In the last class we saw certain examples on
the applications of finite element analysis for real life problems. This was done for
companies, famous companies as probably you would have seen in our slides before. We are
going to continue on these examples. The whole idea here is to give you an overview of where
all finite element can be applied in the industry. This will be very useful for us to later conceive
a problem, workout a model and look at the results. Let us now see further examples of
the application of finite element analysis. This list is not complete, there are lot more
applications we are going to talk, but that we are going to do later in the course. But
before that let us continue further and look at certain more complex examples rather, that
we can do using finite element analysis. Let us start with the first example in the second
class. This example is for the application of finite
element analysis in the design of what are called as piston rings. Piston rings though
looks very nice and simple and small are not very easy to design due to various aspects.
These guys, these piston rings are one of the components which are abused to very great
extent in an engine and hence it is important that we understand how the piston ring behaves
and what will be the stresses and how the stress analysis can help us to design better
rings and so on. Especially the piston ring becomes important because of the fact that
we are now talking about Euro I norm, Euro II norm and other very stringent pollution
control norms and hence it is important that the ring performs quite well in the engine. We are going to only have a bird’s eye view
of what can be done. Lot more can be done, right now we do not have the time or the expertise
to go into various aspects. But at least it is important to understand how this technique
can be used? Now let us look at how that can be used for the design of piston rings? Let
us now look at how we develop the force for the piston ring in our first slide. Let us
now look at that slide. This slide actually gives you an idea as to
how forces in a ring can be calculated. You can see that the complete analysis of the
dynamics of the engine has been carried out using what is called as multibody dynamics.
As the ring sits on the piston and as it goes up and down, the rings actually tilt; they
start hitting the sides. The piston starts tilting and along with that there is some
sort of a tilt and a flutter for the ring as well. It is important for us to understand
the forces that go into the rings. For that we do the multibody dynamic analysis. We will not talk about multibody dynamic analysis
in this course but nevertheless multibody dynamic analysis becomes important for certain
components to get the forces. In these multibody components or multibody analysis, most of
the time we treat the body as rigid. It is also possible to treat them as flexible but
most of the time we can treat it as rigid and get the forces that act on the component.
So, we can find out for this particular ring what would be the forces that would act? Let us look at the next slide and see what
it tells us as far as the ring is concerned. But actually this slide gives us what is called
as the finite element model. We are going to discuss more and more about this model
later in the course but let us now accept this as a finite element model. We will discuss
those lines and what are called as elements which happen to be there towards the end of
the class, but nevertheless you see there are two regions. As you see, there are two
regions; one region is some sort of a white region and the other there, is a red region.
These rings, these piston rings consist of what are called as molybdenum coating. The
red region in the ring depicts the molybdenum that has been coated on a steel ring. Ring
can be steel, cast iron or whatever it is, but in this case molybdenum is coated onto
a steel. This particular design is called as inlay design. You can also see that or you can understand
immediately that it is possible in finite element analysis to get what is called as
the combination of materials. Like it is possible to say that we will have steel in one part
and we have what is called as molybdenum in the other part and do an analysis together.
