 In this lecture, we are going to talk about field balancing. Well, as you saw in the last class that balancing is necessary to remove this amount of unbalance, which we have in the shaft, because the unbalance can lead to the fatigue failure of the rotating system and so on, but these rotors or shafts can be of many different sizes and lengths or weights and lengths. I can have a very very large rotor, which could be as long as 4 meters or as small as may be 10 centimeter. And as you can imagine, if we have a large rotors of 4 meter length, they cannot be treated as rigid. They will be flexible. There will be many critical speeds, but still again in this class also we are going to discuss about the first critical speed of frequencies, operational frequencies below the first critical speeds, but to balance the masses, we can always bring in a shaft or a short shaft or a small shaft, a small rotor into a machine, wherein we have two spindles and one spindle is rotating, one is supporting, wherein I can put a rotor and then have and then balance it. So, these are the rotor balancing machines. Such rotor balancing machines are available in the market, tabletop rotor balancing machines or a balancing machine taking half the size of the studio and wherein you bring in a rotor supported it between two spindles, one spindle you allow to rotate it and then there are transducers, which will measure the viruses and with a vector calculation find out the vector of unbalance vector and then find out the correction mass. But in this class, we are not going to talk about such rotor balancing machines. These machines are available in the market, wherein we can balance to as high as 2400 rpm and so on, but I am talking of the cases wherein in the industry, we have rotors installed in machines like in fans, blowers, turbines. Obviously, for large fans, blowers, turbines, I cannot bring it to the laver and to mount it on such balancing machines. So, in this cases, we have to balance at this site or in situ balancing has to be done or what is known as field balancing. So, in this class, we are going to talk about how such field balancing of rotors, which are already present in fans, blowers, turbines, which are installed in a rigid foundation in a plant, how do we balance them? Just to give an example, this is a case of a paper mill. You can see this is the this roll here. This roll rotates and there is a felt, which is going over this roll and then there is a roll on the top, roll on the side and then many more rolls. As I was telling you, in a paper mill or a paper plant, there are about 100 to 200 similar rolls of length of 4 meters and particularly in a paper mill, the linear speed of the papers coming out and this is the felt on which this pulp will be spread and then in a pulp as I was telling you, is full of water and then will lot of presses down stream, wherein and finally, eventually we will have papers and then which are dried, stream dried on the rollers because inside the rollers will have heated steam going in and they will dry. Now, in paper mills, this typical speed, linear speed is about 1200 meters per minute. That means in one minute, you are having 1200 meters of paper coming out and if there is an amount of unbalance on this shaft, many things can happen and it has happened in few paper mills I have been to. Because of an unbalance, this bearings are going to have a fatigue failure. If once this bearings fail, this roll is going to fall, fail and fall. This falling roll may damage few other rolls and the because this is a very continuous serial process, if one roll breaks, the entire production has come to a standstill unless you repair it. So, in fact, that is the reason why all these bearings in a paper mill are very critical and they are monitored real time round the clock by having pre-installed sensors on this bearings and where in round the clock, they may monitor the vibration levels coming on to the bearing and by which they can also detect what are the possible causes of the bearings faults. Is it because of unbalance? Is it because of something got deposited because of some sludge getting the seals here? We are not proper and then the sludge got into the bearings and the or the heating was so high that the lubricated bearings, the grease or the lubricant burnt and the black carbon residue became a hard particle and that particle went in the bearing and damaged the bearing. So, as I was telling this is dominoes effect, one affects the other. So, but imagine such a roll cannot be brought to the shop to be to the lab to be balanced and many a cases such rolls when they are initially manufactured, they are actually balanced at the long manufacturing machines itself wherein we can have we have the process of rotating it and supporting it on bearings. But in a plant where already such rolls are rotating and existing, how do you balance them is the problem we have in hand. So, again we will see what are the methods of field balancing. One is as I was telling you for the case of the static balancing, we will do the single plane balancing wherein we measure the amount of unbalance and put a balancing mass or a compensating mass 180 degree from the unbalance mass and then they balance it. So, that is either you through a single channel phase and variation measurement or through a 3 point variation measurement is what we are going to discuss in this class. And I am not going to talk about multiple in balancing in this class, but there are many commercial softwares which are available wherein you all need to do is measure the bearing vibrations at the both the outward in one inward and outward bearings or both