 Friends, I am Mr. P. P. Mitra Guthri, Associate Professor in Mechanical Engineering Department at Valchand Institute of Technology, Solaapur. In earlier session, we have studied velocity triangle and velocities in metal cutting. So you already know there are three velocities in metal cutting. That is chip velocity that is flowing along the tool chip interface, shear velocity flowing along shear plane and cutting velocity in the direction of tool travel. So we have to calculate, we have to solve numerical on these velocities and outcome of this session is you will be able to solve problems for establishing relationship between cutting velocity, shear velocity, chip velocity. So the problem statement I will read which is visible on the screen that is during orthogonal turning with single point carbide tool having rake angle of 10 degrees, a feed rate of 0.2 mm per revolution at cutting velocity of 100 meters per minute. Chip thickness after cut was measured to be 0.42 mm. We have to calculate chip thickness ratio r, we have to calculate shear angle phi, then we have to calculate chip velocity vc and shear velocity vs and we have to calculate it in terms of shear cutting velocity, shear angle and rake angle both velocities. So first step to solve this problem will be to understand given data. So given data uncut chip thickness, chip thickness after cut cutting velocity v and rake angle alpha 10 degrees from this data. Chip thickness ratio is denoted by later r which is ratio of uncut chip thickness divided by chip thickness after cut. All of you know this uncut chip thickness is t, chip thickness after cut is tc from given data t is 0.2 that is feed rate and tc is 0.42. So this ratio comes out to be 0.48, it is a simple calculation. Now once we know r, we can very easily determine shear angle phi by the formula phi is equal to tan inverse of r cos alpha divided by 1 minus r sin alpha where alpha is rake angle of the tool and r is chip thickness ratio. We know value of r, we know value of alpha that is 10 degrees, r is 0.8, 0.48 alpha is 10 degrees. Taking these values in this formula, we can write the formula as shear angle phi is equal to tan inverse of 0.48 into cos of 10 degrees divided by 1 minus 0.48 into sin of 10 degrees. We can calculate this angle as 27.8 degrees. By solving this equation, we come to the conclusion that our shear angle phi is 27.8 degrees. After knowing the shear angle, we have to use the formulas to calculate cutting velocity and shear velocity. The formula for calculation of chip velocity is Vc is equal to V cos phi divided by cos of phi minus alpha. We know value of V is equal to 100 meters per minute, value of phi is 27.8 degrees and alpha is 10 degrees. So Vc is equal to 100 into cos of 27.8 degrees divided by cos of 27.8 minus 10. So 100 into cos of 27.8 divided by cos of 17.8 which comes out to be 48 meters per minute. This chip velocity can be calculated by another formula because we know Vc upon V is equal to Tc upon T. So from this, we can say that Vc is equal to R into V. This means Vc is equal to 0.48 into 100 which is tallied that is 48 meters per minute. Now we have to calculate shear velocity in terms of cutting velocity and shear angle and rake angle. For that, we have to use the formula shear velocity Vs is equal to V cos alpha divided by cos of phi minus alpha where V is cutting velocity which is given as 100 meters per minute, alpha is rake angle which is 10 degrees, phi is shear angle which is calculated here as 27.8 degrees. Now shear velocity Vs is equal to 100 into cos of 10 degrees divided by cos of 27.8 minus 10 means Vs is equal to 100 into cos of 10 divided by cos of 17.8 by calculating it with calculator value of Vs comes out to be 103.8 meters per minute. From this, we can establish relationship between cutting velocity, shear velocity, chip velocity in terms of rake angle and shear angle and from this, one point can be noted that is chip velocity is always lesser than cutting velocity, shear velocity can be lesser or can be greater than cutting velocity and cutting velocity is nothing but cutting speed which is dependent upon various factors such as type of material to be cut, type of operation to be performed, machine condition whether coolant is employed or not and all other factors. From this, we will conclude that all velocities are interrelated and for further reading I will recommend held machine tool engineering and textbook of production engineering by PC Sharma and hope you will be able to solve numericals on velocity triangle very easily. Thanking you.