 Hello friends, I am Mr. Sanjeev B. Knight, working as assistant professor in mechanical engineering department, Walter Institute of Technology, Salafor. In this video, I am explaining about the forces acting on the worm gas during power transmission. At the end of this session, students will be able to determine forces acting on the worm and worm wheel while they are transmitting the power. As you know, the worm consists of a worm wheel and worm and worm wheel as you show over here and the power is transmitted from the worm and worm wheel. So, before determining the forces, certain assumptions are made in the analysis such as the worm is driving element while the worm wheel is driven element. So, if you see, this is the worm which is considered to be a driving element which transmits power to worm wheel and whereas the worm wheel is a driven element. As we know, the worm is essentially in the form of helical screw. It has got either right hand threads or left hand threads. Here it is assumed that the worm has right handed threads and also the worm rotates in anticlockwise direction. So, we consider the direction of rotation of worm as a anticlockwise. So, these are certain assumptions made before determining the forces. Now, let us consider the worm and worm wheel which is acted upon by the resultant tooth force acting on meshing teeth which is further resolved into three components. One is a tangential component force, axial component force and radial component force. The tangential component force is abbreviated as PT, axial is PA and radial is abbreviated as PR. Whereas, the suffix 1 is used for these three components acting on the worm. For example, it is a P1T where is a tangential force component acting on the worm. And if I refer P2T, 2 is a suffix for worm wheel. So, P2T is a tangential force acting on the worm wheel. So, likewise we consider suffix 1 for worm and 2 for worm wheel. So, just pause the video for while and you recall the forces acting on the helical gear. Now, let us consider the forces acting on the worm. The resultant force acting on the worm consists of two components. One is a component of normal reaction between meshing teeth and components of frictional force. So, force analysis of the worm wheel is somewhat different than the force analysis of all other gears because essentially the worm is in the form of the helical screw and the worm wheel is in the form of helical gear and that is why linear motion of the worm is converted into rotary motion of the worm wheel and that is why the sliding friction is predominant in this case. That is why the frictional forces become predominant and they have to be considered which are been neglected in other gear forces and that is why we have to consider two component that is a component due to the normal reaction. So, if you just see here P is a normal reaction acting on the meshing teeth which has been resolved into three components PR, PT and PA. And similarly we have to consider the frictional force which will be acting in the perpendicular plane to this plane and that is why it is here and we know that frictional force is mu into P and it is further resolved into another two components. So, we have to consider the component of frictional force as well as component of normal reaction and then the total component force are been called as the resultant components which have been obtained by superimposing the two forces. So, first we consider the component of normal reaction between the meshing teeth and that we consider as the first calculation. So, we know that this is similar to helical gear. So, just remember the helical gear force analysis and that is why it is a resultant force P acting on the meshing teeth which is resolved into component PR, PT and PA by considering two planes. One is a normal plane as you see over here it is A, B, C and D. So, we consider one plane A, B, C and D in which we consider the normal force P which is been resolved as P n as one fact and PR as another component. So, this is a pressure angle alpha as you know. The another plane considered is a top plane that is A, E, B and F in which we are able to analyze the force PT because this is parallel to A E. So, we consider this PT and then this is axial force component PA because it acts along the axis. So, this is the way we consider two planes to analyze the forces. So, from this A, B, C, D plane we calculate P n is P into cos alpha and PR is P into sin alpha. So, by simple geometry we can able to know what is P n in terms of P and PR in terms of normal reaction P. We consider another plane as I said A, B, F in which we convert P n this component into further component. So, PA if I consider PA it is a P n into cos of gamma, gamma is a lead angle. PA is P n cos gamma and PT is P n sin gamma. So, once again from geometry of this plane we consider P n, P n in terms of P n. Now, substituting this P n from A we can get further components resolved as PT acting on the worm is P cos alpha sin gamma because P n is P cos alpha and then sin gamma. Similarly, PA is P cos alpha cos gamma whereas PR is absent in friction and it is just it is PR is equal to P sin alpha. So, this is the way we can get the normal reaction forces of PT, P and PR. Now, the second component we consider is the force components due to frictional force mu P and that is been shown over here because of this sliding friction the frictional force are predominant in case of these gas whereas in other gas rolling motion is been there where friction is very less which is been neglected. So, this resultant frictional force mu P is resolved into two components and the direction of this frictional force is tangent to the helix as shown over here. So, it is resolved into two components one is mu P cos gamma as you show see here it is in the tangential direction. So, it is in the same direction as PT of normal reaction whereas mu P sin gamma it is along the axial direction. However, it is opposite in the direction of PA we have got PA just now as a normal reaction component. So, these are opposite. So, now to get the total resultant force we get superimposing these components. The total tangential force acting on the worm is due to the normal reaction that is we have seen P cos alpha sin gamma and its frictional component both of them are in same direction. So, they are added to get total value. So, mu P cos gamma similarly axial force total if you want in the worm gear is a component due to the normal reaction and this is a component due to frictional force but they are acting in opposite direction. So, it is minus. So, P cos alpha cos gamma minus mu P sin gamma. So, this will be the resultant value whereas radial component has got only normal reaction component that is why it is a P sin alpha. Further these components that is P1A that is axial force component is converted into tangential taking the ratio P1A by P1T we can get this bracket cos alpha cos gamma minus mu sin gamma upon cos alpha sin gamma plus mu cos gamma rearranging the term we get axial force in terms of tangential force of the worm and that is why we can get it something like this. So, similarly P1R also can be converted into P1T. So, getting P1R upon P1T we can get P1T into this bracket sin alpha upon cos alpha sin gamma plus mu. So, this is why we are knowing all these three components P1T P1A in terms of P1T and P1R in terms of P1T as a total resultant components acting on the worm. So, now in practice the tangential component is called as useful force and that actually transmits the torque. So, based upon the torque transmitting capacity required for the worm we calculate its tangential force. So, we know that torque upon pitch radius that is empty upon D1 by 2 which is a pitch radius we arrange the terms 2MT upon D1 we can calculate what is required tangential force to develop that much of the torque which is required to be transmitted. So, based upon that we calculate the tangential force once we know the tangential force the remaining components such as axial component on the worm can be calculated just by using previous equation shown over here where alpha is a pressure angle gamma is a lead angle mu is a coefficient of friction of worm and worm wheel meshing teeth and that is why we are able to know what is axial force component on worm what is radial force component on worm and what is tangential force component on the worm. So, this is the way we can determine all three force components acting on the worm. Once we know the forces acting on the worm we require to know the force components acting on the worm wheel along the meshing teeth. So, here we have shown the balance of forces acting on the worm and worm wheel. So, from this we know that tangential force component on the worm wheel is nothing but axial force component on the worm. So, this is a tangential force component is balanced by axial force component under equilibrium condition and that is why P2T is P1A. So, we are knowing this so we know this. Similarly, axial force component is P2A axial force component worm wheel is P2A is equal to tangential. So, axial force component on the worm wheel is a tangential force component on the worm. So, that is in balance whereas radial force they are equal and opposite acting on both and that is why they are equated. So, this is the way all components acting on the worm and worm wheel are known and are determined. This is my reference. Thank you.