 This is a lecture on misalignment detection like we had in the last class discussed about unbalanced detection and how balancing can be done to prevent unbalances. But if you look at mechanical systems there are many types of mechanical faults which can happen one of course is unbalanced which we have discussed and the next most serious is the occurrence of misalignment between two shafts and of course there are related defect to misalignment like eccentricity of the rotor, shaft being bent or bored and may be cocked rotor and then because of misalignment why things become loose, what happens if the foundation has become loose or what we known as soft foot foundation. So how this occurs in machine is what we are going to discuss in this class and then what are the methods to detect them and then also tell about some things about how we can reduce the occurrence of misalignment etcetera in a system. So if I was to talk about misalignment essentially in any plant as you know basically we have two systems one is a prime mover and other is the mechanical unit or the driven unit this is the prime mover and this is the driven unit and this is the coupling and most important point here is the center line of the shafts. So basically this dashed red line is the shaft center lines between the prime mover and the driven unit and they have to be when one same straight line horizontal to the ground if you look in the vertical plane or if you look in the side view this should make one sink projection. Now if this does not happen how do you maintain this coupling basically brings about the two shafts together basically this two shafts are brought together by this coupling of course I have exaggerated it and then they are bolted the parts of the coupling are bolted and then the shafts are held together. So if this is not held together we will have certain problems ok. I will come to a description as to in the laboratory how we have discussed misalignment but before that there are two serious types of misalignment which can occur in the shaft systems. Suppose I say this is shaft A and shaft B by misalignment I mean that shaft A and shaft B and this is the end of the coupling ok face of the coupling. This was one scenario wherein this shaft is offset the accesses are offset and this is known as to be and but they are parallel ok. This amount of offset could be about you know two to ten microns or more depends on the speed of the machine. In fact there is a standard which specifies for rotational speed the maximum amount of misalignment and these are available in hand books. So if it is a 500 rpm this will have a certain value if it is 1500 rpm will be some other value and so on. So in one case we have what is known as the parallel or offset misalignment. In another case we have the shafts at an angle to each other some theta of A shaft B. So this is what is known as the angular misalignment. So we have the parallel or offset misalignment and the angular misalignment. So what happens in such a case is this will give rise to certain forces in the bearings because as you know the shaft systems are supported on bearings if my coupling they are supported on bearings ok. If they are misaligned either angular or offset they gives to give rise to additional forces and moments ok at the bearings. So we will have failure of the bearings because of misalignment and then we notice defect because you know there will be excessive vibrations of the bearings. But when there is excessive vibrations of the bearings you know people are misled that they will say that the bearing as at a fault. But the problem is the misalignment created a fault in the bearing or in the previous case like we had seen unbalances when which went undetected created a problem at the bearings by giving in excessive loads fatigue loads of the bearings. So bearings are going to fail. So to monitor a misalignment we need to look into certain special characteristics of misalignment which I will discuss later on in this class. But usually people in the industry are alarmed by having excessive vibrations of the bearing and everywhere that is a problem you will face while doing a CBM because we do vibration monitoring or measurements at the bearing locations invariably people will always say that the bearing is at fault because bearing is vibrating excessively that is the and then if this went unnoticed the bearings would fail and then people will say the bearings fail so my machine failed. But actually the reasons could be something else reasons could be like the misalignment which went unnoticed which was not corrected gave rise to this kind of an excessive force in the bearing and then the bearing failed or unbalance which went undetected gave rise to excessive forces on the bearing some bearings failed. So to diagnose or detect faults in misalignment we need certain special vibration monitoring or signature analysis and the typical characteristics of misalignments are something which you will see in the vibration spectrum or spectra measured at the bearing locations. In a invariably when you shaft is rotating at you will have a vibration at 1 x. But there will be some other components at other frequency like 2 x, 3 x, 4 x and so on when you see high levels of harmonics or an excessive vibration in a particular direction we may be sure that this is misalignment. So, let me tell you what we did to study the misalignment in the laboratory. This is the setup which we are using in the laboratory and in fact we will be using this