Mod-01 Lec-09 Tire Construction and Force Development

Mod-01 Lec-09 Tire Construction and Force Development


okay let us continue what we were doing in
the last class we were looking at rolling tires we were looking at what we called as
free rolling and we were also that is what we were doing free rolling and we were going
in deep into the concept of how contact pressure influences various things that are happening
at the contact patch to the small you know the slip of tongue in the last class please note that when i drew the tire okay
i think that is how we drew the tire and that is the velocity so whether it is braking or
accelerating the velocities the direction is the same so i think that instead of acceleration
being in this direction i put velocity please note that is acceleration so the acceleration
is in that direction so the ground we said will be you can have that stationary and the
ground moving in the opposite direction we said that that is the relative velocity
so please note that it is the acceleration and it is obvious but nevertheless i just
wanted to make it clear as to what we were talking about right there were some questions
on tires like how tires are built and so on this is a vast topic in fact tire mechanics
can be a course unfortunately this is only a part of this course so we would not be able
to go into the details of tire mechanics completely we will only talk about tire mechanics from
the perspective of vehicle dynamics how the tires interaction is going to affect the vehicle
performance that is what we are going to talk about we are not going to talk about tire
design and so on i know that is a topic by itself but nevertheless it is important that
we talk about how or what is the construction of the tire okay and courtesy jk tyres i am giving you the slide you know which talks
about how tires can be classified so tires are classified based on construction into
what we call as a radial tyre or a bias tyre today radial tires would become extremely
popular and all passenger car tires are radial tires in this country in india about 10 to
25 percent of the tires in the truck are radial but elsewhere in for example north america
90 to 95 percent of the tires in the truck or the bus segment are radial tires still there are bias tires running in india
but in most of the developed countries the tires are radial there was a lot of advantages
of radial tires the foremost amongst them being the fuel efficiency practical data shows
that the fuel efficiency or the difference in fuel consumption can be as high as 5 percent
so radial tires are extremely popular in the truck market now and it is becoming popular
rather in the truck market the other tire is what is called as a bias tire let us understand what these radial tires
mean okay this is a cut section of a radial tire the cut section of a radial tire so you
can see here that there are say look at that there are steels steel what are called a steel
belts okay and this is what is called as a ply let us get a cut section so that you understand
this much more clearly okay that is a truck radial tyre look at that it
is extremely complex it is complex from two points of view one is that it has a number
of materials and several reinforcements that make it stable that make it efficient that
make it last longer gives you a good ride and as far as possible reduces the fuel efficiency
reduces the fuel consumption it increases the fuel efficiency okay again courtesy jk
tyres we will look at what are other sections i mean look at the different components in
the sections and what the section is made up you would see that there is what is called
as a body ply okay you can see that the body ply which is which consists of a number of
wires and number of wires so they run like that okay from one bead to the other so you
would see that it keeps running like this right so they are radial in nature that is
why it is called radial tyres so the body ply has steel reinforcement in
a truck tyre we are talking about truck tyre here so that is the body ply here you can
see it may be here more carefully you can see that that is the reinforcement okay in
the body ply and you see that the body ply the body ply has rubber on either sides the
most important there are number of times i am not going to explain each one of them the most important which is towards the inner
side okay it is called as the inner liner inner liner okay so in other words it is inside
if this is the body ply and then what is inside this is what is called as the inner liner
okay and outside this outside this you can see that predominantly that is what is called
as the sidewall in other words the questions are what is sidewall so this is the sidewall of the tyre okay so
in between the two okay there are some components let us not worry about it so there is a reinforcement
for us as well we are concerned there is a reinforcement steel reinforcement which is
rather protected on either side okay by rubber and this side this is what is called as the
sidewall this region of the tire is what we call as the buttress okay buttress of the
tire now you can see that the steel reinforcements
go all the way and then wraps around what is called as the bead or the bead core you
can see that here there is a bead and then the reinforcement the steel reinforcement
wraps around and comes out in the other direction so you can see that here very clearly that
it goes like that and then comes around and then okay wraps around the beam right okay now around that portion of bead the solid
heavy you know this is a very important guy last time itself we saw that he is the guy
who is going to interact with the rim in order that the loads are properly transferred and
so on so that portion is a is made up of a number of reinforcements okay there is what