Let us look at the next slide and we will see how the results are? You can see that the molybdenum coating has
an effect on the stresses and you can see that there are regions where the stresses
are high and there are regions where the stresses are low as well. Let us not worry about what
is the stress value, what is the allowable stress value and so on, but it so happens
that in this particular design the stresses are high. Let us look at another design and
that is depicted in the next slide. You can see a second design here and now you
see again there is a red region and there is a white region. This red region gives the
molybdenum part and the white region gives the steel part. This design is what I would
call as a sandwich design where the molybdenum is coated throughout the thickness of the
ring. Remember that we are looking at a cross section of a ring and we call this problem
as an axi-symmetric problem. Let us look at the results for this problem or for this design. That is the stresses; though you may not be
able to clearly see what the stresses are, but I can assure you that stresses happen
to be slightly lower than the previous design. That does not mean that this design is good,
but it means that for these stresses or for the forces that act on this component which
has been derived or arrived at from our previous model of multibody dynamics, this design happens
to be better than the previous design. There are lot more issues to rings, but we will
stop this example at this stage and may be if time permits we will continue it at a later
part of the course. Let us look at our next problem which is a very, very interesting
problem. The problem is the design of a connecting
rod. Please remember that in the previous problem, the material which we considered
was steel as well as molybdenum; a part of the component was steel, a part of the component
was molybdenum. Now we are going to consider a material which is porous, which has porosity,
whose density is not complete. For example we are going to consider a P/M component,
powder metallurgy component, where the normal densities are not attained; not necessarily
attained but only about 90% of the density is attained. This is a connecting rod for
a two wheeler and now let us look at how we develop this particular component using finite
element analysis. The next slide gives the solid model of an
existing connecting rod for the same engine. It is a very nice picture. You can visualize
that it has an I- section and that this connecting rod is performing or it performs very nicely
and you can ask me why do you want to change this connecting rod. All the time we always
strive to achieve excellence; we want to reduce the weight, we want to reduce the cost and
so on. So, from that angle it is now realized that if this forged connecting rod, which
is existing connecting rod is replaced by means of a powder metallurgy connecting rod
with certain special processes, the cost can be considerably reduced. From that point of
view we are redesigning the connecting rod. The next question that you may ask me is why
not I use straight away this connecting rod with a new material or the new process? That
may not be possible because the stresses that may result when I use this kind of technique
are not conducive for the new material. In other words the stresses may not be withstood
by the new material which is a P/M material. Number 2, the process which I am going to
have, which I am going to use in order to manufacture this connecting rod also may not
be very palatable or may not be very friendly for the existing design. Hence I have to change
the design. The next question you may ask is why do you
want to go through finite element analysis, why not straight away do it by a small hand
calculation and start developing certain prototypes and then arrive at an optimum design. There
is a problem to it because if you want to arrive at an optimum design, you have to do
a number of trials; maybe you may have to do 4 or 5 trials in order to achieve at the
correct result. Because certain cases hand calculations may not give you, analytical
solutions may not exist, the results that you are looking for and the stresses may not
be predicted correctly. So, if you have to do about 5, say examples of 5 prototypes,
then you are going to spend a lot of money in order to do this. Hence what we do is we
simulate the actual condition or determine the stresses in the actual condition using
finite element analysis and then say that look these are the 2 or 3 designs. These are
what are called as suboptimal design and I will use now these designs, so reduce my trials
to 1 or 2 in order that I can save lot of time as well as money. Let us look at the
next slide and see how exactly we are going to do this. This is the solid model of a new connecting
rod; connecting rod which has been designed after a number of trials in the computer,
which does not cost me much and the time also required in order to do it, is very small
or in other words I can do the whole thing in a matter of about 4 days. Let us now look
at the results. The next slide gives me the results of the existing connecting rod. This is the stress levels; very nice connecting
rod with performing very well, there is no doubt about it. Let us look at the next slide
and see the stress analysis of the P/M connecting rod. The stresses have been so adjusted that
the maximum stress that exist when the connecting rod is put in operation, put in an engine
is less than what could be withstood by this particular material, by this particular P/M
material; that has been taken care of. The thicknesses have been optimized and hence
it is ready for manufacturing. The manufacturing itself can be continued after this stage,
a finite element analysis as shown in the next slide. You can see that it is possible to integrate
completely CAD and CAM with finite element analysis sitting in the middle. We started
with a solid model, we went ahead, we did finite element analysis and we optimized the
shape. Now it is possible for me to push this geometry to CAM and then get the dye assembly
for this P/M connecting rod, get the cut location data and machine this and so on. Today the
technology is available as an integrated piece to start a design from solid model, visualize
it, do analysis and then completely prepare for the manufacturing process. So, that is
an interesting example. This piece is under trial. Let us look at the next, again an interesting
example from the field of machine tools. All of you know that a chuck is a very important
component of a lathe. Today, we are looking at very high speeds at which this chuck operate
or in other words these are high speed chucks and there are lot of problems of wear of these
chucks. When there is wear of this chuck, all of you know that it will not bite or hold
the component properly and there are problems of quality of the component and so on and
I need not explain all these things to you; you are mechanical engineers you know these
things. So, the whole idea here is, is it possible to enhance the performance of a high
speed chuck by completely redesigning this chuck. Let us look at the first slide in the
series. That slide shows you a solid model of an existing
lathe chuck. This problem is very interesting and very complicated because the chuck is
in contact at number of points to the body of or this chuck jar rather is in contact
at number of points to the body of the chuck. This is what is called as the jaw of this
chuck and hence my interest here is to find out what are the contact stresses that exist
in this jaw? The next slide shows you the contact stresses
of this chuck jaw as it operate in a chuck. Now, it is possible to look at this stresses
and tell whether these stresses are nice enough for you to not to wear or is it going to be
subjected to wear. There are lot more issues of wear but nevertheless this gives me a first
hand figure whether stresses are going to be critical. It so happens that the stresses
happen to be critical and we redesign this chuck and the redesigned chuck looks something
like this, which you can see in the next slide. So, that is the re-modified chuck or the redesigned
chuck and the stresses were lower for this particular chuck. So, performance enhancement
by modifying a machine tool component is possible using finite element analysis. Let us now
look at the next example. The next example is from the world of manufacturing.
