules may have several components of assessment and may
require a pass in all elements. For further details, please consult the
relevant Module Guide or ask the Module Leader.
Typical (hours) required by the student(s) to complete the assignment: hours
Date Work handed
out:
Week 32
Please check your
timetable for your time
slot.
Date Work to be
handed in:
Week 36
Please check your
timetable for your time
slot.
Target Date for the
return of the marked
assignment:
4 weeks after the
deadline
Type of Feedback to be given for this assignment:
Comments will be given on marked report through Canvas.
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Generic feedback will be given in classroom.
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UNIVERSITYOF HERTFORDSHIRE
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7AAD0054 - Automotive dynamics and safety | Quarter car
modelling | Assignment Brief
To improve the quality of the lab sheet please report any errors.
Please report all calculations / simulations within the provided template.
Active Suspension System
For road vehicle users, comfort is an important issue. To move from one
place to another, road vehicles usually encounter various vibrations and
shocks from ground, for instance, in traveling on a bumpy surface, or
crossing over an obstacle. Prolonged exposures to vibrations cause
some problems, such as pain and fatigue, for the passengers. To
alleviate these problems, momentary loads from ground should be
absorbed and damped out. Automotive suspension systems are intended
to absorb and decrease the shocks and vibrations transferred from the
ground to the passengers as well as the vehicle body. Passive
suspension systems which consist of spring and damper components
have been traditionally utilized on different types of vehicles, such as
motorcycles, passenger cars, trucks and even bikes. Active suspension
systems with separate actuators to apply controlled forces provide
better ride.
Quarter Car Modelling
A quarter-car model of a passenger sedan with active comfort and
improved handling. The suspension system shown below represents the
vehicle system at each wheel. It consists of a spring, ks, a damper, bs
and a hydraulic actuator, Fa. The tire stiffness and damping properties
are also shown by kt and bt, respectively. The effective vehicle body
mass is shown by Ms (sprung mass), and Mu (unsprung mass) represents
the effective mass for the wheel and axle. The vertical displacements
from the static equilibrium for Mu and Ms are shown by xu and xs,
respectively. The road profile is represented by xr. The suspension travel
xs - xu is measured and compared to the set point (r = 0). The required
actuator force is determined by the controller to eliminate the error, and
thus, to reduce the vehicle oscillations.
Spring ks
Damper bs
Hydraulic actuator Fa Tire
properties:
Stiffness kt
Damper bt
Effective vehicle body mass
Ms
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Figure 1. Schematic of a
simplified quarter car active
suspension
Effective mass for wheel and
axle Mu
Tasks
Please consider an active suspension system with elements shown in
Figure 1 and complete following tasks.
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 mases.
Solution
The suspension system is classified into sprung and unsprung mass. the
free body diagram is obtained as,
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UNIVERSITYOF HERTFORDSHIRE
School of Engineering and Technology
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.
m1 ¨x1 ( t ) =−Cs ¿
m2 x2
' ' ( t )=f (t )−Ct ¿
Performing a Laplace transform with zero ICs,
m1 s2 X s (s)=−Cs ¿
m2 s2 Xu (s)=f ( t ) −Ct ¿
Simplifying further,
X s ( s )= Bs +K1
M 1 s2+ Bs+ K s
Xu ( s )
Xu ( s ) = 1
m2 s2+ Bs+ k1+ K 2
F ( s ) + Bs + Ks
m2 s2 + Ks + Ku
Xs(s)
It is expressed as a block diagram as illustrated below,
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.
For the free undamped vibrations, the force term is expressed as a zero.
The assumption is that the two sprung and unsprung masses undergo
harmonic motion based on a similar frequency and phase such that,
ms xs
'' ( t ) + ( ku+ ks ) xs −ku xu =0
mu xu
' '+ ( k2 +k3 ) xu−ku xs =0
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UNIVERSITYOF HERTFORDSHIRE
School of Engineering and Technology
Combining the like terms,
The results determine the normal mode of vibration using modal vectors
or eigenvectors. They form the mode shapes of a given system and in this
case, the system vibrates in its first mode.
For the forced vibration analysis,
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UNIVERSITYOF HERTFORDSHIRE
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When simplified further, it results into,
Task 4 (3 marks)
Please simulate the system using a MATLAB program. You can consider
the assumption made in previous tasks and use the supportive
information provided for this assignment on the Canvas. These should
lead you to develop your own Simulink model with a potential design
choice which can be assessed against the model derived in previous
tasks.
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UNIVERSITYOF HERTFORDSHIRE
School of Engineering and Technology
Task 5 (3 marks)
Please used the model created in Task4 to simulate the suspension on
various road profiles. You are encouraged to evaluate the function of the
suspension on example road profile. Key calculations and assumptions
need to be explained and justified adequately. As a result, displacement
and acceleration of the suspension should be plotted. Please assume that
forces are applied uniformly.
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School of Engineering and Technology
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REFERENCES
[1] F. Andronic, M. Rasu, L. Pătuleanu, “PASIVE SUSPENSION MODELING
USING MATLAB, QUARTER CAR MODEL, INPUT SIGNAL STEP TYPE”,
TEHNOMUS.
[2] A. Mahmoud and S. Ferdinand, “Preview Control of Semi-active
Suspension Based on a Half-car Model Using Fast Fourier Transform”,
10th International Multi-Conference on Systems, Signals & Devices
(SSD) Hammamet, Tunisia, March 18-21, 2013
[3] M. Agostinacchio, D. Ciampa, and S. Olita, “The Vibration Induced by
Surface irregulation in Road pavements – a Matlab Approach,”
Springer, vol. 6, pp. 267-275, 2014.
[4] B. Marek, S. Asok, G. Litak, et al, “Vibrations of a vehicle excited by
real road profiles,” Springer – Verlag, pp. 99-109, 2010
[5] D. Rao, Solving Vibrational Analysis Problem Using Matlab, New Age
Publication, 2007.
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