 In this class, we are going to discuss about ball and journal bearings. As you know by now that everything depends on our bearings. We put our transducers at the bearings, but the bearings themselves could be having fault. So far, we have discussed about faults in the rotating systems, be it the shaft misalignment, shafts having unbalance, shafts having cracks in them, but eventually all the measurements are done at the bearing locations. And we in the earlier cases, we had assumed that the bearings were ok, but that is not true. Bearings themselves have so many rotating elements that themselves could be defective. So, in this class, we are going to focus on these two important classes of bearings, the ball bearings or the anti-friction bearings and the journal bearings. In our class in Rotodynamics, we have seen the importance of journal bearings because of the fact that journal bearings can take huge amount of static loads on to them. And they are practically there, the shaft is actually supported on a fluid film. So, there is no contact between the shaft and the journal. There is no metal to metal contact and they can take heavy loads. However, in the journal bearings, there are issues of stability and particularly in flexible systems. The stability in journal bearing is of a critical concern, which is not apparently so in the case of anti-friction bearings, but in large gas turbines, you know steam turbines, wherever we have journal bearings, stability is very very important. So, the oil film thickness, the clearance between the journal and the shaft, all these in the load on the shaft, the rotating speeds, all these control the stability of the system and that is very very important, which we will not discuss in this class, which we had discussed, I think in the class on Rotodynamics. But in this class we are going to focus on what happens or what indications we get when there is a defect in the ball bearings and defect in the journal bearings. So, well why do we have bearings? We have bearings to reduce friction between two moving parts and the bearings support these rotating shafts. So, if I have a shaft, which is rotating, shaft is carrying lot of weight, so they have to be supported on bearings and I have to give very very less friction to the rotating element, that is my requirement, less friction and support the load. So, one way to reduce less friction is to have them finely polished surfaces, hard surfaces, which will not wear off and then they will support load. Another is put an oil film, now when you have this oil film here in the journal bearing you have an eccentricity, because of the converging diverging room there will be this fluid pressure, the fluid here and because of the fluid pressure this shaft is going to get lifted off the journal and then the shaft is going to support. So, we have the case of the journal bearing and of course, the anti-friction bearing. But, in the journal bearing particularly there is a layer of oil or lubricant, it is actually this oil. So, this lubricating oil can give different amounts of friction depending on the z n by p, where z is the viscosity and p is the pressure of this oil and is the speed r p m and this is the famous Petrov's law and then you will see that some some extent this will go up and this is the case of the boundary layer, where the boundaries are almost touching mixed layer and then the hydrodynamic. And we are talking about bearing in this hydrodynamic region, wherein the friction is less. So, this anti-friction bearing could be of many types, could be ball bearings, roller bearings. Similarly, an anti-friction bearing has an outer race, an inner race and this could be the, this is the outer race, this is the inner race. These are the rolling elements which are usually balls, rollers or even sometimes tapered rollers and then there is a cage or a retainer which ensures that no two rolling elements come together, the thin metal they are actually they are actually riveted here and this is the cage or retainer. At sometimes the inner race rotates with the shaft, typical cases or sometimes the outer race rotates like in the case of the ceiling fan, ceiling fan bearing, the hub is actually stationary, hub is attached to the ceiling, the shaft coming, ceiling fans outer race rotates in typical other cases all the electric motors etcetera it is the inner race which is rotating rotates sometimes you call them as race or ring. So, the idea behind this bearings, anti-friction bearing is they have to in any bearing they have to produce give less friction. So, to give less frictions they have to be moving very, moving without any obstruction. So, these elements are manufactured to be very fine surface, hard surface and they are lubricated once they come out of the factory, they are lubricated at the factory and sealed forever, thin layer of lubrication. This is the first class, first type the anti-friction bearing or the ball bearing or the roller bearing, this is how it looks like and the hydrodynamic bearings basically we have journals where there is pad and then where there are grooves for the oil