 Hi everyone. In this video I want to talk a little bit about threaded fasteners, threaded components, but mostly focus on power screws. I'm not going to spend much time talking about threaded fasteners, mostly because when we analyze threaded fasteners we primarily treat those as cylinders, and we generally assume that it'll be sufficiently threaded that we won't have to worry about stripping the threads. So we might talk about shearing of screws, but again in that case we're only really treating them as cylinders of a given diameter. So with that in mind, power screws really just have more going on, more things of interest to talk about. We shouldn't discount threaded fasteners though. The book gives some interesting information where it talks about how screws, bolts, things like that are probably the most common component that we would find. And it says that in a typical airplane we might expect to find somewhere around 2.4 million threaded fasteners, and that it often represents 3% of the cost of an airplane. So for something like a standard like a 737 that would be somewhere in the neighborhood of 1.5 to 2.5 million dollars in screws and bolts. So they're not something that should be taken completely lightly. They are important components. Just when it comes to examining them from a from a failure standpoint there's not as much new information for us to look at. So I want to talk a little bit about power screws. Power screws are threaded rods, threaded components that transmit power, turn torque into linear translation. They also can be used for fine positioning. So something like a linear stage, I might have a little dial that I turn that very minutely position something. That's something I used to do a little bit in my PhD for some stuff I was doing there. And they're really just useful. And the one common thing that we might look at because it's a good example is something like a floor jack. So if I have a screw type floor jack it's useful because it's pretty easy to understand that we have a weight applied down on something and then we turn a screw to raise or lower it depending on what we're doing. So if we talk about threaded fasteners a real key thing that we want to think about is how the geometry of the thread affects what we're doing. And for a lot of things we might stick with kind of a standard ACME thread. And an ACME thread really has a similar to like a screw profile but something like this. And the standard ACME thread is going to have an angle here of 14.5 degrees. So that's kind of our standard for this. And this is alpha, the angle alpha when we when we do our equations. So if we're taking a screw and we're using a screw to transmit a torque, so torque used to turn the threaded screw into a force applied to something, we have to think about how we actually look at this. So let's say we're looking at and I'm just going to kind of pretend that we've taken a screw thread. I'm going to exaggerate the angle here a little bit. But suppose we have a screw thread that we've unwound from our screw and kind of flattened it out. So we're looking at it. So if I have a screw and I have a thread that goes around this you know in a helix and I've taken one turn of that screw and unwound it and then laid it flat on my screen, it would have a slight angle to it like I've shown in the picture here. And this slight angle, so let's suppose I draw a center line through this. If I gave a triangle and drew this out I'd have an angle here which we might call gamma and I'm going to move this gamma because it's in the way of what I want to write next. So we have an angle gamma and we have then a length which is going to be in this direction and that's going to be pi dm which you might recognize basically as circumference. So it's if we wrapped this around the shaft of the threaded rod. One time we'd have one circumference and then we have what we're going to call l which is basically the change in position in the axial direction as we traverse one thread around. Now another thing that we want to look at is if I looked at this from a side view I'd have my thread like this. Now I said up here that we have an acme thread with an angle alpha of 14.5 degrees. Now the trick here is that when I look at this angle of 14.5 degrees really what I'm doing is I'm looking at the thread from a straight on axial view. So I've cut through the thread this way and I'm looking at it from the side there. If I rotate my head slightly such that I'm looking at a cross-sectional view of my thread like this is drawn then my angle is slightly different and the angle I'd have here I call alpha sub n. So it's just like a very slightly rotated view of that thread angle. So if I want to think about what it takes in order to turn this screw and transmit a force then I'd have to zoom in on a little piece of material sitting on this thread and kind of treat that as a free body diagram. So that piece of material has some weight of say my load using that screw jack example. I have a weight of a load pushing down on it. I'm going to have some force of friction applied. I'm going to have a normal force where this is touching my screw surface including an angle in here to rotate this out slightly to you know say like a normal to the surface or to the ground and then rotate it for my angle of my thread. And then I have some driving force which is pushing this forward let's call it q but it's not really important what it is. So if I can if I perform an equilibrium analysis of this in let's say the the tangential and axial directions I can use that to come up with you know my torque. And I'm not going to walk through that whole analysis because the derivation of it isn't really that important for us but there are a few things that are of interest. One is that we can calculate this angle alpha sub n as equal to the angle of our thread which if we're talking acme would be 14.5 different thread pattern might have a different angle. And this angle lambda which is basically the the the thread angle so you know a horizontal thread wouldn't be very useful it'd be straight across with an angle of zero straight across our screw that's not terribly useful but we have some angle lambda which is our thread angle. Then what I get as a result of this equilibrium analysis is if I want to raise my my part up I get something that looks like this. See if I can write it without making any sign errors. And so we can look at you know some of what we have in here we have the weight so that's our force or our load that we're lifting we have our diameter over two and then we have a friction coefficient pi diameter again l which is that that change in position as we lift the one through one rotation cosine alpha n uh over pi dm cosine alpha n minus mu l. And this is to raise to lower we see basically the same thing with some sign changes so raising the load versus lowering the load and of course we expect those things to be different in one situation we're fighting against gravity in the other situation gravity is is helping