In other words next example talks about process modeling of what is called as a P/M gear rolling
process. The next slide tells you or shows the model of this, for this process. What is that we are doing in this process?
All of you know that most of the gears are forged gears and few of them may be cast as
well depending upon the component or rather the material. In this particular piece the
gear, which is the bottom part is made up of powder metallurgy, it is a P/M gear. Today
world over what they do is to look at a P/M component and see whether it is possible to
selectively densify those areas where the stresses are higher. For example in this particular
gear is it possible to say where the stresses would be higher and is it possible to densify
only those areas? For example the flank and the root of the gear may be subjected to high
stresses and is it possible to now compact only those places and leaving out the center
of the gear? If you do that, that is good enough for us to use a P/M gear for many of
the load bearing applications which again means that we can save lot of money. Let us go back and look at that model. You
can see from the model that there are two pieces. That model will now show you that
there is a bottom piece which is actually the gear and the top piece which is what is
called as the dye. The gear actually starts rotating under the influence of the dye and
the dye starts compacting. The next slide will show you what happens because of this
process? The results are quite clear from the next slide. Now, what is that we are looking at in this
slide? We are going to look at what is the compaction or how efficient has there been
as the compaction takes place? In other words what we are going to do is to look at what
is called as a relative density of the gear. As you can see that in the gear this is the
root and that it is important that we have higher densities only in this region and that
the densities need not be that very high in this region. So, as the dye rolls, it is,
it is a regular rolling process, gear rolling process. As the dye rolls in one direction
and then in the other, the material gets densified on the surface to that extent that it can
withstand all the loads or all the stresses that would come during the operation or it
can withstand the operational loads. It is possible now to design the process using finite
element analysis. Let us now look at or let us stop for a moment
and look at this quite closely. You can see the equivalent plastic strain during rolling.
As I was just explaining to you, the top one is the dye and which is considered to be rigid,
the bottom is the component. You can see the plastic strains developing which gives rise
to what is called as compaction. Let us look at the next slide and that gives
us a better picture of the relative densities or compaction efficiency of the process which
we have been talking about. You can see that as it rolls, the flank slowly gets compacted.
Maybe 4 or 5 different cycles are required in order to completely compact the surface.
