 Hello everyone, I am Sachin Rathod working as an assistant professor in mechanical engineering department from Valtryan Stop Technology, Swallapur. So today we are going to see the part 2 of the rolling content bearing. So already we have seen the classification of the bearing and in that bearing you should know which kind of the load is going to act on the bearing according to that we have to select the suitable type of the bearing. That part we had seen in the previous session that is the rolling content bearing part 1. The learning outcome of this session is the learner will able to design the equation for the static load carrying capacity of the ball bearing. So the introduction about the static load carrying capacity of the bearing. So you can think about this. If our shaft is stationary then how to find out the load acting on the bearing that we are knowing that to support the shaft or to reduce the friction between the relative motion between the two rotating element at that time we can use the bearing. So how to find out the forces acting on the bearing because you should know the how much amount of the forces is going to act on the bearing depending upon that we have to select the proper, we can give the proper designation to the bearing. Means we can choose the bearing that is depending upon the forces. So which forces are acting on the bearing you can think about this and which direction it is going to act. So we will see how to find out the forces acting on that bearing. So to learn the forces acting on that bearing for the static load. So you should know what is in the static load. The static load is defined as the load acting on the bearing when the shaft is at stationary. Means certain application in which the shaft is at stationary at that time also the load is going to act around the bearing. So you should know how much amount of the load is going to act on the bearing so that we can identify which bearing is suitable for that shaft. So the force or the load produces the permanent deformations in the balls and the recess which increases the increases in the load. So as we are knowing that the certain amount of the load is going to act on the bearing so definitely the deformations of the balls and the recess is going to occurs due to the load. So as the load is increases the deformation is increases. So if you observe that in this figure this is your the inner recess, this is the balls and here the outer recess is going to place. So as the load of this shaft, this is the C0 it is indicating the load is going to act in the downward position so that your the balls and the recess will get deformed. So as the load is going to increase the deformation will get increases. So what is in the static load carrying capacity of the bearing? It is defined as the static load which corresponds to the total permanent deformations of the balls and the recess at the most heavily stressed point of contact and it is equal to 0.0001 of the ball diameter. So this is called as the static load carrying capacity of the bearing load is going to act in the downward position so that your the balls and the recess will get deformed. So as the load is going to increase the deformation will get increases. So what is in the static load carrying capacity of the bearing? It is defined as the static load which corresponds to the total permanent deformations of the balls and the recess at the most heavily stressed point of contact and it is equal to 0.0001 of the ball diameter. So this is called as the static load carrying capacity of the bearing. So for finding the static load carrying capacity of the bearing you should know the forces acting on that bearing. So following are the assumptions they have made for finding the static load carrying capacity of the bearing and the static load carrying capacity of the bearing has calculated by the Stibach equations. So certain assumptions they have made for calculating the static load carrying capacity. So the following are the assumptions. assumption is that the races are rigid and retain their circular shape under the applied load. So, we are doing that, these are the inner race and the outer race. It will retain their circular shape under the applied load. The balls are equally spaced. So, if you are observing these balls which is in the cage, they are having the equally spaced and the third assumption is the balls in the upper half do not supports the load. So, if you are mounting the shaft inside of this bearing, the upper portion will not carries any kind of the load. So, these are the three assumptions they have made for calculating the static load carrying capacity of the bearing. So, for calculating the static load carrying capacity of the bearing, you should know how the forces are going to act on the balls and the races. So, if you observe this, I will use the pointer. If you observe this, this is the static load. Load is acting from the shaft to the balls and the races. That is the load is going to act in a vertically downward direction. It is indicating by the letter C0 that is the static load carrying capacity of the bearing. So, equal and opposite forces or the reaction is going to occurs from the balls to the races. So, as the C0 is vertically downward, the reactive forces from the balls is acting like this. P1, P2 that are the balls are equally spaced and from the balls, the reactive forces are going to act in the upward direction that is the P1, P2, this is a P2, this is a P3. So, these are the equal and opposite reaction is going to acts opposite to the static load. And as the balls are equally spaced, it makes an angle beta. So, this is nothing but the force analysis or the reactive forces acting due to the static load. And one more thing, as the deformation is going to occurs in the