 Hello, students. I am Bhargesh Deshmukh, Mechanical Engineering Department, Palchian Institute of Technology, Solapur. This session is on design of Bevel gear. We have seen how to derive the beam strength of a Bevel gear, how to derive the wear strength of a Bevel gear. We have also seen that what are the different mounting methods, such as overhang mounting of pinion and gear, saddle mounting of either pinion or gear, and third, the saddle mounting of both pinion and gear. We have seen that it was useful to use both saddle mount, where we can avoid the deflection of the shaft of both the gears. It will be a precise arrangement. Let us now see how to obtain the rated power of Bevel gear. At the end of this session, you will be able to calculate the rated power of a Bevel gear. It is a very common type of problem in design of Bevel gear, and the logic for this problem needs to be developed. Let us see what is the beam strength of a Bevel gear. If we consider this Bevel tooth, the circle represents a0, which is the cone distance, b is the face width, dx is the elemental zone, which we have considered to derive the beam strength, gamma is the pitch angle, rx is the radius at the elemental section, R is the radius at the larger end of the tooth, and we have seen that we have to consider the larger end of the tooth to derive the beam strength of a Bevel gear. However, we have taken elemental section under consideration, and for elemental section we have defined what is the beam strength. Therefore, delta SB is taken as mx, bx, sigma b into y. Where this delta SB represents beam strength of the elemental section in Newton, mx is the module at the section, bx represents the face width of the elemental section in millimeter. y is the levy's form factor based on virtual number of teeth. It is very important that y should be taken on virtual number of teeth. It is not based on actual number of teeth. We know that the torque, the equation is mb, sigma b, y into r into bracket 1 minus b by a0 plus b square by 3 a0 square. We have obtained the other equation of torque assuming that the beam strength SB is the tangential force acting at the larger end of the tooth. We have seen over here beam strength is the tangential force acting at the large end of the tooth. And hence the other equation of torque is mt equals SB into r because SB is acting at this particular point where the radius is r and hence mt equals SB into r. Comparing these two equations, we have defined what is SB? SB equals mb sigma b y into bracket 1 minus b by a0 plus b square upon 3 a0 square. However, we know that b equals a0 by 3. Hence, this third term in the equation of SB, it is very negligible. It is always less than 1 by 27 and we can neglect it. Neglecting the term, the equation of beam strength changes to mb sigma b y into bracket 1 minus b by a0. After doing this, in addition to the spur gear equation of beam strength, this bracket comes in picture which is called as a bevel factor and we represent it as 1 minus b by a0. Let us solve a problem related to the rated power. A pair of state bevel gear consists of a 25th teeth pinion. It is an actual number of teeth on pinion meshing with a 48 teeth gear. 48 teeth gear means again 48 are actual number of teeth on bevel gear. The module at the outside diameter is 6 millimeter and the face width is 50 millimeter. b is 50 and module m is 6. The gears are made of gray cast iron FG 200, 20. That means SUT is 220 Newton per mm square. The pressure angle is 20 degree, alpha 20 degree. The teeth are generated. This is most important, generated teeth. Accordingly, we need to select the velocity factor and assume that the velocity factor accounts for dynamic load. Here, we are supposed to use velocity factor. The pinion rotates at 300 rpm, NP is 300 and the service factor is given as 1.5. We are asked to calculate the beam strength of the tooth, the static load that the gear can transmit with a factor of safety of 2 for bending conception and the rated power that the gears can transmit. Let us recall the forces on gear tooth. For typical spur gear, a driven gear at the pitch point, tangential force is in the direction of rotation of the driven gear. Radial force PR is always directed towards the center of the gear. PN was the resultant force acting on the gear tooth at an angle equal to alpha. The tangential force PT, there it was given as 2 MT upon D dash. The radial force PR was given as PT tan alpha. The tangential force can be obtained from MT equals 16 to 10 to the power 6 kilowatt upon 2 pi N, where kilowatt represents the power. From power, we can get the torque. From torque, we can get what is the tangential force. The value of tangential compound therefore depends upon the rated power and rated speed. To obtain the rated power, what we need then? Let us see the given data for all the problem. Speed of the pinion was given as 300 rpm, Zp equals 24, Zg equals 48, modally equals 6, phase width B is 50 millimeter, service factor CS is 1.5, factor of safety is given as 2 and SUT equals 220 Newton per mm square. To obtain the rated power, we need to obtain the rated torque. To obtain the rated torque, we need to obtain the rated force. More precisely, to obtain the rated torque, we need to obtain the rated tangential force. Tangential force is given by beam strength or wear strength. Let us follow step one to calculate the beam strength. In this problem, there is no data regarding the wear strength. We can follow the beam strength and solve the problem. Material for the pinion and gear is same. Hence, we need to conclude that the pinion is weaker than the gear and we can continue with the design of pinion. Dp is equal to mZp, 6 is the module, number of tethon pinion at 24, therefore diameter of the pinion is 144. Similarly for the gear, module into number of teth, 6 into 48, diameter of the gear is 288 mm. When we get these two, we can find out what is the cone distance. Why we need the cone distance? We can think upon it. Cone distance a0 is given as square root of dp by 2 bracket square plus dg by 2 bracket square. We obtain the value of dp and dg. We can substitute it in the equation of a0 and a0, the cone distance is obtained as 161 mm. Now we need the value of tan gamma. Tan gamma equals Zp by Zg. Zp is 24, Zg is 48, tan gamma equals 0.5 or we can get the value of gamma equals 26.57 degree. We obtain gamma in order to calculate virtual number of tethon pinion. Virtual number of tethon pinion Zp dash equals actual number of tethon pinion Zp divided by cos gamma. Let us put the value 24 upon cos of 26.57. Virtual number of tethon pinion comes out to be 26.83. With this data, calculate the Levis form factor. Levis form factor from the standard table we can get y equals 0.3473. Let us use this value and calculate the beam strength. m is 6, b is 50, sigma b, SU t by 3, we can get sigma b. y is the Levis form factor and 1 minus b by a0 is the Bevel factor. We can get the beam strength equals 5267.74 obviously in Newton. Next step is to obtain the static load. For that, let us use v. v equals pi dp np upon 16 to 10 to the power 3. Diameter of the pinion is 144, speed of pinion is 300. We can get the pitch line velocity equals 2.262 meter per second. As the tethes are generated, we need to use the formula of cv equals 5.6 upon 5.6 plus root v. Let us put the value of pitch line velocity equals 2.262 and get cv equals 0.7883. We know that sb beam strength is given as p effective into fs. The value of p effective fs we can put. cs we know, cv we know, fs is given, sb value is known. Let us calculate the tangential force pt equals 1384.19. When we get this force, rated torque is given as mt equals pt into dp by 2. We can get the torque in Newton millimeter. Let us calculate the rated power as power equals or kilowatt equals 2 pi n mt upon 60 into 10 to the power 6. The power comes out to be 3.13 kilowatt. Hence, the rated power that the gear can transmit is 3.13 kilowatt. Thank you.