is called as a steel chipper wrap around okay to protect the bead and then you have the
chafer and so on the chafer and chipper all of them help the
beat to actually interact with the rim alright so there are other things there let us not
worry about it so the first thing is that this body ply important component either side
of it has rubber sidewall and inner liner wraps around the bead then when you come to
the top you have what are called as belts okay these are what are called as the belts
you can see it here they are in this case this is all steel radial so this is this ply is steel as well as these
belts are made up of steel right they are steel belts they give the stability for the
tread and you can see though that there is not only one belt there are a number of belts
that is what is called as a transition belt and there are 2 working belts and then there
is a protective belts so these belts have steel wires running say for example if you
look at it from the top so you have wires running like that okay one of the belts and then running like that in another belts
okay and so on so the two belts working belt one and two are very important belts and as
i said that gives that stiffness the lateral stiffness and the longitudinal stiffness to
the tread okay the construction there is very complex we will leave it for a minute because
we are only looking at the mechanics of the tire and not into the mechanics of load carrying
and stresses and so on into the tyres so we are not going to look at the design
from design point of view how you place that belt what is the width of the belt what is
the angle and all these things how many belts are used all these things become important
there can be 4 belts there can be 3 belts and so on then on top of it okay there are
some layers again of rubber and then ultimately you have the tread about which we were talking
about so these are the this is the tread we will
see that in a 3 dimensional picture and this is the tread okay tread is the one which is
in contact with the ground and the mechanics has lot to do with the tread as well as the
belt okay and how that interacts with the road that is becomes very important and that
is what we have been talking about and we will continue to talk about that okay in this
class professor student conversation starts tread
is made up of elastomers rubbers okay we will see i am not going to the details of what
is this composition how it works and so on okay it can be a natural rubber natural nr
plus natural rubber is usually called as nr butadiene rubber br styrene butadiene rubber
which is sbr and so on okay so it is a combination of all these materials so we will not go into
the details of these materials okay professor student conversation ends nevertheless to say that oh that is the passenger
car we will come to that in a minute yes so you can see that a passenger car tyre for
example as well as the tractor is made up of a number of different components of elastomers
in other words different regions of the tyres have different compounds of rubber so it is
not one rubber rubber or elastomer is a very generic term it is not that there is only
one compound that covers the complete tyre in other words tyre is just not made up of
only one compound the number of compounds as i said that is not the intention in this
course now okay that is the passenger car tire essentially the construction is similar
but not exactly the same the body plies are not necessarily made up of the same you know
steel but it can be of different materials okay and then as i said we will not we will look
at the bias tire biased truck tire unlike that radial tire where you had one body ply
and then you had belts okay here you have what are called as plies which run throughout
okay 1 2 3 plies as you can see okay which runs throughout okay and are arranged in a
position okay arranged in such a fashion as you can see that they are crossing each other
okay and that gives the strength for the tyre because of the way these are arranged there
is a performance difference between the bias and the radial tire but since the bias tire
is almost given way to radial tires we are not going to talk much about there is no point
in now comparing bias tire and radial tires okay so we will concentrate on radial tires
and how that works i just wanted to say that there is also what is called as a bias tire
bias tires are still used in trucks okay now that is a typical passenger car tire you
can see the treads there okay the treads are very clearly seen there are various ways in
which treads are designed you can see that there are grooves there there are grooves
in the tread okay these grooves this is a passenger car tire and these grooves are there
in order to carry water or minute sand you know as you go over say a sheet of water in other words they are channels for the water
to escape as you go in under wet conditions right the tires are basically classified into
what are called as rib tyre there is a truck rib tire okay you can see that there are ribs
there are 4 ribs in this tyre and lug tires these are what are called lug
tires the rib tires are usually used in the front in the front wheel not necessarily that
it should only be used in the front because there are buses which uses this in the rear
also this basically this is a steer axle tire performs very well when it is in the steer
axle so this is a rib tire okay which is used in the steer axle and that is a lug tire which
is usually used in the drive axle that is the rear okay so these are rear tires and the one the front
is a rib tyre but in a passenger car you cannot have two different types of tires so you have
tires which are a combination or hybrid of these two which would say all wheel tires
so all wheel tires are a combination of this kind of lug pattern and a rib pattern okay
