 This lecture is on engineering applications of vibrations. So, far we have studied about the basics of engineering vibration. Today, we will see in this class what are the basic engineering applications of vibration and towards the sometimes in the middle of the class we will see how vibration is used for the health monitoring of machines or condition based maintenance of machines. Some of the topics which we will be discussing today are essentially what happens during the case of a base excitation. For example, if you have a surface and because of certain forces there is a motion on the surface and how by putting a sensor we can measure this motion y and sense it as a response x of the sensing element. This is the case of base motion. Usually, typically when we have a vibrating surface we try to know what y is. How do you do that? We put an sensing element x or what is which will be essentially housed in a transducer. So, is proportional to y or what is the relationship between x y as a function of the frequency etcetera. So, once I can measure x I know how it is related to y and that is what we are going to study in base excitation. Another very important applications of or unwanted vibration is this rotational unbalance. Essentially what we have is any shaft which is supported on bearings. Suppose it carries a set of blades like in an impeller and this undergoes rotation. Imagine in this impeller if there is an unbalance mass m or m e and this unbalance was at a radius of r from the axis of rotation of the shaft. You can imagine the unbalance radial unbalance force f unbalance will be m e omega square r where omega is the speed of rotation. Now, you see this unbalance force because of the centrifugal action of the unbalance mass is proportional to omega square omega is the rotational speed. It is almost very small if m e is small r is small and omega is small, but even if m e and r are small, but omega is large like in the case of gas turbines rotating at 30,000 rpm. A small amount of unbalance mass is going to give rise to unbalance force and what will happen essentially is because of this unbalance force there will be forces coming up to this bearings that depend this f 1 and f 2 depend on the position of the impeller and so on. And further this will be complicated if there are sets of impellers like in a gas turbine as you will see there will be different stages of compressors. So, one set of compressor having a lot of vanes in that impeller and if one such vane has an unbalance it is going to lead to unbalance force and this unbalance force in different planes is going to give rise to couples and then this is going to have a complicated effect in the life of the machine. It is going to affect the bearings, bearings will be subjected to fatigue failure, there will be clearances will increase and it is going to complicate the matter. So, we should try to avoid this problem. Now, another situation we have in the engineering application is vibration isolation wherein suppose I have a machine which is put on a foundation because of the dynamics of the machine certain forces are being subjected to the ground and this ground is going to then vibrate and this waves will get transmitted and then at some other place I have another machine and they are going to affect this machine's operation. So, I have to device a mean wherein I reduce this energy which is getting transmitted from one machine to another this is one way of looking at it. The vice evers also happens for example, you are driving on the road on a vehicle there are lot of roughness potholes etcetera. So, these are going to give rise to forces and these forces are going to get transmitted and then you are going to get a sense of vibration to the human being who is sitting in the car and obviously we would like to isolate this frequency which is coming from the ground this motion which is coming from the ground by a proper selection of what is known as the vibration isolators we will discuss about them in subsequent sections. So, the vibration isolation is another serious problem in engineering vibration and then we will see how we can avoid it how we can reduce it and so on. Another application of vibration is this tuned dynamic absorber what happens suppose I have a body suppose I have a body which has mass m and stiffness k. So, omega is equal to root over k by m this is the primary this is its natural frequency and this is the primary mass. Now, to this system if I if I see the response of this system I will get a natural frequency a response at its natural frequency which is omega is equal to root over k by m and say for example, this amplitude x which I have got here is something which I do not like I would like to reduce this vibration amplitude. So, what I could do is I could attach to this system another system wherein this omega is also equal to its k s and m s. So, this system now is going to have a response which will look something like this because there are two bodies there will be two natural frequencies and there will be a natural frequency shift and most important thing is this amplitude of vibration has reduced. So, the primary mass though the natural frequencies have shifted then, but the amplitudes of vibration has reduced and particularly this has applications in for example, large skyscrapers for example, because of the wind blowing talk about the tall hotels in Dubai or the skyscrapers of New York or San Francisco