 In this lecture, today I am going to discuss on Gearbox Fault Detection. As you know Gearbox is a very important machinery component which is there in almost all plants. Particularly Gearboxes are used for speed reduction and of course, power transmission with the reduced speed. Many operations in a plant are at very slow speeds and typical the prime movers in any industry are typically the electrical motors as you all know. An electrical motors invariably run at a constant speed may be at the just little less than the synchronous speed. It could be 2 pole it is around 3000, 4 pole around 1500 at little less, 1440 rpm or so on. And, but there are many operations where the plant needs to run at 3 rpm gearboxes in lathe machines which run at various speeds. So, there is a requirement of speed reduction and power transmission and of course, power transmission which is nothing but the torque times the rotational speed. So, essentially Gearboxes are used to transmit power by playing with these 2 parameters changing the rotational speed and torque for a given power. Now, another important feature of this Gearbox is the direction of power transmission. For example, we have a shaft which is rotating I suddenly want power in a direction 90 degrees to it. So, obviously, I have to have some sort of an arrangement in the gears. So, that this power can also be transmitted in an angle of 90 degrees to the incoming shaft. So, if you look at a Gearbox I have an input shaft and then I have an output shaft and there are on the shafts there are gears mounted and the shafts of course, will not be in the gear. So, they will be mounted on bearings and they are put on a casing. This shaft is also this is having another gear and this is also another shaft which is put on a bearing here. This is just to demonstrate to you how a simple Gearbox looks like this is the casing. These are the bearings and this is usually known as the pinion gear, pinion and other gear. One fundamental principle in gearing is the number of teeth times the speed should be equal to number of teeth in the other gear and its speed. So, this is always obeyed and as a rotational speed. Now, this gear are basically if I have to draw a gear file of course, I am not going to give you a lecture on gears, but essentially some of the important features of a gear. So, this is if I just draw one tooth gear and then there will be such tooths all around the circumference of the and this is the root of the gear tooth this is the flank. So, as if and this is going to mess with another gear some the pinion gear and so on one gear that goes this way other gear goes this way. So, lot of things happen on this gear. So, there has to be a constant velocity otherwise we would be getting jerky motion and so on and there will be forces coming on to the flank forces on the flank. So, there are lot of metal to metal contacts between the gear tooth. So, for gear to be strong enough you know this tooth is also behaving like a cantilever beam. Obviously, it is going to deflect each time it messes with a gear tooth from another gear. So, along the gear box this pinion is there gear is there and each time they are rotating one tooth messes with its corresponding tooth from the other gear and so on this kind of gear machine happens. Now, question is when the gear tooth are in contact with the other gear tooth there will be forces and because of the contact there is friction and so there will be wear and there will be heat generation. So, lot of these things happen in the gear box this kind of mechanics happen in the gear box. So, for some reason if this gears are not able to sustain the heat generated because of the friction not able to generate the forces they are going to fail. I will come to this a little later, but now let me tell you what are the different types of gear available. So, this gear depending on if I look at the top view of a gear this gears can be all straight and this are usually known as the spur gear or they could be at an angle and this are known as the helical gear, but spur and helical gear are used to transmit power in one the same direction, but whenever there is a power transmission in 90 degrees we have what is known as a worm and a bevel mechanism. So, gears look something like this and this is one shaft here and another shaft which is rotating in this direction. So, this is the bevel gear arrangement and such gear boxes such gears you will find in windmill and automobile differentials and of course, they all have to obey the law of gearing while they are in motion. Now, this gears are put in a casing I just mentioning to you and because we have to remove the heat which is being generated from the gear boxes because of the frictions many things happen in the gears and this will lead to the if un go unnoticed they will lead to the failures of a gear box. So, this is a typical automobile gear box I just wanted to show you what are the things which we have see for example, this one is one of them is an input shaft other is the output shaft and this is an intermediate shaft because in an automobile gear box we can bring about different types of speed reduction this is a 4 speed gear box and you see these kind of gears which are at an angle they are all