 Hello, students. I am Dr. Bhagesh Deshmukh, Professor in Mechanical Engineering Department, Palchian Institute of Technology, Solapur. This session is on design of spur gear. At the end of this session, we will be able to derive the effective load on a gear tooth. Please recall what are the forces acting on the gear tooth. The components of forces Pn is the resultant force which is acting at the pitch point when we consider the driven gear. At the pitch point, this resultant force is resolved into two components Pt and Pr. Pt, which is horizontal and Pr is vertical. Pt is the force which is responsible for driving the gear. The tangential force Pt is given as 2 mt upon d dash where d dash is the pitch circle diameter. The radial force is given by Pr equals Pt tan alpha. Tangential force is obtained from the equation of torque 60 into 10 to the power 6 kilowatt upon 2 pi n. The value of the tangential component therefore depends upon the rated power this kilowatt and the rated speed n. The torque required by the driven machine also varies. Sometimes the balance is obtained by means of a flywheel. The service factor. In the gear design, the maximum force due to the maximum torque is the important criteria. A service factor accounts for variation of power, torque or speed. The service factor CS is given as maximum torque upon rated torque. Service factor is also expressed as mt max upon mt. It can be also mentioned as Pt max upon Pt. Realizing these terms, we can get that Pt max that is the maximum tangential force equals CS Pt. Let us consider electric motor. Service factor for electric motor is equal to CS equals starting torque upon the rated torque. Service factor for speed reduction gear boxes. Working characteristics of the driving machines or the prime mover is taken on this end and working characteristics of driven machines or the application is taken on this end. Accordingly uniform, uniform if the characteristics matches then it is 1. Accordingly we can select what is the CS for typical application. Let us see the examples of driving machines with different working characteristics. If I take uniform category, electric motor, steam turbine, gas turbine falls under uniform category. Light shock, multi-cylinder internal combustion engines fall under the characteristics of operation of light shock. Likewise medium shock, single cylinder, internal combustion engine. While we are talking about the driven machines with the different working characteristics, medium shock can be for main drive to tool machine, heavy elevator, turning gears of crane likewise. And in case of heavy shock, press heavy feed pump, then rotary dealing, apparatus, these kind of driven machines fall under the category. Now, let us see what is the dynamic load. For the gears rotating at very low speed, almost at zero velocity, the transmitted load Pt can be considered to be the actual force present between the two machine T. But what happens practically? In most of the cases, the gears rotate at an appreciable speed and it becomes necessary to consider the dynamic force resulting from the impact between the mating teeth. The dynamic force is induced due to inaccuracies in the tooth profile, error in tooth spacing, misalignment between bearings, elasticity of parts and inertia of rotating disc. Then what are the methods to account for dynamic load? First one is the approximate estimation by the velocity factor in the preliminary stages of gear design. And the second one is the precise calculation by Buckingham's equation in the final stages of gear design. Let us see how approximate estimation can be done for dynamic load. Calculation of exact magnitude of dynamic load in preliminary stages of gear design is difficult. Hence, what we need to do is, we need to consider a velocity factor Cv developed by Barth to calculate the dynamic load. There are three cases where ordinary and commercially cut gears fall under the category where the velocity is less than 10 meter per second. The velocity factor Cv is 3 upon 3 plus v. For the case two, accurately hop and generated gears where velocity is less than 20 meter per second, Cv equals 6 upon 6 plus v. The third case where precision gears with shaving, grinding and lapping operations with velocity is greater than 20 meter per second, Cv is considered to be 5.6 upon 5.6 plus root v, where v is the pitch line velocity in meter per second and is calculated using v equals pi d dash n upon 60 into 10 to the power 3. Effective load by the velocity factor, it can be calculated as p effective equals Cs pt upon Cv. The velocity factor is an empirical relationship developed by past experiences. Calculating dynamic load using velocity factor, it has some advantages. It eases the calculation of velocity factor and design of gear. Velocity factor have sanctions from the American Gear Manufacturing Associations. That means we can use it. It is used in the past for many years and has given satisfactory results. But when we say that there are advantages, there are some typical limitations also. In case of these factors, mass of gears, mass connected to the gear shaft and properties of the gear material like modulus of elasticity are considered. A gear tooth of a material with low modulus of elasticity will deflect more than the gear tooth of a material with higher modulus of elasticity and the other things being equal will absorb the energy of impact and deduce the dynamic load. Velocity factor methods neglect these factors. It assumes that the dynamic load depends upon the pitch line velocity. Therefore, use of velocity factor is restricted to a limited range of pitch line velocities. It is not possible to extrapolate the values. Hence, effective load is obtained using dynamic load. PDE, the formula is given. It is Buckingham's formula. C is the deformation factor and E is the sum of errors between two meshing teeth. All other terms are known. Deformation factor C is calculated by the formula given, where E are the modula of elasticity of pinion and gear respectively, e p and e g. K is the constant depending on the number of terms. It is the form of tooth. Generally, K equals 0.111 for 20 degree full depth involved tooth profile we use. And, steel-steel combination, commonly 11400 is the value of C. Effective load is given in that case as CSPT plus PDE. Error E, it depends on sum of error between pinion and the gear. It is given as e p plus e g. e p is error in pinion, e g is error in gear. This error depends on quality of gear and the method of manufacturing. 12 grades 1 to 12 are available in the decreasing order of precision. Expected error on the gear tooth is considered to be equal to tolerance. Now, the tolerance on the adjacent pitch, say if it is grade 1, error equals 0.8 plus 0.06 phi. Then, what is phi? Phi is given as tolerance, which is equal to m plus 0.25 square root of d dash, where d dash is again pitch circle diameter. As we do not know this in the early stages of gear design, we cannot calculate this dynamic load using Buckingham's equation. Hence, we need to calculate using velocity factor. Thank you.