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So, this is a flywheel and those are some gears that you can see, and I am going to show that to you in little greater detail, but that’s how the energy gets transferred to the flywheel and then re-released from the flywheel. So, I just make it a little bit more transparent. So, you can see what we are dealing with here, you just see an opaque box here which is holding the mechanism, I will start making it a little transparent. So, you can see how the mechanisms. (Refer Slide Time: 18:24) So, you can see inside these two wheels are there I showed you that this is a gear, that was the only gear that was visible at that point, now you see more gears here you see one more gear here and you see some more gears here right. So, a lot of such gears you begin to see, and then if I make it more transparent you see one more gear here right. So, all of them are they are there here also you have one okay so. So, now, I will just remove all the wheels and we just have the gears up there. So, that you can see what is happening so, but the point being when you push this vehicle on the ground. So, this means this wheel rotates this way because this is the forward direction, you are trying to push this vehicle forward and then the wheel rotates backwards. So, when it rotates this gear, let me say this is gear 1 also rotates in the same direction, that forces gear 2 which is out here gear 2 to rotate in this direction ok. So, gear 1 is rotating clockwise, it is forcing gear 2 to rotate anti-clockwise that is forcing gear 3 which is attached to gear 2 also to rotate anti-clockwise, that forces gear 4 to rotate clockwise and that that gear 4 is attached to the flywheel. So, the flywheel also rotates clockwise ok. So, the flywheel is here. So, that is the flywheel. So, the flywheel is also forced to rotate clockwise, but you will notice here that this gear 1 is larger than gear 2. So, therefore, it forces the gear 2 to rotate very quickly relative to you know whatever rpm is, therefore, gear 1 gear 2 will have a much higher rpm, the gear 3 is attached directly to gear 2 therefore, gear 3 will have the same rpm as gear 2, and then gear 3 is attached to a smaller gear out here which is gear 4 and so, the gear 4 will operate at higher rpm than gear 3 and that higher rpm is now available to the flywheel. So, that is how you know as you rotate the as you move the toy, progressively you are increasing the rpm and therefore, the flywheel is rotating at very high rpm. So, I will remove all the rest of it so that you just see the gears here. (Refer Slide Time: 21:03) So, that’s what that’s the exact thing that you see here like I said this rotates this way that rotates the other way, that rotates that way and when that happens this rotates this way, the flywheel rotates this way. And you can see progressively it is getting faster and faster and faster. So, the flywheel rotates very fast ok. So, the flywheel rotates fast. So, that is how this flywheel is operating and so, if you just go back here this is the toy. (Refer Slide Time: 21:38) You can see the gears that are there and you can see all of the gears now and you can see how they are operating and then you have I separate all the other components and you only see the gears right. So, this is what we have. So, in this process, the flywheel gains a lot of energy and it has that energy in it is rotating very fast, and the gear ratio is such that it will be able to deliver that power back to those wheels, once you know to pull this vehicle back down. It will run slower, the wheels will run slower than the flywheel because that’s the ratio in which the gears are there, but there will be a lot of torque that will come available from the flywheel, because of this advantageous gear ratio and therefore, the vehicle will run. So, that’s how these toys run and that is why I said I guarantee you that you have used a flywheel, and most likely you have used a flywheel and this is the flywheel that you have used. You can see you know even if you have some children in the house and they have a toy that is broken, you open it you will see a mechanism that looks exactly like this. So, this is the flywheel. So, we have all used for the flywheel. (Refer Slide Time: 22:40) Another example. So, that’s a simple example. So, these were two household examples. (Refer Slide Time: 22:44) That we that I showed you, many houses do have sewing machines or you can certainly see it in shops at different places, toys we all have seen or used. We also have the same kind of thing in a reciprocating engine. So, in a reciprocating engine, you have you know a cylinder in which you have this you know fuel-air mixture that comes and then there is it explodes it is lit up and it expands. So, when that happens it moves this piston down okay and so, there is energy stored there is a power stroke this is the power stroke, this is the this is where the power is delivered from the engine energy is being pushed out of the engine. So, that makes this wheel rotate ok because it is linked here. So, that forces this wheel to rotate. Now, the piston has to go back up. So, that it will get ready for the next stroke right. So, now, there is no reason for it to go back, the only reason it goes back is that this wheel is rotating. So, for example, this is how it will look, as it completes the rotation this is how it will look. So, the reciprocating engine as it completes the rotation during the after the energy that has been stored during the power stroke is used for the next intake stroke. So, this next in intake stroke that you see here happens only because of the power that it got that this wheel picked up during the power stroke. So, during the power stroke, it is rotating, and it pushes back to the wheel it pushes back this piston, and that is how the because this is rotating and then it will