Please refer this file just as reference material. More concentration should on class room work and text book methodology. Force acting at machining

1. CHAPTER
METAL CUTTING
Presentation Prepared by
Prof. Naman M. Dave
Assistant Prof. (Mechanical Dept.)
Gandhinagar Institute of Technology

2. • Definition of Manufacturing
• The word manufacturing is derived from Latin:
manus = hand, factus = made
• Manufacturing is the economic term for making goods and
services available to satisfy human wants.
• Manufacturing implies creating value to a raw material by
applying useful mental and physical labour. Manufacturing
converts the raw materials to finished products to be used for
some purpose.
• Whether from nature or industry materials cannot be used in their
raw forms for any useful purpose.
• The materials are then shaped and formed into different useful
components through different manufacturing processes to fulfil the
needs of day-to-day work.
INTRODUCTION

3. MANUFACTURING SYSTEM AND
PRODUCTION SYSTEM
Manufacturing system:
• A collection of operations and processes used to obtain a
desired product(s) or component(s) is called a manufacturing
system.
• The manufacturing system is therefore the design or
arrangement of the manufacturing processes..
Production system:
• A production system includes people, money, equipment,
materials and supplies, markets, management and the
manufacturing system.

4. Production System - The Big Picture
Raw materials Manufacturing
Process
Manufacturing
Process
Finished
product
Manufacturing System
People, Money, Equipment, Materials and Supplies, Markets, Management

5. Material Removal Processes
A family of shaping operations, the common feature of
which is removal of material from a starting work part
so the remaining part has the desired geometry.
 Machining – material removal by a sharp cutting
tool, e.g., turning, milling, drilling.
 Abrasive processes – material removal by hard,
abrasive particles, e.g., grinding.
 Nontraditional processes - various energy forms
other than sharp cutting tool to remove material.

6. MACHINING
Machining is a semi-finishing or finishing process
essentially done to impart required or stipulated
dimensional and form accuracy and surface finish to
enable the product to
 fulfill its basic functional requirements
 provide better or improved performance
 render long service life.
Machining is a process of gradual removal of excess
material from the preformed blanks in the form of
chips.

7. Why Machining is Important
 Variety of work materials can be machined
◦ Most frequently used to cut metals
 Variety of part shapes and special geometric
features possible, such as:
◦ Screw threads
◦ Accurate round holes
◦ Very straight edges and surfaces
 Good dimensional accuracy and surface finish

8. Examples of Cutting Processes

9. Disadvantages with Machining
 Wasteful of material
◦ Chips generated in machining are wasted material, at
least in the unit operation
 Time consuming
◦ A machining operation generally takes more time to
shape a given part than alternative shaping processes,
such as casting, powder metallurgy, or forming

10. Diagrammatic Representation of
Material Removal Operations

11. Mechanism of Chip formation
The form of the chips is an important index of
machining because it directly or indirectly indicates :
 Nature and behavior of the work material under
machining condition
 Specific energy requirement (amount of energy
required to remove unit volume of work material)
in machining work
 Nature and degree of interaction at the chip-tool
interfaces.

12. Mechanism of Chip
formation
The form of machined chips depend mainly upon :
 Work material
 Material and geometry of the cutting tool
 Levels of cutting velocity and feed and also to some extent
on depth of cut
 Machining environment or cutting fluid that affects
temperature and friction at the chip-tool and work-tool
interfaces.
Knowledge of basic mechanisms of chip formation helps to
understand the characteristics of chips and to attain
favourable chip forms.