so you would see that a passenger car tyre is sort of a combination of these two even for truck you have a combination okay
all wheel tires where you can use which you can use the front as well as in the rear okay
so this is a sort of a very brief introduction on how the tires look like though we are not
going to use that knowledge in this course okay we are going to go more into how the
tires interact but nevertheless i think it is good to know how the tires look like and
so on now coming back to our contact patch coming
back to our longitudinal forces and all that what we did in the last class remember that
we were looking at a tire which is under free rolling condition let us get back to what
we were doing in the last class we will switch and go back and look at some practical aspects
of this contact patch as we go along okay so that was a tire which was rolling
we talked about the varying radiuses in this tire we talked about r0 becoming re and then becoming
rh and so on and under this we had drawn 3 figures we talked about the contact patch
okay we just given a two dimensional representation of the contact patch okay and let us now look
at three dimensional representation of this contact patch two dimensional sense that is
just cut at the centre and looked at it it is very yes it is very theoretical but
let us look at it from a very practical point of view actually how the contact patch looks
like okay so this is a finite element model again courtesy jk tyres we have a contact
patch you know finite element model of a contact patch different colours here indicate the
magnitude red being that the contact pressures are higher okay and blue being the lowest
right so in other words you see that the contact
patch is not uniform and as you go to a say for example a truck rib tire the contact patch
is absolutely not uniform okay though we assumed that a shape in order to understand the fundamental
interactions the contact patch is not uniform let us understand a bit about contact patch
because that is an important parameter for the vehicle road interactions right okay if this tyre is to be made up of membrane
whose bending stiffnesses are very low okay say for example you take a balloon blow it
okay and then just press it on the ground right the contact pressure will be uniform
contact pressure has to be just equally break this the inflation pressure and so the contact
pressure okay will be uniform strict conditions that has to be the case or theoretically that
has to be the case when there is no bending stiffnesses and other things that are that we are going
to talk about are involved unfortunately our tyre has a lot more things than balloon all
right the first thing is that the tire is not straight like that so it has you can see
that it has say grooves that is what you see here that it has this kind of grooves okay
so contact pressure is actually let us look at that let us say that is the inside i am
just extrapolating or i mean exaggerating or gluing or zooming to the area at the centre
okay now here is the inflation pressure that is
acting and here is the road surface okay that is the road surface so in other words there
are grooves the grooves become quite complex if you really look at that kind of tires you
know the grooves become complex and here again you have grooves if you now again we will
do a thought experiment if you go and sit here this part is not supported okay that is not supported so because of which
there is going to be a local bending so there will be you know this part of it will now
start bending because it does not have a support right there is an inflation pressure that
is acting that is going to sag okay that is going to get deflect or in other words there
are lot of local deflection number 1 when compared to a nice membrane or a balloon which
you keep it at the surface they are going to be local deflections professor student conversation starts yes
we are now right now we are not talking about water or anything entering there we have just
as it rolls you know this is exactly how it looks like in that picture okay as it rolls
right fine so we are not in other words we are not looking at a soil road i mean sorry
a tire in a deformable soil we are looking at tire which is running on an asphalt road
okay which does not deform right for all practical purposes that is fine right okay if the soil then the whole analysis is very
different okay how it how the soil deforms all those things have to be taken into account
okay that is why you have what is called off the road tires which is called a otr off the
road tires we are talking about truck tires is running on a as follow a flat roads right
okay professor student conversation ends so the first thing is that the constant pressure
is affected by this kind of local bending right so the pressures in this region on either
side in these regions they are going to be affected that is going to be affected that
is the first thing right so as one factor the other is the sidewall so that is the sidewall
so actually what happens is this so under look at that you know under pressure the sidewall
will be like this and so there is a deformation of side wall and the shape of the sidewall
is different from what it is now and when it is under pressure then the sidewall
shape changes right and that is going to have an effect which is very important for this
contact pressure distribution in other words you will see that if this is the undeformed
sidewall then under load this becomes that deformed side
right so under these conditions there are a number of forces that act on to this tire
there is going to be tension or in other words a membrane force that acts there and there is going to be an inflation pressure
force that is going to act at that point okay so there is going to be a membrane there is