etcetera when this wind is blowing this skyscrapers have a motion and this at the top could be about one meter imagine a hundred storey building on the top it is swaying about one meter. And this kind of motions could be arrested suppose we put such structural tuned dynamic absorbers in the structure itself. So, that they are going to arrest this motions and reduce the amplitude of oscillations this is one application of tuned dynamic absorbers. There are lot of applications of such tuned dynamic absorbers in automobiles for example, if you know the drive shaft or the propeller shaft, propeller shaft also undergo a lot of torsional oscillations. So, we can put such torsional tuned damping absorbers to reduce those oscillations at the natural frequencies because by tuned dynamic absorbers we can reduce the oscillations of the primary mass because of the resonant frequency of the secondary mass. Another engineering application is this torsional dampers you recall you know I had written this equation i t theta dot plus c t theta dot double dot sorry k t theta is equal to some function forcing function torque. So, by introducing this damping term in oscillating systems by having torsional damper I could reduce the oscillations of the rotational response of the system. For example, a crankshaft of an engine which is under which is having rotary motion and its torsional oscillations could be reduced by putting a torsional damper. So, these are the some of the applications and we will see some practical examples now to begin with if I look into this case here in the case of a tractor platform isolation. Here we have a tractor for example, of course this is the platform where you put the foot in case this is a me in my younger days you know is to test on a tractor and this is a platform here and if the driver sits here because of the engine's dynamics none of the vibrations from the engine should get transmitted to the platform to the seat etcetera. So, how do they arrest that if you will look closer here there are actually what are known as the anti vibration rubber mounts in this location here between the platform and the chassis of the tractor. So, the chassis of the tractor is actually supporting the engine. So, the forces from the engine because of the engine's excitation of the engine's excitation forces and the inertia forces the engine excites the structure. So, this chassis is going to have large motion and if this platform was rigidly connected to the chassis it was it all this energy is going to get transmitted to the platform. Instead we put a flexible element you can think of it as a structural fuse or you can think of it as an structural impedance mismatch the energy which is if you analogous to an electrical circuit if I put an if I have an impedance mismatch in the system the current is not going to flow of the power flow will not be maximum and same is happening here also the mechanical power flow is reduced by having an impedance structural impedance mismatch which is created by this vibration isolator. So, depending on the payload being subjected to the isolator depending on its mass the frequency of operation I can decide on the natural frequency of the oscillator I can decide on the stiffness characteristics of this oscillator of this isolator. This is another such view of this isolators and this isolator just need not be elastomer or on a polymeric as a polymeric mounts they could be also spring mounts because you know this elastoric mounts they wear out with time the elastomers sometimes they react with the oil and they lose their property sometimes they react with the saline atmosphere etcetera around you and then they will lose their structural stiffness and their bonding strength. So, sometimes in many harsh applications people use other kind of mounts which I will come to later on. Now, this is the case of a gas turbine you know where in this turbine rotates at about 30,000 rpm and then there are series of such impellers which will be the compressor and then the turbine and this compressors you know there could be many such blades in the or vanes in the impellers and if one such set of compressor ring undergoes an unbalance it is going to give rise to a radial force suppose another one has another amount of unbalance it is going to give you a radial force so there could be a couple. So, in this couple this is they are going to give rise to lot of forces though this turbine is put on a structure here or a platform and this platform is rigidly mounted to the hull of the ship or fixed to the wing of the aircraft. So, now this is a closer view of this compressor imagine that this all of these rotate at 30,000 rpm or 20,000 rpm imagine if one such vane either has a small amount of unbalance mass you can imagine the kind of forces which are coming on to the bearings which are supporting them. So, unbalance at high speeds is very very dangerous and in fact this amount of unbalance depends on the severity of the machine suppose it is a very high speed machine we will have serious consequences. So, for example, you are talking about a high speed machining operation where we have a spindle and there is a amount of unbalance mass in the spindle suppose you are doing a vertical boring and if there is an unbalance mass and because of this there are radial forces you will never get a true bore there will be ovality in the bore. So, all these are going to affect the performance or the your