helical gears. This is one particular gear which is meshing this is the counter shaft of the lace shaft and these are again the gears and these are what are known as the synchronizers which can be shifted while you shift your automobile gears. So, that they will mess appropriate gears will mess and then we will get a speed reduction and this is an another gear. So, in automobile gear box you know we have a synchronizers and I will show you how this defect can be because see each of these gears these tooth will deflect under load they will get heated up because of the diffraction. So, there is always this gear boxes are having in this casing some sort of a gear transmission oil or a oil basically used for its lubrication carry over the heat and many of the automobile gear boxes or in gear boxes per se people also monitor the oil condition gear oil condition in terms of its temperature because there should not be a case when the temperature of this oil has gone to a level where the physical and chemical properties of this lubricating oils are lost the molecules bonds etcetera break and another is the presence of wear particles or wear and debris in the oil because what happens with time when this tooth teeth mess with each other the rub against each other once the rub because they may be shoved the proper heat treatment is not done this particles may flake off and can deposited in the oil. So, a very important manufacturing requirement of gear boxes such that is the tooth are hardened they are you know case hardened in that in the sense that the tooth are very hard to or wear resistant. So, many times what I have seen if proper heat treatment is not done on the gear tooth or on the gear on the top these particles will flake off and these particles will get deposited in the gear oil. So, to find out the defects in gear boxes many techniques can be used in which you will come one by one I will just show you another type of gear box and these are some of the defective gears. For example, this is some experiments which we are doing in the laboratory wherein we could artificially seed faults in the gear by an wear EDM machine because these are very hard and normal milling operations you cannot perhaps cut this and remove the gear tooth. So, this is where we have removed two teeth because we are trying to do some experiments on vibrations of the gear boxes because of such defects. So, we have to do that and of course, they are so hard that we have to use wire EDM to cut the gear tooth. Now, the kind of faults which can happen is I will list them in the next slide and subsequent slides. So, this is how a healthy gear looks like and this is what I meant by the flank, the land, the root and these are all helical gears and we have removed them. What happens because of the change in the gear tooth and mind you when the two gears are messing against each other there is always a variation in the stiffness in the stiffness by stiffness I mean you can imagine one gear making contact one tooth making contact with one tooth it would have left and then the other tooth will come up. But imagine if suddenly one of them is absent some of them is absent. So, what is going to happen a momentarily it will not going to withstand that resistance or it is not going to have that resistance on it. So, this will lead to a change in its stiffness material is not there. So, this variation in stiffness leads to sudden change in the response or deflection change in the deflection of the gear. So, these deflections will be responsible for creating a vibration. So, because a vibration has been generated because of a gear box fault we will see that the fault has occurred. So, one is the gear oil conditions in terms of its temperature and physical changes because of the wear debris particles other is the vibration in the gear box. And this vibration is transmitted to the shafts which are mounted on bearings and then which are conveyed to the casings and on the casings we can mount our transducers or accelerometers. So, to detect gear faults we can have so many conditions number one is the oil condition other is the vibration. So, in oil conditions we have temperature and the debris. But interesting thing about the vibration is that in a gear box there are bearings there are gears. So, how do you know that the vibration is not because of the bearings and it is only because of the gears that is the power of vibration signature analysis that is every mechanical component its vibration is manifested at its characteristics frequencies. So, what are the characteristics frequencies of a gear box? Of course, we know the fundamental characteristic defect frequencies of bearings and in the earlier classes I had told you how to find out the defects in bearings because of the faults in the bearings and you would have seen the frequencies of ball spin frequency ball pass inner frequency outer frequency. So, these frequencies and their harmonics show up when there is a bearing fault. But when there is a gear fault something known as the GMF it is known as the gear mashing frequency will show up and there will be side bands around the gear mashing frequency because these gear boxes are subjected to change in load change in speed. So, there will be