going to be an inflation pressure okay and there is going to be a of course the ground
reaction and so on so because of this effect okay if i call this as tx okay because of
this effect we have a bending okay this is actually you can imagine that first let us
look at it physically then we look at that equation okay it has a tendency so there will be actually
this will be the inflation pressures that will be acting and so there will be a force
which will be acting okay in that direction the sum of this inflation pressure forces
okay it may be not here okay maybe somewhere you can say here acting and so on so because
of this there is a bending because of these forces these forces and all that okay there
is a bending that is bending moment that is created okay the bending moment is the sum and substance
of all the forces that are acting okay one in the positive direction the other in the
negative direction and so on right so that bending moment what really we will look at
that bending moment closely now so that bending moment let us s get into this and let us just
expand that so that is the side wall now assume that this whole thing is now bent and so we
have a bending moment acting at this place as you had seen there okay so now what would happen because of that
bending moment there will be more reaction forces here okay there will be a reaction
force in depending upon who wins there are a number of forces there who wins there will
be a reaction force at this edge in other words this bending is going to alter the contact
pressure distribution this bending is going to alter the contact pressure distribution
clear here okay suppose the bending wins over or one of the
forces here wins over and the bending is like this what would happen to the contact pressure
in this region the contact pressure would increase okay the contact pressure here would
increase so in other words the side wall geometry and configuration would result in a bending
moment at the ends because of which okay the pressure here the bending moment here will
be compensated by the that will be the reaction okay this is the action and the reaction and because
of which there will be contact pressure will be here higher or higher contact pressure
would result at the edges so that is what you see here in this in this figure at the
two edges you would see that the contact pressures are higher it is not necessary that it would
be like this it depends upon a number of forces that are acting number one is that there is
what is called as the membrane force okay this which we had drawn there as t and the
membrane force depends upon 2 things one is that it depends upon the radius of curvature
the radius of curve please understand that there are two radiuses of curvature okay one
for example here is a radius of curvature the radius of curvature here is going to change
and then there is a radius of curvature in the other direction okay so there are two
radiuses of curvature in the tire right and so the both the radius of curvature have
an effect on this tx right both the radius of curvature have an effect on tx of course
the other things that have an effect on tx or the inflation pressure and the force in
the ty direction right we will not go into the details of this equation i just want to
say that there is a force in the sidewall which you could loosely call as a membrane
force okay which acts as a sidewall which has an effect of course on the bending okay
at the contact patch edge right that is the first thing that the only thing
i want to point out is that this force is affected by the shape of the or the profile
of the sidewall as well as the inflation pressure to which you subject the tire okay these are
the two things when i say geometry it is rx and ry are included right that is the first
thing the other things that affect the moment are the inflation pressures okay the inflation
pressure and the inflation pressures so that is that
there are two ways in which it acts you know you can resolve it in two directions vertical
and the horizontal direction okay that is what you see there the inflation pressure
is acting in the horizontal and the vertical direction so they have a tendency to okay
have a bending moment in this direction one direction and this tx has a tendency to have
a bending moment in the opposite direction with the result that there is an addition
and there is a subtraction right so if in other words it is very simple to understand
so if this is the w okay what is that w let us get back so say this is the w this distance
is the w okay so hence you will see that everything here depends upon the geometry so if that
is the w then you can see that there is a minus sign here which acts in one direction
and then the other things is in the opposite direction due to inflation pressures in opposite
direction and acts okay like this so ultimately what is this moment bending
moment that decides the variation or the difference in pressure just to summarize what it simply
means is that the inflation pressure that is acting would have been the same as that
of the contact pressure but for the presence of local bending which we saw here as well
as a global bending i would call it as we had seen here so because of this bending and
of course because of the membrane forces and so on the contact pressure is not the same
as that of the inflation pressure clear okay that is the first important point now there
are a number of design parameters which affect the contact pressure let us agree that it
is not the same okay actually we were looking at the rolling tire right and right now our
explanations are more to do with the stationary tyre rolling tire has other factors which
are very interesting right before we go to the rolling tire it is a free rolling tire