output of the machine it could be a machine surface it could be an gas turbine it could be an effect on the it could affect the bearings. So, these are actually the causes by which the machines fail or the reasons behind which machines fail if one such unbalance goes unnoticed and we only get woken up when the bearings fail, but the problem could have been an unbalance usually has created this. So, it is very I mean people do that once they install a machine they ensure that the machine is balanced perfectly to its operating speed and in the subsequent classes I will also be telling you how to do a field balancing of a such a large gas turbine or a fan which is rotating rotating at high speeds basically you know what happens I should briefly tell you here in the radial plane. For example, if this has lot of you can call it vanes blades whatever if there is a small amount of unbalance mass and this is rotating and in this machine and this of course in there in a casing etcetera and I measure this response here by some technique if I can find out this amount of unbalance and if I know the location of this unbalance physically with respect to a certain marker in this vane I could put a correction mass in a single plane and then I will have a balanced rotor or a balanced disc, but if there are multiple such discs along a along the length of the shaft I have to make sure that each one of them is balanced otherwise I have a balanced here if I have a balanced mass unbalance mass here and a balance mass here I may be balancing it in one plane, but the couples will still be there this is also something which we have to be careful about. Another application or I should show you this anti-vibration mounts for example, this is a setup from our lab when you have the system running there will be lot of forces coming on to this structure and this structure will eventually transmit to the foundation. So, these are what are known as anti-vibration mounts you can see one mount here another mount here. So, imagine if next to this machine I had a very sophisticated laser based measuring systems an optical table wherein this is a table and there is a laser beam being produced and then it has certain target which it has to hit a strike. If there is a small amount of oscillations because of certain ground vibration. So, what is going to happen that this source is also going to have a motion. So, I can never hit my target by laser beam and there are many engineering applications wherein lasers are used. Lasers are used in microscopy, lasers are used in machining, lasers are used in surgery. Imagine if such laser beam imagine a doctor coming to your eyes to do a laser surgery and his hands are shaking. And now I will bring it back here in an optical measurement table because I have a imagine you have a large forging hammer in your workshop next door. Of course, you have made a nice building and then there are nice walls etcetera. So, the workshop and then you have a lab here here being a laser lab because of the forging hammer lot of forces are coming and then this forces come to the ground and then this are going to get transmitted through the ground and then they are going to affect the laser. And this is not a science fiction, it does happen. There has been instances you know where I have measured vibrations of the level of micro G, micro G is 10 to the power minus 6 G. In fact, wherever when we have laser based measurements the vibrations have to be less than 10 to the power minus 6 G meters per second square whatever that low vibration level. But question is how do I achieve it? Suppose I have a forging hammer next way or I will give you a more realistic picture. I had visited a lab where we are doing some oscillation selector for a laser machine, laser measurement system, laser microscope to be precise. In this building there was an elevator. Each time the elevator was going up and down the shaft they were having problems in the laser based measurements because you know once we have an elevator going up and down the shaft because of the elevators movement the vibrations were getting transmitted from the elevator shaft through the foundation to the laser lab. And the measured vibration levels were even 10 to the power minus 6 G and that is small enough to create problem in a laser based measurements. So, as an engineer as a vibration specialist we have to decide on what is known as this isolators. Isolators both for motion and both for forces because you think about earthquakes. When earthquakes occur why do buildings fall because excessive forces have come through the foundation. So, we have to design and decide on isolators vibration is the motion is one. Next we will talk about cases when we have impulses, nuclear blasts, shock waves. What happen when we have shock waves? What happen when we have a missile firing on the deck of a ship? So, how do we arrest that the ship should not rock? Other electronics in the equipment in the control panel should not get affected because once we have such shock waves coming in they are going to give rise to fatigue loading. Shock coming once, shock coming twice repeated shocks they will induce fatigue load on the machine and then the structural components may be the electronic shoulders would feel. Imagine a printed circuit board wherein we have lot of shoulders and this printed circuit board is kept on a platform wherein very close to it we are firing a missile and there is no