What is that we are trying to do using finite element here? We are trying to say or predict
how this compaction takes place in the rolling process? Why is that we are doing, because
again here we can reduce number of trials that are required. This is a very expensive process or the trials
may be quite expensive. So, we can reduce both the money as well as the time by doing
this kind of simulation and then arriving at the optimum design of both the gear. After
all what I have to do is I have to add some material or I have to redesign this gear so
that when it gets compacted my profile stays good. It should be good to perform or the
profile should be such that the performance of the gear is not affected. So, that is one
thing. The next one is how is that I am going to design the dye? Is there modifications
that are required to the dye or can it be a regular rolling dye itself. I can do all those kind of simulations, arrive
at what should be the shape and also arrive at what would be the speeds at which I have
to rotate and also look at how many number of rollings are required and so, all things
can be done beforehand. After all we may follow two processes; one process to just compact
only material at the surface and the other what is called as root rolling process where
we may be interested to compact what is in the root. In other words we may require special
dyes or special shapes of the dye in order to compact material which is existing at this
root. So, this kind of geometry optimization in a process is also possible by using finite
element analysis. Let us look at the next slide and see what
we get. The process is complete and the distribution after two rounds, we can keep on seeing 2
rounds, 3 rounds and so on; the distribution of this density is complete and that is shown
in this particular slide. Let us go to the next slide and see the next problem. Now, it is not that we are going to or is
it possible to simulate only this gear? It is possible to simulate a whole range of manufacturing
processes. We are going to study these things in this course as to how to simulate manufacturing
processes. In IIT Madras we have developed a non-linear finite element code to simulate
forging processes and this is operational in a company and you can see the results of
such a code in the next slide. May be slide is not very good but nevertheless it will
become clear in the next slide as to what we are trying to achieve. We are trying to achieve or we are trying
to see whether the filling of a dye is complete and the next slide clearly shows the type
of other results that can be obtained from this kind of work. From this slide it is very
clear that it is possible to predict plastic strains using finite element analysis. You
can see that actually a cup has been formed and the process as you may recognize is what
is called as a forward backward extrusion. During this process the slide shows what would
be the maximum plastic strains? If you have the data to find out whether maximum plastic
strains that are achieved in this process could be withstood by the material, if you
have that data, then you can see or you can say whether this process is good; that is
number one. In other words, you can also look at the process beforehand, simulate the process
beforehand and say whether I am going to achieve this process or not? If not what is to be
done? Number 2 - it may be that the dyes and the
punch that are used in the complete manufacture of the dyes are not good enough to withstand
the stresses that may be generated during the process of manufacture. It is possible
for us to find out what would be the stresses during manufacturing as well. So, it is possible
to say whether a punch will break. If it is going to break, then what would be the modifications
that are required and whether these modifications will successfully alleviate the problems or
remove the problems? All those things can be determined beforehand using finite element
analysis. Let us now look at the next example and see
what is the lesson it teaches? Not only are forgings possible, but whole set of manufacturing
processes can be simulated. We are not going to list them now because it is quite a long
list. But just to give a variety it is also possible to look at compaction, powder compaction
process and see what the density distribution is in a typical component. We will come back
to these examples later. We will first have a bird’s eye view of where all this process
can be achieved. Let us look at the next slide and see what it teaches us? This is another manufacturing process. The
manufacturing process that is involved here is the study of welding of thin sheets. All
of you know about distortions in welding. What are the things that are involved in welding?
There are two things that are, two problems that are important in order to study welding.
One is that there is heat transfer; as you weld, there is a weld pool and heat transfer
takes place. First of all, you have to do a temperature distribution study or we have
to determine the temperatures. What is the next step? Using this temperature
is it possible to solve a mechanics problem and find out what would be the distortions?
We are interested in distortions ultimately. These are coupled problems; a heat transfer
problem followed by mechanics problem, again a heat transfer problem, mechanics problem
and so on. We are going to study this kind of things in this course but nevertheless
it is important to understand that finite element can also be applied to study heat
transfer problems and coupled problems as well. Let us now look at the result of the study.
You can see the temperature distribution, first of all, during welding; as the torch
moves how the temperature gets distributed. You can see very well that it is quite concentrated
zone in the zone which is very close to the welding zone. Let us look at the next slide
and see what it teaches us. This gives the result of distortion after
welding or in other words this is the complete, this is the result of the complete study,
both heat transfer as well as the mechanics problem; you can see that the sheet is completely
distorted. What are we going to do with the sheet? You remember that in the last class
we had talked about undulations on the surface of a coach. This coach is made up of this
kind of such kind of welded sheets. They are 2 mm sheets very, very thin sheets and hence
there are problems of such kind of distortions. This is what manifests as undulations; apart
from the design or the assembly, the coach, it is the fundamental process of manufacturing
the coach itself which happens to be welding which gives rise to distortions. How are we
going to avoid this or is it possible now to see to it that we can get a straight sheet
or straightening as the process, is it possible? Yes, that is possible. World over people whoever
manufactures it; whether it is manufactured in Japan or Germany people straighten out
this piece. How do they straighten it? That is what is called as a magnetic forming process. Let us not worry about this process because
it is quite involved but electromagnets are used to straighten this piece, make this piece
go to a plastic deformation or make this piece go to plastic range and they make it straight.
