The document discusses Merchant's circle diagram, which is used to analyze cutting forces in machining. It explains the different force components in the shear and friction zones. The construction of the Merchant's circle diagram is shown, with key points labeled including cutting force (Fc), thrust force (Ft), normal force (Fn), shear force (Fs), and friction force (Ff). Equations are provided to calculate different forces from the diagram using angles and force vectors. Limitations of the diagram and conclusions from it are briefly covered. The reader is assigned homework to derive machining force relationships from the Merchant's circle diagram.

1. Dr.Jayanta Kr.Mahato
Assoc. Professor
Mechanical Engineering Dept.
ShobhitDeemed to-be University
Contact: jayanta.mahato@gmail.com

2. Shear & Friction Zones and Different Force Components
Shear Zone Fs
Ff
Fn
N
Friction Zone
Fc
Ft
 Cutting Force (Fc): Acts in the
direction of cutting speed and
parallel to the work piece surface
and supplies energy required for
cutting.
 Thrust Force or Tangential Force
(Ft): Acts in a direction normal to
the cutting velocity, that is
perpendicular to the work piece
surface.
Dr. Jayanta Kr. Mahato, Asst. Prof., Mechanical Engineering

3. Different Force Components
Shear Zone
Friction Zone
Fs
Fn
Ff
N
Fc
Ft
Dr. Jayanta Kr. Mahato, Asst. Prof., Mechanical Engineering

4. Different Force Components
Dr. Jayanta Kr. Mahato, Asst. Prof., Mechanical Engineering

5. Different Force Components
Dr. Jayanta Kr. Mahato, Asst. Prof., Mechanical Engineering

6. Different Force Components
Dr. Jayanta Kr. Mahato, Asst. Prof., Mechanical Engineering

7. Concept of Merchant’s Circle Diagram
Merchant’s Circle
Diagram
Dr. Jayanta Kr. Mahato, Asst. Prof., Mechanical Engineering

8. Construction of Merchant’s Circle Diagram
Dr. Jayanta Kr. Mahato, Asst. Prof., Mechanical Engineering

9. Construction of Merchant’s Circle Diagram
Dr. Jayanta Kr. Mahato, Asst. Prof., Mechanical Engineering

10. Construction of Merchant’s Circle Diagram
Dr. Jayanta Kr. Mahato, Asst. Prof., Mechanical Engineering

11. Construction of Merchant’s Circle Diagram
Dr. Jayanta Kr. Mahato, Asst. Prof., Mechanical Engineering

12. Construction of Merchant’s Circle Diagram
Dr. Jayanta Kr. Mahato, Asst. Prof., Mechanical Engineering

13. Construction of Merchant’s Circle Diagram
Dr. Jayanta Kr. Mahato, Asst. Prof., Mechanical Engineering

14. Construction of Merchant’s Circle Diagram
Dr. Jayanta Kr. Mahato, Asst. Prof., Mechanical Engineering

15. Construction of Merchant’s Circle Diagram
Dr. Jayanta Kr. Mahato, Asst. Prof., Mechanical Engineering

16. Construction of Merchant’s Circle Diagram
Dr. Jayanta Kr. Mahato, Asst. Prof., Mechanical Engineering

17. Construction of Merchant’s Circle Diagram
Dr. Jayanta Kr. Mahato, Asst. Prof., Mechanical Engineering

18. Construction of Merchant’s Circle Diagram
Dr. Jayanta Kr. Mahato, Asst. Prof., Mechanical Engineering

19. Construction of Merchant’s Circle Diagram
Dr. Jayanta Kr. Mahato, Asst. Prof., Mechanical Engineering

20. Construction of Merchant’s Circle Diagram
Dr. Jayanta Kr. Mahato, Asst. Prof., Mechanical Engineering

21. Construction of Merchant’s Circle Diagram
Dr. Jayanta Kr. Mahato, Asst. Prof., Mechanical Engineering

22. Construction of Merchant’s Circle Diagram
Dr. Jayanta Kr. Mahato, Asst. Prof., Mechanical Engineering

23. Construction of Merchant’s Circle Diagram
Dr. Jayanta Kr. Mahato, Asst. Prof., Mechanical Engineering

24. Construction of Merchant’s Circle Diagram
Dr. Jayanta Kr. Mahato, Asst. Prof., Mechanical Engineering

25. Construction of Merchant’s Circle Diagram
Dr. Jayanta Kr. Mahato, Asst. Prof., Mechanical Engineering

26. Construction of Merchant’s Circle Diagram
Dr. Jayanta Kr. Mahato, Asst. Prof., Mechanical Engineering

27. Construction of Merchant’s Circle Diagram
Dr. Jayanta Kr. Mahato, Asst. Prof., Mechanical Engineering

28. Construction of Merchant’s Circle Diagram
Dr. Jayanta Kr. Mahato, Asst. Prof., Mechanical Engineering

29. Construction of Merchant’s Circle Diagram
Dr. Jayanta Kr. Mahato, Asst. Prof., Mechanical Engineering

30. Construction of Merchant’s Circle Diagram
Dr. Jayanta Kr. Mahato, Asst. Prof., Mechanical Engineering

31. Solution of Merchant’s Circle Diagram
R
R/
A
Q
B
P
L M N
Fc
Ft
Fn
Fs
Ff
N
R a
a
φ
φ
a
Fc = AS + SR/
Fc = Fn sinφ + Fs cosφ 1
Ft = OB - AB
Ft = Fn cosφ - Fs sinφ 2

32. Solution of Merchant’s Circle Diagram
R
R/
A
Q
B
P
L M N
Fc
Ft
Fn
Fs
Ff
N
R a
a
φ
φ
a
Ft = AL – OL
Ft = R/N - OL
Ft = Ff cosa - N sina 3
Fc = LM + MN
Ft = Ff sinja + N cosa 4

33. Calculation of Forces from Merchant’s Circle Diagram
Dr. Jayanta Kr. Mahato, Asst. Prof., Mechanical Engineering

34. Solution of Merchant’s Circle Diagram
Dr. Jayanta Kr. Mahato, Asst. Prof., Mechanical Engineering

35. Need of Analysis of Forces
Dr. Jayanta Kr. Mahato, Asst. Prof., Mechanical Engineering

36. Advantages of Merchant’s Circle Diagram
Dr. Jayanta Kr. Mahato, Asst. Prof., Mechanical Engineering

37. Limitations of Merchant’s Circle Diagram
Dr. Jayanta Kr. Mahato, Asst. Prof., Mechanical Engineering

38. Conclusions from Merchant’s Circle Diagram
Dr. Jayanta Kr. Mahato, Asst. Prof., Mechanical Engineering

39. Home Assignment
following
 Derive the
different machining
force relationships
from Merchant’s Circle
Diagram shown in the
figure.
Dr. Jayanta Kr. Mahato, Asst. Prof., Mechanical Engineering