 Well, this is a lecture on unbalanced detection. In fact, this is the first of the series of this module wherein after having understood the rudiments of signal processing and of course, the elements of machinery maintenance and condition monitoring. We are now specifically coming to how do we detect different kinds of faults in rotating machines and to begin with we are going to start with unbalanced the most common form of mechanical defect in any rotating machinery. Well, now before we begin into this lecture, let me tell you what we mean by unbalanced. As you all know in this machines of ours, we are always going to have shafts which will be rotating and these shafts are supported on bearings and these shafts will be rotating at very high speeds, low speeds whatever. Now, if for some reason there is an unequal distribution of the mass which is rotating around this central line, geometrical central line of the body and there is a small mass m. This mass because it is not uniformly distributed is going to give a force m omega square r and this force is going to be radial in nature, going to be a function of the speed, function of the distance of the unbalanced location from the center of axis and because of this extra force which is coming on to the system the rotor of the shaft in this case, there will be extra reaction forces or in effect the bearings are subjected to forces much more or beyond what they were initially designed and selected for. When a designer selects a bearing they know the radial loads coming to that bearing and then they design and select and design the bearings, but on top of it if I have this extra force they are going to add to it and another problem you will see is this force is not a constant force as a function of time, since it is rotating this force is also fluctuating. So, this compounds the problem fluctuating force. So, if you will recall your random fatigue design of shafts because of such fluctuating forces the material of the shaft is going to fail quickly in comparison to the case of a static force. So, presence of an unbalanced force leads to such excessive fatigue force and then that leads to a failure of the system. So, now let us look at it from a different perspective let us look at a desk which is rotating this has an initial mass has a mass m rotating. So, this has a radius r at some location E I have a small mass sorry small mass m at a location of E. So, the amount of unbalance can be unbalanced force can be written as given by this expression. So, we can define the for a particular take this back here I will define the unbalanced mass I will come to this expression later on wherein we can define the amount of unbalance I will first define it and then come back this slide. Now, this desk could be thin which is rotating above the shaft thin disk with an unbalanced mass here. So, in this case if I support this desk on knife edges like this and this is going to always come down because of gravity this location and this is the case of a static unbalance where the forces are only in one plane unbalance force is in one plane. Now, imagine instead of this desk I have a long rotor like the rolls of a paper mill if I have an unbalanced mass at this location and if I have an unbalanced mass at this location. So, this is giving me an unbalanced force in this direction and this is giving me an unbalanced force in this direction. So, my from a force point of view this is balanced, but you see this because they are in different planes they give rise to a couple and this is what is termed as dynamic unbalance some in some books or some literature they say this is a couple type of unbalance and then they have a dynamic unbalance where these forces are actually inclined to some axis, but in our class we are going to treat one as the static unbalance and other as the dynamic unbalance. So, in the case of static unbalance you know it is very easy to balance it by estimating what is the amount of unbalance I can put and another mass opposing to it and then balance it. In the case of dynamic unbalance just balancing these does not happen we have to balance put some more weights in another planes. So, that the couples are also reduced or couples are balanced we will come to dynamic unbalance later on. Now, of course, one of the fundamental assumptions we are doing in this balancing is or unbalance is these are rigid rotors, but you know from our class of the rotor dynamics that the rotors have many degrees of freedom and then they have they have need to be treated as flexible rotors, but as long as the operational speed speed of the rotor is less than the critical speed of course, to begin with the first critical speed I can consider it to be a rigid rotor and balancing at one location or putting weight at one location balances the shaft, but when I talk about you know steam turbines or gas turbines where there are where it is a long shaft having sets of compressors vanes and turbine vanes these are long shafts and as you know there will be many critical speeds critical speeds. So, balancing may not be possible in one plane because if I think of the mode shapes of the shaft and many speeds this could be a mode shape this could be the second mode shape this could be the first mode shape and so on. Sometimes because of mode locations this may have no motion, but then if I balance here try to reduce it, but then I am not doing anything here. So, in case of flexible balancing we have to balance in different planes and of course, you know we always should not run at the critical speed away from the critical speed just so that we do not have the conditions condition of resonances, but in this