Quarter car modelling

UNIVERSITYOF HERTFORDSHIRE, SCHOOL OF ENGINEERING AND COMPUTER SCIENCES

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COURSEWORK ASSIGNMENT

Module Title: Automotive dynamics and safety

Module Code: 7AAD0054

Assignment Title: Quarter car modelling

Individual Assignment

Tutor: Mahmoud Chizari

Internal Moderator: Gbanaibolou Jombo

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 %:

Please see “Penalties for Late Submissions”

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 apply for an extension to the hand-in date, provided the extension is requested a reasonable period in advance of the deadline. However, you are warned that lateness due to network congestion (either at the University or on your local network), difficulty with filenames, poor time management and similar 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 collusion is given at this URL: http://www.studynet.herts.ac.uk/ptl/common/LIS.nsf/lis/citing_menu

If the assignment is laboratory based (though not computer-based), or involves offsite activity, please attach the risk assessment form for the Internal Moderator to see.

UNIVERSITYOF HERTFORDSHIRE, SCHOOL OF ENGINEERING AND COMPUTER SCIENCES

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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 and compare the theoretical and Simulink models. In final stage a comparison

should be made on those found from modelling/simulation.

Please provide a report with your assumptions, calculations, solutions and observations as follows:

• 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 the methods 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 follow the requested tasks and report findings.

➢ The report must be submitted using provided template.

Please see brief below in this document for upload information.

UNIVERSITYOF HERTFORDSHIRE, SCHOOL OF ENGINEERING AND COMPUTER SCIENCES

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This assignment is worth 15% of the overall assessment for this module.

Marks awarded for:

The assignment contains modelling and simulation tasks must be reported by all students.

Report must be completed by following the instruction of the provided template.

The marking scheme has been specified on the template of the report.

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.

Generic feedback will be given in lab/classroom.

UNIVERSITYOF HERTFORDSHIRE, SCHOOL OF ENGINEERING AND COMPUTER SCIENCES

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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 calculation modelling and computer 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, Cs and a hydraulic actuator, Fa. The tire stiffness and damping properties are also

shown by kt and Ct, 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.

Elements Parameter Value

Effective mass for vehicle body Ms [kg] See your class list

Effective mass for wheel system Mu [kg] See your class list

Spring; vehicle suspension ks [N/m] See your class list

Spring; wheel system kt [N/m] See your class list

Damper; vehicle suspension Cs [Ns/m] See your class list

Damper; wheel system Ct [Ns/m] See your class list

Body vertical displacement Xs [m] See your class list

Wheel vertical displacement Xu [m] See your class list

Road profile xr [m] See your class list

Figure 1. Schematic of a simplified quarter car passive suspension and its specifications

Tasks

Please consider a passive suspension system with elements shown in Figure 1 and complete

following tasks. Report must be completed within the provided template.

Task 1: Theoretical modelling

• Perform free body diagram (FBD) for the system to satisfy the Newton’s 2nd low. Please

develop your own assumptions to address the applied forces onto the identified mases.

• 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 either free or forced vibration and complete the results. The assumption made

in previous step can be used here. However, your defined assumptions should be based on

Cs

Ct

UNIVERSITYOF HERTFORDSHIRE, SCHOOL OF ENGINEERING AND COMPUTER SCIENCES

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clear and specific metrics which you may use to assess these solutions. The vibration

characters, e.g. frequency of oscillation and response of the system, need to be appropriately

calculated based on your individual data.

Task 2: MATLAB simulation

• Please simulate the system using a MATLAB program. You can consider the assumption made

in previous tasks. These should lead you to develop your own individual Simulink model with

a potential design choice which can be assessed against the model derived in previous task.

• Please used the model created in Task1 to simulate the suspension model. You are

encouraged to evaluate the function of the suspension on specified road profile. Key

calculations and assumptions need to be explained and justified adequately.

• Please plot the displacement and acceleration of the car/suspension. You can assume that

possible forces are applied uniformly.

Useful references:

1. Control Tutorials for MATLAB and Simulink,

http://ctms.engin.umich.edu/CTMS/index.php?example=Introduction&section=SimulinkModeli

ng, (last seen 11/02/2020)

2. Duc Chung Tran, Quarter Car Modelling,

https://uk.mathworks.com/matlabcentral/fileexchange/46316-quarter-car-modelling-zip, (last

seen 11/02/2020)

3. Jonathan Sprinkle, Quarter car suspension model, published on 30 Aug 2013,

https://www.youtube.com/watch?v=TKbChGz4-mw, (last seen 11/02/2020)

4. James Allison, Simulation and Animation of a Quarter-Car Automotive Suspension Model,

https://uk.mathworks.com/matlabcentral/fileexchange/35478-simulation-and-animation-of-aquarter-

car-automotive-suspension-model, (last seen 11/02/2020)