the support bearings and then the software once you give the amount of unbalance at different locations, the software is going to tell you in which correction plane what kind of unbalance is to be put at what degree is because in methods of if I look at a method of balancing the very very important thing in balancing is from a reference axis. This is very very important what is this theta and what is this amount of unbalance? Once I know the amount of unbalance and the location my job is done. Then next what I have to do is at another location this is pi I will put the correction mass and then the forces will balance and I would have done static balance the shaft, but the problem is so I have two unknowns one is theta other is m and then I have to define my reference axis because when a shaft is rotating usually people take you know in a shaft we have the is the key way and as I was telling you when you talked about the case of the velocity transducer, whenever I put a transducer above the key way and this shaft rotates for every rotation I am going at a pulse and this is the time period and if I know the speed I will know this corresponds to 360 degrees for the time period one time period. So, I can define at what time the what is the degree from this reference axis. So, this is how phase measurements are done with respect to the with the reference to the variation pick up which could be a tachometer tachoprobe which could be an axiometer as well because whenever the unbalance mass comes below this I am going to have a high variation. So that again if I have this unbalance mass coming here I am going to have a high level of vibration this means that my unbalance is at this location how much away from this the unbalances we can detect it and I will show you how this is done. So, first we will discuss about the single channel phase and vibration measurement I will just show you what I have here is a this is a motor if you can see here this is a motor and this is one this is a coupling here the black one is a coupling and then I have a bearing one of the bearings you cannot see the other bearing here and there is a shaft on which we have a rotor this everything was to begin with perfectly balanced we created an unbalance by just putting in a bolt onto this rotor. So, we created an artificial unbalance and you will see here I have measured I have put one axiometer in the vertical direction to measure the acceleration or the vibration and this is the tachoprobe which will shoot a light onto the shaft here which has a reflecting tape and then we will measure the rpm or know when the because this tachoprobe basically on the shaft I have I have a reflective tape thin reflective tape. So, this tachoprobe shoots a light beam and then it gets reflected and the shaft is rotating. So, I it will give the this is my 0 degrees I will start my 0 degrees from this location sorry and then when it comes to the next cycle I know 360 degree has occurred. So, it has rotated and at the same instance I have in fact this shaft yeah you can see here if you see this marker here this is the reflective tape this means this is 0 degree and right at 0 degrees I have put my unbalance here this happens to be the case when I could have put it in arbitrary anywhere, but there is always a relative phase between this rpm detector and the axiometer and that is fixed. So, whenever I measure this the phase of this is always with respect to this and that is fixed. So, initially I gave an unbalance at 0 degrees I put some mass of unbalance and made the system unbalanced and then we measure the vibration level and what we did here is the initial unbalance response this is the vibration as recorded by the axiometer mounted in the vertical direction and this was run at 1440 rpm, but we got 24.06 watts and the initial vibration level is 11.5 millimetres per second square. Now, with the FFT analyzer I am giving one as the vibration and one as the TACO probe say channel x channel y what I have done here is basically plotted s x y y sorry s I am trying to see the response of vibration with respect to TACO probe. So, this will have this is a complex quantity this will have a magnitude and also the frequency this is magnitude and also I will have the phase of and this phase you will see all this lines these are up from measure from 0 to 500 hertz, but I am operating at 24.06 hertz and if you look here it is a very very strong component coming at 1 x and if you can see the red cursor here this is the vertical cursor the peak is somewhere here at 24.06 I have 11.5 millimetres per second square is the level of vibration measured by the axiometer and at the same frequency I am measuring the phase angle phase between the vibration and the rpm indicator is 64.8 degrees. So, this is my initial phase. So, this gives me some clue as to what or how or where the unbalance is located with reference to the with reference to the measured acceleration. Now, this is initially now I have to find out what is this amount of unbalance and then how much I have mass I need to give. So, this gives a vibration level but it does not tell me what is the mass and that is what I need to do. So, the very first step once I have measured the unbalance response and know the phase angle with respect to the rotational speed and the axiometer I have to give a trial mass. I will give a known mass of about 6.14 gram I have just measured it here and then I will attach it at some location. So, this was my initial unbalance at another location I have put 6.14 as the trial mass and then this is another way you can see the axiometer where in I am measuring and of course, this side there is a taco probe. So, I