class our attention is focused to this rigid rotors and we are looking at operational speeds less than the first critical speed. So, balancing can be a very very complex phenomena when you are talking about long rotors large rotors when there are sets of disc could be compressors could be turbines could be you know some sort of blower fan sets when if it is a long rotor it is a flexible rotor there will be many critical speeds and it is a difficult task to balance those multiple in balancing. Though people do that there are software which you can do that, but in this course we will focus our attention to very simple may be a Jeffcott rotor with a shaft which is rotating below the critical speed it has a disc which has an unbalance mass how do we balance it and what are the effects of it and how do we how do we detect such unbalance and that is the first part which you need to look into it. Well, before I go in going to how we detect the unbalance what are the possible sources of unbalance one of course, if if the component for example, many many components in rotating systems are casted for example, in an automobile flywheel is a very very important component in a in a IC engine could be particularly in the single cylinder or two stroke engines couple of cylinders of course, if you have more number of cylinders the cycles are balanced and then the flywheel will be will be of a lesser size, but I am talking about a single and a four cylinder three cylinder engines wherein the flywheel is mounted after the clutch sorry after the crankshaft so that we reduce the cyclic engine variations and imagine such a flywheel has an amount of unbalance mass. So, this is going to give an unbalance force onto the shaft and this is not desirable and usually flywheels are casted. There are many engineering applications I will tell you for example, you would have seen the alloy wheels in the automobiles wheels on particular they are the rims say on which we have the this is the tire this is the rim and this could be an alloy wheel rim and which is actually casted you can understand if this casting has a defect or there is some sort of an unbalance mass every rotation of the wheel you are going to get a force like this and imagine the scenario it can be complicated if you have a vehicle which four wheel drive or four wheels and everyone is giving a force they may not be in phase and one is giving the force in this direction other is giving it in this direction other is giving it in this direction other is giving it in this direction. So, imagine you would have an erratic motion of a vehicle and these are undesirable bumpy rides forces coming from the wheels because of unbalance. So, I am sure all of you must have realized it or witnessed when you buy a tire and we mounted on the rims or rims they have and if you go to any automobile garage they have wheel balancers they advertise that because and then if you notice particularly not in the alloy wheels from the front you cannot see, but if you go to the casted steel wheels you will see a small amount of weight given here depending on because of the balance they would have attached a balancing weight to it. And those of you who are riding bicycles must have experienced it if you have a bad tire we always do that when we are students if the tire was weak we did not have enough money to change the tire we would go to the cycle guy then you would put a layer of cut tire in between and then you would have a patch work and then if you rode that kind of a cycle you would get a periodic hits on your seat bumps this is because of unbalance. Now, imagine if this kind of things rotated at very very high speeds omega the forces will be very very high and this forces are finally taken up at the supports. So, bearings will be subjected to fatigue damage and then they will fail much quickly. First is unpleasant ride quality in vehicles and then bearings will be getting subject to fatigue load this will be this will be not good for the machine on cycle or automobile in this case. This is true for the case of fans and blowers particularly in industries I will come to that this in just in a while little bit. So, one possible source of unbalance is whenever we have casted components there could be a casting defects blow holes which leads to uneven distribution of the mass and thus we have the case of unbalance. One is another one the next one is the case of certain installation issues imagine we have a large system and which has to be put in place perfectly between the bearings and they have to be in the geometric central line of the system. Now, imagine if you imagine if this was not in the central line and there was a slight offset. So, this is going to give rise to unbalance. So, when the geometric center does not match with the line which connects the center of mass then there will be a problem and then things will wobble. So, wobbling will lead to the case of unbalance as well. So, while installation people have to take care of these issues also. Another case which happens is the case of in the case of maintenance particularly in the plants wherein we have lot of blowers may be a F D fan post draft fan F D fan F D fan basically what happens when you have this is chimney and then we put an F D fan here gases which are after burning the coal actually. Then you lot of fly ash in this gases what happens. So, because to give an extra draft to the fan we put a fan and this fan basically pushes out the gases out of the chimney because the chimney is at a certain height because we do not want to release the gases all around us. We send it high up and then send it for that dispersion can fly off to large places. The