to come in and so on and which we discuss in the case of protodynamics. I will not go to journal bearings right now, we will focus more on the anti-friction bearings and because most of the case a small machine search etcetera they only have search of anti-friction bearings which could be self-aligning also. So, this is how what are the main components of a rolling element which we just saw, the inner race, outer race, the rolling elements could be either ball, roller, cylinder, tapered roller, needle etcetera, cage separator, retainer they are the same things. Now, why do vibration signals from the bearings occur? That is the characteristics of vibration signals from the bearings because once bearings are put on housings I have a bearing here and this is some shaft and I have put a transducer here, this is my transducer. So, these shafts are carrying loads and sometimes these loads are directional, speed may be fluctuating. So, the load coming to the system or the excitation coming to the bearings is varying with load, varying with speed. So, these are responsible for this vibration signal which is coming out of the bearings to modulate them by modulating them I mean suddenly the amplitude will increase decrease. So, actually so this this sorry these are the amplitude modulations which are occurring because of the load and speed variations. On top of it this all this rolling elements have different relative motion. One is the balls are for example, the balls are spinning about their own axis and also going about the about the about the circumference. This is if this outer race is fixed this inner race is rotating at an rpm n. So, I can assume that this is rotating at n by 2 the train the fundamental train of this rolling elements are moving at and speed of n by 2. This is a fair assumption because this is 0 this is n n by 2 linear assumption. So, you see all these individual components here the cage, the inner race or the outer race one is either stationary either the inner race is stationary in the case of a ceiling final like I told you or the outer race is stationary in the case of an electric motor. So, these elements are all rotating at different frequencies and that is what gives rise to the high frequencies in the even in a good bearing you will see sorry even in a good bearing you will see these frequencies coming up in the vibration spectrum of the vibration which we measure. The best part about the bearing vibration is for example, if I have a shaft which are bearings these are my bearings and I have put my transducer somewhere here. Transducer will record the 1 x vibration because of the rotational speed, but they will also find out the bearing frequencies plus bearing frequencies, but you will see the bearing frequencies you will see the bearing frequencies you will calculate any time they are actually some fractions either 0.6 of x 1.2 of x. So, and they depend on the bearing geometry by bearing geometry I mean the pitch diameter, the ball diameter or the rolling element diameter the number of balls small n, the rotational speed, the contact angle, the contact angle. So, these frequencies are no way related to 1 x, 2 x, 3 x which we saw in the case of rotating shafts and that is again why you will be wondering well always I am putting my transducer on the bearing mounts. What if the bearing frequencies are contaminating or mixing with my actual shaft defect frequencies of missile and man crack unbalance that will not happen because they are at different frequencies. The bearing frequencies themselves are at a different value compared to the shaft frequencies and that is actually helping us and like I told you in spectrum analysis every peak in the vibration spectrum corresponds to a particular defect in a particular mechanical element it could be a bearing fault, it could be a shaft fault, it could be an unbalance, it could be a gearbox fault they are all different frequencies and that is really they are just really saved the work for us. But another thing also happens in the bearing is because there is a defect in a bearing lot of high frequencies get generated and I will come to that just in a little while but what are the sources of bearing vibration? So, once we manufacture this bearing when you say this outer rays inner rays to be a perfect circular ring we manufacturing them through a grinding process through a polishing process through a buffing process to make a perfect circular ring. But after this ring has been manufactured if you take a dial gauge and measure the ovality of this ring it will not be circular, it will be surprised to know that it will be somewhere this is not a sharp peak here but these variations a ring a circle which should happen the green circle actually looks like this and this could be order of 2 micron very very small but this is there in a new bearing also and this is known as the waviness of the ring or what is known as the out of roundness through a precision measurement precise measurement of the wave of the surface profile you will see that it is not a perfect circle it is something like this. So, bearing