 In machinery condition monitoring, we come across many defects, machine defects like unbalance, misalignment, bearing defects, gear defects which we have discussed in some of the previous classes. Another important defect so called in machines is looseness and rubs. So, in this class we are going to focus on looseness and rubbed direction, what are the characteristics of such defects and how through vibration analysis such defects can be distinguished. Well, what is this looseness we are talking about? So, if you think of a machine, basically any machine has many such rotating shots which are supported on bearings and these bearings could be anti-friction or general bearing and these shafts may be carrying a gear, pulley, set of impellers. So, all these components could be there, may be one of them could be there or all of them could be there and this shaft is rotating. Now obviously, if this was in a machine, this should be housed in a casing, this should be housed in a casing and so on and perhaps near the location of the bearing, we may be picking up a virus in signal, we may be picking up a virus in signal from a transducer. Now it is this characteristics of the signal which you measure by putting a transducer near the bearing locations and from this how do we identify looseness is our objective. Just to recap, as you know in machinery condition mounting wherein we are using vibration analysis, the fact that vibration analysis is so powerful is for the fact that every defect has a characteristic frequency in the vibration spectra and this is the most important fact for which this vibration signature analysis is very powerful, convenient, easy to implement in finding out faults in machines. So, we all know that for the fact that when we studied about bearing faults, we knew how the characteristic defect frequencies of bearings showed up in the spectra. We know about misalignments, how the axial components of the 2x vibration frequency showed up more prominently than the others. In gears how side bands occur around the tooth machine frequency, in you know you will talk about fluid machineries, particularly in fans, blowers, pumps, turbines, how the vane pass or the blade pass frequency shows up in the frequency spectra. Similarly, the question is what happens because of looseness and then how do we detect them. See as I telling you here, the characteristics of vibration signals due to looseness, there will be significant amplitude variation. These signals in the time domain would look truncated, I will explain one of them. They will be having certain harmonics and sub harmonics and then there could be a beating of the signals and unstable phase between signals, we will see each one of them one by one. For example, if things are loose what happens, the components would be flying around all the places. So, they would be hitting against each other, so there will be series of impacts or hits. So, if I look at the time domain signal of a normal signal, this is something normal normal signal. So, what happens when there is an impact or a hit, you all know the characteristic signal of a hit is something like a impulse and we actually mathematically represent them with a direct delta function when we do the integration to find out the response. It is something like this, time period tau and may be amplitude is A by tau or something like that and this exists only for a short duration of time and this is the mathematical representation of an impact, but this is what the real world signal looks like because of an impact and imagine such a signal, such impacts are occurring on the time signal because of a looseness. So, what would happen is these amplitudes would go blow up and so on. So, first of all these are high amplitudes, significant variations. Now, in vibration monitoring you know that once we have the transducer, this is followed by a data acquisition system and in the data acquisition system, I will come to come back to this figure later in the transducer, I have a A to D system and then of course we have the digital signal which goes to a computer, this is my transducer. There is a range of this A to D system and this could be may be 10 volts, maximum range you can have or plus minus 5 volts, but what happens if this transducers have of very wide dynamic range. It must have happened because of this impact because there is no physical device which is controlling this amplitude, there is no limit to controlling because if I have an impact because of a looseness, it is going to produce a high vibration signal and this is limited by the dynamic range of the transducer. Sometimes it may go beyond the dynamic range, so there may be a case where I will over range go beyond the capacity of the transducer. In such a case what happens, these signals will be truncated because my A to D system will say understand this is plus 5 volt and this is say minus 5 volt, so the A to D card will not try to understand anything beyond plus 5 or minus 5. So my signal will look truncated, if I draw on the, so this is the red one is the truncated amplitude signal. So such a signal will appear in the time domain where you are measuring because of the impacts or impulses which occur due to looseness, so if I have to draw them again. So these are signals which can very easily be seen on an oscilloscope, for example my normal periodic stationary signal out of a machine could look something like this, but the truncated signal would, so these are the limits. So what happen, they look like chop signals or truncated signals, so looking by the physical nature of the signal characteristics of course, how do I know in an automated system it is not possible for anybody to look at a signal. So we have to study the time domain features, by some of the time domain features I meant RMS, mean, kurtosis, skewness, crest factor etcetera. We studied about this in some of the earlier classes on time domain signal analysis and you know by now how to calculate this parameter. So the characteristics of truncated signal would be different having a different kurtosis, skewness and crest factor and in the time domain they will look like truncated like I showed you in the earlier red plots, this kind of plots I showed you here. These are the characteristics of the truncated time domain signals and they will look something very close to may be a square wave and with some signals with some oscillations and so on. So if somebody was going to do an frequency domain analysis of such signals and the normal method of doing such