problem is with fly ash, fly ash on top of it if it is wet and moist they will become like a sludge and then they will you know this fans have blades I am just. So, with time what happens these fly ashes get deposited the stick to the fan blades and then once the stick they may not stick uniformly in some location they may get stuck and then this gives rise to a fan which is unbalance and then I have seen cases wherein these fans are filled the blade shear off the bearings get damaged because of this excessive fatigue force which went unnoticed because things got deposited in the blades. This happens in lot of chemical plants and food processing plants also. When you are talking about dry milk powder you have seen how the dry milk powder becomes sticky once it gets in contact with moisture or water. Imagine when you have in the milk processing plant they have lot of agitators and mixtures agitators and mixtures are nothing, but again some high speed churning devices in a tank churning devices. Again the same thing if I feed in certain material which is susceptible to moisture and then it becomes sticky they will they will stick to the blades and then because it is rotating then unbalance and finally you will say some find a this thing has failed because of excessive fatigue loading again this things happen. So periodically in many of these plants be it the FD fan in a power plant be it an agitator in a food processing plant periodically in regular maintenance they scrape off and there are alarm levels also if suddenly they see that the weight increases etc. they know that something is getting deposited. You are talking about iron ore centering plant a lot of things happen lot of places where things can get stuck they will create an unbalance and then things will break off. So the sources of unbalance are manufacturing defect installation issues maintenance issues and so on and then the question is what is the tolerable limit of unbalance. See everything can be balanced but how less should this force be reduced to and how much should be acceptable this is a function given by this curve here one it says the speed of the machine and other is the acceptable residual unbalance per unit of rotor weight that is given is gram per millimeter per kg that the denominator is the so acceptable unbalance mass because if I unbalance force is m e omega square if I if I remove the speed unit out F by omega square is equal to m e. So as I can I can say as gram per millimeter and then if there is a particular speed I know what is residual and the mass this is the mass of the rotor in kg. So for large levels you know g 830 means a very very high mass rotor and if you will see this is 0.04 and with speed the amount of unbalance which you can tolerate obviously will reduce because with speed any way we have a very high force omega square. So obviously at the same grade will have higher levels of unbalance acceptable unbalance at lower speeds that is obvious intuitive and this is the case of a precision balancing imagine in in in watches etcetera if there are other this was not precision balanced then we will have lot of problems but when I am talking about you know may be a steam engine or or a big drum big cement mill drum which is rotating at a very low speeds I can this the numerator can be very very high. So depending on the grades of unbalance this chart is given as per the ISO 1940 standard they have classified the grades of unbalance as to how much of acceptable quantities unbalance how much is not balanced when we should go for unbalance unbalancing and so on. So this is a great it is a reference because we never know I have got a residual unbalance of 100 sorry of 1 gram rather than 0.1 gram is it ok is 1 gram ok is 0.1 gram ok is 0.1 ok or 1 kg ok we did not know then we have to follow the standard and accordingly we have to specify that. Another very important thing we have to keep in mind is of course you know we will we will talk about this in the next class balancing or unbalance is defined or specified at a particular operating speed. If I have balanced a component or particular rpm n and n by n rpm ok I obviously the amount of unbalance will get magnified if I make an n if I operate it at n star which is much much higher than n because of the omega square term. The residual unbalance which was there will get magnified if I increase the speed. So it is always safe to balance system at a at its operational speed ok. Otherwise if I operate suppose I balance it at 2400 rpm and then try to operate it at 4800 rpm I am magnifying the amount of residual unbalance which was there. So usually best rule of thumb is you know suppose it is operating at 600 rpm you also balance it at 600 rpm ok. But usually there is a problem that we do not have high speed balancing machines. So usually people try to do it at a lesser rotational rpm and then try to operate it at a higher rpm. But we have to be careful that we do not run it at too much of a higher speed than it was intended to balance for. Now this is a typical balance quality grades this is from the same standard of ISO 1940. Now you say this balance quality grade it says g 0.4 this is basically for spindles disc armatures or precision grinders and gyroscopes. I will just come to g 100 this is the crankshaft drives of fast diesel engines with 6 or more cylinders complete engines for cars and trucks g 100 grade ok. When you have say g 1600 crankshaft drives of rigidly mounted large 2 cycle engines and marine engines etcetera. So for small gas turbines, steam turbines, rigid turbine generator sets it is g 2.5. So balance quality grades which we have to balance is actually specified by