Mod-01 Lec-01 Introduction to Vehicle Dynamics

Mod-01 Lec-01 Introduction to Vehicle Dynamics


welcome to this course on vehicle dynamics
we are going to spend the next 35 hours on understanding the dynamics of vehicle as the
name indicates vehicle dynamics simply means that we are going to study vehicles in motion
so we are going to look at how vehicles are going to behave before we go into a formal
introduction of this course let us first look at what are the books that i am going to follow we will follow that with the syllabus and
then brief introduction this will be the first class this class will be towards motivating
you to look at vehicle dynamics so these are the text books that i am going
to follow the text books are you know gillespie fundamentals of vehicle dynamics a very well-known
textbook in this field reza jazar vehicle dynamics theory and applications springer
book hans pacejka tire and vehicle dynamics slightly advanced when compared to the first
2 books and then bernd heibing chassis handbook where we will take some data in order to illustrate
the practicality of what we are going to see in this course so i suggest that you periodically look at
these books in order to understand what is being done in this course okay let us now
start with the formal introduction this is going to be chalk and talk i may use or i
will use the power point presentations especially when the figures and the drawings are bit
difficult i may use that if it is difficult to draw in the board or else it will only
be with the chalk that i am going to talk the reason is that i want to give you time
to assimilate things especially there will be lot of derivations in this course and it
is important that you have the time to assimilate as i write down these equations hence the
course will completely be based on this method okay we will have the class on mondays tuesdays
tomorrow at 8 o’ clock and wednesday at 12 o’ clock okay it has been 3 hours okay as i told you vehicle dynamics is a dynamics
or the vehicle in motion and we are going to study what happens in motion of course
when you talk about vehicle a number of things come to your mind the first thing that come
to your mind is the part of the vehicle so if you study this as a course what constitutes
a vehicle just briefly let us review quickly what are the components of vehicle that will
be involved in what we are going to study now so if you look at the vehicle per se you can
broadly classify them into the power module okay which involves engine and so on the chassis
module and if you want to add you can further divide
this and say that you can involve this what i call as a body module say anything and everything
of the vehicle can be brought into these 3 categories for example if you look at the
power train or the power which gives the power to the vehicle you can include the engine which is of course
the most important thing for power as well as other subsidiary equipments or the components
which actually take the power to the wheel so if you look at the power that is given
to the vehicle it is given by the engine and the power that is developed by the engine
goes to the wheel so you can include all those transmission systems that go to the wheel
which you can say gearbox etc okay now if you want you can also in this category
include also the axles it does not matter we are only categorizing them okay if you
are looking at the chassis then you are looking at a number of subsystems which is say for
example the suspension systems you are looking at the steering system and you are looking at tires and wheels which
you can include here or you can include in the axle system okay of course you are the body okay which makes
you comfortable to sit in the vehicle or carry goods and so on so broadly in other words
this is not complete but i know that you know all these things you know the mechanisms of
many of these things so i am not going to cover that broadly vehicle consists of a number
of subsystems all these subsystems are going to act in order that you carry from one place
to the other and so what is the fundamental requirement
of a vehicle or what does these subsystems do when you go in a vehicle? or in other words
what are the requirements of the vehicle? of course it has to carry people do not tell
me that it has to carry people yes of course it has to carry people but they have 3 important
requirements when it carries people obviously safety it has to carry people safely it has
to carry people comfortably and of course economically
okay so these are the 3 fundamental requirements if you look at vehicle as it moves the second category i am not saying it is
not important as important as the first one is the driver interaction with the vehicle
so in other words the vehicle has to listen to the driver it has to do what he wants him to do and it
has to do that again in a prompt and effective way so in this course this is what essentially
we are going to study what are the factors which affects safety? now when i say safety we are not looking at
things like crash that is not our interest okay that is not our interest so for example
when we say safety what is that we mean? for example when a vehicle takes a turn okay how
does it behave? okay when you brake how does it behave and so on? so when we say safety
we are not looking at situations like crash okay so we are looking at safety for our dynamics
point of view comfort we are going to look at how your comfort as you travel in the vehicle
is affected? how do you characterize comfort? what are the subsystems of the vehicle which
you are going to have an effect on comfort? okay how does the road profiles interact with
the vehicle and affect your comfort? and more importantly what defines comfort? so these are the things that we are going
