Good vibrations - modeling methods part 2

What is vibration? Vibration is the periodic back -and -forth motion, or oscillation, of an object. We encounter vibration in many different ways in our daily lives. Nearly all musical instruments utilize the periodic vibration of mechanical elements to make sound. For example, pianos and guitars use the vibration of a string and connected soundboard, clarinets use the vibration of a small reed, and trumpets use the vibration of the player's lips. The vibration also exists in nature and the motion of the tides is an example of a very low frequency vibration that is produced by the gravitational force of the moon and sun. This motion is an example of forced vibration and resonance in the case of the Bay of Fundy. A sudden gust of wind acting on a tall pine tree can also produce a periodic low frequency vibration of the tree, an example of free vibration resulting from an initial impulse. The wind blowing on aspen leaves produces a continuous periodic motion of the leaves, an example of self -excited vibration. Machines, because of internal and external forces, also vibrate. Machinery vibration involves the periodic motion of rotors, casing, piping, and foundation systems, all at the same time. Usually this vibration is so small that sensitive equipment is needed to detect it. To illustrate the small size of machinery vibration, we can compare it to the diameter of a human hair. The average diameter is approximately 130 micrometers, about 5 mil. This is an unacceptable vibration level on some steam turbine generator sets that are the length of the house. Vibration in machines causes periodic stresses in machine parts, which can lead to fatigue failure. If the motion due to vibration is severe enough, it can cause machine parts to come into unwanted contact, causing wear or damage. Now that's the opening of a book called Fundamentals of Rotating Machine Diagnostics by Don Bentley and Charlie Hatch and I thought it was the most fitting way to

give context to what we're gonna be talking about today. We're gonna talk a little bit about vibration monitoring in general, its use in the detection of machine faults, and then in the diagnosis of it. And then we're gonna close talking through a couple examples of ways to diagnose faults or ideally get closer to root cause by looking just at vibration. So first let's talk about what to monitor with vibration. So anything that spins vibrates. Anything that spins or reciprocates vibrates. This vibration is caused by a slight imbalance, a misalignment, or just other kind of drivers of the geometry of a machine like a centrifugal pump's impeller or say like the number of rolling elements in a rolling element bearing. These are all drivers of forces that create vibration in a machine. Now one bit of context. Large rotating machinery like a steam turbine generator set or a gas turbine hooked up to a generator will be set up to trip if it exceeds 1 inch per second in vibration. For context, your dryer at home when it's running runs way higher than that. So we're trying to pick up vibration. Vibration is very small because of the amount of energy in those machines. So with that one inch per second as a trip limit where we would typically alarm well before that, but

that mass or the energy in that spinning mass is really all the difference. And And this goes back to earlier in my career, I was involved in gas turbine design, and we saw a number of examples of these horrific pictures of the rotor of a gas turbine that's a quarter of a mile or about 400 meters down the road from the power plant because of runaway vibration. I think the most notable example I can remember is a steam turbine that an overspeed event, meaning it lost its load, so it lost its connection to the generator, and a steam turbine, when you are continually applying steam to it, there's nothing to slow it down other than the generator. So in that overspeed event it continues to spin faster and faster and faster and broke itself free from its casing and went up through the roof, down across into the field next to the power plant. So just a terrifying amount of energy there, but all the

reason why vibration is critical to pay attention to. So we're monitoring anything that rotates or reciprocates and now let's talk about how to monitor it a little bit. So when monitoring vibration there are like three different ways we can measure it. One is direct displacement, the second would be measuring the velocity, or the third would be actually measuring the acceleration itself. Now those all could be multiple different devices so displacement could be a non -contacting eddy current probe or a proximity probe but the point is it's measuring the actual displacement of the spinning shaft and then that can be integrated into velocity and then integrated yet again into acceleration. Velocity would be measured by again a sprung mass in something that you would call a velometer. It is less used today. Typically we will use an accelerometer. And we'll either use piezoelectric accelerometer that I think I talked about earlier, where you have a crystal element, you have a sprung mass on top of it, and that can detect the acceleration. And then, I apologize, when I was talking earlier, instead of the integral, we're actually taking the derivative to go from displacement velocity to acceleration, from acceleration back to velocity, and that's when we're integrating. So in any of those instances we're getting to the vibration. It's just kind of which measurement you're actually taking. It matters when you're getting into actually interpreting things. Another thing to take into account is are these measured with a wired sensor like a wired displacement proximity probe, a wired accelerometer. For larger machinery it is almost always the case because those are used for protection but for less critical machinery it becomes quite common to either do operator rounds or like we propose use one of our wireless vibration sensors and have that permanently mounted whether it's threaded on or using a mag mount or epoxied on but that wireless system