such standards ok. Now question is with this brief understanding of unbalance what are the effects it can have on systems because many machinery components actually start failing because of balance unbalance. You see what happens unbalance gives rise to excessive forces at the supports. So supports the bearings will then get damaged. So we may be alarmed because of a bearing failure. The initial problem could be something else could not be bearing failure to say that again unbalance if it goes undetected unbalance is going to give rise to forces at the bearings. The bearings are subjected to high forces the bearings are going to fail and then we will be maybe if the bearings are making noise etcetera bearings fail shafts are going to fail. So eventually we will be drawn to a fail bearing or a fail shaft but the initial culprit could have been unbalance which was undetected just for that examples I told you something is getting deposited on the vanes and blades which went unnoticed ok. There are many ways to find out unbalance and vibration again is a helpful tool to help us detect vibration then I will give you two specific examples how vibrations helps us detecting unbalance in couple of cases. In one case we have a rotor may be on this rotor we have a disc which has an unbalance and then we have this rotor supported on bearings. And what I do here is I put a accelerometer say axle 1, axle 2 and there is an unbalance so I am getting m omega square e unbalance force. Now of course you know if you look in the from the side the rotor will look something like this. So this is my vertical direction this is my horizontal direction and of course this is my axial direction ok. In this example I am measuring the vibrations at two locations this is bearing 1, bearing 2 because I can obviously only put the accelerometers at fixed rigid locations and these are essentially bearing 1 and bearing 2. So imagine what is going to happen because of this unbalance this shaft is going to bow ok. So because of this bowing because of the unbalance force I am going to have very high vibrations ok. They will be this vertical or horizontal this accelerations will be much much higher than the axial and they will be at the 1 x frequency by 1 x frequency I mean it is at the rotational speed fundamental rotational speed fundamental rotational speed ok. And this is strongly harmonic because you can you can understand if the rotating unbalance with every time it is going to change it is going to be a sinusoidal motion ok. So because this sinusoidal motion I am going to have it is a harmonic and obviously with speed because of the omega square term the vibration amplitude is going to increase like a parabola with time sorry this is with omega ok because of the square term. And another very important thing which you have to notice in detecting of such unbalances this is in phase between the support of the bearings that means by in phase I mean whenever the acceleration at location 1 is a maximum the vibration at location 2 is also a maximum. So that means the phase relationship between them is 0 degrees or close to 0 degrees that means they are in phase. If I was to plot in an oscilloscope if I if I if I draw two lines here is for a V 2 time ok this is for bearing 1 and this is for bearing 2 by in phase I mean whenever this guy is maximum this guy is a maximum whenever this guy is a minimum this is a minimum they are all in phase or the phase difference between them ok. But this is very ideally speaking it is nice to tell it in in in notes but once you go to the fields to measure because no system is perfect when I when I when I drew a sinusoidal if I show you an unbalance time history of a signal this is no way close to this because in a machine everything is mixed up you know this sensor which you put on the bearing ok. This this measures lot of things this measures the bearing vibrations this on top of the unbalances ok this this measures the suppose the shaft had some other problem like a loose things were loose shaft had a crack shaft were misaligned. So, all these vibration signals are going to come into this accelerometer here. So, these are the diagnostic techniques or routines which we have to follow to ensure that it is unbalance on and not looseness or misalignment or crack shaft. So, these are the processes by which we can know or we can be sure that yes there is an unbalance because I am having an high radial force or high radial vibration compared to the vibration in the axial direction and then of course the vibrations between the two bearings are in phase or they are 0 degree. You may not quite get 0 degree you may get 10 degree 20 20 degree, but you know while this is this is not 0 because of other reasons, but then we are going to get a sure test that this is the case of unbalance ok. And this configuration is true when the rotor is in between bearings and as I told you right in the beginning that we are talking about the balancing of rigid rotors in bearing where the rotational speed is less than the critical speed, but there could be another configuration I am sorry yeah there could be or before I go here I just want to show this and this is what we have measured here. Now, you see we measured signal 3 is 1 accelerometer signal 2 is 1 accelerometer which you have mounted on maybe if I go back and try it here again this is my channel 2 channel 3 wherein we have a disk. I will show you picture of this setup in the next class. And if I look here and this is the internal phase vibrations and the top plot is the cross spectrum ok cross spectrum establishes the delay between each other. In this case we have the phase and the magnitude