Mod-01 Lec-06 Tire Mechanics – An Introduction

Mod-01 Lec-06 Tire Mechanics – An Introduction


in the last class we were looking at the tractor
trailer right and we were looking at breaking we also looked at how breaking affects the
performance as well as in other words the breaking distances as well as we saw how when
a tire is locked whether the front gets locked or the rear gets locked or the trailer gets
locked how that is going to have an effect on the vehicle motion so obviously we also gave a sequence on how
it should be locked and obviously the breaking forces or the percentage of breaking forces
which are distributed would depend upon the w’s that are acting as well as on this sequence
which we set you know that should take place okay without dealing much into that tractor
trailer you have done some assignments so that will give you an idea we will now move
over to a very important and interesting topic on tires so in other words we will understand what
are tires and then we will go ahead and understand what is the mechanics of tires mechanics of
tires is a very interesting topic as well as a difficult topic though one would say
that what is in a tire i see this everyday in every car what is so important about tires
if you look at in automobile there are 2 components which are extremely abused abused to the greatest
extent one is the tire the other is the piston rings okay both of them are abused abused in sense that
they are subjected to all sorts of loads friction and so on in their lifetime and what happens
between the tire and the road is extremely important for the safety of the vehicle whether
you are accelerating or breaking and whether you are taking a corner or manoeuvring the
vehicle for all these things what happens between the tire and the road is important
so in other words we have to understand this carefully in the last class we said that we will dump
all the effect the effects that happen between the tire and the road in to one constant and
we call this as mu and we said that this is friction constant or friction coefficient
i put that within the inverted commas friction coefficient because it is not as simple as
what happens or what this equation says or what happens in just a block so friction coefficient is only a simple equation
to depict the behaviour of the forces or depict the relationship between the forces but the
phenomenon is very deep we will answer the question okay one by one as to why or how
this friction coefficient or friction is developed and how it enhances the grip and so on now before we go further let us look at just
the forces that are acting on the tire since all of you know you have done a course on
automotive systems you know what is a tire and so on i am not going to deal too deeply
into the specs of the tire and so on but we will maybe indicate this as we go along we
will not go into the construction of the tire and other aspects of materials but we will
suffice it to understand what all is required to understand we will do that right now so first let us look at the forces that act
on the tire there is a longitudinal force okay which is in x direction okay but that
force is exactly not along look at that it is not along the wheel plane suppose this
is the wheel plane okay then you would see that the tire direction of rolling or the
travel is not exactly along that direction but is at an angle which makes let us say
that this lambda or alpha and that angle is what is called this slip angle why is it so
we will see that in a couple of lectures so the first thing is that it is very interesting
to note that the tire just does not as it travels it does not go along the plane let
us say that the x direction is the direction perpendicular to the normal direction or normal
to the wheel plane okay so in other words the tire does not travel along the wheel plane
so it takes a direction that is what i call as direction of wheel travel and that direction
is at an angle of alpha or lambda which is called the slip angle okay that is the first
thing there are a number of forces that act as well
as moment that act on the tire of course there is a longitudinal force okay we saw that the
longitudinal force is along the x-axis okay but we modified it by saying that whenever
a tire travels it may not travel along the x axis okay now the slip angle is necessary
to generate what is called as a lateral force if the lateral force is 0 slip angle becomes
0 and the vehicle or the tire travels along x direction so in other words lateral force is developed
because of the slip angle okay so we have a let us call this as longitudinal force
that is the fx force that is breaking acceleration and so on then we have the lateral force which
is fy okay which is the result of the slip angle this you would see that this is the
result of what is called as slip we will define all these things carefully the longitudinal force is the result of what
is called slip very interesting when there is slip longitudinal force is produced when
i say that it really sounds this is what an oxymoron rather that when you slip what is
this that there is a longitudinal force developed how is that that is what we are going to see
so there is a relationship between longitudinal force and what is called a slip what is called
slip i want to define that slip carefully as we go along so we have a lateral force fy and that is
due to what is called as the slip angle in other words when the lateral force does not
exist the slip angle does not exist and the direction of travel is along the x direction
then of course we have what is called as the normal force normal force which is fz is normal
to the wheel plane okay that is the ground reaction as we called it in the last class all directions have an accompanying moment
okay so let us look at the fx first that fx force is accompanied by what is called as
the overturning moment i would call that as mx and that is what is called as the overturning
moment you have a moment which acts along the ez direction which is called as the restoring
torque or a restoring moment so here we have what is called as the restoring torque or
moment and along the lateral direction there is a
force as well as a moment and the moment is nothing but the rolling resistance moment we said that that moment or rolling resistance
torque is what can be converted into a force okay that acts in the x direction so we said
that they are equal you cannot put both of them so we said either there is a moment or
there is a force so when we analyse vehicular dynamics the whole of the vehicle then we
replace the rolling resistance moment by means of the force in the x direction this is what
