Lecture Notes - Part 1 Sorniotti

Modern Vehicle Systems

Design (ENG 3170)

A. Sorniotti Senior Lecturer in Advanced Vehicle Engineering (16AA03)

Email: [email protected], Ext: 9688

S. Fallah Lecturer in Vehicle and Mechatronic Systems (11AA03)

Email: [email protected], Ext: 6528

mailto:[email protected]

mailto:[email protected]

Modern Vehicle Systems Design – Dr. A. Sorniotti

The Vehicle Engineering Group •Coordinator of the FP7 E-VECTOORC project;

•Principal investigator in the FP7 projects iCOMPOSE, PLUS-

MOBY and FREE-MOBY, WP leader in AUTOSUPERCAP;

•Optimisation and testing of novel transmission systems;

•Development of novel automotive controllers

www.e-vectoorc.eu

http://www.e-vectoorc.eu/



Examples of results

• Three driving modes (sport, normal, eco) selectable by the driver;

Torque-vectoring controller

• Vehicle response ‘designed’ through the controller

Skid pad test

results

• Three driving modes (sport, normal, eco) selectable by the driver;

Torque-vectoring controller

• Vehicle response ‘designed’ through the controller

• Reduced delay

Step steer results

• Increased yaw damping;

Examples of results

Examples of results Drivetrain modelling

and testing

Outline


•Part 1: basic theory of vehicle dynamics;

•Part 2: hybrid electric and fully electric vehicles

Final Mark

•40% coursework due on Tuesday week 11 (report dealing with

the set of design calculations that will be assigned in week 6);

•60% final exam (2 hour duration, including exercises, multiple-

choice questions, open questions)

Main References

•Milliken WF and DL, Race Car Vehicle Dynamics, SAE

International, 1995, ISBN 1-56091-526-9;

•Reimpell J, Stoll H and Betzler H, The Automotive Chassis,

Butterworth-Heinemann, 2001, ISBN 0 7506 5054;

•Limpert, R., Brake Design and Safety, 1999, SAE

International;

•Ehsani M, Gao Y, Gay SE, Emadi, A, Modern Electric, Hybrid

Electric and Fuel Cell Vehicles, CRC, 2010, ISBN

1420053981;

•Chan CC, Chau KT, Modern Electric Vehicle Technology,

Oxford University Press, 2001, ISBN 978-0-19-850416-0;

•Lecture Notes



Part 1 - Topics

•Revision of basic concepts relating to tyre behaviour;

•Derivation of analytical formulas for the calculation of the load

transfer in traction/braking and discussion of the criteria for

braking system design;

•Derivation of the analytical formulas for the calculation of the

load transfers in cornering conditions;

•Fundamentals of braking system design;

•Discussion of vehicle pitch dynamics


Part 1 – General Philosophy

•Many of the concepts to be presented in this module have

already been discussed in the level 2 vehicle dynamics

module;

•This module aims at the analytical and quantitative description

of these concepts;

•Real engineers must be able to carry out design calculations;

•By the end of the module it is expected to be able to carry out

load transfer calculations, basic suspension analysis and

design, simulation of vehicle longitudinal dynamics


Revision – Tyre Behaviour

Longitudinal force

𝑆𝑙𝑖𝑝 𝑅𝑎𝑡𝑖𝑜 =𝜔

𝜔0− 1

• Various possible definitions according

to different textbooks;

• According to this definition the slip ratio is positive in traction and

negative in braking;

• As a consequence, it is:

−1 < 𝑆𝑙𝑖𝑝 𝑅𝑎𝑡𝑖𝑜 < ∞

Wheel locked during braking

Wheel spinning in conditions of

vehicle standstill



Longitudinal force

𝐹𝑧

• The location of this

peak depends on the

tyre and surface

characteristics;

• The presence of this

peak justifies the

difficulty of tyre slip

control during anti-

lock braking and

traction control

𝜇𝑥,𝑀𝐴𝑋 =𝐹𝑥,𝑀𝐴𝑋

𝐹𝑧



Longitudinal force

• The variability of these

characteristics is very

significant;