would measure at a less frequent or measure less frequently than the continuous system but all that said we're measuring either displacement velocity or acceleration it's most common to measure either acceleration with an accelerometer wired or wireless or displacement with a proximity probe. So now that we get all of those measurements in there there are a couple terms I want to talk about. First we're going to talk about frequency and just to be very clear frequency is the rate of vibration per unit time. It's measuring the amount of time it takes to complete one cycle of that vibration. We'll typically talk in cycles per second cycles per minute if it's cycles per second or hertz and that's the the reciprocal of the period in seconds. Now in frequency there are a number of other terms that are very common to use when we're talking about vibration. The first one is synchronous vibration otherwise known as 1x vibration. This means it is vibration that is aligning with the rotating speed of the machinery, or you could call it the rotor speed. So that x is equivalent to how many times it is rotating. So 1x is synchronous, 2x is 2 times the running speed of the machine. So synchronous is that first term. Then you would say non -synchronous is anything that is not 1x. Also, as you would think, sub -synchronous is anything below 1x. this could be integer ratios, it could be decimal ratios, or they end up being

subharmonics that we'll talk about in a second. But subsynchronous is anything below the running speed. Supersynchronous is anything that is greater than the running speed. So that's frequency. Now the other key piece is the amplitude. So it's the magnitude of vibration. Now at the signal level it's going to come out as like a millivolts or milliamps but then that is translated into units whether it is mils in displacement or millimeters per second or inches per second in the terms of velocity. In acceleration you would then have inches per second squared. Now on that amplitude there is another bit of nuance and since vibration is an oscillation or going back and forth you could measure it and we would use common terms like the peak vibration or a peak two -peak vibration. That would be if you were looking at a pure sine wave, so a really clean oscillation of vibration, the peak -to -peak would be the top minus the bottom, whereas the peak would be the top minus the midpoint. Another common measurement is referred to as RMS or a root mean square of vibration. So let's say for the scope of this discussion it's just letting you know that these are all, quite frankly you could view them as

engineered, featured, or calculated variables from the amplitude itself. So we have frequency, we have amplitude, and now I think the last thing I want to talk about is the frequency of measurement. And there are kind of two pieces I want to talk about here. One is the sampling rate of how frequently is it measuring that vibration, and then for that that data set, and then the one would be how frequently the vibration sample is taken. So that would be if it is continuous you could really be continually measuring that but if it were say one of our wireless vibration sensors we would have it configured to look once every hour or once every six hours taking a measurement. Now for the first part the sampling rate there's the question of how quickly is it measuring the vibration. And the reason I bring that up is there's what really in signal processing there's something called the Nyquist limit or I think you'd call it like the Nyquist frequency or a folding frequency. And really the whole point there is just noting that for sampling data that you would then run a fast Fourier transform on, half of that sampling rate is the maximum resolution that you can actually see in the FFT. And this is more of a discussion around aliasing and kind of bandwidth limitations. Really we don't have to go into great detail about that