manufacturers when they manufacture bearing they ensure that they do good amount of finishing operations in the buffing final polishing operations so that this happens. And on top of it if you will see that we have this rolling elements actually riding on these waves. So, if you if you put it flat on a surface so we have a wavy surface on which these rolling elements are moving this strain is moving at a high speed. So, this gives rise to the vibration response in vibration you must have studied when you go over a wavy surface what kind of amplitudes you get all of you must have experienced going on a motorbike on a wavy road you would have experienced those amplitudes coming up same thing happens in a bearing. So, this is why even in a good bearing we have vibrations because of the out of roundness while they have manufactured it. On top of it if you look at another important component that is the surface roughness of the components this surface it was any of the surface was supposed to be manufactured all the surfaces were supposed to be manufactured as nice flat surface with an r a of the of the central line average of the surface roughness to be very very low. But, if you look under the microscope there will be lot of valleys and pits and this is because of the valleys and pits valleys and peaks and they are not smooth they have an surface roughness. So, imagine a rough surface moving over another rough surface this rough surface could be that of a ball or a rolling element or a roller riding on an inner and outer rest which also has a surface roughness and which is wavy and this is what is actually there in a bearing at a microscopic level. So, all these wavy surfaces they are having motion and that is why this vibrations come even if you have a good bearing. To reduce this manufacturers what they do is they ensure that they have good amount of manufacturing operations in terms of polishing operations. On top of it at the factory when the bearings are manufactured they put a layer of lubricant right once the bearings are manufactured. So, this lubricants will go into this pits and valleys and make try to make a smooth surface. So, if you hold a new bearing and if you just play around with the bearing you will not feel any roughness to your hand because of these lubricants. To remove the lubricants if you take this new bearing and wash it with kerosene and remove the lubricant you can all do that and feel it you will feel very too much amount of roughness in your feel because the vibrations have increased because you have removed the lubricant by washing it with kerosene. So, that is the reason why new bearings also have vibrations. It is not true that new bearings will not have a vibration. New bearings have vibration because of these two reasons waviness and surface roughness. On top of it things become more complicated. In the sense let us come to this case of the presence of dirt. Now, imagine on a surface smooth surface you suddenly come across a bump or a pothole. So, these and then you have a rolling element. So, these bumps or potholes these bumps could be because of presence of a dirt on the surface of the inner race and outer race. Very hard silica particles sand particles they are very hard they will not disappear. So, they are going to scratch scrape the surfaces. They are going to corrode or if there are some scratch markers there is like potholes. So, imagine when you go on a bicycle over a pothole you get this impulse. So, these rolling elements are subjected to a force of this nature an impulse force in the time domain. If you look at the force they are subjected to pulse like this and this is an impact. So, this rolling element which are rotating in the inner or the outer race are subjected to such impact forces because they came in contact with a hard dirt particle which is like a bump on the road or there are some pits on the inner race because of some corrosion something has happened there is a pitting mark some scratch marks. So, these impacts basically these forces impact the bearings elastic structure. The bearing has mass bearing has elasticity. So, bearing also has a natural frequency of its own bearing has a natural frequency k by m it has mass it has a stiffness. So, it has a natural frequency. Now, if you look at the frequency response of an impact force it is basically a random force in the frequency domain an impact would look like this force impulse short time force would have lot of frequency lot of forces in the frequency domain a white noise. Now, imagine if the bearings equation if I write some force this force happens to f sin omega t where it is omega is equal to 1 infinite for that matter because this goes all the way up. So, that means this bearing is getting excited at all frequencies agreed why did they get excited at all frequencies because there of this impact force or impulse force. So, the right hand side of the equation has got all the frequency components. Now, it may happen. So, these are the forcing frequency it may so happen that the forcing for a frequency is equal to the natural frequency of the rolling element