most important is the phase here and this was rotating at 24.06 hertz and close to about 1440 rpm this corresponds to about 24 hertz. And you can see this is about 24.063 because you know this is what the finally the shaft was rotating at 1440 rpm and then sorry if you will see this dotted line here if you can see it here the cursor has been put at 24.063 hertz and the y in phase is about 13.149 degrees. And if you of course the cross spectrum you cannot see here actually it should have been the magnitude. And you will see a very strong component in the cross spectrum of course you would have seen the outer spectrum as well and this indicates that there is a y level of vibration. I have not shown you the axial vibrations that was too less in this case and this was actually a simulated in an experimental rig wherein we introduce an mass of unbalance and rotated it and measured the phase between 2 and 3. I did not report here the axial directions because it was too less but all you have to I wanted to show you regarding the in phase vibrations and they are in phase. Another case is when we have a case of an overhang rotors. In case of an overhang rotors the configuration is like this I have a shaft onto which I put a disc and they are supported on 2 bearings and this is the overhang part and they are rotating. Now in the previous example when the shaft was supported in between 2 bearings I had told you that there will be strong radial vibrations. In overhang unbalances there may be also strong axial vibrations this direction as well as this direction and though the axial vibration may be unsteady and axial phase between these 2 may be little unstable they may not be stable and this is again a case of an example wherein on the overhang rotor unbalance can be detected. The problem with unbalance detection is many. So, what are the problems associated with unbalance detection? One problem is whenever we have an unbalance or we have a machine rotating at a particular speed I will get a harmonic vibration because it is periodic vibrations. If I look at it in the frequency spectrum I will always get a 1 x component and this is because of the rotational speed. But think of it any machine it has to rotate at its rotational speed and so in any vibration measurements I am bound to get this rotational speed in the spectrum. So, this may be misleading I have seen many times people when they see a rotational speed they say well it is unbalance that is not true because this rotational speed is fundamentally because of the physics of the problem it is there. Of course you know this can be less this can be more but think of it this way if this was misaligned this was bearing I am still going to have a rotational speed coming up. So, just seeing in the spectrum of frequency at 1 x you should not be biased to detect unbalance. So, 1 x does not mean unbalance this is very very important because the reasons of 1 x are many it is a fundamental rotational speed it is there could be looseness there could be misalignment there could be cracks there could be bearing defects. So, how do you say for sure that this is an unbalance and that is when you look into the phase relationship between few transducers that is when you look into the relative amplitude between the radial and the axial. So, because many times another problem is only radial data is available. Number 3 which is common to any machine is rotational speed not known for a system simple rotor system wherein we can measure the rotational speed of the shaft is not a problem but think of a multi stage gear box think of a multi stage gear box wherein I have an input shaft and of course there are lot of intermediate shafts and then I have bearings at every location these are all there. So, the speeds of this intermediate shafts sometimes are not known because I do not know the gear ratios and there could be a problem of unbalance here because of 1 tooth broke it fell it created an unbalance but I am I can put an accelerometer here and measure. So, if I do not know the right rotational speed I am not able to pinpoint what is which shaft is having an unbalance. So, these are the problems associated with unbalance another thing is very very careful is when we have to compare the radial that is the vertical and horizontal with axial we have to be sure that they have been calibrated the accelerometers are calibrated and when I say I mean 10 meters per second square in a particular direction I also mean that this has been calibrated for that level. Otherwise you know when I am when I am getting a value of 10 meters per second square here and this was not calibrated I am getting a value of 8 meters per second square there is no way I should be able to compare I should be comparing these two. So, people mistake or miss these instances when they do the unbalance detection we have to be careful that these kind of problems are taken care of. So, to summarize in this class we looked into the causes of unbalance or in fact first we define what is static unbalance and what is dynamic unbalance how we define the grades of balancing and then most important is to know what is the source of unbalance in a system and then how do we detect unbalance. So, the source detection is very very important. Now, once we have detected unbalance as opposed to other mechanical systems faults like looseness, misalignment cracks through signal processing or through the signal processing of the measured vibration we can pin point and be sure that an unbalance has occurred in the system and in the next class we will see that how this balancing can be reduced and then how we can balance a system which is rotating. Thank you.