for this discussion but I suppose the main takeaway here is how fast you are sampling the vibration measurement dictates what you can actually see in the frequency domain. And that's both kind of how quickly you are measuring things from kind of point to point from vibration point point or from that amplitude point to point and the duration of that measurement. So how that becomes a little bit more practical is looking at our wireless sensor. When it takes that burst of high frequency data that's analyzing, depending on how long that is, that's going to determine how low of a frequency you can pay attention to. So if you have a machine that's moving very slowly it may be difficult to see that in the frequency domain. So more detail than you're likely interested in right now, but just letting you know the Nyquist limit exists. Another corollary to that that is more relevant is kind of if we zoom out to like a PF interval in saying you're you're trying to detect a failure with say a week's lead time or two weeks lead time. The general corollary here is saying that whatever lead time you're looking for you need to measure at least twice as frequent as that. So if you want one week lead time you need to be measuring at least once every three and a half days. That type of thing. So last thing around that

frequency side of things. So now that we talked about some of the measurements so frequency amplitude and kind of some of the ramifications around sampling rate Let's talk about resonance, natural frequencies, things like that. So any mechanical system has a natural frequency or many natural frequencies and from a simple perspective that natural frequency for a sprung mass is the square root of the stiffness divided by the mass or root K over M if you're paying attention to the equations. This is the same thing with guitar strings, tuning forks, piano wires. It's a function of the mass and the stiffness. Now to kind of zoom out or think about another event, the Tacoma Narrows Bridge. That's an example of there was a natural frequency that was excited. So you'd have something like the Tacoma Narrows Bridge is self -excited vibration. I think earlier in in the intro we talked about the Bay of Fundy, which is more of tidal resonance. These are instances where there's a natural frequency defined by kind of stiffness or geometry and the point is with some level of excitation or an external force whether it is wind or the tides coming in you can actually excite that and you end up seeing a an increase in vibration. One last little bit around kind of resonance would be if you're driving in your car on the highway and if you open up one window it is quite common to experience

a kind of lumping or kind of a periodic sound like a low frequency driver. Now that is referred to as a channel resonance and or a Helmholtz resonance. So there's this concept of resonance and how that's relevant for us in machinery diagnostics is knowing that large machines like a gas turbine actually run In their normal running speed, so whether it's 50 Hertz or 60 Hertz, so 3000 or 3600 rpm or cycles per minute They're actually running above their first resonance or their first natural frequency So what that means is as it is starting up it's going to pass through that natural frequency and if you were to kind of stay near that natural frequency the 1x or the driving speed of the machine would dramatically increase the vibration So, back when steam turbines and gas turbines were first designed, they were actually kept

underneath their first critical. So it's really an aside, but the main point is that first critical is the first natural frequency. So when that forcing frequency is near the natural frequency, so the running speed is near the natural frequency of the machine, you end up getting a high response amplitude that that ends up being amplified and if you you stay there it ends up becoming highly amplified. That's just what I wanted to kind of note around kind of resonance but now I want to talk about how we do something useful with it and first I'd like to talk about you know what are you trying to do in monitoring things and I'd like to talk a little bit about the difference between detection or diagnosis? Now a former colleague of mine liked to use the phrase that's the answer what's the question and that quip was really talking about machine learning and applying it but I think you can just apply it as appropriately here for vibration monitoring. So the question is are you trying to detect a problem or are you trying to diagnose the cause of the problem? So detection as you're probably guessing ends up being far simpler. So from a detection perspective you can go in and say if your vibration increases from a historical baseline at a similar load or speed you can be very confident that something is causing that. Another way of putting it is vibration doesn't lie so if vibration is increasing there is a reason. A corollary is that if vibration is increasing it is very unlikely that it is just going to resolve itself and go down. So there's some kind of reason. Really that only only subset would be if there is

some type of interference or a rub inside of machine and material gets removed so that rub goes away. But if you're trying to detect, easy to do it from overall vibration. But if you're trying to diagnose, that's where it gets a little bit trickier. And that's where high frequency vibration analysis comes in. So now the last bit of this episode is really talking about examples of typical faults you might see and how one might diagnose this. Now to put some context here when we're talking in our rotating condition monitoring and our physics -based models this is essentially what we are looking at. So as we know on the detection side of things you're looking for overall levels of vibration and you know a vibration goes up there's a problem. Now there are even ISO standards for the amount of allowable vibration or a vibration severity. I think it's ISO standard 2372 and we can copy a link in here or you can google that and there's a chart that talks about good satisfactory unsatisfactory and unacceptable by machine size or machine class and that's just really an anchoring point. But so you detect a problem and then you're saying okay well what do I want to do or how do I want to figure out what that