to look at in terms of comfort we are not going to spend lot of time on economical part
of your travel but we are going to concentrate here and there the economics of vehicle operations
in this course we are not going to cover for example engines that is the separate course
okay but we will talk about certain other subsystems like tires how that affects the
economics of vehicle motion? so essentially we will be concentrating on
these 3 aspects safety is linked with the second part of this categorization safety
is the result of the vehicle properly listening to the driver hence that is why i have put
that as a second category and that the vehicle has to listen listen in such a fashion that
it is safe for the people inside so we are going to look that as well okay so for example we are going to pick up the
difference between a formula 1 car and for example the cars you drive what is the difference
between that 2? we are going to look at that kind of very exciting things in this course
right so these are the things that we are going to look at it the same thing can be
looked at in different perspective in other words there are various perspectives to look
at these 3 aspects and that is what we are going to cover in the next 30 minutes in other words a broad picture emerges when
we talk about this in terms of a driver this is simple maybe you very easily understand
this and already know it but this gives us a picture of what we are going to do a driver
a vehicle a response and then effect so the most important thing is that triangle the
driver interacts with the vehicle because of his interaction say for example what is
meant by interaction? he may give a steering input he may accelerate
the vehicle he may brake the vehicle and so on so he interacts with the vehicle okay by
means of things which are around him okay because of that there is a response of the
vehicle the vehicle responds the vehicle decelerates the vehicle takes a turn and so on so this
is the response to the input okay and the response may make him modify or not you know
depending upon what is the response so there is a lot of feel depending upon what
is the response the driver may modify his input okay so in other words there is a very
close interaction between the driver vehicle and the response okay the response has another
effect the response has an effect on the occupants of the vehicle so in other words the effect
on occupants okay is also important right now this is what we are going to look at we will not be going into details of what
is the effect of the occupants and so on but we will definitely point out under normal
circumstances what is the effect on the occupants? okay so we are going to look at these 3 things
very carefully so the driver of course as i said accelerates and brakes now how are
we going to study this? we are going to study this using mathematical models now what do i mean by mathematical model?
so i have a vehicle is represented by means of a set of differential equations so vehicle
which was introduced 5 minutes back to have subsystems consisting of a number of them
okay can be also looked at from a very different perspective okay as a set of differential
equations okay so this forms a very important part of this course or the core of this course
a mathematical model of the vehicle so what are the things that participate in
this mathematical model will come to that in a minute so this mathematical model will
have an input okay which will be from the driver so we are going to deal with this input
and you will get a set of output so in other words the vehicle will be reduced to a system
with an input and an output of course you can add a feedback you can modify this like
in what you did in control systems and so on we will do that we will use a lot of control
system concepts in this course okay we will of course revise some of them as we go along
but the perspective now of a vehicle is that of a mathematical model okay so what is this
mathematical model and what is it based on? very simple all of us know it okay when you
talk about dynamics we have to talk about newton we have to talk about euler of course
we have to talk about newton-euler equations and so on so these equations okay will form the basis
of our development of mathematical model so that being the basis the language of defining
the vehicle is going to be different it is not in terms of the subsystems which we had
defined it will be in terms of mass of the vehicle we will talk in terms of moment of
inertias of the vehicle moment of inertia and say i xx i yy and i zz and
so on okay we will see that we will use 3 moment of inertias
and not i xy and so on we will talk about stiffness or in other words we will include
in this stiffnesses we will talk about the stiffness of the springs which form a part
of the suspension system we will talk about damping so damping stiffness these are the
things that enters into the mathematical model the other things which enter into the model
are compliances just opposite of stiffnesses and there are going to be very special terms
which may also be used here and we will introduce that as we go along so in other words the
mathematical model looks at the vehicle from a very different perspective or in terms of
very different quantities whose definition most of it at least you already know clear
okay so i hope you remember all the dynamics that you did in your previous classes which
will be used and which will be applied in this course clear from another perspective the vehicle dynamics
study can be broadly classified into what is called as longitudinal dynamics lateral dynamics
and vertical dynamics in other words a mathematical model covers the vehicle behavior in the longitudinal