we saw in the last class right so these are the things that happen in a tire the question is how is developed what is the
mechanism of this development of these forces okay that is what we are going to see one
of you of course no how a tire is specified okay if you go to a shop to buy a tire you would
see that i want to say for example you are buying a passenger car tyre so you would say
that i want a passenger car tire which is say a 215 okay and you would specify one more
55 or something like that 55 or 65/55 okay then you would specify r okay and then you
would specify another number 15 okay this is what usually you would specify right sometimes you would go ahead and specify a
number okay and a letter each one of them have a meaning p is the passenger car tyre
215 is the biggest section width of an unloaded tire let us look at a section of the tire
okay so that is a section of the tire so this distance okay this is the section width the
maximum distance okay or the maximum width is called as the section width so you specify
that section width note that the section width specified in terms of mm millimetre then you have 55 45 65 whatever it is that
is what is called as the aspect ratio and it is in percentage
what is the ratio when we say aspect ratio what is the ratio the ratio of the height
here this height which i would call say ht okay to the section width right so it is a
height this height to the section width so if i have a tire like this then that is the
section width then that is the height the ratio of the height to section width multiplied
by 100 okay that is what is called as the aspect ratio in percentage lower the aspect ratio okay it is called as
the low aspect ratio tires colloquially called as a low aspect ratio tires 35 is a very low
aspect ratio tires in fact if you see today many of the high-end cars you would see that
this height you notice that they are very small okay and these are low aspect ratio
tires these tires have a specific property or characteristics that it makes handling
much safer on other hand ride becomes quite wobbly or
in other words it has an effect on ride a negative effect on ride and a positive effect
on handling so the low aspect ratio tires are compensated usually by a good suspension
system okay r is what is called as the radial tire today almost every or why almost all
the passenger car tires are radial tires we still have tires which are not radial in the
truck segment that depends upon the country for example in north america you have 90%
or 95% of the tires are radial tires or even more but where as if you look at a country like
india maybe about 25% of the tires are radial tires and still what you call as radialization
is going on where bias tires are converted into radial tires we will see what is biased
tire what is radial tire again in the next class through some pictures just note that
2 types of tires are there one is the radial tire and other biased tires we will just see
quickly a section and see what is the radial tire but we will go from micro up from micro
to we will go to the macro okay now this is 15 is the rim diameter in inches
so that is the rim diameter in inches due to some peculiar history or legacy you have
mm combined with inches when you specify the tire then you have a load rating you have
a table from which you can find out the load rating of the tire okay and then you have
what is called as the speed rating so you have a load rating and a speed rating okay
a quick look at the section before we go further and explain the micros that is a typical section okay cut section
of a truck tire courtesy jk tyres one of the leading manufacturers we have a section of
their tires you would notice that there are a number of reinforcements okay there are
a number of reinforcements okay you would also notice that these reinforcements in this
tire are made up of steel okay and you would notice there are chunks of steel on either
side okay actually that is what is called as a bead okay so the rim is here the tire sits on this rim
and it is inflated right so there are number of parts of this tires we will explain that
in the next class we will go into the details of what is the material that this tire is
made of how it works and then we will look at the different parts of the tires the way
the reinforcement is done is not first of all it is not a pure rubber it has reinforcements
number one the way reinforcements are done the tires
are classified either as a radial tire or what is called as the bias tire
radial or a bias tire okay though you see that there are all steel radials it is not
necessary that all the reinforcements are made up of steel okay some of the reinforcements
you see here which is called as the ply the reinforcements which come here okay section
of which we will see in the next class is made up of polyester materials and the belt
as it is called these are the belts okay the reinforcements are made up of steel so in other words you can have a combination
of materials which can reinforce this so the reinforcements are basically made up of steel
nylon polyester rayon and so on okay before we deal deeply into tire per se we will go
from the material of the tire then to the construction of the tire this is just to give
you a background so let us now look at what are the materials and what or how does it
behave right all of them all the tires which are used in
the automobile basically consists of what are called as elastomers of course tires are
classified into pneumatic tires which we use all the time or solid tires and are non-pneumatic
tires which has very specific applications but now we are in this course we are going
to only see the pneumatic tires so the first thing is that we should understand
elastomers and how it helps the tires to develop the forces that are required for it to accelerate
break take a corner or manoeuvre and so on okay so we will go into small bits of information
which we will collect together in order to understand how a tire interacts with the road
in other words we will understand the elastomers we will understand the road then we will understand
how these 2 guys talk to each other in order to develop forces that are required right
okay now what are these elastomers the elastomers
are basically long chain molecules okay they are long chain molecules now these long chain
molecules are vulcanised through what are called as the sulphur bonds in other words
these long chain molecules do not exist it is not that there is one long chain molecule
and there is another long chain molecule like that okay they are independent long chain
molecules that exists no these long chain molecules are bonded by what
are called as sulphur bonds and that is what we call as vulcanization now if you leave