have just put an unbalance mass sorry a trial mass of known weight 6.14 gram and then I need to again rotate it again at the same location I will measure the vibration and the phase angle. Now, this vibration has come become 12.8 because of the trial mass and the phase angle at that same frequency has become 121 degrees and this is all I need to do. Then what I will do is I will calculate the compensation mass and angle by this formula. So, m 0 will be nothing, but what was our initial V 0 initial V 0 was 11.5 and trial I am getting a 12.8 times 6.14 this approximately comes to about some I think this is not 6.14 some little higher, but anyway this 6.18 grams. So, this is how I calculate just by knowing the relative vibration levels once the original unbalance then once the vibration level of the original unbalance vibration level with the known mass and then multiplying this I will get the compensation mass of 6.18 grams. So, this has to be put again at another direction is this alpha compensation is given by alpha d whatever I would have got this angle 121 degree and then alpha naught was by initial and then 180 degree and this happens to be 67.7 degree measured from the trial mass axis and once we know this we put it back at that location and then we got the residual unbalance to about 6.02 the same location the balance amount has got reduced. So, we started with somewhere around 11.5 millimeter per second square and a very crude way we just did couple of runs and then we measured it. Now, the problem is why we have not got less than that is because of this reasons. So, this disc there are actually holes around it and this holes are placed at about the 18 holes are about 20 degrees. So, if I calculate this is my 0 degrees if I calculate any angle it has to be multiples of 20 degrees, but I got some reading as 67.7 degrees. So, either I put it at a 60 degree mark or an 80 degree mark because of this problem the residual unbalance is not quite less. But, so this is very important that this errors happen in practice also that is one location another is regarding the radius the same amount of unbalance m r is equal to m star r star I can have a higher mass put at a lesser distance and create the same kind of an effect this also there. So, radially I can change and then select about the play around the mass also. Suppose, it comes with the mass of 6 grams, but I only have 5 gram of unbalance mass weights to put. So, I can put it at different radius by maintaining this relationship. So, these are practical limitations as to where to put the unbalance mass at which radius and how much of unbalance is to put and for this this problem we in the lab we did not get more than or less than 6.02 because of we have problem placing the mass at the calculated angle because the rotors did not allow us because these are these are because these are all at 20 degrees you know I do not know 18 such. So, if the angle comes somewhere here I have a problem I cannot put it and that is why this problem is there. So, to summarize this single plane balancing with a single phase measurement phase and frequency phase and acceleration measurement we have to see that we have to have the rotational speed measurements and we require a phase measurement and then we have to do a vibration measurement. So, in this example we use an accelerometer for this phase we use an FFT analyzer and then we use a tachopro. This is very expensive in the terms of the equipment we have used. We require 3 equipment to do this, but another very easy way to do the vibration balancing of shaft is what is known as the 3 point balancing. As it says this requires no phase measurements. So, we do not require a tachopro or an FFT analyzer, but of course it requires 4 sets of vibration measurements requires 4 sets of vibration measurements, but to measure vibration only on vibration metric can be used. Rotational speed measurements is not required, but we need to frequently start and stop the machine because 4 measurements have to be done. In this 3 point vibration measurement basically what you do is we do not know where this unbalanced mass is. I will all I have to do is initially I have to measure the vibration and prove that in the earlier example I showed you the screenshot of an FFT analyzer, I showed you the tachoprope and then accelerometer. In this example, in fact if you can see here this is the same rotor where there are 2 bearings and then I have attached the accelerometer here and accelerometer here. In the previous class of unbalanced detection I was talking about the phase measurements. It was phase between this transducer and this transducer. So, phase would be close to 0 degree and we got something around 13 degrees, but here in this previous example I had used this accelerometer and used a photo probe which is somewhere here and this is the rotor. In this 3 point measurement what we have done is we have just put an accelerometer and just got a vibration meter to see the initial level of vibration level measurements and which comes to about 1.3 minutes. It is 1.3 meters per second square. So, to begin with I have an initial unbalance of 1.3 meters per second square and this gives the overall vibration level and this vibration meter is set from 3 hertz to 1000 hertz. This is giving the overall. I am not specifying the rotational speed. I do not care about what speed it is rotating as long as it is rotating at constant speed. Some speed it is rotating I will just put an accelerometer, measure it, initial is 1.3 meters per second square that is my V naught. In the next instance what I do is a switch of this machine and at location 1 some location which