signal domain analysis, frequency domain analysis is by the FFT process. You will see lot of, this is your typical 1 x 2 x 3 x by 1 x I mean the normal rotational speed and you will see again one thing I should drive home the point that in vibration monitoring it is essential that whenever we are doing vibration monitoring beat in the laboratory beat in the field it is very very important and implied that you are always measuring the rotational speed. It is a good practice many a times when you go to the industry you know people assume you know this machine is running at 1440 rpm or it is running at 2900 rpm etcetera. That is fine that is what the motor rating says if we have no knowledge about the speed of the machine that is good to follow. However, wherever possible try to install a rotating speed measuring device like a reluctance probe like an optical tachometer like a laser based system. So that any time whenever you are measuring the vibration you also have the corresponding rpm trace this is of course, in a time domain signal rpm and how you will usually get a peak some voltage some voltage and this is your time period and the rotational speed F s or F r is equal to 1 by t. So it is always good to measure of course, vibration and then the rotational speed. Because once you have the rotational speed you will get a good estimate of 1 x and then you will get 2 x 3 etcetera, but the characteristics of such signals in the frequency domain is that we will get harmonics to lot of fractional harmonics. So, this will be 1 half x 1 and half x 2 and half x and so on and maybe even fractional 1 third x 1 sixth x and so on. So these are the because they see end of the day your this FFT analysis is being done by a computer and this computer does not know whether your machine has a looseness or not. It is the signal which tells the computer once we analyze we interpret that there is a looseness. So, this interpretation of the signal is only by a mathematical process it is the signal analysis which gives us harmonics harmonics and subharmonics. This is what is given by the computer the harmonics and the subharmonics. So as long as the signal looks something which will give us harmonics and subharmonics we then interpret that there is a looseness in the system otherwise this computer will not be able to tell whether it is looseness. So that is where the signal analysis comes in the hell and again because this is looseness no suddenly a component may get stuck may not be though it may be loose momentarily it may get frozen it may get jammed with some other another loose device. So this signals are very erratic you can say to some extent they are non stationary and of course because you know if the rattling looseness another mean word means rattling this rattling may be at frequencies which are close to each other. So if frequencies are close I will get what is known as the I will have beating occurring and once beating occurs we will have amplitude modulation well I will not have amplitude modulation but the signals will look like amplitude modulation and then because they are all independent process you know these two frequencies which are rattling and close to each other will produce and they are independent they will produce beats and they will look like amplitude modulated signals. Now we did not mention something about phase see phase is a very relative term first defined phase if this is my some signal x. So if this is pi by 2 the first this is my reference the first occurrence of maximum amplitude from the reference plane and is the phase. Now question is if I have many signals say another signal there is of course a phase difference between I will not draw another signal may be I will just there is the phase difference may be of between the blue signal and this is the phase difference phase is always relative. So when I said here pi by 2 this blue one it is with reference to this plane but between these two signals there is again a phase difference of pi by 2. So when you do signal analysis there is an unstable phase between signals. Now what do you mean by unstable phase between signals? So when I talk about two signals when I talk about two signals x and y how do I find out the phase of these two signals? So what I can do is there is a process known as the cross spectrum phase. So in an FFT analyzer I can always find out the auto spectrum s x x which is nothing but. So if this was signal was if I do an FFT of the signal x t if I do an signal FFT FFT I will get a signal which is in the frequency domain will have and similarly I will have y real in the frequency domain plus imaginary part of y imaginary in the frequency domain. So s x x I will remove the F's here these are all in frequency domain and this will be x R plus I x I times the conjugate and this will be x R square plus x I square. So this is the auto spectrum of the signal x similarly auto spectrum of signal y will be square, but there is another component which is known as this cross spectrum between s x y f is nothing but x R plus I x I times y R minus I y I and you will see that this is the complex quantity and the this will have I will not go into the details of this. So this will have real part of s x y f plus imaginary part s x y f and so on. So the magnitude will be nothing of the cross spectrum this is the this is the auto spectrum this is the auto spectrum. In other words this is the power spectrum if you look the unit has squared and this is the cross spectrum. The reason I am telling you this is this is how in the FFT analyzers the phase between few signals are calculated. So the phase between signal x and y phi x or phi of phi of the cross spectrum x x y f is nothing but tan inverse imaginary of s x y f by the real part of s x y f and from this equation if you multiply them you can find out the real and imaginary. So this phase angle which is a function of frequency this phase angle which is a function of frequency will actually vary with time and this will be from plus pi by 2 to minus pi by 2 and then this will be varying and this variation for a stationary signal and this depends on how many resonances occur and this is fluctuating and usually for usually for stationary signals when in signal processing the random error in measurements is actually reduced by signal averaging. So what I mean to say is suppose I am finding out the transfer function by the way the transfer function between this two signal h x y f is nothing but the auto spectrum sorry and this is again a complex quantity and these