setup to demonstrate other defects like the eccentricity like the bent shaft, the rubbing in the shaft, the cocked rotor etcetera. Basically here you will see this is a motor which is my prime mover in this case and this rotor on a shaft supported at 2 bearings you see one bearing here and another bearing here which is my system and this black one is the coupling. So, the by to introduce misalignment we have this dials here which could be turned around and this system could be loosened and so that we can push either both of them away and create an offset misalignment or if I just push one of them by holding one constant then I can create an angular misalignment. Basically to explain it to you again if you look at the top view of the system with the top view motor this is the coupling, this is the drive end bearing, this is the non drive end bearing and this is the yellow rotor. So, in fact you will see this 2 white dials here this dials is one dial here and another dial here. So, these 2 white dials they could be turned and then I can force this move it. So, that I will create an angular misalignment and if I move or if I move both of them I can create a parallel misalignment. Now, to measure the vibrations I can measure at each of this bearing locations in x y and z directions and similarly here in x y z direction. So, this kind of vibration measurements can be done and then basically this is my axial direction along the longitudinal axis y happens to be the horizontal. For clarity I have just moved it here this point, but this is actually at location A and location B. So, basically I will have 6 measurements in location A x y z location B x y z total 6. So, this kind of vibration measurements can be done in any machine in this case to what is the angular misalignment we are not moving point A. Now, this misalignment amount of misalignment does depend on the flexibility of the coupling and that is very very important. Couplings play a major role in the prevention of misalignment you would have heard of this flexible coupling rigid coupling or the universal coupling. Basically in flexible coupling there are elastomer elements cap which will take small amount of offset offsets can be accommodated. Rigid couplings do not allow per say any offsets, but then there are universal coupling wherein these angles could be as high as you know 7 to 10 degrees. A good example of universal coupling what we known as hooks joint is in the automobile drive shaft or sometimes it is known as the propeller shaft they can take good amount of angular misalignment. So, the couplings play a major role to accommodate such parallel or offset parallel or offset or angular misalignment between the driver and the driven unit. But despite having these couplings we will still see lot of forces and moments coming at the bearing locations I mean why at all misalignment is a serious issue in machinery because for the fact that misalignment will load the system. So, when I give a power to a machine to run it I am unnecessary wasting the energy to rotate a misaligned shaft for rotating the same misalignment shaft misaligned shaft and the perfectly normal not misaligned shaft I will require less power to rotate the normal or perfectly ok shaft then compared to a misaligned shaft. So, I do not want to waste power and the other effect is if misalignment goes unnoticed for a longer time the forces and the moments occurring at the supports are going to increase the bearings are eventually going to fail and large clearances may occur in the bearings and then things will be lose and so on. So, once we are talking about misalignment the some of the related issues with the other mechanical defects are let me list them now related mechanical defects one is rotor eccentricity other is cocked rotor band or board shaft soft looseness. We are going to discuss about soft foot and looseness in few classes down the road, but the reason I wanted to tell you is you know once we look into the vibration spectra the signature of the defects like rotor eccentricity cocked rotor band board shaft are almost very similar at times. So, we should not be misled as to a misalignment has occurred though there are means by which misalignment can be detected and then separated out, but particularly at high speeds the behavior is almost similar and then we should at least know what would we mean by a rotor eccentricity. For example, if I look at a rotor by rotor eccentricity I mean the rotor's center of mass is not at its center of rotation. Another way to look at this is may be I should draw the figure the other way I have a large disc this is my center of mass, but I am rotating it the hole has been made here and this is my center of rotation. So, you can understand the rotor is going to wobble and make an ellipse like thing at some point if I you should draw it. So, this at some point I will have large forces large displacement and less displacement. If this was a perfectly balanced eccentric rotor the displacements at locations like they are called you know the 12 o clock position, 3 o clock position, 6 o clock or 9 o clock position will be same, but if they are eccentric or the center of rotation is not at this mass center they will be wobbling and one level will be less compared to other and here may be another level this is more compared to this. So, the displacements along the circumference are not same and that is because of this eccentricity in the rotor it is very easy to measure it and there is an instrument all of you