this long chain molecule okay just leave it it now what happens it becomes something like
a bundle of twine or wool or something like that okay it is very interesting to note how
they behave independently and how that is different in their behaviour or what is the
difference in their behaviour when it comes to these molecules okay these molecular environments have other molecules
as well in other words it is interesting to know the difference between how one molecule
behaves how a number of molecules or molecular chains okay they behave right okay now if
you look at one molecule then the molecule can be like that let us say that i take these
2 points and then i stretch it okay when i stretch it it increases the length
increases okay what is length note that that is the original length we call this as original
length now when i stretch it that is the final length the first point you have to notice
is that this stretching is different from the stretching that you would notice in a
metal for example if you look at steel steel does
not have molecules like this obviously and that the elastic behaviour of steel is due
to what is called as lattice deformation in other words they have depending upon the
type of steel the type of structure the steel let us say that it is fcc and bcc or this
is an austenite or is it fcc and so on okay now when you have the steel subject to a force
then the lattice gets deformed and that is what we call as lattice formation and when
we leave the forces okay the lattice goes back to its original position so lattice distortions
are deformations are responsible for the elastic forces that are developed in steel you also
know that the plastic deformation are due to a phenomena called slip and slip is due
to the presence of dislocations and so on look at this so you have a wire say for example
if you take the mouse okay let us say that this is the length from my left hand to right
hand this is the length of this long chain molecule as you see it outside so now let
us see what happens when i stretch it okay look at how much i am able to stretch look
at how much my hand moves actually i’m not disturbing the bonds like what i did in the
previous case okay but what i did was to straighten this out okay look at that difference so the phenomena of deformation of an elastomer
is different from that of steel and the phenomenon is controlled by with our entropy now you
imagine that the entropy which you normally understand it to be what higher the entropy
higher you imagine that very simple way of understanding entropy is that higher entropy
means that there is more chaos more disorder and so on and so forth okay this is what you roughly understand from your
let us forget about the mathematics here we say that it is the configuration which decides
the entropy when it becomes straight the number of configurations that this molecule macromolecule
can take is limited okay and so the entropy actually drops so when i leave it the entropy
actually increases and so it goes back to this position so in other words there is an entropy change
that is responsible for the deformation of these macromolecules okay so at one level
you can imagine that these molecules are like a spring okay so you can say that i will fix
it here i will pull it when i pull it okay it becomes like this and then when i leave
it it goes back to this position the same thing we can say or imagine the same
situation when you have the springs which are bonded by sulphur so if you have the spring
bonded by a sulphur here spring bonded by a sulphur here the springs bonded by sulphur
the spring bonded by sulphur and so on okay this keeps increasing and so you apply a force
okay a similar thing happens fine so this gives that kind of spring effect so on one
hand this can be modelled as a spring do not forget that there are long chain molecules
though they are bonded okay they are not arranged like happily like that right so when they
are pulled these long chain molecules start interacting with one another or with itself
and so on okay in other words the long chain molecules have
let us say some sort of a friction it is actually not a friction let us say that it is some
sort of a friction between the other molecules right so when i pull it they also interact
with other ones okay and that gives a very interesting effect which is the viscous effect
or the dashpot effect you can for a moment imagine that these molecules
are in a tube this is called as a tube model and that elastomer consist of a number of
tubes okay into which these molecules are placed and these tubes now start interacting
and you can say that there is one more okay the chain as it goes there is a tube like
that and they start interacting with one another right so because of this interaction i said there
is a viscous part two factors become important in their interaction
one is what is called as the frequency and the other is what we call as temperature these 2 become important and interestingly
we will see that the mechanisms are similar and hence there is a relationship between
the 2 what do i mean by frequency frequency tells me how fast i am going to pull let us
say that i am pulling it and releasing it how fast i am going to do this okay i can
do that slowly okay and say one cycle per second 10 cycles per second or i can do it
in a very fast fashion that i can just keep doing it at 10 to the power of 8 10 to the
power of 10 cycles per second now what is the effect of this frequency on
the mechanism just we said what we indicated right now that there are interactions at very
low frequency since we had put a viscous affect which means that velocity has a role to play
at very low frequency okay the force that when you apply the force okay the chain have
the time to react to that force and hence they would react to the force almost in the
same fashion as you had applied it and since you are going to release the force
again in a very slow fashion okay it has time to react and come back to its original position
so at low frequencies the effect of time i mean the time available is quite large and
because of that the molecules have the ability to expand then come back so in other words
at low frequencies it behaves something like a spring okay and so all the forces are dumped
into the spring so the force here is same for example a very
simple model the force here kx x is the displacement and for a dashpot it is always cx okay so
the forces that act are able to get back or in other words the whole rubber behaves like
a spring what happens when i increase it let us look at the other spectrum the other end
of the spectrum is that i am applying the force at a very high frequency so when i apply the force at a very high frequency
