 Hello friends. I am P. P. Mithra Uthri, associate professor in department of mechanical engineering at Valchand Street Top Technology, Solaapur. In earlier sessions, we have studied merchant circle diagram and forces acting along tool chip interface and shear plane. But we have not spoken anything about velocities in metal cutting. These velocities are very important in determining tool life, in determining tool forces, in determining heat generated during metal cutting. So we have to consider velocity triangle in metal cutting. And outcome of this session will be to establish the relationship between cutting velocity, shear velocity, chip velocity in terms of rake angle and shear angle. For that first of all we have to assume that our cutting is orthogonal cutting. And what we require to know is cutting velocity. Now what is this cutting velocity? Cutting velocity in general term is a cutting speed that we select depending upon type of material to be cut, depending upon type of tool, type of operation and various factors that cutting speed in vector format is called as a cutting velocity. And cutting velocity is always represented along the direction of tool travel. Rake angle of the cutting tool is the angle made by the tool face with vertical. And shear angle phi is the angle made by the shear velocity along the with cutting velocity. Now along with cutting velocity there are two more velocities that is one velocity is one velocity is acting along shear plane that is shear velocity. And another velocity along with the help of which chip flows along tool face is the chip velocity. So chip velocity is denoted by later VC and shear velocity is denoted by later Vias. We have to establish relationship between these three. Before that we can graphic once we know cutting velocity and shear angle and rake angle we can graphically represent shear velocity and chip velocity. And we can graphically calculate values of shear velocity and chip velocity that is shown by the animation. So for that first of all we have to draw a vertical line and then a tool face making an angle alpha that is rake angle with the vertical line. Now from tool point we have to draw the line with proper scale which will represent cutting velocity V and this will represent proper magnitude. This line is shown by later this line is nomenclated as OA which represents cutting velocity. Now next line will represent shear velocity that will make shear angle and that will be represented by later sorry that will be represented by OB. OB will represent correct magnitude of shear velocity or before that we will draw the line at angle phi then we will draw line from A cutting line OB parallel to tool face which will be OAB. So this AB line will represent rake angle equal to with vertical you can understand this angle can be none other than alpha that is rake angle. Now this AB represent VC and if you measure the magnitude of line AB it will be magnitude of chip velocity. If you measure magnitude of line OB which represent shear velocity it will be representing magnitude of shear velocity. Now after that we have to calculate we have to find out analytical method to establish a relationship between shear velocity chip velocity and cutting velocity because we have to analytically calculate shear velocity and chip velocity for that we are drawing one line from point A which will cut OB that is Vs at point C and AC is perpendicular to OB AC is making an angle phi with vertical. So angle CAB will be phi minus alpha so if you want to from triangle OCA you can very easily understand that AC is equal to OA sin phi OA is nothing but cutting velocity V. So AC is equal to V sin phi this is equation number one similarly from another triangle BAC you can say that AC is equal to AB cos of phi minus alpha. So AB represents VC so AC is equal to VC cos of phi minus alpha this is equation number two. So we have to equate equation number one and equation number two so V sin phi is equal to VC cos of phi minus alpha. So chip velocity VC can be represented in terms of cutting velocity shear angle and rake angle as VC is equal to V sin phi divided by cos of phi minus alpha. In this case we can very easily understand that VC can never be greater than chip V or cutting velocity VC is always less than cutting velocity and generally it is half of chip will half of cutting velocity then we have to establish relationship between shear velocity and cutting velocity for that again we will consider velocity triangle but now we have to carry out another construction we have to draw line OD perpendicular to AB this line OD is making angle phi with AB OA sorry cutting velocity. So remaining angle will be phi minus alpha now from this we can understand we can consider triangle next triangle OD if we consider we can understand that OD is equal to V cos alpha this is equation number one now from triangle OD be another triangle OD is equal to VS cos of phi minus alpha. So equating one and two V cos alpha is equal to VS cos of phi minus alpha therefore shear velocity can be represented as cutting velocity cos phi divided by cos of phi minus alpha. So from this we have we are able to analytically represent relationship between cutting velocity chip velocity and shear velocity with shear angle and rake angle. So hope you have understood this and you will be able to solve numerical problems on this. So for further reading I will recommend book by J. R. Nakpal titled Machine Tool Engineering and Textbook of Production Engineering by P. C. Sharma. Thank you.