would have been familiar must have it is a very common instrument in the lab that is a dial indicator or a gauge basically it is a spring loaded stylus spring inside it and then we will have an indicator which is either it could be 0 here plus and this direction minus and this direction and this stylus will be contacted contacting on a surface this surface is going to have a motion this way it is going to swing and this direction if it is going to have motion in this direction it is going to swing the other direction and these readouts are usually in micron. So, dial indicator or gauge can be put on a rotor which is rotating at these locations this is basically the dial indicator. So, by knowing the measurements in the dial indicator at these four locations on the circumferences circumference one can decide the amount of offset which has occurred and usually these measurements are taken on the flange which is there which is mounted on the shaft if I have a shaft because the shafts only meet at the coupling. If I was to align these two shafts A and B whatever motion this is going to happen this also going to have the same motion. So, I can see the dial gauge reading here I can see the dial gauge reading on this surface and then as I rotate it they should all get the same reading if not we will have to play around with the system and that is how I will tell you. For example, in this system we see that the level in this has increase in particular in this direction. So, in fact in all of these foundation there are very thick steel plates which are known as sims. Sims are very hard wear resistant steel plates or inserts which are introduced right at the time of installation and then we put the foundation bolts. Similarly, so by removing adding or removing sims adding or removing sims this can be taken care of. And in this system we had the provision of putting sims at these locations if you look here you can remove this is the foundation of this bearing and then sims could be introduced and then we can align them as to they are in perfect horizontal displacements. So, this kind of shimming is done right at the foundation by measuring the radial runouts and these distances which we measure are known as the radial runouts. The radial runouts in the 12 o'clock position 3 o'clock, 6 o'clock and 9 o'clock positions should be same. So, they are concentric and another relatively between shaft A and shaft B they should be also same and if they are not we have to play around with the sims to adjust the level ok. Maybe this is only in the horizontal in the vertical plane you have to move something in the horizontal plane as well ok. For example, in the top view I have sims here I have sims here I have sims here I have sims here. If I add or remove in one plane I can reduce the angular you can you can understand if there are this is at elevated locations this location is elevated compared to this this will be having a rotation like this base plane it may be like this ok and this gives rise to what is known as the angularness alignment. So, by adding on removing sims I can take care of the missile alignment by either reducing the radial runouts or in both in the angular sense or in the normal vertical or horizontal sense. So, what are the factors which affect the missile alignment of course, one is the machine speed because the machine speed is high the forces will be high and the missile alignment could be there. Coupling stiffness plays a very very important role in the missile alignment as you have seen we allow a flexible coupling or a hooks coupling to accommodate certain missile elements which is required by our functionality. For example, in an automobile popular shaft the reason we give a missile hooks joint is because of this fact that if this is my wheel and engine is here. So, my output shaft is at a higher location than the driving shaft axis. So, to account for this kind of angular deviations of course, we have to give rise to a coupling which can take care of and that is what is done by actually the hooks joint or the universal joint. So, missile elements are sometimes required and sometimes it has they have to be of course, reduced in a rigid machine and that is where the coupling stiffness plays into account. So, that is why we have a flexible coupling in a flexible coupling if you look at the bolt holes I was doing four bolt holes in every bolt there will be provision to have an elastomeric insert which can take little bit of radial play and reduce the amount of missile element. These are there kept in the machines to take care of. Now, what are the effects of missile element? So, additional forces and moments are the bearing locations and these forces can be calculated forces and moments and this class on the preliminary condition based monitoring I am not going to the details of how these forces and moments are derived, but out of our research work these are there in the published paper and you can visit this website of ours iitnoise.com wherein you can refer to the journal papers in the research section and then see the papers on missile element basically this missile element in systems which are carrying a normal shaft as to crack shaft etcetera. How these forces and moments are computed and why because of the if you look into the x axis and the y axis there will be deflections of delta x delta delta y and if you are looking at three dimension delta z. So, these deflections because of missile element and the system already have stiffness. So, as you know f