is 0 degrees by 0 degrees I mean V naught was in this direction. I put this is my reference axis because reference axis is very very important because once I come up with some angle it has to be always measured with relative to some axis. So, initially I decided that wherever I have put my this axis and with this I am measuring V naught and I will put V 1 here. This becomes my V 1 because this is V naught I am measuring V 1 aligns with this and this is my 0 degree to begin with. So, henceforth any angle calculation I do I will state this as 0 to this point as 0 degree and then move along the rotation of the direction. If I move opposite to the direction of rotation the angle will be negative. So, this is my 0 degree going clockwise in this direction will be the positive axis and then what we did is at 0 degree I got my V 1 as 1.56 meters per second square in the first run and of course, V naught was 1.3 meters per second square. And mind you these are all vectors though I am writing it as magnitude, but they are at a particular angle these are all vibration vectors. So, 1.56 meters per second square next is I removed the mass from V 1 switch of the machine remove the mass from location V 1 move to this location V 2 mounted and then rotated the system. So, vibration level at 120 degree that means when I have put the mass at 120 degrees this is the vibration level and that comes to 2.03 meters per second square. Now, imagine if this was a perfectly balanced machine out of got all this as same and then in a next case I moved it to 240 locations and I am getting V 3 as 0.735 meters per second square. What did I say? This is 0.735 yeah 0.735 meters per second square you all will appreciate that if this was a perfectly balanced rotor V 1 should have been equal to V 2 should have been equal to V 3 and which is not the case in our case because we have put some unbalanced mass at some location and now what you are do is a very simple thing you have to find out a vector V t which is nothing but the of course, I will denote it as vectors now V t is nothing but V 1 plus V 2 plus V 3. So, this will give me the effective residual unbalance and which happens to be in our case V t is equal to V 1 plus V 2 plus V 3 and this you can measure it now this is this if you have one of those calculators you can find out the V t magnitude and V t phase and once we have done that you take the this equation M naught is equal to V naught by V t times M t and V naught was this and we had given a mass to begin with I think in this case we had given a mass of M trial was about 6.18 gram. So, using this equation M naught is equal to V naught by V t times M t I will get the mass M naught and then once I know this angle I have to just put it V t plus 180 degrees from this location because this is my starting point. So, I will get a V t angle I will place it on this and then add. So, I will know the location of the V t angle that is my unbalance mass direction and then 280 to that I put this unbalance compensation mass whatever M naught I calculate and I finally, line up with 0.629 millimeter meters per second square to start with I started with 1.3 meters per second square and then I line up with 0.629 meters per second square again in this example you would see that we have not quite reduced it because of again the same reasons that the mass which we measure may be it is always a problem sorry the mass which you measure 6.14 grams is quite not what it was expected may be if it says 6.23 grams I may not be having very close manufacturing trial weights. So, I took the closest available to me was 6.14 grams. So, this is a mass in a accuracy other is angle location. So, in practice how do we overcome this again in practice there are lot of trial weights of different sizeships, but usually in many of these rotors you will see many times the weld either weld masses the final mass or grind off this you will notice in the ceiling fan hubs in the rims automobiles you will see people either weld masses or fan or remove them and I am sure all of you must have tested if in a in a ceiling fans very good example many of the ceiling fans the high and ceiling fans they come with a set of blades which are many a times balanced to that particular fan. And if you if you change the blade orientations of one which is the other and or may be now you have seen the effects of how unbalanced this whole thing could be and they could be wobbling. So, balanced set of blades even by changing the orientation of one blade angle this is going to give rise to an unbalance this has to be taken care of. So, in practically you can choose many method there are few other methods also ok, but the one advantage over the other is in a in one you are accurate in the sense you are accurate in both the cases your accuracy depends on your mass location a mass trial mass and the angle location. But in one case we need to do more measurements and we need to frequently start and stop like in the three point balancing, but the measurement is very simple all you require is just a portable handheld vibration meter and you do not require any phase measurements ok. And this is a very simple experiments which people do in the students do in the lab as well just we have a rotor mark 120 degrees sectors of 3 3 meters 120 degree to each other put a trial mass measure the unbalance again rotor put it at 3 different locations of 0 degree 120 degree 240 degree measure the vibration levels I will calculate that find out v t and calculate the compensation mass and then put it at whatever angle you get in v t plus 180 degrees and that is the most simplest way of doing single plane balancing, but another one