continue to do that. It will come back to this site, the next power stroke will push it down and that will continue. So, even in a reciprocating engine, which is based on some you know internal combustion that is happening, this kind of mechanism ensures smooth delivery of power. I was telling you, you know that we need to have the power delivered smoothly because here also you see the power stroke is where the power is coming, the intake stroke this now no power that is coming right. So, but this ensures that since the wheel is rotating it is generating this movement that looks relatively smooth on the outside. So, that is the reciprocating engine. (Refer Slide Time: 24:45) Another example is regenerative braking. So, in a regenerative braking situation normally in a break in an in a vehicles brake you press the brake of the vehicle, all that you have is that you have the brake pads which press against you know some rotating disc that is there and then there is friction. So, you have the disc that is rotating and then you have this brake pad that it clips on to that disc because you have pressed the brake, and it grabs it tightly and in the process, you have a lot of heat that is generated. You have a lot of heat that is generated and that is essentially that heat is the entire kinetic energy of that car that you had, that kinetic energy of the car is lost as heat in the when you do the braking. Now, you can think of other implementation. So, I am just showing you one implementation, where instead of just wasting it all as the heat you have a situation where let’s say this is the brake pad, this is the brake pedal and you are inside the car you have this brake pedal at your disposal and you press the brake pedal right. So, now, this wheel is rotating. So, the vehicle is moving forward the wheel is rotating and it continues to rotate. So, you have another wheel here which is not in contact with that wheel, which is not in contact with your rotating wheel. So, right now there’s a gap here. So, right there’s a gap that you can see here. So, there’s a gap there. So, that thing it is not in contact, but the moment you press the brake right the moment you press the brake. So, you are here you press the brake. So, when you press the brake, the wheel comes the two wheels come in contact. (Refer Slide Time: 26:22) Two wheels are in contact, the two wheels are now in contact when you press the brake. You are here you press the brake you get the two wheels in contact. Once you get the two wheels in contact when you have this rotating this way, you have this other wheel also rotating the same way right. So, you have the wheel rotating that way, then you can have a generator here and from that generator, we have electricity going to a battery ok. So, that is how we generate electricity put it into a battery ok. So, and this when these two wheels come in contact there is going to be strong resistance from this wheel that is pressing against this smaller wheel when it presses against this larger wheel it is going to resist the movement of the larger wheel. So, it is going to press against a larger wheel and resist the moment of the larger wheel and so, when that happens, you are breaking you know you are providing the braking energy. So, you are providing the braking energy and it slows down the working of this wheel and therefore, the vehicles slow stall. So, whereas, previously all that energy was just being wasted as heat, and being you know unnecessarily released to the end where I mean atmosphere, this time when you press the brake you are charging you are running a generator creating electricity and charging a battery. So, this idea is called regenerative braking. And I will also point out that regenerative braking you know because it is you know set up in this manner, it is often not ideally suited for sudden braking ok. So, sudden braking where you want you to know abruptly you want the vehicle to halt, this may not provide you with enough resistance to the movement of the vehicle to the movement of the wheel, to complete you know to stop the wheel abruptly. So, usually regenerative braking is additional braking in over and above the normal, you know standard kind of break that we have, where we have a pad holding on to a brake pad which presses onto a disc. So, that’s always there. So, you always have a regular brake which is available in the vehicle, and you have also this regenerative braking if you decide to implement it. And particularly you will implement it if you have an electric vehicle because you will already have all the electrical infrastructure associated with the vehicle which includes a battery and so on. And so, when you press the brake, automatically some energy goes from the vehicle instead of all of it going into heat, it will go into the battery and a particularly in slow city kind of driving where you are gradually accelerating, gradually decelerating a lot of things are going on, this is a very useful way in which you can recover a lot of energy. And of course, at the moment you hit the brake hard then there will be some control system which will ensure that your regular brake also comes immediately and then stops the vehicle. So, this is the way you would do it. And this is an implementation I am showing you where we are using our generator to generate the current and put it into a battery. If you are trying to use flywheels, in this case, we can think of a more or less similar implementation except that it would pick up it would give this energy into a flywheel, as opposed to this implementation where this energy is now being given into a battery. So, you can instead of giving it to a battery you can give it into a flywheel and so, that is another possible implementation of this system. (Refer Slide Time: 29:59) So, for example, you would have a situation, which looks where if the brake is pressed