bearing has been designed. So, and we always design a bearing to ensure that its natural frequency of a bearing of the bearing is away from the operating frequency. My operating frequency means I am in the shaft rotating speed and few harmonics of it. So, it should not interfere in the operating frequency usually a bearings natural frequency are in the order of 20 to 30 kilohertz because we never operate at these frequencies. So, the bearing would never undergo resonance conditions, but the problem is because I have excited it here by an impulse force which has all the frequencies the natural frequency gets excited. So, I will have a large response at its high frequency. So, resonance of components occur that means the bearings have got excited at its natural frequency. So, if I see a high frequency vibration in the order of 20 to 30 kilohertz in the ultrasonic range if I see a high increase in the vibration level I can say for surely a bearing has undergone a fault and that is what actually people use in an instrument called as a shock pulse meter. So, shock pulse meter is actually nothing, but an hand held instrument for bearing fault detection it is nothing, but and high frequency bearing vibration measurements. So, basically essentially a high frequency 20 to 30 kilohertz vibration measurement or monitoring device and because high frequency vibration occurs in defective bearings because the resonant frequency of a defective rays because of a pit scratch dirt gets excited and you know the physics why it got excited because I excited the right hand side of the equation by a forcing function which happens to have the natural frequency of the system. Obviously, so, resonance happened and then I have high frequency vibrations. So, a bearing vibration a bad bearing vibration would have the frequencies of these inner rays, outer rays, cage, retainer etcetera plus a sure case to say that the bearing has failed is when you see a high frequency vibration in the 20 to 30 kilohertz range. So, to understand this we did a small experiment in the lab and basically what we have here is a motor driving a 6 to 0 through a bearing and all we have to do is put an accelerometer and put a filter have a n i data efficient card and we take all the data to the computer and then we have a photoelectric probe to measure the rotational speed. Because as you will see every all the bearing frequencies are dependent on the rotational speed of this shaft and this frequencies can actually be calculated and in fact, the rolling element bearing defect frequencies we can call them as defect frequencies we can call them as bearing frequencies as also and they are given by these equations. The outer rays defect frequencies given by n by 2 times r p m by 60 times 1 minus ball diameter by pitch diameter times cosine of the contact angle beta and 1 is minus 1 is plus and then the ball defect frequencies where small n is the number of balls r p m is the relative rotational speed between the inner and outer rays b d is the ball diameter p d is the pitch diameter and p beta is the contact angle. So, these can be calculated from the bearing manufacturer where all the bearing manufacturer give this data some of them give only the ball diameter not the pitch diameter sometimes they do not give the catalog in the catalogs the number of balls but, you can always find them at in the internet or measure them or talk to the manufacturer. So, here what you have done in this experiment is we took a 6203 bearing which had a ball diameter of 6.747 millimeters pitch diameter of 20 point 28.7 millimeters the number of balls in the rolling element bearing was 8 contact angle was 0. So, cosine beta is 1 speed of motor it was running at 1800 rpm is 30 hertz. So, this motor was running at 1800 rpm we have bearing here and in this bearing actually we had a series of 6203 bearings manufactured by a company who wherein we could artificially create defects in the inner rays by putting an electric scratch mark through an electric itching pen we could create scratch marks in the rolling elements we could create scratch marks in the outer rays. So, then we one by one we introduce we manufacture bearings defective bearings and put them in the shrink and then we measure the vibrations. So, the theoretically calculated values for a rotational speed of 30 hertz the fundamental train frequency is 11.4 hertz, ball spin frequency is 60.3, outer rays frequency is 91.8, inner rays is 148.2 you will see here nowhere this wall the bearing frequencies are multiples of 30 hertz we are some decimal fractions of the inner rays outer rays of the of the rotational speeds. So, that is a good indicator. Now, this one here just to give you a feel of the bearing vibrations how they look like when there is no defect and there is lot of defect. So, when there is no defect the amplitude levels of vibrations are very very low if you compare to the second one which is the case of a defective bearing and if you look at the time history they are almost periodic and then there are very small peaks, but the magnitude is very very low 0.01. But in this case