suppose you are not allowed to switch off the machine may be one just to put the trial mass you can do the phase single channel phase and single channel vibration measurement. But there are many commercial software available for balancing I will just show you the screen sort of one such balancing software which we have in all laboratory and this is how it looks like ok. And there are in this balancing software there are many options you can do single plane you can do multi plane multi plane you can go as high as 2 to 4 planes ok, but in this class we just discuss about the single plane balancing and then you know it will these are GUIs which will tell you do the initial do the trial runs do the calculations and do the final mass and you can select the trial mass at different angles what is the radius it says that what is the trial mass values and then vectorially in a in a graph it is going to show you the rotor and show you where the mass is to put and basically what we did in the previous calculations are the same things which are there in the software and it is a very simple balancing is the most easiest thing to do in machinery troubleshooting field balancing only thing that you should have the perfect instrument to measure the vibration and the phase or the phase and then of course you have to measure the rpm also many times what happens this is you know while you are doing the balancing if it is a maybe this balancing operation takes about couple of hours to do the you know large plant it takes couple of hours to switch on a system switch off the system and while you are doing the measurements what if the speed has changed and that is very very important. If the speed changes earlier vector diagrams have no meaning because they would have changed as well the magnitude would have changed. So you have to have ensure that always the speed is the same in the laboratories we can make sure that it runs on constant speed. In fact while we do measurements in the laboratory we actually have our systems run on EPS and constant voltage and current supply but now it is in many of the industries we have this V F D drives with closed loop composition so that the speed invariably does not change. Once the speed is does not change and speed you have measured correctly and what are the ways by which you can measure speeds from an industrial rolling system is usually tack of probes or laser based probes because we cannot measure this with having a contacting type of probe. And we may not be allowed to go very close to the rolls. Rolls rotating at high speeds high temperature think of a steel plant a cold rolling will CRM and HRM the rolls are rotating at very very high speeds. We cannot even go close to them because of safety issues because of temperature issues. In those cases we can shoot a laser beam get the reflected beam back and measure the angular speed or some of them are pre-installed with digital RPM indicators wherein they have a reluctance type pickup which are used to measure the rotational speeds. Once we have a good feel of the rotational speeds only requirement in balancing is obviously if you have to balance you have to add weight or remove weight. So, we need to stop and start the machine to do the field balancing no where you can do balancing without switching off the machine because we have to put weights and remove weights and so on. Of course, nowadays many smart systems are available where balancing using counter weights wherein you are monitoring the vibration level and then at a particular phase if you see that unbalance is occurring there will be systems which will move the counter weights or other inward or outward. There will be guides by which this can be moved so that you take care of such unbalances. There are smart systems I mean there are many ways but we are not talking about these innovations yet. But in this class in the previous class we just introduce you to the case of unbalance how we detect unbalance and in this class I just told you two simple measurement techniques to do field balancing. In one case it was the single plane measurement by phase measurement and the acceleration measurement or the vibration measurement wherein we need not switch off so often and the second example I told you about the three point balancing wherein we have to just have a vibration meter which is very cheap and handy and we do not require to measure the rotational speed or the phase. So, it is very cheap that way but only disadvantage is that you have to stop it about four times three to four times to add on the masses and then commercial softwares are there where we can do balancing in many planes. Of course, there of course it you require software along cannot do the balancing you have to do the measurements in situ at the bearing locations. Sometimes the problem happens that how do I do the locations measurements along the rotor suppose I am talking about large systems. So, far we have discussed about rigid rotors and suppose this is a flexible rotors large steam turbines or gas turbines. In this case what happens there may be because of mode shapes. So, what we can do is I need to measure along this length of the shaft. So, I can shoot laser beams on to the shaft and then find out the points where large motions are there and then again use through software I can find out how to how do we take care of some balance and how do we reduce it. But this is something which we are not going to discuss in this class and we have not discussed is the flexible rotor balancing. So, as long as we know how to balance rigid rotors field balancing we are doing good. I think with this I will stop this class. Thank you.