are all functions of frequency that be careful about how you put the conjugates and then this magnitude will look something like this with averaging there will be lot of such noises which will reduce noise reduces pi signal averaging. Now similarly for this if you look at the phase phase also is pretty nicely defined phase of the transfer function. However, when you do such analysis between two signals which are coming from a machine where there is lot of looseness you will see that this phase there will be lot of it will make no sense because if you do an average signal you will not get any meaningful information and that is what I mean by unstable phase between signals. So these are clear indications that a system has looseness. So, through signal looking at the signal in the time domain I will see very very high amplitudes overloads occurring repeatedly overloads occurring though you do what is known as an auto ranging etcetera. But if you look at the signals in the time domain their features their features may be very high the mean the RMS values will be high. But again in the frequency domain a very easy way to find out such defects is the occurrence of harmonics sub harmonics and the reason behind harmonics and sub harmonics is because of the fact that the signals almost look like square waves they are truncated they are clipped and then because if things are rattling moving around there will be lot of beating occurring and then there will be unstable phase between signals because these signals are have no constant basis of generation in the time domain. I mean in one instance one virus in signal is coming out another instance another virus in signal is coming out because an impact has occurred. So, they all give us to a signal which has lost is stationarity is another definition by which we can also find out looseness. Now once we have all the techniques of non-stationary signal analysis non-stationary signal analysis can be done to detect such defects. And what are the non-stationary signal analysis we will go to them I will I will before that I will before coming to rub I will I will conclude this in the sense in the non-stationary signal analysis we can do what is known as the STFT I can do what is known as the wavelets. And these are the two important techniques which can be used to find out looseness though in this course I will not go into the details being the very basic course on STFT and wavelets I will not go in the details of this. But, however if you want to know more about this you can refer to my website IITnoise.com or you can contact me over my mobile or you can also email me these are my contact details if you want to know more about these non-stationary signal analysis STFT and wavelets. But this is not in the domain of this course however this being in the web if anybody is interested to know about more about non-stationary signal analysis they can contact me at this website or through my mobile or email. Now, another very important characteristics of this looseness signals is that they will be associated with noise because things are hitting against each other. So, they will be impact noise and this noise can again be captured by a certain process which are total of the SPL. But now it is techniques of acoustical holography are available by which the sound field can be detected say for example, I have a machine and there has been some defect inside. So, it is radiating noise. So, what I can do I can bring about another plane around it I can do the noise measurement either through an array of microphones and when this microphones are located at every grid location. And they can we can do a special transformation of the sound field by using such an acoustical holography technique and if there are defects in the machine and then the noise will be removed then the noise can be of a very high level. And if I look at the sound field for every frequency I can get some maps special noise map. And because these are non stationary these maps are going to change these maps are going to change. And this is an advanced fault detection technique which is being used to know from the sound field what is the noise which is getting generated. And we can then detect looseness in a system, but sometimes we purposefully have things made loose for example, a rolling element bearing. There is a cage or a retainer which sits on the between the races these retainers are actually riveted. However, they are free to rotate, but the purpose of the retainer is ensure no two rolling elements come in contact. But then they are loosely rotating if the shaft is rotating they will be spinning at their frequencies. And we will come to each other if this retainers were not there or the cage or the retainer. If this cage or retainer was not present what would happen is these two rolling elements would come and contact with each other. And that happens when if they are two balls spinning at high speeds and come in contact with each other there will be lot of wear they will get deformed. And then they will be not perfectly round and then they will have more friction and then more noise more vibration. So, and that is what we are coming to the next topic about rubs. And if these things are rotating so we should avoid and come back to this rubs. So, in a machinery if anything is contacting each other rotating devices are contacting each other they will rub against each other rubs will occur. And I just told you the case of a rolling element bearing where if the cage or retainer shown in red was not present these two rolling elements when they were spinning and rotating they would come to and touch each other and then they will be severe wear because of hersian contact because of hersian contact stresses would be developed. And they again they same phenomena will occur they will be because of this excessive forces load they will be high stress there will be wear increased friction and then there will be of course, noise kind of a streaking noise. So, this would happen and they will be speed dependent this kind of happens. So, we should avoid this rubs to be occurring. And then I will while I talk about rubs I will also tell you when I talked about machines many a times this looseness will also introduce the two parts either rotating or sliding or stationary come in contact to each other. And these machines are usually usually I am not drawing the other side which is hidden usually are having a foundation. So, because of this foundation being loose we call this as a soft foot. Now, soft