we have bearings which where there were lot of defects and you will see this impact nature this is because of the potholes or the dirts so it is ringing. So, this is if you look just look at the time domain signal of a good vibration from a bearing and a bad vibration of a bearing you can right away say looking at it this is a bad bearing. So, you will see time domain analysis itself is very very helpful to identify bearing faults and if you will do the feature calculation from these signals like its mean RMS you will see. Obviously, the RMS value of this is much higher than this, but there are factors like the kurtosis of the bearing signals. If I measure the kurtosis you will see the kurtosis values of this bad bearings are pretty pretty much high more than about 4 or 5 and then you can say for sure that this is a bad bearing and this is how the spectrum looks like. Now, the earlier example was for the case of the time domain and then these are both time histories the same now has been converted to the frequency domain and from 0 to 500 you will see for a good bearing the amplitudes are low and you see the fundamental 10 frequency and the sharp frequency showing up nothing else. But once you have defective bearing first of all the amplitudes are high and almost in this case there was an inner rest defect the ball defect or outer rest defect all these frequencies are showing up and these are sure cases and in this bearing we are not even monitoring the high frequency vibrations I told you about 20 to 30 kilo Hertz. But the reason I told you to monitor the high frequency vibrations from 20 to 30 kilo Hertz is for the fact that bearings are actually put in systems where could there could be frequencies of faults from other defects like in shaft missile and band unbalance etcetera. So, they will smear the spectrum it will be very difficult for you to distinguish many frequency other defect frequencies unless you have a very fine resolutions or really a good eye for it. So, a sure test is that high frequency monitoring through a shock pulse measurement and this is how this waviness and out of round is looks like. So, this is the good bearing acceleration signal this is the bearing signal with outer rest defect you can measure you see 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 0.2 by 18 that would be approximately how much about 0.3 is it on a time period is 0.2 seconds. So, 200 by 18, 0.01 seconds and this is 1 by 30 is actually 0.3 is not it 0.03. You can actually looking at this you can say whether the more what is this special spacing of this defects whether 2 defects are there or 1 defects are there. In fact, I am not sure about what defect we have put here. I am but this is that no defect case only with outer rest defect the multiples come up it is not only the single frequency but also there multiples. Yes, 2 outer rest defects 180 degree apart in this case what we did as we created one defect here and another defect here and this is for the inner rest defect sometimes you will see the shaft frequency is showing up because the inner rest is attached the shaft and here when we have the ball defect only defects in the ball the ball frequency will show up and how are these frequencies calculated? This is inner rest outer rest ball all 3 were there. What I am going to show you is I am sorry these equations. So, these equations are there in the books these equations you can know only thing that you have to know the ball diameter pitch diameter and find out this and then you can find out. So, this is usually what you will see when you measure the viruses out of a bearing in case of the defect free and in case of defect and this kurtosis value gives you an indication as to why this faults whether the fault has occurred in the bearing itself. You blindly pass it through our signal processor where in you just calculate the kurtosis of the time domain signal and usually kurtosis gives the pickiness of the signal and usually kurtosis value greater than 5 is case of a defective case and less than 3 is the normal case because if this bearing faults go unnoticed for example, a crack in a bearing outer rest. If it goes unnoticed we are going to have problems the bearings are going to fail and many a times I will I will tell you in other case studies in a many a times when in a particularly electrical motors when there is a electrical conduct turns occurring through the bearings because the shafts carry are carrying a rotors and there is lot of magnetic flux and this flux gives rise to small ground voltages and this at the bearings because of the oil film that is a sparking very significant sparking occurs. So, this grounding is not done properly the sparking is going to occur and the sparking is going to giving rise to pits. So, if a bearing goes dry not lubricated not properly care for pitting marks will occur pitting occurs because of electrical sparking. So, this is going to give rise to the initiation of these defects. So, good bearing has to lubricated made kept in dirt free environment and ensure that pitting dirt do not enter and then you also do not