direction the lateral direction which is perpendicular to the vehicle and in the vertical direction
okay as it goes over a bump or as it goes in a rough road and so on so basically the mathematical models are the
ones which are written in such a fashion that we understand what happens in these 3 directions
clear okay now you may ask a question what is this input? say steering behavior what
do you mean by steering behavior? what is deceleration acceleration and so on? because
the question that may come to your mind is when i drive my vehicle in a crowded road
okay in the traffic then i give all sorts of inputs okay it can be a sudden braking or i can do a maneuver
which is very fast maneuver i can do lane change and so on in other words there are
so many things that i do when i drive the vehicle and what do you mean by this input
and what are the types of input that you are going to give or in other words are you going
to create every scenario that happens outside on the road here in order to understand the
vehicle behavior very important to understand that first that
we are not going to build scenarios in this course and that is not what when you develop
a vehicle v2 there are a set of standard tests okay which are available in order to understand
the vehicle in other words there is an iso standard which tells you what are the inputs
that are required in order to understand the vehicle behavior so we have iso standard for understanding
the vehicle behavior these are called by different names and there are number of them okay so
i am going to list a few of them not going to complete list here but we will see that
later in the course so when we come to the input part we are going to talk about say
for example you want to overtake a vehicle in the actual scenario okay suppose you are driving in a highway and you
want to overtake a vehicle of course i want to understand how my vehicle is going to behave
if i want to overtake a vehicle okay and so what do you do? suppose the vehicle is going
like this and there is a vehicle before you so in order to overtake the vehicle you go
okay and then you go back right so you do what is called as double lane change so there is a test called double lane change
okay or you can just do a single lane change right in other words which to a great extent
mimics what happens in reality but there are other tests which may not exactly mimic but
is used in order to understand the dynamics of the vehicle they are much more technical
for example there will be a test which we will talk about a lot in this course which
is called as the pulse test or pulse steer in this test i am going to give a steering
input okay 40 degree change in less than a second okay so i just change it and then bring
it back right this is called a pulse test you may ask me are you using this anywhere?
may not or will not be using it in your day to day driving but it brings out the dynamics
of the vehicle okay so this is one of the tests that we will be doing or which will
be given as an input to this in other words input has been very carefully
defined by this iso standard in order to understand the dynamics of the vehicle okay or to bring
out certain scenarios there is other tests like constant radius cornering or constant
radius tests and there are tests okay which say for example there is a test called j-hook
test and so on which bring out extremity conditions so in other words what is that we are going
to do or what is usually done? there are tests the tests involve either an
input through steering or through brake and acceleration we will mostly be using braking
conditions okay so these conditions there are number of tests these tests are given
as an input to this mathematical model which is based on a good old newton-euler techniques
and so on now what are the outputs that we are going to look at? okay ultimately as i said i want to look at
comfort level i want to look at safety this is what i said the whole ideal of studying
vehicle dynamics is to study the safety economics and so on let us take the condition of braking
let us say that i want to brake a vehicle okay suddenly i see some obstacle and i want
to brake the vehicle okay so i said that i want safety during braking actually what does
it mean or how does this output look like? if i want to be safe then i have to look at
braking distance for example i cannot have a vehicle whose braking distances are large
we will see what typically they are later is large right if the braking distances are
large then obviously i am not going to satisfy this condition of safety and i may go and
crash with that obstacle so in other words we are going to look at as outputs okay quantities
which are related to what i said before this at least is simple braking distance okay
so we are going to look at that kind of output distance and there are other outputs that
typically what i said is that we are going to go back to newton “professor – student
conversation starts” so what are the things when you look at newton’s equation? what
are the things that comes to your mind? lateral and longitudinal dynamics “professor – student
conversation ends” yeah so what comes to your mind is accelerations
what comes to your mind is velocity and so on right so the outputs will now be in terms
of these quantities distances accelerations velocities and so on there will be other things
we will see that later but all of them are to do with the dynamics clear now how is this
related to say for example comfort? i may ask you a question okay you get acceleration how do i deduce my comfort
levels or in other words what is the effect? so this is the output response is the output
yes i can understand that if the braking is not happening as the driver wishes it to be