There is a small problem here. These equipments are expensive. So, if I have to get an equipment
in order to do this kind of work, then I have to spend quite a lot of money. If you look
at this kind of magnetic forming process equipment, there are about five varieties of equipments
that exist What is the hitch here? If I have the first
variety say variety one and get it and use it for this kind of straightening process
then, if the sheet does not become straight then I lose lot of money. We have to import;
in India, we have to import these pieces so, we have to lose lot of money. The question
here is can I beforehand find out what is the type of equipment that I have to use in
order to straighten? What should be the specification of the equipment in order that I can straighten
this piece? Yes, it is possible. Let us look at the next slide. The next slide
is the result of such a simulation, finite element simulation and you can see that it
is possible to even simulate a magnetic forming process and then look at a straight piece
and arrive at what is called as the optimum configuration of the equipment that is used
in order to make this kind of flat sheets. Let us pause for a moment; let us get back
and see the things that we have seen so far or in other words let us now look at what
are the applications of finite element analysis? Let us get some answers from you. Let us see
where all we have applied? Summarize, what are the applications. Let us start from the
first example and see what are the areas in which we have applied finite element analysis?
Let us get some answers from you. Yes, the first one is rotor. LP rotor; LP
loader is the first example but what is that we got? Yes, stress analysis; in other words
it is possible to look at a new design; so for stress analysis for design. Quite a few examples; in fact whether it is
repair or whether it is a original design whatever it is we can do stress analysis for
design. What is the next type of examples that we saw? Non-linear analysis; we did contact
analysis. For example for the wheel we did contact analysis to predict failures. It may
not be that when we do stress analysis for design as a first step we may be interested
in a very complicated problem. Many times we do a simpler analysis but sometimes when
we have to investigate failures then we have to do a much more complex and thorough analysis.
We have to predict where we have to do much more complex and thorough analysis. So, non-linear
analysis to predict, I would say performance; yes, it is that you may argue that why not
we do it here itself? Yes, it is possible that you do this kind of analysis right in
the beginning. But as a tradition most people do not do a very detailed analysis when we
start the design … a performance because 80% to 90% of the components go through with
the simple linear stress analysis. But that may not be sufficient when the problem becomes
complex and we have trouble in the component hence we have to do a thorough non-linear
analysis. This may involve difficult things like contact with what is called as material
non-linearities and geometric non-linearities and so on. All these things are possible by
using finite element analysis. What is the third example? It is even possible
to look at assembly processes. We used it for assembly processes and look at deformation
during assembly; so, stress and now deformation assembly process deformation. What is the
next issue or what is that we got as the next issue? Contact analysis we have already covered here.
When you look at say for example piston ring, then automatically you saw that there are
two materials. So, material is not a constraint. That is the lesson that we learnt. One part
of the component can be of one material and the other can be of another material. So,
material is not a constraint. What is the next lesson? Yes Process model; so, process modeling using
FEM that is the reality. This process modeling consists of both heat transfer sometimes,
heat transfer analysis and a mechanics problem or stress analysis and it can be coupled as
well. What is the next thing we saw? Is there any other lesson you learnt? Equipment selection;
lastly it is possible to use this for equipment selection. This list is no way complete; you
know it is not that the list is complete. In fact today finite element analysis is used
in biomechanics, extensively used in biomechanics. Unfortunately we will not have time to cover
all the applications in this course, but biomechanics is one of the areas where finite element has
really taken off. From I think 87 to 97, there have been 1000
papers published on finite element analysis to human bodies, different parts of the human
body. There are nearly I think 350 papers; 300 to 350 papers on heart alone, human heart
and other things that are important to us or cardiovascular system if I can call it,
in that alone there are about 300 to 350 papers. There are extensive finite element studies
for dental applications. So, biomechanics is a very important area today for the application
of finite element analysis. There are lot of things that can be determined using finite
element analysis in biomechanics and if there is time we will see one or two examples, maybe
towards the end of the course. But let me warn you that many of these things are very
difficult. They are not very straightforward and easy because of the way nature has designed
us. The behavior of each and every part in our body is much, much more complex than the
material which we use in order to do things. There is no comparison between how our tissues
behaves and say metal behaves; they are totally different and hence the problems that we get
in using finite element for biomechanics are much more complex. There are other areas as
well. For example in electrical engineering there are lot of applications in electrical
engineering. Here again the applications are quite recent and again we are not going to
talk more about these things in this course. We will restrict ourselves to design and manufacturing.
