 I am Mr. P. P. Mitragootri, Associate Professor in Department of Mechanical Engineering at Vulturen Institute of Technology, Solaapur. Today we are going to study what is merchant circle, what is merchant circle diagram and how it can be utilized for graphical representation of forces acting along shear plane and acting along tool chip interface during metal cutting process and how we are able to graphically calculate magnitude of shear force, normal to shear force, magnitude of tool force and normal to the tool force with the help of this diagram. And outcome of this particular session will be, learners will be able to draw merchant circle diagram and will be able to calculate various forces acting along shear force, shear plane as well as along tool chip interface by orthogonal cutting and this is graphical method of representing the forces. Now, for drawing this diagram and for further things, first and basic assumption is our metal cutting is orthogonal cutting, orthogonal cutting is two dimensional cutting, it is strictly confined to two dimensions. Now, for drawing merchant circle diagram, required data is we have to measure cutting force denoted by letter fc which acts in the direction of tool travel or tool feed and thrust force denoted by letter ft which acts perpendicular to the cutting force. These two forces are measured by tool dynamometer during metal cutting operation, rake angle of the cutting tool is denoted by letter alpha is recorded from specification of the cutting tool that we are employing for orthogonal turning or orthogonal cutting. And uncut chip thickness denoted by letter t and chip thickness after cut denoted by letter c are to be recorded. Now, we will begin the procedure for construction of merchant circle diagram. Now, first of all, we have to draw a vertical line parallel to y axis and we have to draw a tool face making an angle alpha that is rake angle with the vertical line. After that, we have to draw a cutting force fc which is measured by letter tool dynamometer acting in the direction of tool travel with proper scale of correct magnitude as shown in the diagram. Then, we have to draw a thrust force perpendicular to the cutting force with the same scale and with proper magnitude. Then, we have to draw the resultant of these two forces. This resultant cutting force and thrust force will form a triangle. Now, next important thing is we have to carry out geometrical construction which we have studied in school days to find out midpoint of the resultant because this midpoint is going to act as a center of the circle which we are going to draw through these three points of the triangle and that is called as merchant circle. This merchant circle is visible in the diagram now along with merchant circle we are observing cutting force and thrust force. Then, next construction will be we have to show uncut chip thickness with proper scale and as uncut chip thickness is measured along the direction of tool travel, line representing uncut chip thickness will be parallel to the cutting force as shown in the diagram. Then, chip will always flow along the tool face. So, cut chip thickness will be parallel to the tool face and cut chip thickness is denoted by later TC. Now, these two lines intersect somewhere and that point of intersection is visible in the diagram. Now, through that point of intersection and through the tool point we have to draw the line cutting the circle at certain point. This line represents shear force denoted by later FS and you have to understand the angle made by this line with cutting force. I think you can understand it this is reflection spot in our video. I will wait for a moment. I understand that you have followed it and this angle can be no other than shear angle denoted by later Phi. Now, we have to draw the line perpendicular to the shear force which will join the resultant force and this shear normal to the shear force is denoted by later Fn and resultant top shear force and normal to the shear force is also the resultant top cutting force and thrust force that we can very well understand from this diagram. We have constructed shear force and normal to the shear force we have to measure their magnitude and this magnitude with proper scale and we have to transform them into Newtons or KGs as per the scale that we have adopted and angle between cutting force and shear force we can measure and we can say that this is the shear angle. Then we have to draw a tool force along the line of the tool face from the tool point and that will cut the circle at point shown over shown in the diagram this tool force is denoted by later F. Then we have to draw a perpendicular line joining the resultant which will represent normal to the tool force which is denoted by later N. We have to measure the magnitude of F and N and these magnitudes if transformed into proper scale they will give us the number that is the value of Newtons and this way we can graphically represent and graphically calculate all the forces. Now I will once again rapidly repeat the procedure that we have followed what we require we require to know cutting force and thrust force we have to draw cutting force thrust force and resultant triangle then we have to find out the midpoint of the resultant by geometrical construction with that midpoint as a center we have to draw and resultant as radius we have to draw the circle which represent merchant which is called as merchant circle. Then we have to draw a line representing uncut chip thickness parallel to the cutting force and we have to draw the line representing chip thickness after cut parallel to the tool face and through the point of intersection of these two lines and through the tool point we have to draw the line cutting the circle which will represent shear force and we have to draw the line perpendicular to that which will be represent now which will represent normal to the shear force and angle between shear force line and cutting force line is none other than shear angle similarly line along the tool face will be tool force and perpendicular to that will be representing normal to the tool force hope you have understood the procedure to draw the merchant circle and procedure for calculating various forces acting along the shear plane and tool chip tool interface by merchant circle diagram for further reading I will recommend a book by machine tool engineering by book machine tool engineering by jr nakpal and textbook of production engineering by pc sharma thank you