us. Generally for this type of equation we might expect a coefficient of friction in the or for this type of application a coefficient of friction in the order of 0.08 to 0.2 so that's just kind of a broad range there and we also might have bearing friction so we have to have bearings for to be able to rotate something and lift a load without rotating the load we have to have a bearing and so if that bearing friction isn't negligible we might have to add a term for bearing friction where we have weight again mu sub c which would be like coefficient of friction for the collar or or where the bearing is diameter of the bearing and all over two. So great we have some equations for raising and lowering we could also calculate efficiency it's on the page on on canvas or on our website so I'm not going to on canvas so I'm not going to spell that out but we have efficiency that we could calculate in the same way. Now I want to take a look at a little example so suppose I have let's see if I can draw this all here. I have a screw jack if I can talk and that's my bearing and sitting on this bearing is some sort of platform that's going to act as the thing that raises my load and up here I have my load let's call it a thousand pounds so this is where the bearing is so give it a collar diameter of 1.5 inches I have an interface between my my threaded screw and my collar that's going to ride up and down that and we'll say that the screw has a diameter of one inch we have a collar friction of 0.09 we have a friction at the thread of 0.12 and we'll say this is a one inch akme double threaded then you know what we could imagine and again this is a kind of a rudimentary thing but let's imagine we have a handle attach this thing and that's where we apply you know some force in order to turn this and thus raise our load now of course you know most likely this isn't turned by hand we probably have a motor attached to it and we're rotating it and and all that so what we want to then find is okay what torque do we need in order to lift this thousand pound load using using our screw so the first thing we need to do is we can look in the lookup table I think it's table 10.3 in the book and what we find is that for a one inch diameter akme threaded rod we would expect to have five threads per inch and this gives us a pitch of 0.2 inches great now for double threads what this means is that the the l or if you remember from my drawing above that l is the the amount of distance that I expect to move as I travel one turn around for a double thread that's going to be equal to two times p so because we have two threads going on at the same time we're raising our load two times p or in this case 0.4 inches for one rotation of that thread now we can find our major diameter if you refer back to some of our geometry from the textbook we would find that this is equal to d minus p over two which in this case then would give us a a d sub m of 0.9 inches and we can start calculating from equations lambda and you know referring to the geometry we had before I can do the arc tangent of l over pi dm this is just using that angle that we showed in the just a few minutes ago so this gives me 0.4 over pi and we get something in the range of 7.63 degrees great small relatively small angle from this we can calculate alpha sub n that I described so so arc tangent of tan alpha cosine lambda and plugging in our values if we're talking acme then we're talking tangent of 14.5 cosine 7.63 and this equals 14.38 degrees so 14.38 degrees is not all that different from 14.5 degrees you know where I said that the angle changes slightly because it depends whether we're looking at the thread from a side view like this or from a side view like this because that angle lambda is so small the difference is actually very small in those two angles so it actually probably doesn't affect things too much but you know we still want to be be accurate so from that then we can basically just plug and chug into our equation that we just looked at so without rewriting all the variables we have our weight of 1000 pounds times we were given our friction collar error so that's l times cosine of alpha sub n pi 0.9 cosine 14.38 minus 0.12 times 0.4 now because we're given collar friction we can probably assume that we can't neglect that so I have to add that term on 1000 0.09 for friction 1.5 diameter over 2 and if I calculate all these values out I get something like 124.6 inch pounds plus 67.5 inch pounds for the collar so comparing those two you can see that the collar friction is not particularly negligible it's you know roughly 50 percent of the the screw friction and what's needed there so not really negligible 192.1 inch pounds so that's the torque necessary and I used the the right raising equation in order to do that so that's the torque necessary to apply to my screw in order to raise my load 192.1 inch pounds now it's important to realize that the frictions here are typically like running friction so it's it's dynamic friction we can expect a little bit higher you know if we're starting from not moving at all you can probably increase that by about 30 percent in order to get the the starting friction now I could also look at what it takes to lower the load so this was for raising this we can do the same thing for lowering which if you recall the equation was changing some signs on our on our in our equation so I'm not going to write that all out but I'll show the numbers here what we end up finding is minus 4.74 inch pounds which you might ask well what does that mean that it's minus well minus would actually then imply that we actually have to apply a torque to slow it down otherwise setting the weight on our on our screw would just drop it to the ground right there's not enough friction there to hold it up but this is the value without considering the collar friction so we can add the collar friction in 67.5 inch pounds and that you know in theory should hold the load so we get 62.8 inch pounds in total necessary to lower our load now really you know that that torque that we're putting in then really all that's doing is overcoming friction in the collar right because it was negative on the screw and we're just basically assisted by gravity and lowering that down all right so that covers what I want to get through for power screws the main thing to remember is that you know we have to take some geometry into account we we have to consider friction whether or not it's it's negligible in the collar as we saw in the example it's probably not negligible in a lot of cases but you know it's one of those things that sometimes we neglect and then ultimately one thing that was kind of interesting was that we saw you know it is possible that we actually don't need any torque to twist to lower our load you know it can just in theory free fall if the load is sufficiently high it would just just push the screw down and that would be important to know right we'd want to know whether or not it's that's going to happen all right thanks