protection to arrest the vibration cause once we fire this missile. And this forces are going to excite the shoulders and shoulders will give away eventually and then we will have a component failure. So, the reliability of the equipment has to be also ensured that they do not fail under repeated shock loading, repeated forces, repeated motions. So, this has to be also ensured. This is one another example which I was talking about and you must have seen this. When we have this generator driven by an engine and because of this motion of the engine because engine itself because of the inertia forces and the gas forces are going to have and you must have studied in your dynamics of machines that some of these forces are not balanced whatever we call a perfectly balanced machine, but then there are some orders at which balancing forces are there and these forces will also excite the foundation and this has to be isolated by I could have elastomer mounts, but nowadays you know people are using cable mounts. Now, this cable mounts it can flex in both directions longitudinally, transversely. So, it can take up forces in any direction because if I was talking about an anti-vibration mount which you will see that the mount which we have is usually in one direction. But suppose the motions are in three directions it becomes very cumbersome to put you know three isolators in three directions rather the convenient we have doing it is through cable mount or sometimes in people also known as wire, rope, mount because of the fact that there are no elastomers here. So, they can be subjected to weathered conditions in the saline atmosphere in an oily oil mist full atmosphere. So, they will not wear out with time and because of these are made of high strength stainless steel they will not corrode they can take more load for the same available space. So, cable mount is people are particularly in the defense they are using a lot of cable mounts because it can survive a lot of harsh environment. This is another case of a missile launcher and then here you see again the cable mounts have been put here. In such a system could you put on the deck of your ship then once you have the missiles firing none of the motions are going to go through the deck to the other systems in the ship. Of course, you know you will see we will be doing certain numerical how to do we calculate the stiffness how do we estimate the damping how do we estimate the payloads of the mounts. Well this is from a catalog of a manufacturer of isolators I will just show you some of the examples here. These are the normal helical springs which are used as mounts and some of these are actually pads where there in there are pockets here. So, for example, when you compress them they are going to flex in and take in the load. These are the cable mounts and these are some of the conventional spring helical mounts and they could be series of such springs and then there could be a damping associated with damper associated with it and so on. I will now give you a typical example as to say for example, I have a machine I will just draw the base of the machine and suppose it is put on four isolators and then there is this machine has a certain mass m each one of them has a stiffness k. So, springs and parallel the effective stiffness is nothing k effective is nothing but summation of the k's and this will be 4 k and the natural frequency of this system will be m by 4 k. Now, imagine the question is what is the motion of this or the vibration which is transmitted to the ground because of this system. This system say for example, it is rotating at a certain speed omega. There is a rotating component which is rotating at a speed omega and which is known as the driving frequency. So, we will define a ratio r is equal to omega by omega n. So, the ratio which is transmitted or the displacement is actually given by where zeta is the damping coefficient factor and r is the frequency ratio. Now, if I plot this what happens is if you look at the typical vibration response plot. Now, if I increase the if the damping reduce is very less what happens is this amplitudes go up. And if I increase the damping so at resonance I can always reduce the motion vibration motion by introducing damping. Now, how is that done? Actually we can there are many ways to introduce damping in rotational systems. They use what is known as torsional damper particularly in crankshafts of engine. Another is by coating or sandwich beams and they are both constrained unconstrained. So, basically if I have a surface sheet metal in the constrained layer damping what I could do is I will have another thin structural material and here I will put a viscoelastic, elastic damping material. So, because of the relative motion of these two members there will be an hysteresis loss and then the energy will be damped the energy will be reduced and then the oscillations of vibration will reduce. This is one another is just coating with unconstrained we just coat it with a damping material which is known as the kind of a coating. Commercial lot of damping paints are available to measure such or to put on the structures to reduce the motions at resonance. Coming back to this figure here so this is how the structure of the internal of a vibration oscillator looks like. This is a steel base plate and here there is a neoprene rubber body which acts which gives stiffness and sometimes also gives some inherent damping in it