1. Theory of metal cutting, 2. Concept of Rake Angle and Relief Angle, 3. Shear Angle and Shear Zone, 4. Orthogonal and Oblique cutting.

1. MANUFACTURING TECHNOLOGY
ME 405
ME 405
THEORY OF METAL CUTTING

2. GENERAL PRINCIPLE OF METAL CUTTING
• Metal cutting operations can be represented by a
process where a wedge shaped tool is made to move
relative to the workpiece in such a way that a layer of
metal is removed in form of a CHIP.
metal is removed in form of a CHIP.

3. PRINCIPLE OF METAL CUTTING
CUTTING TOOL basically consists of two
intersecting surfaces to form the cutting
edge.
Surface along which the CHIP flows is
known as RAKE FACE.
Surface along which is relieved to clear
Surface along which is relieved to clear
the newly machined surface is known as
FLANK.
γ = Rake Angle = Angle between cutting face
and normal to finished surface.
α = Clearance Angle/Relief Angle = Angle
between Flank and new workpiece surface.

4. CHIP FORMATION
Portion of the metal that has been cut away from the
Work material by the cutting tool is called CHIP.
When force is Applied to the Tool, the material of the
workpiece ahead of the cutting edge deforms due to
SHEARING action.
The shape and size of the chips obtained from a
machining process indicates the type and quality of
the process.
Types of CHIPS:
•Segmental or Discontinuous Chip
•Continuous Chip
•Continuous Chip with Built up Edge
•Non homogeneous Chip
Φ = SHEAR ANGLE

5. SHEAR PLANE
Metal is removed during metal cutting
operation by Shearing action.
Material is sheared in a narrow zone extending
from the cutting edge to the work surface.
from the cutting edge to the work surface.
For the purpose of analysis, this zone of Shear
is treated as a single plane commonly known
as SHEAR PLANE.

6. CUTTING RATIO
During metal cutting, the mean chip thickness (t2) is
always greater than the undeformed chip thickness
(t1), which is actually the feed in Orthogonal cutting.
Ratio of the thickness of the chip before removal (t1 )
to its thickness after removal (t2) from the material
to its thickness after removal (t2) from the material
bring cut is termed as Cutting Ratio.
Vc = Velocity of the tool relative to the
tool.
Vs = velocity of the chip relative to the
workpiece.
Vc acts along the tool face.
Vs acts along the shear plane.
Cutting Ratio = rc = t1/ t2
t1 = underformed chip thickness
t2 = mean chip thickness.
The inverse of cutting ratio is known as Chip
Compression factor.

7. SHEAR ANGLE
• Shear Angle (ф) is the angle made by the Shear plane with the direction of
Tool Travel.
• Shear Angle (ф) is the angle made by line AB with the direction of Tool
travel.
• The value of this angle depends on the Cutting conditions, tool
Geometry, tool material and Work material.
• If Shear angle is small, then Chip is thicker.
• If Shear angle is large, then Chip is thinner.
(ф)
(ф)

8. SHEAR PLANE or SHEAR ZONE
• Deformation of Metal in the process of separation of chip, does not
occur sharply across the Shear Plane.
• Grains of metal ahead of cutting edge of tool start elongation along the
line AB and continue elongate until they are completely deformed along
the line CD.
• Region between the lines AB and CD is called SHEAR ZONE.
• Angle made by plane of Shear with the direction of Tool travel is known
as SHEAR ANGLE. (ф)
as SHEAR ANGLE. (ф)
TOOL
B
A
D
C
SHEAR PLANE
(ф)

9. FORCE RELATIONS
In Orthogonal cutting, the force
system can be represented as acting
on a Single plane.
The force system is arrived at by
assuming that the chip is isolated as
a free body in stable equilibrium
a free body in stable equilibrium
under the forces acting on it at the
Tool face at the Shear Plane.
For equilibrium, the Force R between the tool face and the
chip along the shear plane should be equal.

10. For equilibrium, R = R’
i.e.
Force R between the tool face & chip = Force R’ between work
piece & chip along the Shear Plane
R and R’ is assumed can be assumed to act at the tool point and
are represented by diameter of a reference circle.
FORCE RELATION IN ORTHOGONAL CUTTING
CHIP
TOOL
PZ
PS
ф
γ
PY
PN
PD
PT

11. FORCE RELATION IN ORTHOGONAL CUTTING
CHIP
TOOL
PZ
PS
ф
γ
PY
PD
The FORCES can be resolved into
number of orthogonal components:
I. In horizontal and vertical
directions, Pz and Py.
II. Along and perpendicular to the
shear plane, Ps and Pd.
III. Along and perpendicular to Tool
face, Pt and Pn.
Pz = Main Cutting Force and is in direction of Tool travel.
PN PT
Pz = Main Cutting Force and is in direction of Tool travel.
= It represents the total Workdone by the Tool in
cutting the material.
Py = Feed force and acts in direction perpendicular to
main cutting force= Py acts perpendicular to Pz.
Ps = Force along shearing plane, represents the force
required to shear the metal.
Pd = Force acts normal to Ps and results in compressive
stress applied to plane of shear.
Pt= Force acts along Tool face = Pt represents frictional
resistance met by the chip as it slides over the Tool.
Coefficient of Friction is given by the ratio of Pt and Pn.
Ps = Pz Cosф – Py Sinф
Pd = Pz Sinф + Py Cosф
Pt = Pz Sin γ + Py Cos γ
Pn = Pz Cos γ – Py Sin γ

12. COEFFICIENT OF FRICTION
Coeffient of Friction (µ) between the Chip and the Tool face is
measure of the resistance to sliding encountered by the chip
as it passes over the Tool face.
Coeffient of Friction,
µ = PT/ PN
= ( Pz Sin γ + Py Cos γ ) / (Pz Cos γ – Py Sin γ)
= (Py + Pz tan γ) / (Pz – Py tan γ)
Coefficient of friction can be controlled by using effective cutting fluid,
by varying the rake angle, by using higher cutting speed or by adding
certain chemical additives to the workpiece material.

13. TEMPERATURES IN METAL CUTTING
Temperature generated in the region of Tool
point during metal cutting control the rate of
Tool wear, the practical cutting speed and the
metal removal rate.
Workdone in deforming the material to form
the Chip and to move the Chip and freshly cut
work surface over the Tool is converted into
Heat.
The figure shows the region where Heat is
primarily developed during Metal Cutting.
primarily developed during Metal Cutting.
Total heat generated ,
Q in metal cutting = Total Amount of Work /
Mechanical equivalent of heat
= (Pz . V) / 427 , kilocalories/min
Where, Pz = tangential cutting force
V = Cutting speed, m/min
Heat Dissipated per minute by the Chip,
Qc = Ts . W. Cp / 1000 kilocalories/ min
Where, Ts = Increase in Temperature, W = Weight of
Chip, Cp= Specific heat of work material.
Ratio of Qc / Q indicates the
percentage of Heat generated that
can be dissipated by the chips.
80% of heat generated is dessipated
by Chip.
18% of heat generated is dessipated
by Tool.
Rest os heat is dessipated by Work