then the guy does not have time to get back to its original shape okay because by that
time it gets back you have applied the force again right it is a viscous effect we said
so what happens it would behave like a very stiff material because when you want to release
it it does not come back when you want to again apply it it will not again go back so
it would become very very stiff so at very high-frequency they behave as a
very stiff material okay so in between the 2 at very low frequency it is a nice spring
because the guy has enough time to recover and at very high frequency he does not have
time at all to recover okay and hence it becomes very stiff and in between the 2 it has is
a spring and a dashpot effect so if i now plot say for example this frequency
versus what we call as the stiffness in other words modulus how would it be that it will
be like this like this and like that here is the spring here both the effects are there
the spring and the dashpot and here it is quite rigid okay now clear so these are the 3 affects
so to summarise at low frequency the time required is good enough for the rubber molecules
to come back and so they are springs and at higher frequencies they do not have time and
hence they become rigid on the region of interest in this whole thing
is this that is our region of interest if i now plot a stress-strain curve for that
region of interest which i would call as the viscoelastic region of interest okay how would
it look like let us say that i apply stress like this
okay then the strains do not follow the stress in other words if it were to be an elastic
material like steel then so let us say that that is how the strains would be pressure
being the x modulus on the other hand here in this material because of the viscous effect there is a time delay between the stress and
the strain or in other words there is a phase lag okay between the stress and the strain
right so there is a phase lag between the stress
and the strain and that is a very important that phase lag is what gives you what is called
as the hysteresis and is an important property of the rubber and which gives advantages and
disadvantages in the case of functioning of the tire clear so in other words what does
that mean it means that when i apply the stress the strain is not immediately developed okay
it takes time to develop when i release it okay it does not immediately
get back to its original position it takes time for him to get back to its original position
okay so this is a very important property which we will see more and more we will recall
this phase lag as delta okay this is the phase lag we will call this as delta between the
stress and the strain right now let us look at the effect of temperatures and then get
back to this again the temperature has just the opposite effect
when the temperature is high the temperature aids these let us say i am fixing the frequency
i am taking the temperature to be high what would happen when the temperature is high
then it aids in the recovery of these molecules to its original shape and hence it would behave
as if you are at a low frequency so if i now plot the temperature at high temperatures
since it aids the molecules to recover the modulus would be something like this at very
low temperatures what would happen at very low temperatures just the opposite okay the
molecules are under difficulty to get back to its original position so the modulus is
high intermediate temperatures the modulus is between the 2 so if you compare this graph with this you
would notice that the temperature effect is the inverse of the frequency effect okay that
is the inverse of the frequency effect we will see that there is a relationship between
the 2 which is called as the wl of relationships okay right now if i now plot for that frequency effect
let us say that i plot for the frequency effect the energy loss versus the frequency then
the curve would look something like that there is a region which is that central
region at which the energy loss is high that is that region okay and that is the region
at which we are going to use our tires the same case temperatures would also look something
like this right clear okay so the temperature also would have the same
type of behaviour there is one particular temperature of interest which is called as
the glass transition temperature popularly denoted by tg so tg is the glass transition
temperature below which the material is vitreous and above which that is this region above
which the material becomes very soft okay so the glass transition temperature
would obviously depend upon the frequency because both of them have an effect right in other words if i do a test at one frequency
at a temperature and i now do with that same frequency at another temperature the effects
would be different vice versa if i do a test at one temperature with 2 frequencies again
the effect would be different so there is an interaction between these 2 in other words
there is an equivalence between the frequency and the temperature the equivalence is inverse so it is usually said that when the frequency
increases by a factor of 10 there would be a change of temperature to 7 to 8 degrees “professor – student conversation starts”
what is this change when the temperature would increase or decrease
when i increase the frequency what the temperature be increase or decrease decrease decrease
okay “professor – student conversation ends” so you go this side in frequency you would
come the other side in the case of temperatures there are equations for this and these equations
are given by williams landel and ferry this wlf equations we will not go into the details
but we will understand this more physically okay now why are we talking about this how is that
the behaviour of an elastomer helps in the development of i say grip that is the first
question which we are going to answer in other words let us define what is meant by grip
so we are now going to the micro level so in other words what we are trying to do is
we are now that is the section and let us say that this is the tire we are now going
to go and sit at the interface between the rubber and the road and understand how this
concept is going to be applicable at that circumstances one of the things we know about the road is
that the road has what are called undulations the undulations can be looked at from a macro
viewpoint or it can be looked at from a micro viewpoint right okay how does
this rubber interact with the road is our next question given that we have these 2 kind
of roughness okay that we will see in the next class

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