• For example, some sources

report an increase of the

longitudinal force vs. slip

ratio on snow

𝜇𝑥 =𝐹𝑥

𝐹𝑧



𝑥

𝑦

𝑉

Slip Angle

Lateral Force

Aligning Moment

Lateral force

Key concepts

• Tyre reference system;

• Slip angle;

• Lateral force;

• Aligning moment

𝛼



Lateral force

Key concepts

• Cornering stiffness C;

• Non-linear behaviour;

• Friction coefficient

𝜇𝑦,𝑀𝐴𝑋 =𝐹𝑦,𝑀𝐴𝑋

𝐹𝑧


Lateral force


Notice that in this case

the tyre has an

asymptotic behaviour

(frequent case) as a

function of slip angle



𝜇𝑦 =𝐹𝑦

𝐹𝑧

Lateral force

Please pay attention!

𝐹𝑧

𝐹𝑧



Interaction between longitudinal and lateral force

These trends justify the regulations about brake distribution and the

adoption of anti-lock braking systems




Rear wheel locking Oversteer

Front wheel locking Understeer




Key concept: friction ellipse

Elliptical envelope






The effect of camber is

much less significant

than the one related to

slip angle



Tyre rolling resistance

Undriven wheel in conditions of constant speed

Rolling resistance is caused by the fact that the resultant vertical force is

applied to the frontal part of the contact patch

𝜔

𝐹𝑧 −𝐹𝑧

𝐹𝑅𝑜𝑙𝑙

∆𝑥

𝑅𝑤,𝑙𝑎𝑑𝑒𝑛

𝐹𝑅𝑜𝑙𝑙𝑅𝑤,𝑙𝑎𝑑𝑒𝑛 = 𝐹𝑧∆𝑥

∆𝑥 = 𝑓𝑅𝑤,𝑙𝑎𝑑𝑒𝑛

𝐹𝑅𝑜𝑙𝑙 = 𝑓𝐹𝑧 −𝐹𝑅𝑜𝑙𝑙




Exercise – What would the free body diagram be for a driven wheel?

𝑓 = 𝑓0 + 𝑓1𝑉 + 𝑓2𝑉2

The rolling resistance coefficient is a function of speed:

Typical values are:

𝑓0 = 0.011 [−] 𝑓1 = 0 [𝑠/𝑚] 𝑓2 = 6.5 10−6 [𝑠2/𝑚2]




Effect of slip angle on rolling resistance

𝐹𝑥

𝐹𝑦

𝑉

𝐹𝑅𝑜𝑙𝑙

𝐹𝑅𝑜𝑙𝑙 = 𝐹𝑥 cos 𝛼 + 𝐹𝑦 sin 𝛼

𝐹𝑅𝑜𝑙𝑙 ≅ 𝐹𝑥 + C𝛼2

If 𝐹𝑦 ≅ Cα (small slip angle) then:

𝛼

Calculation of the Wheel Loads

•Vehicle dynamics is significantly influenced by the variation of

the vertical load between each tyre and the road as a function

of braking and cornering forces;

•In general, the lower is the load transfer, the better are vehicle

dynamics;

•It is necessary to achieve a good understanding of the

mechanisms which provoke load transfers in order to have an

acceptable evaluation of vehicle dynamics


Calculation of the Wheel Loads

ya

xa LFzF ,

Vehicle parameters

RFzF ,

RRzF ,

LRzF ,

Roll angle V


Prediction of the Vertical Load

in Static Conditions

a b

mg

CG

L

a = front semi-wheelbase

b = rear semi-wheelbase

L = wheelbase

FSTATICzF ,, RSTATICzF ,,

O




L

mgaFF RRSTATICzLRSTATICz

2,,,,

L

mgbFF RFSTATICzLFSTATICz

2,,,,

mgbLF FSTATICz ,,

Moment balance equation about point O

L

mgbF FSTATICz ,,

mgFF RSTATICzFSTATICz ,,,,

Force balance equation (vertical direction)