momentarily modulation of this gears gear vibration because of these defects. So, there will be side bands around these gear mashing frequency because of modulation. So, any signal processing technique which can identify this that is the gear mashing frequencies and the side bands around it is good enough to find out the gear box faults, but that calls for a detailed vibration signature analysis. So, how do we do that? We will come to that a little later, but let me continue on my discussions on the other types of gears. So, this is a planetary gear box where inside it we have the gears which are worn and this is how the gear box is used in our fault simulator in the laboratory where this is actually a motor driving the shaft and which we have the pulleys which is the input shaft and then this is the output shaft at this and you will see a clutch device a magnetic clutch which is used to load the gear box. This kind of gear box is used in our lab for the studies and this is actually a gear box in a plant and if you can see here the white one is actually a big motor which is driving a multi stage gear box is a three stage gear box and this is an output shaft where we bring about the speed reduction in the speed and this actually was used to you drive a conveyor belt in a raw material handling plant and this you will see the side glass for the oil which is kept inside the gear box and you will see some the oil is actually leaking from one of these drain plugs here and this gear boxes are put on the foundation here and then this is the gear box base and in fact you will see lot of corrosion occurring and many a times because of this corrosion there the gear boxes will lose their alignment and then the bearings will get unnecessarily loaded because the heavy loads and they will be rotating under load. So, you can imagine it is like a domino effect one leads to the other poor manufacturing of the gear box housing poor foundation harsh environments these all lead to the misalignment of the gear box base which in turn will increase the load because there are heavy bearings here you know there are usually rolling element bearings at this location and this bearings will be responsible for the loads on the unnecessary loads on the shaft here and then there will be uneven wear. So, to find out the causes of gear box faults one is of course, the excessive load because this gears are designed to transmit a particular amount of torque this is some N 1 T 1 N 2 T 2 now the torque which is being carried of course, this is the number of teeth not the torque here. So, GMF is equal to either N 1 times T 1 or which is also equal to N 2 times T 2 gear machine frequency of course, they are doing the same units. So, that we get them in either in herds or in rpm if it is in herds if N is in rpm then we have to divided by 60 then this will be N and N is in rpm rotational per minute. So, because of excessive load sometimes in a gear boxes are designed to carry a maximum load because you know the root the famous Lewis equation is used to find out the stresses at the root of the gear in a gear box design those of you who do gear design is that. And because this is like a cantilever they will be failures and these are usually the root crack and because excessive loads came on the gear boxes. And another thing is on this gear box we will be having what is known as the fluctuating speed and torsional vibration. Lack of lubrication if the particles are not lubricated and the heat is not being taken away by the lubricant there will be lot of heat generation. And many times there is a minimum oil level which has to be maintained in industries you know there could be mistakes and people do not have the entire oil of course, in automobiles you know we have that transmission oil which is almost there. And many times you must have I will just tell you a story see in an automobile there are few types of fluids which is used one particularly for the engine lubrication we call it as the oil which is used in engine oil. And engine oil is exposed to much higher temperatures because they are very close to the combustion taking place and they lose out because of evaporation we lose them. So, every may be 5000 kilometers we top of the lubricating oil that is one but the another one is the transmission oil. So, transmission oil are not at a temperature as high as the engine oil. So, the evaporation loss is less and may be we only check them after 5000 kilometers and this is what is known as the gear oil that is of course, the purpose of both is the same to lubricate and reduce the friction in the mating engine components in the mating gear components. But because this are at a lower temperature than the engine oil we need not replace them or check their levels beyond 5000 kilometers. And some of the modern cars where the transmission oil goes to even very high temperatures they have what is known as a gear oil cooler gear oil cooler a small heat exchanger which is mounted next to the gear oil. So, that it is cooled and put back in the system of course, the key idea here is that this temperature has to be monitored temperature has to be monitored in such gear oils. Now, I just we know about this wear debris analysis in gear boxes and all these