13. A chip has two surfaces:
1. One that is in contact with the tool face (rake
face). This surface is shiny, or burnished.
2. The other from the original surface of the work
piece.
This surface does not come into contact with any
solid body. It has a jagged, rough appearance,
which is caused by the shearing mechanism.
Chip Formation

14. Figure. More realistic view of chip formation, showing shear zone
rather than shear plane. Also shown is the secondary shear zone
resulting from tool-chip friction.
Primary & Secondary Shear
Zone

15. Piispanen model of Card
Analogy

16. Piispanen model of Card Analogy

17. Four BasicTypes of Chip in
Machining
1. Discontinuous chip
2. Continuous chip
3. Continuous chip with Built-up Edge (BUE)
4. Serrated chip

18. Figure: Shear strain during chip formation:
(a) Chip formation depicted as a series of parallel plates sliding relative to each other,
(b) One of the plates isolated to show shear strain, and
(c) Shear strain triangle used to derive strain equation.
Shear Strain in Chip Formation
𝜺𝜺 =
𝑨𝑨𝑨𝑨
𝑩𝑩𝑩𝑩
=
𝑨𝑨𝑨𝑨+𝑫𝑫𝑫𝑫
𝑩𝑩𝑩𝑩
= 𝐂𝐂𝐂𝐂𝐂𝐂 ∅ + 𝑻𝑻𝑻𝑻𝑻𝑻 (∅ −∝)
Shear strain in machining can be computed from the following equation,
based on the parallel plate model:
Where,
ε =Shear strain, φ = Shear plane angle and α = Rake angle of cutting
tool

19. Large shear strains are associated with low shear angles, or
low or negative rake angles.
Shear strains of 5 or higher in actual cutting operations.
Deformation in cutting generally takes place within a very
narrow deformation zone; that is, d = BD in Fig is very small.
Therefore, the rate at which shearing takes place is high.
Shear angle influences force and power requirements, chip
thickness, and temperature.
Consequently, much attention has been focused on
determining the relationships between the shear angle and
work piece material properties and cutting process variables.
Shear Strain in Chip Formation

20. Velocity Relationship in Orthogonal
Cutting
Figure (a) Schematic illustration of the basic mechanism of chip formation by
shearing. (b) Velocity diagram showing angular relationships among the three
speeds in the cutting zone.
The tool has a rake angle of α, and relief (clearance) angle. The shearing
process in chip formation is similar to the motion of cards in a deck sliding
against each other.

21. Velocity Relationship

22. Using sine rule,
)90sin(sin))(90sin( αφαφ −
==
−−
sc vvv
αφαφ cossin)cos(
sc vvv
==
−
)cos(
sin
αφ
φ
−
=
v
vc
rvvc ×=






=
)-(Cos
Sin
r
αφ
φ
)cos(
cos
αφ
α
−
=
v
vs
c
c
cc
t
t
rvv
tvt
0
0
rAs,
v
chiptheupflowingmaterialofVolumeunit timepermaterialofVolume
=×=⇒
×=×⇒
=
Velocity Relationship

23. Forces Acting on Chip
F, N, Fs, and Fn cannot be directly measured
Forces acting on the tool that can be measured:
– Cutting force Fc andThrust force Ft

24. Fs = Shear Force, which acts along the shear plane, is the resistance to
shear of the metal in forming the chip.
Fn = Force acting normal to the shear plane, is the backing up force on
the chip provided by the work piece.
F = Frictional resistance of the tool acting against the motion of the chip
as it moves upward along the tool
N = Normal to the chip force, is provided by the tool.
NS
/
FFR
FNR


+=
+=
It is assumed that the resultant forces R & R’ are equal and opposite in
magnitude and direction. Also they are Collinear. Therefore for the
purpose of analysis the chip is regarded as an independent body held in
mechanical equilibrium by the action of two equal and opposite forces R,
which the workpiece exerts upon the chip and R’ which the tool exerts
upon the chip.
Forces acting on chip in Orthogonal
cutting

25. Resultant Forces
 Vector addition of F and N = resultant R
 Vector addition of Fs and Fn = resultant R '
 Forces acting on the chip must be in balance:
◦ R ' must be equal in magnitude to R
◦ R’ must be opposite in direction to R
◦ R’ must be collinear with R

26. Cutting Forces
Fig: (a) Forces acting on a cutting tool during 2-dimensional cutting. Note that the resultant force, R must
be collinear to balance the forces. (b) Force circle to determine various forces acting in the cutting
zone.