is equal to k times delta x f x f y is a different different k x k y. So, these delta x delta y delta z are because of missile element the system has stiffness k x k y k z. So, we are going to get these additional forces f x f y f z and of course, depending on the length we will have a momentum and this couple. So, additional forces and moments do happen at the bearing locations because of missile element obviously, if additional forces are coming they will oppose the system. So, once they oppose your load we are going to have additional power consumption in the system and then because of these forces are changing in direction at every rotation they will induce fatigue load. So, the problem gets compounded you see a small delta x which has gone unnoticed will create a fatigue load and because of fatigue our systems are going to fail much earlier than they were designed designed for. So, to avoid such fatigue failure because of missile alignment we have to ensure that is delta x delta y delta z are kept to a minimum. So, how can this minor alignments be mitigated of course, you know we just discussed about flexible couplings and then we have the universal coupling and in the industry particularly when we have lot of high torque and power being transmitted or converted we have what is known as a gear coupling. Gear coupling allows for certain linear movement of the shaft for example, if you think of it one gear sitting like this and another gear sitting on top of it. So, there will be a slight amount of movement is allowed this is essential because of temperature particularly in industries you know we have the systems rotating almost round the clock 24 by 7. And of course, there is a amount of force convection or of there are blowers in the in the motors which cool the bearings but sometimes we have large gear boxes gear boxes the temperatures becomes very very hot. So, there will be small amount of thermal expansion. Now, if the things were held rigidly in the both the driven unit and the driver unit they were held rigidly and the shafts underwent a thermal expansion and if there was no space or no allowance for this expansion to take care of by allowing a linear movement they are going to bend because of this shaft are going to bend or bow. So, to allow for such thermal expansions usually gear couplings are used which will by the once the thermal expansion happens they will they will expand and then they will slide and this could be few mills you know very few microns but nevertheless they are going to take care of this. Now, even before this is done this happens later on when you are running the system but once what happens when you are installing in the system using installation alignment has to be checked and that is very very important and the traditional methods are by using dial indicators what is known as the two phase indicator method another is the reverse dial indicator method. Of course, these were the preferred method in the industry where in you measure the radial runouts in the four different locations that is the 12 o clock, 3 o clock, 6 o clock, 9 o clock locations and then try to estimate the average radial runout and then try to use the sims either in the vertical plane or in the horizontal plane or across the two foundation axis as I discussed. And another method is the reverse dial indicator method which is very very popular but of late people are using what is known as the laser based alignment system. This is for the fact that because in the previous first two examples first two methods two phase of the reverse dial indicator our meeting and the or the two shafts have to be very very close to each other. So, that we can take the dial gauge readings through a common shaft but imagine the case of maybe a windmill where the there is a long shaft and then we have this gear box here and then this is the alignment here and then we have the fan here and this is the coupling here and this this this could be about 2 to 3 meters. So, how do you align such a system and that is where lasers are helpful because lasers can travel straight line in straight line and if I put a reflector they are going to reflect back. So, imagine if I have two systems one this is one flange and another flange. So, one scenario second scenario is and this is in first case if I shoot a laser beam it is normally incident. So, it is going to reflect back in this case shoot laser beam it is not normal. So, if this is normal we are going to come out somewhere like this. So, if I have the laser transmitter is here transmitter receiver I should see a single dot come on this is going in and coming in another way if I put a mirror here at some point I have exaggerated it I will be getting two points. So, I can play around with the shims at this locations such that I align it and then bring it back so that they all point down to one point. So, in one of the mirror planes one is this dot and another is this dot. So, I have to play around so that this both the dots come together both the dots together. So, the laser elements are very helpful in this regards and particularly you would have seen that when you go to an automobile garage the four wheels of the shaft of the sorry of the vehicle have to be aligned basically they use this laser based alignment system also they have a reflector they have a mirror and then they will make sure and then here they can change the camber angle and the castor angle and the there are adjustment bolts wherein I can change the camber and castor angle to