and so one component of the structure is attached to the base another component is attached to the top and same is true here wherein we have the neoprene pad or rubber pad on top of it we also have a helical spring. So, depending on the payload we can if the payloads are more we can have a bigger helical spring if the payloads are less even sometimes the pads are good enough to take the payload and as I was telling in the previous diagram some of these pads they have what is known as they are not a thick rubber sheet instead there are pockets. So, what happens when there is a load because of this pockets if you look at the sectional view so I am just doing say two pockets they will flex in so because of a load they will try to move in and then try to take the load and then try to because we have to arrest motion. So, they will flex and take the motion and then less will be transmitted. So, such are the neoprene pads which are used as used as isolators. Now, such vibration isolators are sometimes used to in engineering to isolate you know what is shock for example, you know you would have studied about the vibration wherein in the time domain I have a series of I can break them into in time domain there will be lot of frequency components of such a time history of the vibration signal. But a shock on the other hand is a large motion occurring for a fraction of a time and this amplitude could be very high. For example, impact like a like a gun burst large impact they happen only one in a given period of time they are not repeated we never have repeated shock. For example, a large earthquake initial wave is a shock. So, such shocks have very very large amplitudes. So, immediately what happens the how do we isolate this suppose if a subject my equipment to such shocks they are going to get damaged because of this high oscillations. So, in such a case what if you look at the energy point of view in shock isolators look at the time I will the energy is like this to begin with in shock isolation we try to reduce because and this energy there was no isolators this energy would straight go into your component and damage the component. So, in shock isolation what we do through this isolator try to take in all that energy and it is the same energy, but dissipate at a less lower amplitude with a longer time. So, the energy the area of these two curves should be the same. So, energy dissipation at a slower rate. So, if I have a very fast moving object shocks are coming here. So, this isolators or shock isolators actually try to take this energy and then the same energy goes into the system, but at a reduced amplitude because I cannot I cannot heat up energy energy has to anyway going, but I will give it at a much slower rate. So, this is how because how does that happen this happens by having provisions for this isolators to flex to move unless they move they cannot take up that energy instead if it was a rigid connection everything would go in. So, this is a soft connection here this is a soft connection here. So, they will have low motions and sometimes this cable mounts are also used in shock isolation system we just saw the example of the missile launcher. So, such foundations are also put with cable mounts which also act as shock isolators. In of course, you know this is not a class in vibration because you know engineering shock and isolation or vibration and isolation is a course by itself and I am sure the teacher must be covering all this there, but this is of course and condition monitoring and the reason behind telling this is you know once you go to the machines to do CBM will invariably come across these elements and we have to do measurements of around these elements because these are the elements wherein the energies go in and go out because of an unbalance I will see the forces coming at the at the bearings because of a forging hammer I will see energy coming into the system at the isolators ok. So, this is another example which I will this on a backhoe loader ok in a put typically a backhoe loader or a truck essentially there are two strong components one is this engine and the chassis and if you observe and this is the unit where the operator or the driver sits and this is a cabin ok. And invariably you know this construction equipment be it a bulldozer be it a loader they are always subjected to harsh vibrations because of the terrain because of the work nature because they have to shovel etc. So, these four operators are really subjected to very harsh levels of both vibration and noise. So, these cabins you know they may look very robust, but they have to they have actually supported on four mounts. And again our vibration isolator come into play there and one has to decide on good amount of vibration isolator. This is one example we are talking about say a truck you all must have seen a truck going on the highway, but the cabin where the driver sits actually sits on the chassis and this cabin is actually mounted on the cross frames or the cross frames and the longitudinal rails at four mount locations. So, no matter of what comes through the road because of the potholes because of high speeds because of fundulations on the road all these motions would normally come into the driver or to the driver seat. Imagine I will just give a story here see these the driver gets excited by a forcing frequency and if you think of a human body as a mechanical system the internal organs are supported in a