maybe he can jam or press the brakes hard fine that i understand okay from braking distance
if you want to reduce the velocity or increase the velocity he either presses the brake pedal
all that i can understand okay but you are talking about effect of the occupants
what is that? you know say for example i want to be comfortable sitting in the back seat
and you know enjoying my ride so how does this give me or how does this outputs give
me that feeling of goodness? so whole lot of research has been done as to how say for
example the acceleration levels affect your comfort levels inside the vehicle or in other words we will map certain of the
outputs like for example vertical acceleration okay lateral acceleration and so on we will
map them into your comfort level by lot of research has been done on this topic map them
into your comfort level okay and tell you what is the effect of the occupation so it
is a large topic we are going to give a glimpse of this towards the end of the course as to
the effect the cause and the effect on the occupants
clear so in a nutshell this is what we are going to look at in this course we are going
to look at first the mathematical model input output and so on clear okay in order to understand
the mathematical model itself okay we will introduce to you or i will introduce to you
a certain technical information to write down these equations if you remember newton’s equations on one
side we have quantities or newton-euler equations if you want to call it you have these quantities
on the left hand side or right hand side however you write on the other side of the equation
you have forces moments and so on so we have to understand those as well so i should add
to these lists the right hand side of the equation which i would call as generalized
force moment and so on okay so we also have to understand the source of
these forces how does this force originate? how does it act on the vehicle? how is it
transferred to the vehicle? so this is one of things also when we come to the mathematical
model becomes important just to give you an example if i have to brake the vehicle or
accelerate the vehicle then i need a braking force and a traction force alright yeah you can tell me that the braking force
emanates when i press the brake pedal yes of course that is the braking system but we
are not going to look at you know the braking system per se in this course but ultimately
as a vehicle when it brakes the forces emanate from that interface between the tire and the
ground so we are going to look at actually how the vehicle talks to the road how actually the traction is developed? how
actually the force is developed? so when you take a turn also you should look at what generally
called as the grips in all these conditions i have to talk about
the grip of the vehicle or grip of the tire okay with the road so in that process of understanding
the mathematical model we will go into the details of tire mechanics and tire behavior
because that forms the basis for one of the quantities on the right hand side there are
other quantities as well the other quantity or other force which is
important in that mathematical model is aerodynamic forces so we have to look at the aerodynamic forces
how do they act on the vehicle? and what are the design parameters of the vehicle which
affects aerodynamics? we will follow let say a book at that time i will give you a reference
so we will follow that also in this course okay and there will be a short introduction on
aerodynamics the effect of the body okay on the aerodynamic forces okay so in other words
yes there is i would say an environmental interaction with the vehicle and this is due
to various components body of the vehicle and so on so we are going to look at that
because that forms a basis for the vehicle model right okay this is we are talking about the equation
part of it okay so the point of view i do not want you to get confused is at force is
force and input or an output so you may look at it like that yes okay braking force can
be an input but in the equation that is formed okay the force naturally comes and that is
why i wrote this along with that equation clear any questions? so the view that we are
going to take is that we have a mathematical model we have an input and we have an output
okay because of this mathematical model and how does the vehicle behave or how is
that i convert a vehicle into a mathematical model? so that is the perspective that we
are going to look at in this course clear okay we are going to introduce of course a
number of terminologies no course is complete if you do not understand the words call it
jargons or call a technical terms okay the course is not complete unless you understand
these terms so you cannot converse okay or express your
ideas if you do not understand the corresponding language of a course so from that perspective
there will be a lot of new jargons or definitions or terms that we will introduce in this course
okay how does this jargons look like? okay let us look at it from a different perspective
so we now know what we are expecting from this course? what is that we are going to
do? the other way of looking at it also the another
perspective is look at the course or look at what we are going to study from 3 different
angles the first angle is what i call as driving dynamics same thing but termed in a different
way another what i would call ride comfort and the third one is safety okay so when i
say jargon what are the type of things that we are going to introduce? so of course when i say driving dynamics i
am going to look at the vehicle in driving dynamics the first thing that comes is straight-line