like this, in addition to this you know this wheel which is touching the rotating wheel which is the one on the ground, you can have a mechanism attached to it where you have this flywheel. The same thing that we just saw in the toy. So, you press it and so, it is already there attached to it, I am just showing you as a separate thing for you to understand how they are related to each other. So, you press the brake down and then when the brake is pressed down, the flywheel mechanism that is attached to this wheel. So, it is already attached to this wheel, which is just not shown in this figure which and it would be attached in this manner. So, that will ensure that this gear rotates that will ensure that that gear rotates, that gear rotates and thus let’s show this rotates the flywheel rotates ok. So, in this manner, you again convey energy back from the rotating wheel which was on the ground, which has the kinetic energy of the vehicle into the energy that is stored in a flywheel. So, that is how we share this gather back this energy right. So, this is how you do regenerative braking using a flywheel and electric vehicles do an implement this. (Refer Slide Time: 31:19) So, now what is this flywheel? So, we will now look at this wheel alone, this wheel that is out here which is the flywheel, that alone we will look at a little greater detail to understand what exactly is it doing. So, usually, what it is that, it is a wheel where there is where you are storing energy in the rotating you know as the wheel rotates. So, if you look at the energy stored in a wheel, it is given by this formula E equals half I omega square ok. So, E equals half I omega square where I is the moment of inertia okay. It is an I is the moment of inertia and this wheel. So, and omega is the angular velocity. So, omega is the angular velocity and I am the moment of inertia and the. So, when you rotate it this is how the energy is stored in it. So, you can see here the energy increases only linearly with mass, the mass will show up in this moment of inertia. So, it will show up in I the mass shows up there it only. So, you can see I am here in a linear format, but omega is here in the quadratic right. So, it’s gone. So, as the square of the angular velocity. So, therefore, if you double the mass of the of this wheel you are only doubling the and use the same rpm etcetera you are only doubling the amount of energy that is stored in the wheel. On the other hand, if you double the angular velocity of the wheel, you are everything else being the same you are you know putting four times as much energy into the wheel. So, you can store much more energy into the wheel by simply increasing the rpm of the wheel. So, therefore, many implementations of the flywheels focus on this idea that they should try to maximize the amount of omega that or the angular velocity of the wheel. So, that is the implementation that they aim for. That has some restrictions associated with it that there have some you know limitations associated with it so that we will see in just a moment. (Refer Slide Time: 33:34)
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
But so, for example, if you look at the I have the moment of inertia for a solid cylinder has this form it is half m r square where m is the mass of the wheel the r is the radius of the wheel. So, that is this radius here this is the radius. So, that’s your radius r and this wheel has a mass m ok. So, you must also remember that you know if you look at you know some information you had in your say mechanics course or so on, the moment of inertia of these kinds of objects or of any object it depends on the geometry of the object depends on how the mass has been distributed on the object etcetera. So, for example, this is for a solid cylinder this formula is not going to be the same if you have just a wheel where all the masses on the rim. So, you have to actually if you are implementing a flywheel you should figure out what is the shape of the flywheel, what is how the mass is distributed on the flywheel, what is the orientation in which it is being held in what is you know axis about which it is being rotated. So, a bunch of things you have to take into account, before deciding what is this moment of inertia. So, this formula is not standard, it is not standard for all you know objects. So, whereas, for linear you know for linear kinetic energy we write E equals half mv square right we write that for kinetic energy for of something that is moving in a linear which is having some linear motion. So, there they are fixed, it doesn’t matter in which direction you are moving this equipment, it doesn’t matter if you take a wheel and you throw it this way or you throw it upwards or whatever the mass of the wheel remains the same as long as you are not looking at the rotational aspect of the wheel. The same wheel if I just throw it as a flat object with or without worrying about it is rotation. If I just throw it, then it doesn’t matter in which direction I throw it the mass of the wheel is still m and its kinetic energy will be given by half mv square. On the other hand, if I am not throwing the wheel, but I am rotating the wheel, then it depends on how I rotate the wheel I could rotate it you know about its axis. So, I can have a wheel I can rotate it about this axis I can also rotate it about this axis right I can rotate it about a vertical axis, which is the axis that I have put as a dotted line here or I can rotate it about a horizontal axis which is perpendicular to the wheel that we have drawn here right. So, those two have a completely different moment of inertia. So, you cannot use the same I for those two cases you have to check and you have to calculate what i is, and in that, that is the I that you would use. But in any case, the point is that this is the moment of inertia and them is there. So, therefore, if