 Hello friends, I am Sanju Benike, working as assistant professor in mechanical engineering department at Walton Institute of Technology, Sulapur. In this video, I am explaining the design of rolling-contact bearing subjected to cyclic load. At the end of the session, learners will be able to calculate dynamic load capacity of the bearing which is subjected to cyclic load. So friends, think about what is cyclic load? In certain applications, ball and roller bearings are subjected to cyclic loads and speeds. For example, if you consider a ball bearing subjected to a work cycle which consists of number of elements like 1, 2, 3, in which in first element it is subjected to a load of 2000 Newton and is rotating at 750 rpm and this is the condition of loading for 25% of the cycle time. The next, the radial load changes to 4000 Newton, the speed also varies to 600 rpm and this remains for next 50% of time of a cycle. And third, there is a radial load of 1000 Newton when the bearing is rotating at 1000 rpm for the remaining 25% of the time. That means we consider one work cycle consisting of three elements during which for a particular point of time the bearing is subjected to different loads. And this particular thing is called as a cyclic load or a cycle consisting of three elements of loads as shown over here. Under these circumstances, it becomes very necessary to consider the complete work cycle while finding out a single dynamic load capacity of the bearing. So for that purpose, we have to calculate what is known as equivalent dynamic load. So let us consider an example of a ball bearing subjected to a work cycle consisting of certain x elements as shown over here. Element 1, the load acting is P1 as a radial force and under this load the bearing completes some N1 revolutions. Similarly, in second element it is P2 load acting on the bearing and under such load it completes certain N2 revolutions. Likewise, we can define the x elements subjected to Px load completing some Nx revolutions. So this is the way one work cycle is consisting of x elements having the different force components and number of revolutions they complete. Under such loading condition. So now if I consider a load P1 only, I know that corresponding to this load P1 the bearing will complete some L1 revolutions. So that there is a relationship between load and life such as L1 is c by P1 raised to cube as it is a ball bearing into 10 raised to 6 revolutions. So if I consider just the load P1 the bearing is subjected to then I can get relationship between the life dynamic capacity and the load applied as L1 is equal to c by P1 raised to cube 10 raised to 6 revolutions. So but actually in this case as a cyclic load the bearing is not completing all L1 revolutions it is completing only N1 revolutions. So first I calculate one revolution the life consumed will be 1 by L1 and correspondingly the other side that the load this side is 1 upon this. So that gives P1 upon c cube into 1 by 10 raised to 6 so it is equivalent. So in one revolution the life consumed is 1 by L1 or it can be considered as P1 cube by c cube into 1 by 10 raised to 6. So the first element if I just consider there are N1 revolutions actually the bearing is completing and that is why I consider that the life consumed by first element totally is N1 into P1 cube upon 10 raised to 6 into c raised to cube. So this is the way first element effect is there when the load P1 is acting on that and it is completing some N1 revolutions. So this relationship I can get. Similarly I consider the other elements for example second element it will be N2 P2 cube upon 10 raised to 6 series to cube. So this is the way I cover all x elements and I get summative effect that total life of that particular work cycle bearing is going to complete is something N1 P1 cube upon this N2 P2 cube plus so on Nx Px cube upon 10 raised to 6 c cube. So this gives the life consumed by all the elements in a particular work cycle. Now if I think of that instead of taking all these P1 P2 x life I consider the single load equivalent PE then it is going to complete some N cycles of the life and that is why the relationship in the same way I can get as NPE cube upon 10 raised to 6 c cube where this N is a total life is nothing but the life of all these revolutions together taken as a summation. So total N is N1 plus N2 plus Nx. So I got two equations A and B over here established. So equating these A and B equations what I get it N1 P1 cube plus N2 P2 cube plus so on and that must be equal to NPE cube where PE is an equivalent load acting on the bearing. N is a total life of the bearing under this single value of equivalent load whereas actually this equivalence is obtained for actual conditions of cyclic load that is N1 P1 cube plus N2 P2 cube plus Nx Px cube denominator being same 10 raised to 6 c cube has been cancelled over here. So with this what we get is equivalent load is equal to cube root of this N1 P1 cube plus N2 P2 cube plus so on divided by N1 plus N2 actually this N1 plus N2 is N here and we know that N is nothing but N1 plus N2 plus N3 and so on. So one can get this equation as equivalent load PE cube root of summation of Np cube divided by summation of N so N is life here is individual N1 P1 cube etc. So this is the way one can calculate the equivalent load for ball bearing which is subjected to actually cyclic load having different elements of load P1 P2 P3 etc. So this is the way first we have to convert a given cyclic load into some equivalent load called as a P and that is called as equivalent dynamic load when the ball bearing is subjected to cyclic load. Now by using this equivalent load further we can calculate a dynamic load capacity of the bearing. So once again to calculate the dynamic load capacity of the bearing we have got life relationship as L10 is equal to C by PE raised to cube and this is what expected life of the bearing in million revolutions. C is a required dynamic capacity of bearing which we want to select bearing from manufacturer's catalog so we want to get some dynamic load capacity required by the bearing known. So this C for cyclic loading condition of a bearing is obtained with the help of equivalent load P and we just see that how to calculate P as an equivalent load. We have seen it previously as a derived equation. By knowing this equation we can get the dynamic capacity of the bearing required C as a value P into L10 where L10 is a desirable life in million revolutions raised to 1 by 3. This is a case of ball bearing if would have been a roller bearing this could have been 3 by 10 so it has 1 by 3 that will be 3 by 10. So by substituting that we can just convert the same as a roller bearing in case of cyclic load acting on roller bearing. So this is the way we calculate the load acting on the bearing as equivalent load due to cyclic load and we convert that into required dynamic load capacity. So that this will help to select a bearing from manufacturer's catalog. So this is the reference. Thank you.