 Hello students, I am Bagesh Deshmukh from Valchand Institute of Technology Solapur Mechanical Engineering Department. This session is on endurance limit, the method to obtain the endurance limit by approximate estimation. At the end of this session, we will be able to calculate the endurance limit by approximation method. Dear students, what is the necessity to use this method? You may think upon why it is necessary to use this approximation method. You may recall what were the issues regarding the method by R R Moore, the laboratory method. We obtain the endurance limit by the method on the x axis we have taken number of cycles and on the y axis we have taken the amplitude stress. However, what has happened? I need to take the first trial, obtain the first point. I need to take the second trial, obtain the second point. Every time I need to change the component, because the component is the specimen instead of saying component, it will be better to say the specimen because it is a laboratory method. Component which is to be used in the service. It is basic difference between specimen and a component. The method of R R Moore is used for specimen rather than the component. That means I need to use first specimen, throw it away, second specimen, get the value, throw it away, third specimen, get the point by S and N value, get this point. Same thing I need to repeat for the next, get the next point. For each point I need to use a different specimen. Then draw this curve, then obtain this line and then get the required value of S E. This is for specimen. The method as seen over here is time consuming, laborious and there may be variation in the answers obtained by this method. Therefore, it becomes necessary to use some different method. Let us see the next method which is called as the approximate method. Then how to use this approximation method? I need to use two notations. I need to first correlate S U T value with S E somehow. Then how to correlate it with S E? I need to use the equation S E dash equals 0.5 S U T if it is steel. This is the standard relation that we can use. That means with the help of the mechanical property, because S U T we can call it as a mechanical property, we can correlate S U T to S E dash. Then what is S E dash? We are going to use the notation, the symbol S E dash is the endurance limit of a specimen and S E is the endurance limit of a component. Dear friends, our interest is a component. R R Moore's method was useful for getting the endurance limit of a specimen. What we are doing? Here we are using the approximate relation of S U T and S E dash. We are correlating it with S E. How to do this? I need to use few D rating factors. Then why I have called D rating factors? Dear friends, S E dash is the endurance limit of a specimen. The specimen is highly polished, then it has a size, the minimum diameter is 7.5. The expected reliability for the test of R R Moore is 50% and there is no further notch in the component. Therefore, this value is of ideal specimen. If I am going to correlate it with the endurance limit of a component, I need to use D rating factors as K A, K B, K C, K D and if I multiply these four factors with S E dash, then I am going to get the value S E. Here S E is of the component. My interest is to get this S E value. Then how to get this? K is going to reduce this value of S E dash, K B is also going to reduce the value of S E dash, K C is also going to reduce the value of S E dash, K D is also going to reduce the value of S E dash. Therefore, these factors are called as D rating factors. What is going to happen? That S E will be always less than S E dash or in ideal case, S E equals S E dash. Therefore, all these factors, the highest value will be equal to one. In normal cases, the values are less than one or in fraction. Let us see various factors. The first factor is the K, which is called as a surface finish factor. If I am going to use this surface finish factor, I already told the necessity. The reason is the component is not polished as that of the specimen. Therefore, I need to use this K factor. Let us assume that the tensile strength of the component material is 800 and the method of manufacturing is this line, the forging. I need to then move up. I need to find out this intersection. Let us see the intersection over here. With this intersection, I can get on the y-axis what will be the surface finish factor. Therefore, K, I can get it from the chart. You can see over here, if the component is polished, the surface finish factor is going to be equal to one because it is ideal case matching with the specimen. Let us see the next factor, next derating factor, which is called as the size factor. There is a typical chart given for the size factor. The normal case, the dimension was 7.5 for the specimen. However, there can be varied dimensions of the component in practice. Therefore, there can be different ranges taken. Ideal dimension less than 5 or equal to 5, 7.5, the KB value, the size factor is going to be equal to one. It is the ideal case. In case the dimension under consideration, I am calling it as dimension not the diameter, if the dimension is greater than 50, then the factor is going to be equal to 0.75. However, if the dimension is not known and you are going to find out the dimensions, in that case of ambiguity, you may assume the value of important dimension to be existing in 7.5 to 50 and refer the value of size factor KB as 0.85. Therefore KB, I can say that it can be obtained from the table. The value is 1, it can be up to 0.75. This is the second factor that has been considered. Let us see the third factor. Third derating factor is the reliability factor. The RR Moore's method, it was developed on the basis of 50% reliability. However, in service, there can be different requirement of the reliability. If the reliability is 50% as in ideal case, then the reliability factor is going to be equal to 1. However, if the reliability of the component which is to be kept in the service is going on increasing, increase, this value is increased, the factor is decreasing. Then KC, the value, this is given in between 0.659 to 1 as per the reliability required of the component. Remember, if the reliability is not mentioned in the numerical, if it is given, you may assume that it is based on the 50% reliability. However, in practice, if you need higher reliability of the component, then the designer has to choose the higher reliability thereby reducing the reliability factor. Then what will be the effect of it? If I am using the less number, this number will be lesser for higher reliability, I am going to estimate SE, SE will be lesser in that case because this factor will be 0.659 times this SE dash. I am going to derate this value, I am going to design for the lesser value so that the components dimension will be higher than that of the reliability equal to 50%. In that case, I am going to design the component on the higher end, higher side, the dimension of the component will be larger for the increased reliability. That is what is the significance of this factor. It plays very important role when we design the component. If the reliability factor is going to, reliability is increasing, the factor is going to be decreasing and in that case, the SE value will be going on decreasing as compared with the standard value of SE dash. SE dash is the endurance limit of a specimen and SE is the endurance limit of the component that is to be kept into the service. Then after this, there is the fourth factor which is going to be considered for the design. It is the modifying factor. Modifying factor KD equals 1 upon KF. Then what is 1 upon KF? KF we can say that KF is 1 plus Q into bracket KT minus 1. And in this equation, QE is the notch sensitivity, KT is the theoretical stress concentration factor. Dear friends, it is important if there is no notch, there will not be stress concentration then this factor will be equal to 1 in that case. That means there will not be any effect of this stress concentration notch on the endurance limit of a component. The value in that case will be KD you need to check upon. Then after, if I say that how to get this value of SE, SE will be equal to KAKBKCKD into SE dash. This is what is the final formula of the endurance limit. We are considering only four factors, there can be more factors, however we have limited our scope to only these four factors. It is going to give me the endurance limit of a component which is subjected to this bending. However, if the component is subjected to axial loading then SE for that axial loading condition load axial varying load or fluctuating or reverse load I need to take it as 0.8 times SE. This is also one of the important relations that we may need to use while solving various problems based on this reverse loading. This method is called as the approximate estimation of endurance limit. You may need to use this method many times. Thank you. Thank you.