fluid and then they oscillate. So, this internal organs also have a natural frequency and this natural frequency is about 2 to 5 words very low frequency, but imagine from the road if I have a forcing frequency of 2 to 5 words coming into the seat on which the driver is sitting then what is going to happen the driver is also going to have a resonant at 2 to 5 words the driver will have a nauseating feeling and may be he will fall sick will throw up and I am sure all of you must have experienced this while going in those you know state transport buses wherein the there is not good amount of isolations to the seat and the bus floor there are almost rigidly bolted you would have noticed and then you would be saying people feel uneasy when long distances and such buses on top of it if you think of the luxury buses nowadays when there are good amount of cushions in the seat good amount of isolations they reduce this energy coming in from the road and affecting the passenger or the driver. So, I will just show you one example here in this backhoe loader here this is a particular case wherein if you can see this this actually this yellow one is the chassis of the cab okay and or the backhoe loader and this is the cabin and this is the isolator it is nothing but a thick rubber pad and here we are actually trying to measure the motion these are the accelerometers which are used to measure the motion of the chassis this is in a particular direction this is the transfer this is the longitudinal and this is the vertical direction and there is another accelerometer here to measure the response at the mount location on the cab side. So, the effectiveness of this isolator or the vibration transmissibility can be checked by seeing the ratio of these or the difference between these two levels and this difference is large than this isolator is doing a good job. So, this is how the isolators are actually evaluated and then we can also design as to what kind of isolator this is to be taken in and if you look at the force transmissibility curve suppose I have a body which generates and force F and there are certain stiffener damping etcetera and this is the transmitted force F t if you calculate this force transmitted to the applied force this applied force or the force which is originating because of the dynamics of the machine is given by and if I was to plot this curve where r is equal to omega by omega n omega n is equal to k by m and omega is the forcing frequency. So, this is 1.0 say this is F t by F and this as a plot and this value is root 2 no matter whatever is the damping. So, at a frequency of omega by omega or omega is equal to omega n by root 2 or more. So, that means, if the frequency of driving frequency is more than the root to the natural frequency the force transmitted will be less than the applied force F. So, the F t by F will be less than 1 for r greater than root 2 and this is a very very fundamental design equation which all vibration designers work with and. So, we can decide on of course, you know this because somebody ask you estimate me the values of k and c to be used in this machine where this machine operates at say 1200 rpm. So, 1200 rpm means 1200 by 60 is the forcing frequency I know the mass of the body I know how to find out stiffness and c depending on this equation. And sometimes I can go to the manufacturer's catalogue find out for different payloads what is the available stiffness or available damping and then select the isolators. So, to summarize in vibration applications to engineering the cases of unbalance the cases of base excitation the cases of force transmissibility are very very important tuned dynamic absorber and damping tuned dampers and vibrations occur around us everywhere and these techniques which I told you are actually used to reduce the vibration levels, but sometimes we use them or we use them as an indirect means to estimate the condition of the machine because if there is an unbalance this will give rise to forces in the bearings. If the isolators are not working properly the vibration levels of the engine will go up the dampers are not working the torsional oscillations would be high and the crankshafts would fail in fact many of the industries you will see the crankshafts failing because the torsional oscillations were high they were either not arrested by the dampers you know particularly in ships these dampers are filled with oil somebody neglected filling up the oil dampers when dry and the effects happen. So, we have to be careful as to how we can reduce this vibration levels. In the next class I will be talking actually you know I will be giving you more equations and we will try to solve some problems in rotodynamics how actually rotodynamics is an offset from vibrations and how actually rotodynamics help us understand condition based maintenance. In closing this is one last slide wherein you will see the tuned dynamic sorry the torsional damper here on this engine and if you recall here in this engine we had done lot of unconstrained layer damping to the oil sump to reduce the radiative vibration levels vibration and noise levels. This is actually in an engine manufacturer's test cell where we are doing some vibration studies on the engine and particularly this is the torsional damper because there is a crankshaft here and this is a 6 cylinder truck engine. So, this oscillations are reduced by having this torsional damper over here ok. Thank you.