We will look at only thermal problems, fluid mechanics problem. For example there has been
lot of applications of finite element analysis in fluid mechanics; that again will not be
covered in this course. As I told you, finite element is a very, very
vast subject. There has been tens and thousands of papers published, so we will restrict ourselves
to the fundamental finite element for design and manufacturing. There are some applications
of fluid mechanics in manufacturing but because of lack of time in this particular course
I will not cover all those aspects. With this background saying that these are the applications
of finite element analysis, let us now look at what is involved in finite element analysis. Let us look at the last slide in this particular
series. Have a close look at that. What does it indicate? What are the things that you
see? You see lot of lines or what I would call as network. They intersect at points
which are called as nodes. What is that you see or what is that you get or what is the
information you get out of seeing that picture? You see that there are lot of lines like this
or in some other figure you would have seen lines like this. These lines meet at certain
points and so on; these lines meet at certain points or the bodies which we considered for
analysis have been discretized, have been broken down into what are called as elements.
These are what are called as elements and this is an element and they are bounded by
what are called as nodes which sit at the intersection of these elements. Say for example
that is a node, that is a node, that is a node; that is a node and so on. So, nodes and elements are the ones which
are important in finite element analysis or what is that we have done philosophically?
A complex component has been broken down into what are called as elements. What are these
elements? How does it help us and what are the advantages of using this kind of approach
is what we are going to see in this course. Essentially what is that we are looking for
in a design problem? We have a force
and we have a body and we are looking at what
are the deformations? So, I want a relationship between force and deformation. Let us call
this deformation as simple displacement. There is a difference between displacement and deformation,
…. one, let us say that the body gets deformed and we will call this deformed quantity as
displacement. If I have a bar and if I apply a load say P the end of the bar gets displaced
by a certain amount say u. The body here in this case is the bar. The force that happens
to be there on this body is P and what is that you are looking for? You are looking
for this displacement, right. If this is the L or the length of the bar
we can easily find out what is the strain what is the stress and so on. What is that
we are interested in? We are interested to find out what is this deformation or displacement?
As mechanical engineers whenever I say that there is a force on one hand and displacement
on the other hand what is it that comes to your mind? Stiffness; beautiful. Suppose I have a spring for example and I
apply a force here and I ask you what is the displacement? The first question you would
ask me is what is the stiffness of the spring or in other words if this is the force and
this is the displacement of the end of the spring then F is equal to ku. So, all mechanical
engineers or all engineers generally know that this is a very fundamental equation.
What is the difficulty in applying this straight away to a much more complex problem like what
we have or what we had in these particular examples. For example can we apply this to a railway
wheel or to a side wall and so on? It is not possible, it is not very straightforward.
Why? Because here I could immediately say that the spring displacement is measured or
is characterized by the displacement of the end of the spring. When I say displacement
of the spring immediately you know that I mean how much it is going to displace, this
tip, this guy sitting here. On the other hand if you look at a three dimensional body, which
we encounter in the actual practice I cannot say by one number that this is the displacement.
What does it mean? It means that I just cannot come and tell you that this is the maximum
displacement; your interest is just not in one number. Your interest is in the complete displacement
of the component at every point. You would come and tell me the displacement at this
point, this point, this point, this point and so on. If I take the complete sheet, you
would ask me what the displacement of this complete sheet is. Maybe to make it more realistic
let me put a small window there. It is a complete sheet. Not only you will ask me the displacement
of complete sheet but you would also be interested in strain distribution throughout the sheet.
As we saw in one of our slides that the plastic strains of the forging, for example, was different
at different places. It is not that you are only interested in displacement; it is only
one small part of the problem. You are interested in strains and strain may not be constant
whereas this problem, it is not so and stress in this problem is constant throughout this
bar, but here the stresses may not be constant. Most components are such that stresses will
not be constant throughout. How do you now tackle that problem? Yes, this
is a nice answer that you have spring and you have a relationship with force and displacement.
How do you extend this? Can we develop a concept called stiffness and if we develop a concept
called stiffness is it going to be one number? That is the question we are going to answer
in the next two classes. The next class we look at what is stiffness from a finite element
point of view. We will answer that in the next class