race, as the load is going to act vertically downward, the deformations are delta 1. So previously, this is our the previous figure, this round shape and after applying the load, it will get deformed by an amount delta 1. So, delta 1 is nothing but the deformations occurs in the first ball. This is a delta 2, deformations occurs in the second ball. Similarly, delta 3, so like these the deformations is going to occurs in the races. It is indicating by the later delta 1, delta 2, delta 3 respectively. So, consider the equilibrium forces acting in the vertical direction. So, as the C0, the vertical forces is acting in the downward direction, equal and opposite forces are acting in the upward direction. If you consider the vertical plane, C0 is equal to P1 plus P2, it makes an angle with the vertical plane as a beta. Therefore, we are getting P2 cos beta. Similarly, here the P2 is going to act, so here also the P2 cos beta. So, we are getting P1 plus 2 times P2 cos beta. If you observe the P3, P3 makes an angle with the vertical axis as a toys beta. Therefore, P3 cos of toys beta. Similarly, here the P3 force is going to act. So, here we are getting P3 cos of toys beta. So, simultaneously we can do all the balls which is acting the reactive forces. We can find out the static load carrying capacity of the bearing by using this equation C0 is equal to P1 plus 2 times P2 cos of beta plus 2 times P3 cos of 2 beta plus P4 if there is a ball plus P4 sorry 2 times P4 cos of 3 beta, so like this we can do depending upon the number of the balls. So, this is the equation number 1 and if you observe the relation between your the delta 1 that is the deflection in the recess delta 1 and delta 2, so as this is a delta 1 and this is a delta 2. This makes an angle beta as it is equally spaced delta 1 and delta 2 makes an angle beta, so like this I will draw the figure. It makes an angle beta, this is a delta 1, this is a delta 2, therefore we are getting the relation between delta 1 and delta 2 is equal to delta 2 is equal to delta 1 cos beta. So, from this geometry we are getting the relation between delta 2 and delta 1, therefore delta 2 by delta 1 is equal to cos beta, this is the equation number b. Next, according to the Hertz equation the relation between load and the deflection delta at the ball is given by, so this is a relation by the Hertz equation that is by the context stress theory we are getting deflection delta is directly proportional to the load raised to 2 by 3. So, we can consider the c 1 as the proportionality constant therefore delta 1 is equal to c 1 p 1 raised to 2 by 3. Similarly, we can get delta 2 is equal to c 1 p 2 raised to 2 by 3 as c 1 is a proportionality constant, here also we are using the c 1, c 1 is nothing but the proportionality constant. Therefore, we are getting the relation between delta and the p that is delta 2 by delta 1 is equal to p 2 by p 1 raised to 2 by 3. So, from this equations we are getting the relation that is the equation number 3 and we know that from the equation b delta 2 by delta 1 is equal to cos beta, therefore by considering the equation b and c we are getting p 2 by p 1 raised to 2 by 3 is equal to cos beta that we are equating the right hand side that is the p 2 by p 1 is equal to cos beta. Therefore, p 2 is equal to p 1 cos beta raised to 3 by 2, similarly we can easily calculate the relation between p 3 by p 1 raised to 2 by 3 is equal to cos beta that is the p 3 is equal to p 1 cos of 2 beta raised to 3 by 2. So, as we are knowing this relation we are seeing this relation from the equation number a that is the c naught is equal to p 1 plus 2 times cos of 2 times p 2 cos of beta plus 2 times p 3 cos of 2 beta just we have to put the value of the p 2 p 3 in this equation. So, we will get this relation for the c naught just simplify this equation we are getting p 1 into this bracket. So, this bracket is indicating the constant term that is the angle beta. So, we can consider that constant terms as m we are given as a notation as m where the m is equal to that bracket. If z is number of the ball then we can easily calculate the value of the beta as the beta is nothing but the angle between each ball. Therefore, beta is equal to total 360 degree divided by the number of the balls z we can get the value of the beta. The value of the m for the different value of the z can be tabulated like this. So, in this tables we are getting if you are putting z is equal to 8 we can put this in this equation you will get the value of the beta put this value of the beta in the above equation you will get the value of the m. So, if you are putting z is equal to 8 10 12 15 respectively we are getting the value of the m then divide z by m you will get this the value of the z by m. So, if you observe this value of the z by m we can consider the value of the z by m is nothing but the phi just put the value of the z by m that is a we are getting the value of the z by m is equal to phi. Therefore, m is equal to z by phi just put this value in the equation D we can easily calculate the value of the C naught. Therefore, C naught is equal to P 1 into z by phi from the experimental evidence it is found that the force P 1 is required produce a given permanent deformations of the ball and it is given by P 1 is equal to K D square where D is nothing but the diameter of the ball and the factor K is depending upon the radii of the curvature at the point of contact and the moduli of elasticity of the material. Therefore, we are getting the equation that is the final equation C naught is equal to K D square z by phi. So, this equation is called as Stabak equation. So, based on this Stabak equation we can easily calculate the static load carrying capacity of the bearing. So, I have taken reference as a VB Banda Reboot. Thank you.