[MUSIC] Hi, and welcome back. In today's module we're going to go over how to estimate the endurance limits. The learning outcomes for today's module is to understand the factors that impact the endurance limits and learn resources and techniques for estimating marin factors. So, Estimating the endurance limit. The endurance limit for your operating component is often different than the endurance limit that shows up in the test data. And that's because your test specimen is typically tested in a lab at room temperature. It has a mirror polished finish and it's tested in this very nice air. We are operating component like in a car engine it's going to be operating in a higher temperature. It's either hasn't machine or a cast surface it has not been mirror polished and so there's a lot of differences between. What you see in the test data for an RR Moore rotating beam specimen and what's actually going to happen in real life. And so there are these methodologies and resources to estimate your endurance limit for your actual operating component. So your component in the actual conditions that we'll see in service. Now, keep in mind that these procedures and methodologies have been estimated from data that has high variation. And so it's always a good idea to increase your factor of safety when you're dealing with fatigue and so again, validate with testing. So a couple of definitions. Se prime, that's the endurance limit that you would see of the rotating beam specimen. So that's the endurance limit you would get from testing in these pristine conditions. So hopefully you have data from Se prime. Most steels have test data for Se prime and the MIL HNDBK 5J. You might have a in house, there's some ASTM standards and ASME handbooks, so find the data if it's there. Now, if it's not there you can estimate Se prime on using the equations to the left and that's for steels and it's based off of a number of test run on a number of different steels. And it gives you a rough estimate of what's the pristine endurance limits would be from testing. Okay, so there are these things called Marin Factors. And what these factors do, they were discovered by Joseph Marin and they are factors that will adjust to the endurance limit estimated from your pristine, rotating being test specimen to the endurance limit for your actual operating conditions. So, rarely are your actual operating conditions mere polished. The Marin factors are going to come in, and they're going to reduce the endurance limit you found in test to what's more appropriate for your operating conditions. So there's a number of Marin factors and you can see your actual endurance limit for your operating conditions. That's Se, is equal to ka, times kb, times kc, times kc, times kc, times kf, times Se prime, which is the endurance limit that you found in testing in pristine conditions. And all of these Marin factors account for differences that could occur from testing to operation. Such as differences in surface finish, in size, in loading and the temperature, the reliability and then there's this miscellaneous effects factor. Okay, so let's start with ka, which is surface finish. So, typically the test specimen have been polished, sometimes mirror polished and in reality and what's your designing leg the mirror for a satellite telescope. Your specimen is not going to be mirror polished. So, there always flaws that occur in surfaces due to surface roughness. The stresses are very high at the surfaces, and service flaws, and surface roughness. Adversely impacts your fatigue life and your fatigue behavior. It's dependent on the tensile strength of the object and how rough the services, the surface of your component. And there's a number of resources that you can use to determine ka. From Shigley's mechanical engineering design text book to the fundamentals of machine design text book. Johnson wrote a great paper called Specifying A Surface Finish That' Won't Fail in Fatigue which has a lot of great resources. And then a lot of companies use in house data to get their ka estimates. Here on the left, you can see a figure and it kind of shows the relationship for steels on the increasing strength along the X axis. And then the surface factor is shown along the Y axis and you can see for a mirror polished steel, there's going to be no reduction in endurance strength. Your ka will be 1, for ground steel, you'll get somewhat of a reduction in endurance strength that will increase as your strength goes up. And then for stuff with a rougher surface, you get a quite a reduction in your endurance limit. So, here you can estimate this relation using the equation ka=a(se)b. A and B are constants based off of data that can be found. There's a chart for in Shigleys machine design textbook That gives you these constants. And if you just plugged in, you could see a mirror polished specimen for a 97 ksi straight strength steel has a ka of 1. A forged specimen of 97 ksi steel has the ka of 0.41 And that's quite the difference. So, the forged steel is going to have 40% of the endurance limit as the mirror polished steel, which is quite the reduction. So surface finish is very important to take into account. There's also a size effects, so if you look at a cylinder that's rotating. In either torsion or bending, it has those those uneven stress distributions, where the stresses are really high at the surface and really low in the middle. So the smaller the cylinder, the less area in these really high stress distributions. Where the larger the cylinder, the more material there are in the high stress regions. And when it was found is that. You get a decrease in the amount of endurance limit. So, it decreases your endurance limit as the diameter increases and you get more and more material in theses high stressed areas. There's more and more chance that you'll get a flaw in these high stressed areas, so more adverse impact on your endurance limit. You can estimate the kb factor for cylinders that are rotating, utilizing these equations right here. And this is really important for axial stresses, you have an even stress distribution. Which means that the size does not impact the endurance limit for an axial stress. So, in an axial stress, your kb is going to be equal to 1. Okay, the next is load effects. So, most of the testing done for endurance limits has been done in bending, in that rotating beam for point bending test. And so kc = 1 for all bending tests, or for specimens in bending. because most likely your test specimen isn't the same type of loading as your actual operating specimen. Now, for axial and torsional loadings, that's a little different. So, axial loads would have all of the material in a high stress gradient. All of the materials in the high stress areas, because the gradient is constant, so there's no gradient and the stresses are constant across the cross section. And that causes axial components to have slightly lower endurance limits. Torsional component, you can see if your component is in torsional loading. You're going to reduce the endurance limit by 0.58 or if you'll multiply it by 0.58 and that's due to do the Von Mises or distortion energy theory. So, you need to make sure before using these load effects that your actual test data has been done in bending. If it hasn't been done in bending, then these loading effects don't apply. These loading effects apply for test data that's been done in bending. Okay, temperature effect. So, just like your ultimate and tensile yield strengths decrease with increasing temperature. The same mechanism happens in fatigue and your endurance limit will decrease with increasing temperature. And so typically, what people do is they'll use a ratio of temperatures and they'll go off. If they have it, they'll go off of data for a tensile test at temperature, and they'll say the strength at temperature divided by the yield or ultimate strength depending on, if this was a ultimate or yield on strength. And so if you have data that shows the temperature profile per tensile strength. You should absolutely use that. If you don't and you're working with steels, you can use this equation right here, from Shigley's. And this equation is a fit based off of a graph that looked at data across. I think it was 40 different steels and the behavior at temperature so its going to give you an approximation. But if you have data for your specific steel or your specific metal you should always use that. And then finally, fatigue data has a variation in it. And the more reliable you need your component to be in service, the less variation is allowed. So there is this kd factor. I'm sorry ke factor that should, that reduces your endurance limit based of of the level of reliability you're looking for and note that it's a significant reduction. So if you need to be 99.9999% reliability, your endurance limit is going to be multiplied by 0.62. So it'll be 62% of what your initial endurance limit was, it's quite the reduction. Some other things to take into account is residual stresses, types of plating, corrosion, these can all impact your endurance limit. They're aren't as great methodologies for estimating these, so testing becomes really important in here. Some companies have in house test data for these types of failure modes, but if your in an environment that is going to have high corrosion or your dealing with parts of high risk residuals stresses. You need to reduce the endurance limit because of those factors as well. All right, so what we did this time is we figured out how to calculate the endurance limit and we already knew how to compare the endurance limit to the stress in the part. So, what we're going to work through next time is an example where we have this rotating shaft in fully reversed bending. And it's simply supported and they say they need a reliability of 99.9% and it's going to be operating at 600 degrees F. So, it asks you to determine the fully adjusted endurance strength. Which is the operating endurance limit of your parts. Okay, so that's all we have for estimating the endurance limit. We'll work through the example next time. [MUSIC]