then we will go to a tire which is braking how the contact pressure changes or accelerating
and lastly the most difficult of these cases what happens when the vehicle takes a turn
or cornering right so in this class in todays class we will concentrate only on rolling
tire free rolling tire and we will just get into what we call as braking or traction okay
the next class we will expand it and so on clear any questions professor student conversation starts in the
y direction right in the y direction yes in the y direction x and y x i had given here
y is in the other direction okay fy is in the other direction pressure pi is the inflation
pressure okay let me write down if you have doubts let me let me write down tx and ty
are already explained tx is the sidewall tension in x direction and ty is the side wall tension
in the y direction okay pi is the inflation pressure yeah one minute inflation pressure this is the free body diagram okay from which
we are determining the say i what i have done is essentially i have cut this and then put
the equal and you know forces here right yes see what we are: good question actually in
most of these analysis we have left out centrifugal force okay sorry it rotates in some of these
conditions if you look at let us centrifugal force becomes important okay but under many conditions okay we neglect
the centrifugal force because of rotation okay it will be careful usually in a truck
tire we are looking at the truck tire this centrifugal forces are not that very important
because of the speeds but in a passenger car tires centrifugal forces become becoming poor
okay right now we are not considering that but okay then there will be another force
or other forces and it will there would be some changes here
and so on right so this is only to explain more physically the bending you know what
happens okay i am not going to relay on this equation today most of us do not rely on analytical
expressions we go to finite elements okay so all these things all the results that you
get all the niceties are beautifully brought out in finite element analysis but nevertheless this becomes important in
order to understand what really happens or why the results are what you see in finite
element that is the reason why we explain what is bending you know how does it bend
you know what are the forces which cause bending we cannot do hand waving okay that is reason
why we write down this equations and see look there is a moment and the moment consists
of or the moment is due to various forces and forces act because of inflation pressure because of the force of the membrane or the
side wall forces okay these participate in this moment and so on all these effects okay
are accurately brought out by the finite element analysis and hence we look at the results
ultimately in the finite element you know contact pressure distribution clear in which
case you can also add the centrifugal force and so on so we will look at now rolling tyre there are other things that become important
okay y coming in the x direction this is the way actually the this is the membrane theory
we are not going into the equations okay so we would right now not going to the derivations
of this equation y ry rx rx ry and all that right we will not because then the topic becomes
very difficult and so this is not f this is not f this is fv i thought you are asking
ryv this is fv and fv is this force that is acting here in
this direction okay the force which is acting at the centre here and that is f okay that
is not fy that is fv okay but rx and ry come into picture and that is the f v actually
it is not the total vertical reaction force that is acting okay this is not fy you are
right but rx and ry come into picture because of this radiuses on either x and y directions the m is the bending moment that acts at the
edge okay at the edge right so there what we do is simply we take bending moment due
to the distributed loads okay in due to inflation which is divided into two parts okay that
is what we do this and this right so as if there is a distributed load like that here
okay and this is the result of the bending moment due to the distributed load and that
acts in the opposite direction okay ultimately you have a bending at the edge
yes yes see what does this what do we mean by distribution of these forces if you want
to understand this it is again very simple if you have a doubt let us say that i have
a cantilever beam okay now i have it is a distributed load that is acting on the cantilever
beam okay so there is an action here okay and there is a reaction at this point okay
right so we are talking about the same action and
reaction here so this is something like a cantilever beam when there is an action and
a reaction so the reaction is in the opposite direction which means it should be in this
direction so you will have a load distribution here such that it will oppose this moment
that is acting here in the same fashion as you have in the cantilever beam clear okay so the only thing difference between these
two is that here we have a cantilever beam within quotes cantilever beam and sense that
it is okay curved beam okay and for associate of course there are effects of local bending
you can see that there are there are green in some places that are green and there are
as you near the grooves and then you have again red and so on okay so there is a sort
of a relief here okay that is happening in other words what happens is that when it
really bends okay when it bends then there is a small lift and so on there is a redistribution
and that is why you will see that near the grooves they are not red okay there is a change
right so there is an inflation pressure that is why the two components or what we give
that no there is no this pi only one pressure one pressure that is acting this direction