L

mga

L

bmgFmgF FSTATICzRSTATICz

1,,,,

Combining the former equations, it is:




In the case of race cars it is easy to change the static load distribution

during the vehicle design phase

62% 38% Excluding driver





In this case the mass distribution is shifted

towards the front axle

Prediction of the Effect of the

Aerodynamic Forces and Moments

DRAGCAERODYNAMIF _

FRESISTANCEROLLINGF ,_ RTRACTIONF ,

FCAERODYNAMIzF ,,

CG

CGH

Constant velocity

Rear wheel driven vehicle (like our FS vehicle)

RCAERODYNAMIzF ,,

YCAERODYNAMIT ,

L

O

DOWNFORCECAERODYNAMIF _




Moment balance equation about point O

LT

L

bF

L

HFF

YCAERODYNAMIDOWNFORCECAERODYNAMI

CGDRAGCAERODYNAMIFCAERODYNAMIz

1,_

_,,

YCAERODYNAMIDOWNFORCECAERODYNAMI

CGDRAGCAERODYNAMIFCAERODYNAMIz

TbF

HFLF

,_

_,,




2

__2

1VSCF DOWNFORCECAERODYNAMIDOWNFORCECAERODYNAMI

2

_2

1VSCF DRAGDRAGCAERODYNAMI

2

,,2

1LVSCT YTYCAERODYNAMI

32.1m

kg


S frontal area of the vehicle

air density



2

,,

,,,,

RCAERODYNAMIz

LRSTATICzRRzLRz

FFFF

2

,,

,,,,

FCAERODYNAMIz

LFSTATICzRFzLFz

FFFF

0_,,,, DOWNFORCECAERODYNAMIFCAERODYNAMIzRCAERODYNAMIz FFF




DRAGCAERODYNAMIF _

RRESISTANCEROLLINGF ,_FTRACTIONF ,

FCAERODYNAMIzF ,,

CG

CGH

Constant velocity

Front wheel driven vehicle

RCAERODYNAMIzF ,,

YCAERODYNAMIT ,

L

DOWNFORCECAERODYNAMIF _



Aerodynamic Forces and Moments Typical Data Sets (passenger cars)

Vehicle CDRAGS [m2] CDRAG S [m2]

Renault 5 0.67 0.37 1.80

Opel Kadett 0.60 0.32 1.88

Ferrari Testarossa 0.61 0.33 1.85

Alfa Romeo GTV 0.71 0.40 1.77

Mercedes 190 E 0.65 0.34 1.89

Mercedes 200 0.60 0.29 2.07


Load Transfer during

Traction/Braking

L

HmaF CGx

az x ,

xazF ,xazF ,

If the vehicle is braking or accelerating, there is an additional load transfer which, in a

very first approximation, without considering the effect of suspension stiffness and the

anti-dive, anti-lift and anti-squat designs of the suspensions, can be computed in the

following way:

CG xma

CGH

RTRACTIONF ,FRESISTANCEROLLINGF ,_


Load Transfer during

Traction/Braking

22

,,,

,,,,XazFCAERODYNAMIz

LFSTATICzRFzLFz

FFFFF

22

,,,

,,,,XazRCAERODYNAMIz

LRSTATICzRRzLRz

FFFFF


Load Transfer during Braking

xa

XazF ,

Vertical load

1.5 g

Formula Student vehicle (for an assigned V)

XazF ,

Rear axle

Front axle


Load Transfer during Braking

xa

XazF ,

Vertical load

1.1 g

Typical Passenger Car (for an assigned V)

XazF ,

Rear axle

Front axle


The vertical load

distribution

significantly changes

during braking

Equations for the Prediction of the Load

Transfer during Traction/Braking

Static load distribution 50:50,

centre of gravity height 0.5 m

• Load distribution during braking at 1.1g and 100 km/h?

• What happens for a different number of passengers?


• Load distribution at 130

km/h (constant velocity)?

Lecture Notes - Part 1 Sorniotti

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