This document provides an overview of mechanics of machining and Merchant's circle diagram (MCD). It introduces metal cutting, tool geometry, assumptions for force analysis, and forces acting on single point cutting tools. Key points include shear plane analysis using rake and shear angles, assumptions of orthogonal cutting and constant chip thickness. Construction of the MCD is described to relate cutting, thrust and feed forces. The MCD allows calculation of shear stress, power and friction coefficient, enabling selection of machine parameters and tool/workpiece design.

1. Mechanics of Machining
(Merchant Circle Diagram )
Presented by
Manish Singh
IIT Delhi

2. Contents
• Introduction of metal cutting
• Tool signature by ASA system
• Assumptions for Merchant’s force analysis
• Forces on single point cutting tool
• Construction of Merchant circle
diagram(MCD).

3. Introduction of Metal cutting
Metal cutting is a process in which desired shape and size can be obtained by
removal of unwanted material in the form of chip.
The predominant cutting action in machining involves shear deformation of work
material to form a chip, as the chip is removed new surface is exposed as shown in
figure 1.1
Figure 1.1

4. Why metal cutting is important ?
• Variety of work material can be machined.
• Variety of shapes and special geometry can be produced
such as gears, screw threads and very straight edge and
surfaces.
• Very complex object can be produced.
• Very good dimensional accuracy can be obtained.

5. Tool Signature by ASA system
(Machine Reference System)
ASA ( American Standards Association) system
v or Zm

6. • πR= Reference plane; plane perpendicular to the velocity vector
• πX= Machine longitudinal plane; plane perpendicular to πRand
taken in the direction of assumed longitudinal feed
• πY= Machine Transverse plane; plane perpendicular to both πR and
πX[This plane is taken in the direction of assumed cross feed]
• The axes Xm, Ymand Zmare in the direction of longitudinal feed,
cross feed and cutting velocity (vector) respectively.
Cont…

7. αb
αs
θs
θe
Cs
Ce
Cont…
The main geometrical features and angles of single point
cutting tool in ASA systems

8. •Rake angles
= side rake angle: angle of inclination of the rake surface from the reference plane (πR)
and measured on Machine Reference Plane, πX.
= back rake angle: angle of inclination of the rake surface from the reference plane
and measured on Machine Transverse plane, πY.
• Clearance angles:
θs = side relief angle: angle of inclination of the principal flank from the machined
surface and measured on πX plane.
θe = End relief angle: same as θs but measured on πY plane.
• Cutting angles:
Cs = side cutting edge angle: angle between the principal cutting edge (its projection on
πR) and πY and measured on πR
Ce = end cutting edge angle: angle between the end cutting edge (its projection on πR)
from πX and measured on πR
• Nose radius, r (in inch)
r = nose radius : curvature of the tool tip. It provides strengthening of the tool nose and
better surface finish.
αs
αb
Cont..

9. Assumptions for Merchant’s force
analysis
• The tool is perfectly sharp.
• A continuous chip is produced without BUE.
• Uncut chip thickness is constant.
• Metal cutting occurring under plain strain condition (i.e. width of
the chip is remain constant).
• Shear zone is consider as single shear plane
• Orthogonal cutting is consider (side cutting edge angle Cs = 0).

10. t1
t2
ϕ
( -ϕ α)
chip
work
v
Analysis of metal cutting
α
ϕ
t1
Shear plane area
B
A
C
ᴨ
R
α

11. Cont…
• Chip thickness ratio
• Shear Angle (φ)
• Shear strain
• Shear force

12. Forces acting on single point cutting tool
FZ or FC = Cutting force
FY = FR = Radial force
FX =Ff = Feed force
R = Resultant cutting force
For orthogonal cutting
Cs = 0o
Ff = FT cos Cs = FT
FY or FR
Fx =Ff
FC
R
Ym Xm
Zm
FXY =FT

13. Forces Acting on Chip
Forces in metal cutting:
(a) forces acting on the chip in orthogonal cutting
(b) forces acting on the tool that can be measured

14. Fn
Fs
FC
FT
F
N
R, R’,R”
α
α
(β-α)
ϕ
β
Construction of Merchant’s Circle Diagram
(MCD)

15. Equations derived using MCD
Based on these calculated force, shear stress, cutting power and
coefficient of friction can be determined as

16. • Estimation of cutting power consumption- Selection of
motor for machine tool.
• Structural design of the machine tool, fixture and tool.
• Evaluation of role of the various machining parameters
(such as v, f, d) on cutting forces.
• Study of behavior and machinability characterization of the
work materials.
• Condition monitoring of the cutting tools and machine
tools.

17. ?
Thank you…