that is the inflation pressure the force the result of the inflation pressure can be
divided into two parts okay or two in the x and y direction so what we have drawn here
is the inflation pressure right professor student conversation ends let us come back
here and so we are talking about rolling so this is the what we call as static pressure
rolling has a very interesting thing that going to happen when you when it is rolling
with respect to contact pressure let us see what happens and then we will explain okay that is a contact
pressure of a rib tire look at that when it this is a sudden change okay you will see that there is a change between
the two contact pressure when it is stationary and you can see the whole thing gets twisted
right you see further when it is okay the same thing
with the different limits you would see when it is breaking look at
the way the contact pressure now changes when it is traction look at the way the contact
pressure changes so in other words you can see that let us get back to this so you can
see that there is a change in contact pressure okay there is an adjustment of contact pressure
why does that happen right that is our next question we are looking at contact pressure
in this is the contact pressure now as i travel from one end of the contact pressure to the
other okay in other words just look at the contact so
let us sorry contact patch if this is the contact patch okay as i travel from one end
to the other there is going to be a longitudinal force we saw that in the last class there
is going to be a longitudinal force goes up and comes down remember last time we saw that
okay something like this we also saw that this longitudinal force okay reaches some
maximum re remember that we talked about r variation
of r okay in a to b b to c c to d d to e and so on in the last class and this longitudinal
force has a very interesting effect okay now just see how that is in finite element let
us that is the a longitudinal force okay i hope you are able to see one is in the positive
and the other is in the blues is the negative the red is in the positive so it goes up goes
to zero in the middle comes up and this is exactly what you see here is what you see
in this case but unfortunately since there is no unfortunate
here but anyway the rib all the ribs as you can see here do not have the same longitudinal
force due to the construction of the tire okay let me explain they do not have the same
longitudinal forces they are different in different ribs you can see that okay now the
tire so that is the let us so the first point is that the longitudinal force as we had seen
there is not a constant in all the ribs they are different at different ribs because
of which okay the tire now rotates a bit about the vertical direction so that the total strain
energy total strain energy becomes minimum so in other words this distribution of our
uneven distribution of forces causes that tire to adjust okay adjust or in other words
the contact pressure now is such that becomes a minimum that the total strain energy is
minimum as a system it would like to go to minimum
strain energy and so there is a twist so that you can very well see that here look at that
so it sort of twist in such a fashion that it becomes slightly more okay uniform right
so in other words the longitudinal forces that are acting has an effect on the contact
pressure distribution itself right and for example the longitudinal forces which we are
going to see in the next class due to braking has further look at that has further effect on the contact patch right
any questions okay just to summarize what we what we said we will continue this that
the contact patch is an important or influences the interaction between the tire and the road
another contact patch though one would like it to be very uniform is not uniform and that
there are some local effects and there are some global effects which has an effect on
the contact patch distribution and that the contact patch is also affected
by the uneven distribution of longitudinal forces between the various ribs and the ribs
tend to or the contact patch tends to adjust itself so that the strain energy is brought
to a minimum or there is a redistribution such that the strain energy levels as a system
is brought to a minimum okay so there is a small rotation that is as far as the free
rolling is concerned we will look at braking and then go to the contact patch in the next
class right let us stop here

Only registered users can comment.

  1. Dear Sir,
    Summarize what you taught in Lesson-09.

    Contact patch in a tyre is affected due to following factors.

    1. Local bending (sag) between Treads/ Grooves.

    2. Global bending due to Side wall deformation causing Bending Moment at edge of the contact patch.
    3. Inflation Pressure.
    4. Longitudinal Forces acting on the Tyre when its free rolling causes uneven forces acting upon contact patch, which causes
    contact patch to rotate slightly along the vertical axis.

    Question related to Point4,
    What is the direction of Tyre travel as per the FEA analysis (during Free Rolling, braking and acceleration?)
    On screen (left to right) or the other?

  2. In free body equation and membrane equation, these are dimensionally confusing. T is tension force, should have dimensions: N (Newtons), and if we apply dimensional analysis to P*Rx, P must have dimensions = N/m, that is similar to stiffness constant K, not Pressure dimensions: N/m2.
    All of this confusion about dimensions could be avoided if we assume Tension to be force per unit length. In physics and solid mechanics, sometimes in order to account for the variation of force due changes in properties of the material, we use notion for force per unit length.

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