oils can be used to find out their particles in them and the normal wear debris analysis routines can be followed and there is a particular schedule which has to be followed. So, that the oil analysis gear oil analysis along with the wear debris is done that is for the gear box. But of course, a much quicker way is to monitor the vibration and do some sort of an signal analysis and then find out the fault in this gear box. So, we will come how this signal analysis done. So, the causes of gear box faults are excessive load fluctuating speed and torsional vibration, lack of lubrication, presence of foreign particles, maleficant defects like improper heat treatment. So, that the flank wear will increase many a times in gear box now I myself have seen lot of impurities there in the gear box and particularly impurities like sand or silica particles will be very detrimental for such system and how do we detect that. So, in a gear box the type of failures which can occur is because the pitting of the gear flank this is one tooth and this pitting could occur in some of these areas there could be cracks, there could be the oil film because there is always a thin layer of oil film here, thin layer of oil film, root crack this is the pitting of course, the bearing faults debris fault detection coupling faults on over hitting all this can occur. So, all this will lead to increase in the dynamic response or otherwise vibration of the gear box. So, we can capture the vibration of the gear boxes and then how do we capture the gear box vibrations suppose I have a multi stage gear box from the outside these are the bearing housings. So, I can I have the option on this are on the basis of the gear box usually the good locations to put the transducers are at the bearing locations sometimes we put it on the base just to make sure and just for reference we can put it in one casing of course, the highest signal to noise ratio will be obtained at the bearing location highest signal to noise ratio will be obtained at the bearing location. So, we have to be careful that we mount the axiometer on the bearings and they could be either uniaxial or triaxial. Now, once this vibration from the gear box has been captured we can do what is known as the signal analysis and signal analysis can be done in many types of course, the very basic signal analysis one done does the time domain. In time domain we can of course, always estimate its parameters relevant estimate the features and there are many features we can estimate from the gear box time domain signals one of course, the RMS the mean the kurtosis skewness etcetera. There is there are about you know earlier in the we are told there are about 20 different features which we can find out, but and then of course, we can always trend these features with time and then this may be increasing with time and there will be a level at which I will know this is an alarm point, but we would not like to measure only at such gross levels to only know whether a defect has occurred or not. However, to diagnose it we have to do something further beyond just time domain feature estimation of the signals. However, it has been found in gear boxes which the time domain signals are greater than 6 kurtosis we can say for sure that there is a fault in the system for a faulty system there can be, but how about to diagnose. So, there is a difference between fault detection diagnosis we know grossly this will let us know that there is a fault in the gear box, but we would like to know which gear how where and so on and then we have to go more into diagnosis module of the gear boxes. And there are many ISO standards which I will tell you in the case when we discuss about case studies in general and how such case studies are used to measure the variation of systems. And of course, because we want to go into a fault diagnosis mode we have to do what is known as the we can go in the frequency domain mode by technique of FFT. And I will be seeing certain peaks and then around them there will be side bands and this is the variation level. So, the amplitude of side bands will increase over time and this side bands are around the gear massing frequencies and it is multiple, but what happens many time because there are lot of other signals. So, this side bands are very nicely buried in noise. So, the signal to noise ratio at side bands is poor. So, we have to find out an improved signal processing technique to detect such side bands and that is what is known as the substrum analysis. We had an entire class on substrum analysis and there also I believe I had covered about the gear box signal fault detection. I will give you some examples, but another important thing which happens because of this defects in the gear tooth sorry there will be lot of impacts occurring and this impacts in the time domain will look something like this. So, this kind of they are highly non stationary signals because they are not definitely existing at all times they are not periodic. So, the fundamental signal processing theorems of stationary signals where in the properties of the single ensemble over a given time change is being violated and thus stationary signal analysis like FFT etcetera cannot be done on such signals. So, we