foot can be very easily determined by what is known as an coherence analysis coherence analysis. And how this is done is suppose I will just name them 1, 2, 3 and suppose I have another transducer at location 4. So, what I will do between transducers 4 and 1, 4 and 2, 4 and 3 I will find out what is known as the coherence function. And how does how this coherence function between any two signals x and y denoted as. So, gamma x y is nothing, but S x y by S x x times S y y and this is actually denoted by a square because of the square term. And the value of this is 0 x y square as than equal to 1 and this is known as the coherence function. So, the value of this is in frequency domain does not want. So, when I measured in this case when I measured the coherence you will see this may be if this is loose. So, for example, this loose number 3 is loose or having a soft foot this could be of the order of may be whatever is the 1, 2, 4, 1, 2 of may be 5, 6, 6 and you will see that the vibrations at 3 is no way related at 4 because they are not connected to the system because it loose this could be very, very low. So, this gives us an indication that something is wrong with this machine this foot and then it is not producing a coherent signal at 3 at 4 is not because of 3. So, this says coherence function actually relates one signal to another and just by measuring I can measure them simultaneously or you can measure them by a dual channel signal analysis one at a time. Suppose, your x is 4 y could be once 1, once 2, once 3 and then you could be doing this computation of course, the modern FFT analyzers have this functions built in. So, you can measure the coherence and if there is a soft foot the coherence would be poor in the given frequency domain. So, this is another way such coherences can be detected and then in fact, coherence also has a very important application in experimental model analysis because if I have a system mechanical system or a machine. Suppose, I am getting some output y which is the response because of some input x is the excitation and to know whether this system I can measure gamma x and if this value is I know mostly that the response is because of the excitation and those of you know signal processing or vibrations you know this will be the resonance because at resonance you require very less force to excite and to get a response that is why there are dips in the coherence function. So, this means that the response y is only because of x if I have a good coherence and this is actually very much used in experimental model analysis. I will not go into this in detail, but coming back to the phenomena of rub because this looseness create rub. So, the characteristics of this rub is once for per revision contact for example, blades with casings and rub has lot of detrimental effects. For example, if you think of the turbine of an aircraft the compressor which looks like this in the outside rub blades I will not draw the entire set of blades and so on. This is the rotor casing or the compressor casing and these are the sets of blades. Then because of a misalignment this touches this edges touches this casing. So, if there is a rub there will be fatigue failure there could be high heat generation. So, though the tolerances are very very close you know may be less than 1 centimeter in a in a in a gas turbine engine of may be 2 meter diameter this could be about 2 meter diameter and then this clearance is even less than 1 centimeter and these things rotate at a may be 30,000 rpm. So, you can imagine the serious consequence they will have if the blades touch either and so this rubs are to be avoided. Then this could be because of my bearings which are supporting the long shaft because in an aircraft engine the series of blades the low pressure compressor the high pressure compressor etcetera the combustor and then the turbines of course, which works on the principle of the Britten cycle particularly the gas turbines. So, I will have air flowing in and then combustion and exhaust gas and that gives the thrust, but imagine if these casings touch against each other. So, we should avoid you may be in the class class of turbines I will show you a picture of how this compressor blades look like and how close they are. So, this has to be taken care of. Now, some of this because this looseness and rubs the interrelated how do you detect this looseness many times in many systems what happen the series of belts and then there will be series of pulleys and there will be belts going all over the system and they are all rotating in a particular direction with a linear speed. So, if the belt was not slipping of the pulley was not loose what would happen the relative speed between them is 0 and this can be very easily detected by a what is known as if you flash a strobe light by a strobe scope. So, basically you flash at a frequency which is equal to the rotational speed. So, the belt would look to be stationary on the pulley. So, I have exaggerated this gap. So, between this the belt would look stationary and such can be used to detect looseness if they were not stationary this would gradually look to be sliding on the strobe scope image. I mean those of you who have particular the engine fan belt if it is slipping over the pulley they shoot a strobe light onto the engine fan belt and kind of find out this kind of things. So, this analysis of impact and rub vibration signals which are created because of the looseness are non-stationary in nature and conventional FFT is not appropriate. Non-stationary signal analysis like STFT or wavelets need to be used and another important thing we have to keep in mind that usually because of a rub which has occurred because of a loose signal sorry because of a loose component they will manifest as a vibration excessive vibrations and because this 1 x etcetera will be high people many a times misunderstand them as unbalance and misalignment. So, we have to careful against that while measuring such rubs because of loose components in a machinery. So, associated problems like I told you soft foot belt looseness and bearing damages may occur if this loose components go undetected they will give excessive forces onto the bearings and then there will be problem bearings will eventually get damaged. So, one lead to other and that is the most important thing in condition monitoring if you are not careful the very first time you may another disease may develop into more severe disease and it will be difficult for somebody to diagnose. Thank you.