overload the bearing more than it was designed for. So, bearings if they go unnoticed eventually if a bearing fails a machine has failed your shaft is going to come down loads are going to come down everything is going to fail. Missalignment in the shaft is going to give rise to a high axial force sometimes in the journal bearings, parallel bearings you will see lot of uninformed wear occurring uninformed wear again gives rise to uninformed clearances and then the forces are going to vary the support forces are going to vary again this give rise to fatigue loading. So, it is actually a dominoes effect kind of one leads to another. So, we have to be careful whether now who came first. So, I will give you at the closer I will just talk about a small case in a particularly in a paper mill wherein we have to be careful about the supporting the bearings which are there in the number of rolls which are there in a bearing. So, this is the flow chart of a paper mill basically you have the this area where the pulps etcetera come the paper pulp etcetera come and then they are shredded and a mixed with the caustic soda etcetera clean bleached impurities removed and this pulp paper pulp is actually fed through a wire press wherein there is a steel wire which is going in and then basically they are pressed here in the first stage. So, that the water is squeezed out from this pulp and this pulp is you know this black line is made to pass through rollers wherein we do lot of drying. So, initially once you dry this wet pulp and then slowly this paper is going to get formed and paper will be they pass through about 20 30 dryer big drying drums and each are supported on rollers on bearings and bearings are what and they are steam dried there are steams going through this drums and eventually at the end they are in a hot press after the dryer that is called as the calendron operation and finally, they are put into roll and then the rolls go to the market. So, in the if you will see in a typical paper mill there are about 200 to 300 rolls just rolls rotating at and a typical speed is about 1000 meters per minute this at that speed 1000 meters per minute this paper come out at about 1000 meters per minute and then roll and typical production is about 80 tons per day in 80 tons of paper per day particularly the news prints and this bearings if one bearing fails the because this is operation in series everything has to be shut down. So, this bearings have to be monitored around the clock and this is one view of the press section near the washer wherein the pulp has been fed this is a wire on to which this the take off roll and so a very big roll and you can see my students standing there it is about 1 meter to 2 meter in diameter and then they go in through this rolls and then and this is the pressing section there are few presses here and in other side and you will see this rolls coming in here and in this particular plant and then you will see lot of this drums big drums and in one drum one side of the drums there are actually steam going in heating the drum. So, drums are very hot so the because the water has to be dried after you have pressed and removed the water from the paper pulp it has to be now dried over series of rolls and then these are the bearings I have another view every roll there is a bearing there is a bearing here bearing here and you will see in such a plant the bearings are monitored by vibration you will see this white lines here is a bearing transducer here is another bearing transducer here another bearing transducer here. So, around the clock vibration monitoring of this rolling bearings are being done because and then there are diagnostic algorithms where in a people can know which vibration signal is coming from which bearing what is it is kudosis value what is its spectrum value and if you because this are very very critical operation because imagine if one rail roll breaks and falls it is going to damage few other rolls it is going to damage few other bearings and to put everything together you can imagine the problem one has to face. So, everywhere depending on the criticality of the equipment of the process of the plant monitoring of rolling element bearing is essential and particularly in paper mills etcetera these monitoring of bearings is done sometimes continuously online through these and nowadays the state of the art is right at the bearings they are having transmitters wireless transmitters. So, that in a complicated plant it did not have all this cabling coming to junction rather you have over the wireless and with the proper routers you have the signals you know which are coming in and then sitting somewhere remotely in the control room you can know which bearing signal is where and people are now in fact monitoring them over the internet sitting in Kharagpur you can be monitoring a plant in Malaysia it is possible it is no longer a science fiction you could be having your paper mill in Spain and you can be monitoring the bearing at Kharagpur and then you can be giving them diagnostic measures they have to take. Thank you that will be an effect.