 So in this video I want to talk about a couple of methods by which we might attach things to two shafts. Those are the two things I want to talk about are keys and pins. So keys are probably the most common method by which we might attach something to a shaft and typically just kind of giving a crude drawing of this. If I have a shaft and it has a keyway cut into it so just kind of looking at it from an end view and then around that I have something else which itself has a keyway cut into it and assuming this is well fit here we have this space now and this space is where we would place the key and the key is really just a rectangular piece of material that we fit into this slot here and we assume that the key is well sized and the keyway is sized appropriately such that we have a tight fit and the key isn't getting turned kind of diagonally across that space at all as the torque and rotation is applied to the shaft. So we're going to assume that that's a tight fit. Now generally the key is going to be one quarter in width of the shaft of the diameter so the width of the key here is going to be d over 4 and then and it's not drawn very well the scale on my picture here but the height within the shaft of that keyway is going to be d over 8 and so one half of that width. Now one of the things we may want to know then is you know how to appropriately design our key to be able to carry the torques that we are expecting it to have to carry so there's a few things to think about one we have the shaft itself and it's limiting torque so what sort of torque it's designed to carry and we know from previous analysis that we can write shaft torque as pi d cubed by 16 and we're going to assume that our limit is 0.58 sy so we're assuming that our shear yield is 0.58 sy and plugging that in so this is we'll say more or less our limiting torque for our for our shaft itself now we need to think then about the key and the key in theory can fail in a couple of different ways it can fail by compression in that you know we're applying a load let's get a different color here we're applying a load to the key do the torque of the shaft in one direction and of course an equal and opposite force there and those are more or less in line with each other and therefore it can fail by compression but of course you know really it's loaded in shear in this case at least the the loads aren't perfectly aligned they're slightly offset which means that we can fail in in shear as well so we want to check both conditions so under compression we can take our torque uh that's applied to our shaft and basically we're going to um represent that as a load and in compression it would fail under under yield stress rather than shear yield and we're going to apply it to an area which our area in this case is going to be um equal to the length of our key so whatever that length of the key is which you know we haven't designed um by d over eight so it's a side facing area of one half of the key so we have l d by eight as our area that we're applying this force to and our torque is equal to uh force times one radius so the torque out at the the plate the location of the key is basically the force by one radius so we need to factor that in there as well and this gives us a result of sy ld squared over 16 as our limiting torque we also need to look at the key in terms of shear failure to see if that uh changes anything so we can do basically the same sort of analysis and say that our limiting torque is now in shear failure so 0.58 sy times um the area over the shear now in when we shear the area we're looking at is the cross-sectional area so in this case it's a like a top-down view of the key and it's that area which which would be then l d over four rather than over eight and our torque is also at the same distance of one radius of d over two so if we if we write this out we get 0.58 sy ld squared over eight now what we can do then because ultimately we're trying to design the key and if we want to design the key uh or at least a limiting torque load for the key we can say well we want the key to fail effectively at the same time that the shaft does now really that's not our goal typically in the end but just it's a good starting point so we can say from this analysis that we've just performed if we take the shaft torque and set it equal to the key torque say in compression we can then solve for l in terms of d so if we do that by compression we end up with l equals 1.82 d if we do the same thing but now with shear take the shaft torque uh shaft yeah shaft torque um set it equal to the key shear failing torque we get l equals 1.570 so what this basically says is that if we want the key to fail at the same time as the shaft then it needs to be equal to 1.82 times the shaft diameter for uh the compression case and 1.57 times the diameter for the shear case so we can actually see that the compression is a little bit more conservative because it's prescribing a longer key than in the shear case now in reality when we design a key really we're looking at um we want the key to fail first typically uh the idea being that you know our shaft is more expensive to replace uh and the components on it are more expensive to replace we'd rather replace the key if something goes wrong and only the key so usually we would design the key to be a little bit undersized uh such that it fails first before anything else would have the potential uh such as the shaft to to shear off so um typically we're going to do that now the one other thing to keep in mind is that in this assumption by specifying the shaft torque as we did up here based on the diameter we're assuming that the shaft itself was designed to be an appropriate diameter for um shear failure however the shaft may not be designed for stress it may be designed for deflection so maybe there's a deflection requirement on the shaft which um made it smaller or larger probably larger um that is being taken into account so in that case that might mean that this torque based on this diameter is not relevant because the the shaft strength is um not designed for you know that possible failure condition so it's just something to keep in mind now with the one thing we have to be careful about is we haven't really taken into account any stress concentration due to the key way that's been cut um into our shaft so uh there's a nice diagram from the book which uh talks about this so in a in a runner style key way which you know is as you can imagine being cut by a horizontal mill we have that situation on the left hand side here and a profiled key way being cut you know by a vertical mill we have a slightly different key shape uh and and therefore different stress concentrations corresponding to that so down here we can see some some ranges of stress concentrations depending on the scenario that we're talking about anything from 1.3 up to 2.0 so this is a stress concentration introduced to the shaft by that cutting of the key way and it's it's just something to keep in mind um that we would probably want to factor that in as well when we go ahead and design our shaft and specify the stress of the shaft all right one additional thing I want to mention is pins as another really common um method of attaching things to a shaft and so briefly if we have a component mounted to a shaft a pin base typically involves drilling a hole through our two things together and then pushing or press fitting a pin a thin small pin which can be either solid or hollow into that uh into that hole such that passes through both components so we can specify the pin has a a small diameter of d and then specify our shaft diameter of capital D and in this case uh assuming you know we have a solid pin and that's of course we might have a hollow one and we can represent that but I'm just gonna for illustration say that we have a solid pin we can calculate the shear uh capacity in terms of torque of that pin using an equation that looks like this where basically we're saying we have a solid rod it's in double shear um because the torque is being applied over two cross sectional areas one at the top of the shaft and one at the bottom of the shaft and therefore we get a torque um capacity of this device that looks like this um so it's kind of the same sort of basic principle as we saw with the keys we can figure out what the torque capacity torque carrying capacity is of that pin and then do something with that in terms of design all right i'm going to stop there thanks