have to do signal analysis using certain non stationary signals like the wavelets and then things like short time Fourier transform or STFT. So, some of the advanced diagnostics software which are available have these features by which we can do such signal analysis. Now, I will give you a case study for signal which we had done in the signal analysis in the laboratory. I will just give you a relative field of this is a normal gear box frequency and then you will see about from 0 to 1000 in the gear box which I showed in the laboratory simulator and this is the amplitude of the vibration measured at the bearing location or sometimes in the gear box casing you will see this gear side runs around the gear box frequencies. And these are characteristics of the gear box signals I will you will realize that whenever we have seen the signals of the other mechanical systems we will not see such side bands around GMF and that is the characteristics of a gear box vibration signal. And to find out more about the side bands we have to use the technique of system analysis. So, just to quickly recap you know I did tell you about the gear box debris analysis debris and oil analysis I mean the gear box oil will lose its property the debris will be deposited looking at debris we can get some clue. Next is vibration of course, another technique which we in our group at IIT Kharapur have successfully used is this MCSA motor current signature analysis. And this has been used to find out gear box fault I will I will tell you briefly what is there in this suppose I have a motor here electrical motor through a coupling it is driving a gear box. And this motor there are current which is being drawn by the motor. So, what happens is as a defect in the gear box this gives rise to some sort of a load additional load torque on the motor. So, if this motor is being subjected to an additional load torque the current itself gets modulated at the frequency of the occurrence of this defect. And so, the side bands in the current will also indicate some presence of the mechanical defects. So, side bands around the supply I mean the electrical supply frequency of the motor current will indicate a mechanical fault. So, this we have successfully used to demonstrate gear box fault. And more details about this can be found again at my website. And you can refer to some papers in journals like MSSP or JSV. Again the systems and signal processing or journal of soil and my publications. And then you will see that how these motor current signature analysis has been used to found out gear box faults in the laboratory. Now, when we had a one gear case the amplitude there is a change in the amplitude. In this case showing your comparison actually the amplitudes are from a different gear box though. So, that is why it is not fair to compare between the first graph and this graph, but then there is a difference in the spectrum. But what I wanted to show you here is that the gear box side bands around the GMF have to be found out by the system analysis. And the system analysis of the gear box signals this is in dB they will give you certain Q frequencies. So, the inverse Q frequency will be related to the rotational speed of the pinion or the gear or their multiple. In this case there is a strong multiple. So, you will see which one is more at fault just for the sake of discussion. Suppose, this is running at 600 rpm and this has 20 teeth and this has may be 10 teeth. The speed at which the gear n gear is nothing but 600 times 20 by 10 is about 1200 rpm. So, one rotates at 600 rpm other rotates at 1200 rpm and the inverse time period would be. So, this is 600 rpm will correspond to 600 by 60 that is 10 hertz. So, the time period is 1 by 10 that is 0.1 second is for this one and for this one it will be just twice. So, this will be the time period of gear will be 0.2 seconds. This is going at a much slower speed is that right. I do not mistake here I believe this will be at a slower speed is not it. I have taken this as 10 may be I have drawn it wrong this sort of other way. If the number of teeth here is 10 that is. So, this is rotating at 0.2 seconds. So, in the Q frequency and some d b amplitude because this is in a log scale if I see a Q frequency at 0.1 seconds at or 0.2 seconds I know at a particular and with time if I monitor the Q frequencies I will know that there is a fault in the device which is running at with a time period of 0.2 seconds of the fault in a component which is running at 0.2 seconds in this case it is my gear. So, we can use such a technique sub term analysis to find out pin point the fault in a particular component. So, just to summarize in gear box it is a very very important mechanical component and this component or this device is used almost in every industry. So, two broad ways of fault detection in gear box is one is doing the either the oil analysis and the wear debris analysis and other being the vibration analysis. And vibration analysis itself can be done in many ways just in time domain signal analysis frequency domain time frequency or in system analysis. And then we can not only know the gear box fault conditions, but also actually diagnose and find out the real cause of the fault in a gear box. Thank you.