you just want to write this again as in the with m also included in it, this is E is equal to 1 by 4 m r square omega square ok. So, I will remove this here. So, this is E is equal to. So, half mv square m half m r square I have put for this value of I here. So, therefore, I get 1 by 4 m r square omega square. So, you can see here it stays linear concerning m. So, that is what we say it you know increases linearly with mass, but a square of the angular velocity that is the point that you have to note. And that is why they are as working very hard to find ways to keep the angular velocity as high as possible. (Refer Slide Time: 37:20) So, what is the problem when you raise the angular velocity to a very high value right? So, when you raise the angular velocity to a very high value. So, if this is the wheel and this is the centre of the wheel. So, you are going to have some centrifugal force ok. So, this is a centrifugal force. So, centrifugal force is going to be that; that means, what? That means, the material that is at the rim is trying to go away right it is trying to go away from the centre and therefore, it is pulling all the material in between to move away from the centre and therefore, there is stress. Now any material will you can check it’s you know tensile strength, ultimate tensile strength etcetera there is when you put stress on a material, it will have elastic deformation initially, then it will have some plastic deformation and then it will fail ok. So, it will have elastic deformation, then it will have plastic deformation and then finally, the material will fail. So, therefore, and that is got to do with stress. So, when you have stress, low-stress elastic deformation, high-stress plastic deformation and then even higher stress failure. Failure means the material just breaks okay it just splits up into pieces. So, this is just I mean descriptively I have shown in indicated this, actual values will vary and if it is a brittle material, for example, you will me you may not see a much of plastic deformation, it will go elastic and you badly see any plastic deformation it will fail. So, so that variation is there for material to material. So, generally, but this is generally how the material is going to behave once it is stressed. So, you have centrifugal force, you also have stress which the force leads to stress based on you know you put I mean you calculate the force per unit area that is the stress, you also have stress because the circumference is now trying to move apart right. The circumference is all having centrifugal force heading outwards which means all these. So, if I take any two points here if I make a point here and a point here this point is trying to move this way that point is trying to move that way because it is trying to expand and that is basically what I am showing you here, that is the arrow that I am showing you here. So, it is pushing the material apart that is called hoop stress. So, that’s the stress of the rim, which is trying to push the rim open trying to expand the rim. So, you have a circle because the circle is rotating very fast it is trying to expand, the whole circle is trying to expand. So, that is also a stress that is there and that is usually trying to take all the particles that are in that wheel and you know to separate them to further distances. (Refer Slide Time: 40:20) So, usually, this tensile stress at the rim of the cylinder of this flywheel at this rim know at the rim of the cylinder is the highest stress that is there in that system as it is rotating at high speeds, and it can make it creates a situation where it can exceed the ultimate tensile strength of that material of that rotor material and then the rotor material will simply shatter. So, that is a safety issue ok. So, the rotor material can shatter. So, in other words, if you take a flywheel and you put it at very high rpm, it can disintegrate as it is operated ok. And in that sense in in in a fundamental sense, it is the same kind of safety issue that you have with any energy storage device because that much energy is in there. In all energy storage devices, it is very critical that you safely store the energy and safely extract the energy okay in a controlled manner. The energy should get stored in a controlled manner, the energy should be released in and controlled in a controlled manner. You can create situations or you can end up in situations where either during the energy storage process or the energy retrieval process the process is not in a controlled manner it can go in an uncontrolled manner. When it goes in an uncontrolled manner you are having you know an accident so, to speak concerning that device. So so, that is what we are talking about when we say you know a battery has exploded a battery explode explosion is a situation where the energy from the battery got released in an uncontrolled manner, not in the manner that you want the battery to release the energy, but in an uncontrolled manner; the same thing in a flywheel, if you take a flywheel and you get it to operate at conditions which are beyond its capability, the flywheel will completely come apart; it will just disintegrate into pieces and come apart and that is very dangerous. So in fact, you know all the vehicles were they you know install flywheels for various applications. So, certainly like I said you know for let’s say electric cars where they are trying to put flywheels to do regenerative braking. You have to have a casing around the flywheel, which is in a position to handle a breakdown of the flywheel. So, if the flywheel at high rpm just shatters and comes apas comes apart in pieces those pieces should stay within that casing they should not just you know come out and injure somebody or hurt something or caused other damage. So, it is very critical that when a flywheel is made that it is made in such a way that it is