 Hi everyone. In my last video I presented the Lewis equation as one method for analyzing gears. At the beginning of that video I also laid out all of the limitations of using the Lewis analysis and the assumptions that it makes. So in this video I want to talk about a variation on that, which is a slightly more rigorous stress analysis for gears. So where previously we had an equation that looked like this using what is called the Lewis form factor, and then we compare that against Sn from fatigue. Instead now, as we have with other components that we've talked about, we're going to describe a method that uses more experimental basis in order to determine whether or not we should expect failure and do our stress analysis. So for this new more rigorous form our equation becomes fp over bj kv kokm. And our fatigue analysis becomes slightly different equal to Sn prime clc gcs krktkms. So you may notice that my fatigue equation has changed a little bit. I've added a couple of new terms, new factors onto this, and therefore it takes on a couple different things. And my stress equation for the gear has changed. I've replaced the Lewis form factor with j, which we call the geometry factor, and then I've got some new k values here that are taking into account some other stuff. So in this equation, as I just noted, j is the geometry factor. We read this from figure 15.23, and basically what this is doing is it's taking into account that that Lewis form factor that we've already discussed, but now adding in some consideration for stress concentrations at the fillet locations. We have kv, which is a velocity factor, figure 15.24. This factors in the fact that these teeth, when they come into contact, they're moving with some velocity. So you have a little bit of an impact loading there. Take some of that into account, and it's dependent on the velocity, the speed, rotational speed of our gears, and also the precision of our gears. ko is an overload factor read from table 15.1. This allows for variations in driving torque. Depending on how stable our input driving torque is, that can vary what we see there in the overload factor. In this equation, the last one we have is km, which is a mounting factor, table 15.2 from the book. This takes into account gear alignment as well as face width. The gear is, if perfectly aligned, you remember when I talked about the Lewis equation, that the assumption is that the force is evenly distributed across the face of the gear tooth, where that's not always the case, and often not the case. So this mounting factor takes into account possible misalignment of the gears, as well as the width of the gear, which exacerbates any misalignment. The wider the gear is, the more problematic misalignment would be. All right, so I have these factors built into this stress equation. Now, in my fatigue analysis equation, I have a load factor, which for most gears is going to be equal to 1. I have a gradient factor, which is going to be equal to 1 if p is greater than 5, and 0.85 if p is less than or equal to. We have a surface factor, which we can actually read from figure 8.13. So that's back in our fatigue chapter of the book. We have a reliability factor, which we can pull from table 15.3. We have a new temperature factor, and this is related to the temperature factor that we had for steel, but slightly different. Equals 1 for temperatures less than 160 degrees, and equals 620 over 460 plus T for temperatures greater than 160 degrees. And finally, we have a mean stress factor. So mean stress allows us to take into account what type of gear we're talking about. So it's equal to 1 for idler gears and equal to 1.4 for input or output gears. So what this is doing, what this mean stress factor is doing, is basically taking into account how that gear tooth is loaded. So an idler gear is a gear that's mounted in between two other gears. So it's transmitting say an input to the idler gear. Maybe I'll draw a little picture here just to show what I'm talking about. So this might be in, this might be out, and this is my idler gear. Sometimes it's used just to change the direction of the output. So if two gears are mating together, one's rotating clockwise the other counterclockwise, the idler gear might be used if you want both to input and the output to rotate clockwise. It could be used for a number of other things. But the general reason we need to talk about it here is that an idler gear is making contact with two other gears, which means that any one tooth on that idler gear as it comes into contact with the first gear bends one way and then it comes into contact with the other gear and it bends the other way. So it's seeing a much different state of stress than an input or output gear, which is only contacting one gear and therefore only getting bending stress in one direction. So idler gears basically don't have to factor in this mean stress while input and output gears do have to factor in the fact that they're repeatedly bending in the same direction. So we take that into account. Now beyond this really nothing else has changed. We have a new equation for stress on the gear and we have a slightly modified equation for fatigue limit, but we can calculate both. We can figure that out. We get stress in the gear. We compare that against the fatigue limit for the material and we do our fatigue analysis just like we do with anything else. All right, I'll stop there. Thanks.