ensure that the wheels are aligned. So, the same laser technique laser band alignment system is very popular to do machinery alignments. Now, I will come to what is the best way to find out whether a misalignment has occurred in a system through vibration monitoring. In this what we do as I was telling we will measure at any location the axial vertical and horizontal vibration equations. And if you will see if you will go back to the equations of flexible coupling or the hooks coupling, hooks joint. If I have an input shaft N and if I put a hooks joint the output shaft is actually a function of sorry this is rotating at omega this output speed the output shaft speeds will be proportional to cosine 2 omega. So, this 2 omega comes so if I am rotating at 1 x because misalignment I will have a strong vibration at its 2 x in the axial direction. So, this is the most important diagnostic indicator in a vibration spectrum whenever we have a misalignment as opposed to the unbalance unbalance it was strongly radial here it is high axial at 2 x frequency. If you recall unbalance was high radial at 1 x frequency, but let me just caution you this is very theoretical in the sense high axial at 2 x vibrations. When you go to the lab we see 3 x 5 x sometimes we see even high radials when there is eccentricity with misalignment. So, one has to be careful I though if you go to any hand books on condition monitoring or any trade guidelines they usually give a machinery troubleshooting chart and which says you know we have to if it is high axial and in 2 x frequencies it is misalignment that is well and good, but then one has to be careful that it is not necessarily always true. So, misalignment detection by vibration measurements generally a high axial level of vibration compared to radial levels compared to radial levels that is a good way to look at it in comparison with respect to radial levels, but sometimes exceptions are there at parallel misalignment and so on. And now what I am going to show you is this is a case wherein we had the vibrating machinery rotating at 30 hertz and then we had different amounts of misalignment of course, this is they were all measured in axial directions and we will see usually 2 x and sometimes very close to this is a 3 x and 5 x is occurring. So, what I meant to say is always it is not right to say that always only 2 x will come, but this is characteristically different than the case of unbalance. In unbalance we will very rarely see you know things beyond 1 x of course, another thing is we have to take care of the phase measurements. Phase measurements do help us for example, I had talked about the bend shaft in a bearing of a shaft which has a rotor and if there is an unbalance mass I will see the vibrations at bearing A and B are in phase. So, phi of A minus B is equal to almost 0 degree is the case of unbalance. If the shaft was bend in my drawing I am exaggerating this bend shaft, you will see when you have bend shaft this will be close to about 180 degree. So, these are characteristics of the phase measurements or the characteristics of the vibration spectra when a misalignment case has occurred. So, to summarize in this class on misalignment detection we studied about how misalignment occurs and why sometimes we have to purposefully give misalignment. So, that this thermal expansion between systems can take place and that is why in the industry we have a lot of gear couplings. In the automobiles we have the hooks joints because of the large angular deviations between the engine drive shaft or the crank shaft and the propeller shaft of the vehicle. Sometimes we allow misalignments because of installation defects to few microns and that can be accommodated by flexible couplings. But, despite our best intentions of giving gear coupling hooks joint flexible coupling the misalignment as you have seen will give rise to excessive forces or moments and these forces and moments are time varying and they are periodic and so they are going to reduce fatigue loads at the bearings. So, bearings are eventually going to get subjected to excessive forces because of misalignment and again because of misalignment because these forces have come we are unnecessary using extra energy to overcome this resisting forces. So, the power consumption also increases because of misalignment. So, in an effect this misalignment has detrimental effect into the machine health of the machine which has to be avoided. To detect misalignment basically at slow speeds we can turn around the systems the shafts at the flange phases and measure the radial runouts. The runouts should be same in both the systems that is the driven and the driving unit. If they are not the runouts are not we can play around by inserting shims at the foundation locations. So, that and then we can raise or lower the foundations as to the requirement amount of microns measured in the radial runouts and once we have done that we misalign the system. But for reasons unknown to us misalignment does occur it occurs in machine and then the telly-tale sign to identify misalignment is to look into the 2 x axial vibrations in the vibration spectrum measure at the bearing. Typically to distinguish themselves from unbalance in unbalance we have high radial at the 1 x direction. Of course, when there is overhang rotors having unbalance we as we have seen there could be also the axial components. But usually in the case of misalignment is the 2 x axial direction of vibrations which is very very high. Thank you.