tracking where we are studying we want to study the vehicles interaction with the external
atmosphere we are going to see simple things first we are looking at maneuverability then we are going to introduce some other
jargons we are going to introduce things like self-steer behavior watch out that from the
terms which you understand from pure english we are going to terms which you are not going
to make out that easily unless you know the definitions so self-steer behavior if i am
going to define now you would not understand anything but we are going to do that later is the difference
in the slip angle between the front and the rear tires does not make sense right now to
you okay but we are going to talk about this okay what is called a slip angle? how is slip
angle developed and so on? we are also going to study driving dynamics okay since it is
dynamics okay and this is a dynamical system or system which is controlled by equations
from dynamics immediately you would say that that can be
what are called as oscillatory behaviors and does the vehicle also have this oscillatory
behavior? if so how does that affect the vehicle? there are lot of very interesting things happen
when you give or when you maneuver a vehicle things like what is called as load shift you
would have realized that when you take a turn in a vehicle you would have realized that okay you are
pushed to one side and then you can easily realize that there is going to be load shift
okay in other words certain of this driving dynamics gives rise to certain effects like
for example load shifts so maneuverability changing gives rise to load shifts
okay now one of the things that i want why i am
writing one of the things i want you to realize is that your mathematical model should be
able to capture all that driving dynamics okay which i am going to put forth here so
when i say there is a load shift okay the first thing you have to ask is is this going
to captured by my mathematical model? you will see that mathematical model is a general
term there are simple models the simplest model
you can think of is just vehicle consisting of mass m okay one mass the vehicle as an
acceleration a okay and has a force opposing its motion so a becomes deceleration will
call that s a we will not call acceleration deceleration every time we just call that
depending about positive or negative you can come to your own conclusion so you can look at simple mathematical model
f=ma right this does not talk about various driving dynamics so that is the reason why
i have put this on the other hand this also does not talk about what happens when the
vehicle goes over a bump goes over a rough road and all these things right so mathematical
model is a very general term okay and that you have to understand many of these
things in order to understand the limitations or what can be achieved using the mathematical
model so if i just give you a braking force and if i say mass is this one tell me the
deceleration okay simple calculation back of the envelop you can tell me what is this
from this equation okay now when i say that the vehicle is taking a turn i want to know
what is the role of the vehicle and so on this would not work so in other words what is also required is
a proper understanding of the physics okay which would be the result of your input and
whether your mathematical model will capture that physics okay so from that sense mathematical model can
be very simple like what we had seen or it can be complex and the complexity is increased
as we increase what is called as the degrees of freedom as we increase the degrees of freedom
so that is the reason why we look at driving dynamics suppose i want to look at oscillatory
motion of the vehicle as it goes over a bump okay you would immediately reject this and you
would go back to your vibration class and say oh this we had studied okay that is the
vehicle let me replace all your suspension by a spring okay let me replace the damping
bla bla bla of the suspension system by a damper okay so let me say that the tire is
just another spring and that the tire goes over a rough road and so on so what did i
do? the same vehicle okay a different mathematical
model or a different view of the vehicle’s behavior i have given and the type of degrees
of freedom here what i have chosen is different from what i have given here and so on so the
mathematical model in simple terms should capture what you want to analyze in driving
dynamics okay in other words whether it is a longitudinal dynamics or vertical dynamics
or you can say lateral dynamics because it should be able to capture the vehicle it is usual practice to start with to d-link
the behavior of the vehicle in the longitudinal direction okay in the vertical direction and
in the lateral direction i can d-link them okay and study them with simple models as
if nothing happens in the other directions so this model quite good maybe you would have
done problems in vibration class with this kind of models for the vehicle but if i ask you what happens during a cornering
behavior you know i am going to say that so in other words i will have another model so
the models can also bring out the behavior in a particular direction or a particular
dynamics clear okay we will go into some details on the technicalities that have involved before
we jump into what is going to be the longitudinal dynamics? in other words we are going to have models
which are like this but much more complex than this okay to study longitudinal dynamics
so the intellectual property right of this whole thing belongs to newton-euler and we
have to salute him for whatever he has done to us with that we will stop this class and
we will continue in the next class


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