 Hello friends, I am Mr. Sanjeev B. Knight, working as assistant professor in mechanical engineering department, Walton Institute of Technology, Singapore. In this video, I am explaining about the friction in the worm, which is considered during power transmission and its thermal power rating, based upon which it can transmit safely a power on thermal concentration. So, at the end of the session, students will be able to understand friction considerations in the design of the worm gas and design of worm gas for thermal power rating. As we know that the worm gear pair consists of a worm and worm wheel. The worm being in the form of helical screw and worm wheel is similar to helical gear, this sliding friction is predominant between the worm and worm wheel. So, this is the basic difference between the worm gear pair and other gear pairs and that is why frictional losses are quite heavy and frictional forces are also quite heavy. And that is why coefficient of friction in worm gear drive is an important requirement in design and this is been observed that the coefficient of friction in worm gear drive depends upon its rubbing speed. The rubbing speed is a relative velocity between the worm and worm wheel. So, here we consider a triangle in which we can find out the rubbing velocity v s if we know the peripheral or pitch line velocity of the worm and pitch line velocity of the worm wheel. So, considering this velocity triangle, we can establish to know the rubbing velocity and based upon rubbing velocity, there is a coefficient of friction. So, the geometry is considered here to calculate the rubbing velocity v s which is v n upon cos gamma. Gamma is a lead angle and where pitch line velocity we know that it is pi dn upon 60, 1 and n1 stands for worm speed and worm diameter. So, pi, pitch circle diameter of the worm and speed of the worm divided by 16 into 1000 because diameter is always in mm whereas v1 we require in meters per second. So, that is why considering this equation, we can calculate the pitch line velocity of the worm and once we know pitch line velocity, we can calculate sliding or rubbing velocity in this fashion. Once we know sliding or rubbing velocity, then by using this standard chart, we can calculate or we can know what is the coefficient of friction. So, here two assumptions are made in this standard chart. One is the worm wheel is made of phosphor bronze and the worm is made of case hardened steel. So, normally in many of the cases, the worm wheel is phosphor bronze and the worm is made of case hardened steel. So, this is a peculiar combination is considered for the materials and also the lubrication method is concerned that is having viscosity 16 to 130 stocks at 60 degree centigrade measured at 60 degree centigrade or particular lubricating oil which is a mineral oil. So, considering these two standard conditions, this standard chart is available. So, here we can find out the rubbing speed as we have made use of triangle and we have calculated rubbing speed. So, corresponding to this rubbing speed, we can establish the coefficient of friction. This is the way the coefficient of friction can be established for worm and worm wheel. Now, as I said that the frictional losses are quite heavy in case of worm gate drive, the efficiency also is a matter which has been comparatively less as compared to other gate drives. And how to calculate this efficiency is something like this. We know that the mechanical efficiency is power output by power input. In case of worm gate drive, the output is always been considered to be taken from worm wheel and whereas it is assumed that the input supplied is always to the worm. So, we consider power output from worm wheel and power input to the worm. So, corresponding we take torque into speed is the power if you take torque into angular speed is the power. So, here we consider the torque as tangential load into radius is a torque. So, tangential force acting on the worm wheel multiplied by pitch radius of the worm wheel which is essentially diameter by 2 and angular speed is 2.0 by 60, but here also 2.0 by 60 gets cancelled and we can get just the speed rpm n2 of the worm wheel. And similarly power input is a tangential force acting on the worm multiplied by its pitch radius is a torque multiplied by the speed. So, this is another equation we can use for input power. So, this is the way we get the ratio. Once we get this ratio as efficiency, here we get the n2 by n1 as one factor, n2 by n1. So, this is what the speed factor. So, what is the speed ratio? Actually it is n1 by n2. The speed ratio is speed of the worm by speed of the worm wheel. So, it should be n1 by n2 is equal to i. So, definitely n2 by n1 becomes 1 upon i. So, I get n2 by n1 is 1 upon i. Similarly, I can get d2 by d1 because 2, 2 