well guarded with, against this possibility that it might shatter and therefore, it keeps the energy in you know contained manner. And also I will point out that concerning the flywheels, the bearing is very important. You have to have very good bearings because you don’t want friction you want it to run very smoothly and you want it very well aligned you do not want it wobbling when it is speaking of this high rpm because all those things can be a danger. So, dangerous. So, making the flywheel making good bearings friction as frictionless as possible you never going to have zero friction, but you are going to have as smooth you know well-lubricated bearings as possible, which hold the flywheel in you know proper alignment those are all very critical things you know in successfully implementing a flywheel for some application. So, that is something that we have to carefully look at because we want it to store a lot of energy and we want it to store this energy safely. We don’t want it to store it in a manner where it will just shatter as it is being operated ok. So, this is the point that you have to keep in mind. (Refer Slide Time: 43:56) So, if you look at the scheme of where the flywheels fit into you know energy storage realm of energy storage devices, you can see here we discussed when we spoke about supercapacitors and I have you know built on that same image here. So, capacitors will give you high specific power, but low specific energy. And the opposite end of the spectrum is the battery which gives you high specific energy, but low specific power. These supercapacitors and flywheels come in the middle and in this context the flywheels give a little bit better specific energy, because you know it is there in it are rotating it can hold up that energy for a little longer and so on. So, it gives you a little better specific energy relatively, but it’s roughly in the same realm of existence as a supercapacitor. So, a flywheel just the way a supercapacitor behaves, a flywheel is also something that bridges the gap between a regular capacitor in the battery. So, these two energy storage devices that will give a lot of flexibility when you put together you know the set of equipment that have to come together to run an electric vehicle. So, you have an application as I said you know the application will have a power demand profile, that has a very specific shape or even a shape that is unpredictable and the power supply infrastructure which consists of a battery of flywheel a THE supercapacitor a capacitor some combination of that, we shall be which you have to design, you have to think of what is the right kind of combination what should be the sizing of the flywheel, what should be the sizing of the battery, what should be the sizing of the supercapacitor what should be the sizing of the capacitor. That is a decision that you, as you know the designer of an electric vehicle would have to take into, would have to make and then once you make that decision, you and I will also point out, but there is no single answer for this it is not like there is an if I if one person makes an electric vehicle and another person makes an electric vehicle, both of them even if they did all their calculations both of them are not going to come to the same answer. The reason being we will each of us will have a different idea of what our vehicle should do. So in fact, even today if you look at you know even if you are looking at non-electric vehicles, we are just looking at regular you know passenger vehicles based on petrol running on petrol or diesel; already the modern-day vehicles have different settings. They have an eco setting, they have a sports setting and different settings are there. So, what is the difference? That setting simply changes how the power is extracted from the engine the conditions under which the engine is operating they say the fuel-air ratio that is going into the engine. So, you can optimize the engine to do different things, you can opt if similarly, you can optimize the electric vehicle to do different things, you can put an electric vehicle for racing you can put an electric vehicle in an F-1 circuit fone racing circuit. So, there your optimization is for power, power and torque those are the things that you are optimizing for. On the other hand, you may want a mass-market electric vehicle, which you want to put on the roads where everybody is going to use it and we intend to make it as fuel economical as possible there your optimization is going to be very different. So, in both these cases these two extremes that I am talking off. So, a passenger vehicle and an F-1 race car. If both of these you are trying to implement using electric vehicles your choice of battery your choice of a flywheel or supercapacitor or a capacitor that combination; however, what capacity what sizing and what material you will use and also what will be the logic based on which you will decide which is going to provide the power, which is going to charge, which is going to discharge, how much it is going to discharge all of that will vary based on what is your requirement, okay and that is something that you will have to over decide on. So, this is something that you should keep in mind. (Refer Slide Time: 47:41) So, I will sort of wind up by telling you a few things about the materials here. So, you can use various kinds of materials for the flywheels, and some of the older toys typically apparently have used to lead-based flywheels. So, you can see that it’s kilojoules per kilogram it is kind of low it is only one-kilo joule per kilogram whereas, cast iron can go up an order of magnitude to about 25-kilo joules per kilogram and carbon fibre reinforced polymers can go up to 150-kilo joules per kilogram. So, carbon fibre reinforced polymers can hold much more energy per kilogram related to say cast iron or lead-based flywheels.