problem is because without understanding the cause of the problem you don't really know the effective way to fix it. So here are a couple examples. The first instance of an increase in vibration you would say is due to an imbalance on the spinning shaft. Now how that shows up in high -frequency vibration is the same way shows up in your clothes dryer or your washer if it is unbalanced you get a 1x or every time that that machine spins around that heavy spot or kind of deviate or unbalance is looping around once per revolution so in an FFT or in a spectral plot you end up seeing a strong 1x component so that's the imbalance now a a different example let's say like now that you have imbalance well let's think about misalignment so you could have there are a couple different types of misalignment but suffice to say the misalignment would show up both in 1x and 2x components so imbalance would show up as 1x misalignment shows up as 1x and 2x say if you have mechanical looseness like looseness between say the steam turbine and the generator there's a coupling in between those and it's loose now that's going to show up in, let's call it harmonics, so there will still be a 1x component but you may see 2x, 3x, 4x, 5x and a way that I conceptualize this is since it's loose it's kind of rattling around so you're going to get significant variation in the amplitudes and they may vary over time because of

that looseness. Simple examples around kind of looseness, instability, misalignment. But let's think about what if we had a rolling element bearing. That rolling element bearing meaning like a ball bearing. There are elements in there that roll around. Well, if there is a bearing defect in there, we'd end up seeing an element pass frequency. Or kind of a different way of thinking about it is that damaged element or spalled race within the bearing is going to drive an additional force every time it is spinning around. And each time an element is hitting over that spalled piece in the race, it would drive the number of elements in there per revolution. A similar thing but a much higher frequency instance would be if you're looking at a gearbox and there's some type of gear defect. So again, remember this is all driven by a force and the frequency at which the force is hitting something, but gear defects could be, say, 20x or 200x the running speed. So that's really a function of the number of teeth that each gear have times the rotational speed. I think you're seeing a pattern here. If you kind of deduce back to the cause is or like if you figure out what the cause is driving the Frequency by which that force is showing up in the vibration in vibration now Something outside of the actual machine this could be electrically induced vibration and that could be a line frequency thing So you could pull that at say 100 Hertz or 120 Hertz or a different way putting it is it exactly twice the line frequency whether you're in a 50 Hz area of the world or 60 Hz. So I already talked a bit about kind of gear mesh and gear mesh frequencies, relates to the number of teeth. Something else to note around gear mesh frequencies is the sidebands around them are worth paying attention to. And really as you're getting a taste for, this is really just the start

scratching the surface of a whole field of study, but you can kind of up on the concept of vibration comes from somewhere and if you are observing the signal of how frequently that driver of vibration is occurring, you can attempt to deduce what that cause is. Similar to the number of elements in a rolling element bearing or the number of teeth in a gear, You can think about the number of blades or veins in a pump or a turbine because those are going to be a number of drivers or a multiple of the running speed as well. And that's how you can get in and you can attempt to determine if there's something like cavitation occurring in a pump or you would see something like surging or choking because you're gonna see that kind of align to the veins or the blades of the impeller. So I think maybe that's that that's where we'll we'll wrap up in talking about the concept of vibration. To summarize we talked about how vibration can be measured whether it's whether it's displacement, velocity, or acceleration. We talked about the sampling rate. Then we talked about how really none of this comes from thin air this is all being driven by some type of force and the whole field of diagnosing a problem with vibration is you look at the frequency at which the the vibration the higher amplitudes of vibration is showing up and then you use that to deduce what is actually driving it because if you can figure out what is actually driving the problem then you fix the problem rather than just putting a band -aid on it. So this is a longer episode, but this was going into a little bit more of the details of when we talk about vibration monitoring. We talked about how we would do it for a detection perspective, which is largely paying attention to overall readings, and then how you would diagnose things. And that's really looking at... you could view it as either engineered features of the vibration signature or the as High Frequency Vibration Data Analysis. Thanks.