gets cancelled. So, if I want to know ratio d2 by d1 is here. d2 is a pitch circle diameter of the worm wheel which is calculated as m into z2. So, in my previous videos we have seen terminology we find that pitch circle diameter of the worm wheel is m into z2. Similarly, pitch circle diameter of the worm is m into q. So, that's why finally d2 by d1 is z2 by q. So, just for some simplicity we divide numerator and denominator by z1. So, z2 by z1 is also a speed ratio. So, we have seen in terminology velocity ratio or speed ratio is also z2 by z1. And that's why it is i, z2 by z1 is value i. And tan of gamma, this relationship also we know from lead triangle, tan of gamma where gamma is a lead angle, z1 by q. So, there why we want q by z1, so it is 1 upon tan of gamma. So, tan gamma comes over here. So, finally z2 by q is nothing but i tan gamma. So, that's why d2 by d1 can be replaced by i tan gamma. And n2 by n1 by 1 by i and finally we can find out here something. That efficiency is further p2t by p1t. Then d2 by d1 is i tan gamma and n2 by n1 is 1 upon i. And that's why we get this relationship. That is p2t by p1t into tan of gamma. Further we know that p2t, that is the tangential force on the worm wheel, is equal to axial force on the worm. Just in force analysis in previous video, we have seen that the tangential force on worm wheel is axial force on the worm. So, we can replace this p2t by p1a. That's why it becomes p1a upon p1t into tan of gamma. Further this p1a in terms of p1t, we have seen that we can convert it likewise. So, axial force on worm is equal to tangential force on the worm into this bracket. Cos alpha, cos gamma minus mu sin gamma, cos alpha sin gamma plus mu cos gamma. So, this is the way we can convert p1a into p1t. So, that p1t and p1t gets cancelled. And just we get the efficiency as a tan of gamma into this bracket. Cos alpha cos gamma minus mu sin gamma, cos alpha sin gamma plus mu cos gamma. So, this is the relationship to find out the efficiency of the worm gear, in which we require to know only three parameters. One is a lead angle, one is a pressure angle, and one is a coefficient of friction. So, by this way we can able to know the efficiency of the worm gear, right? Further substituting tan gamma is assigned by cos. So, we can simplify further in this equation also. That is, efficiency is cos alpha minus mu tan gamma upon cos alpha into mu cot gamma. So, this is the two equations which can be used to calculate efficiency of worm gear drive. So, students pause the video and just recall how the efficiency of helical and spur gear is there as compared to the worm gear as just we have seen. Now, being the loss is more as a frictional work done or friction between the spur and worm gear as a worm and worm wheel, they have got comparatively very less efficiency. If you compare the efficiency of spur and helical gas is very high in terms of 98 to 99 percent, whereas in case of worm gears it is very low, it varies between 50 to 98 percent. Sometimes you are less than 50 in self-locking conditions also. So, this is why as this frictional work done is very large, the heat generated is also more and if these gears are continuously been operated, then this thermal concentration must be there. That is, heat generated becomes predominant and that should be known and heat generated is 1000 into 1 minus efficiency to killer. So, whatever frictional work done is a loss of efficiency, 1 minus efficiency is a loss of efficiency and that is directly converted into heat. So, this is equation which we can use for heat generated. So, for smooth working and safe working, this generated heat must be effectively dissipated through the lubricating oil to the housing wall of the gearbox and finally, to the surrounding air. So, that is why the rate of heat dissipated is h d which has been calculated as k into T minus k into T minus T naught into E. So, h d is the heat dissipated through the wall. So, overall heat transfer coefficient of housing wall, T is the temperature of the oil and T naught is the temperature of the surrounding air. So, this becomes a temperature difference and A is the effective surface area of housing. So, under thermal equilibrium condition, the heat generated must be heat dissipated. So, equating these two, we can just know how much power safely the gear can transmit as a kilowatt as k into T minus T naught A upon 1001 minus efficiency. So, by knowing the efficiency, we can also know how much power safely the worm gear pair can transmit without accumulating the heat. So, whatever heat generated continuously, it is continuously dissipated. So, this is the way becomes a thermal concentration in design of the worm gear drive to know its power transmitting capacity. My reference is design of machine elements. Thank you.