27. The following is a circle
diagram. Known as Merchant’s
circle diagram, which is
convenient to determine the
relation between the various
forces and angles.
In the diagram two force
triangles have been combined
and R and R’ together have
been replaced by R. the force
R can be resolved into two
components Fc and Ft.
Fc and Ft can be determined
by force dynamometers.
tc FFR

+=
The rake angle (α) can be measured from the tool, and forces F and N can then
be determined. The shear angle (φ) can be obtained from it’s relation with chip
reduction coefficient. Now Fs & Fn can also be determined.
Merchant’s Circle Diagram
∅
Work
Tool
Chip
Clearance Angle
Ft
Fc
F
N
Fn
Fs
α
α
β
(β - α)
R

28. Merchant’s Circle Diagram
Work
Tool
Chip
Clearance Angle
Ft
Fc
F
N
Fn
Fs
α
α
β
∅
(β - α)
R

29. Clearance Angle
The procedure to construct a
Merchant’s circle diagram
Work
Tool
Chip
Ft
Fc
F
N
Fn
Fs
α
α
β
∅
R

30.  Set up x-y axis labeled with forces, and the origin in the
centre of the page. The cutting force (Fc) is drawn
horizontally, and the tangential force (Ft) is drawn
vertically. (Draw in the resultant (R) of Fc and Ft.
 Locate the centre of R, and draw a circle that encloses
vector R. If done correctly, the heads and tails of all 3
vectors will lie on this circle.
 Draw in the cutting tool in the upper right hand
quadrant, taking care to draw the correct rake angle (α)
from the vertical axis.
 Extend the line that is the cutting face of the tool (at the
same rake angle) through the circle. This now gives the
friction vector (F).
The procedure to construct a
Merchant’s circle diagram

31. The procedure to construct a
Merchant’s circle diagram
 A line can now be drawn from the head of the friction
vector, to the head of the resultant vector (R). This gives the
normal vector (N). Also add a friction angle (β) between
vectors R and N. Therefore, mathematically, R = Fc+Ft = F +
N.
 Draw a feed thickness line parallel to the horizontal axis.
Next draw a chip thickness line parallel to the tool cutting
face.
 Draw a vector from the origin (tool point) towards the
intersection of the two chip lines, stopping at the circle. The
result will be a shear force vector (Fs). Also measure the
shear force angle between Fs and Fc.
 Finally add the shear force normal (Fn) from the head of Fs
to the head of R.
 Use a scale and protractor to measure off all distances
(forces) and angles.

32. αα
αα
sincos
cossin
tC
tC
FFN
GEODCDODABN
FFF
GBEDGBCGCBOAF
−=⇒
−=−==
+=⇒
+=+===
Frictional Force System
angleFrictionWhere
N
F
tan
frictionoftcoefficienThe
=
==
β
βµ
Relationship of various forces acting on the chip with the horizontal and
vertical cutting force from Merchant circle diagram
Ft
Fc
F
N
α
α
β
(β - α)
R
α
α
α
(90-α)
(90-α)
O
A
C
B
G
E
D
∅
Work
Tool
Chip
Clearance Angle
Ft
Fc
F
N
Fn
Fs
α
α
β
(β - α)
R

33. Shear Force System
φφ
φαβ
φφ
cossin
(
sincos
tCN
N
S
tCS
S
FFF
DEBCDEADAEF
RCosF
FFF
CDOBABOBOAF
+=⇒
+=+==
)+−=
−=⇒
−=−== Also:
)tan( αβφ −+= SN FF
Relationship of various forces acting on the chip with the horizontal and
vertical cutting force from Merchant circle diagram
∅
Work
Tool
Chip
Clearance Angle
Ft
Fc
F
N
Fn
Fs
α
α
β
(β - α)
R
∅
Ft
Fc
A
O
Fn
Fs
α
α
(β - α)
R
B
C
D
E
∅
∅
(90-∅)
(90-∅)

34. )tan(
cossin
sincos
sincos
cossin
αβφ
φφ
φφ
αα
αα
−+=
+=
−=
−=
+=
SN
tCN
tCS
tC
tC
FF
FFF
FFF
FFN
FFF
Relationship of various forces acting on the chip with the horizontal and
vertical cutting force from Merchant circle diagram
∅
Work
Tool
Chip
Clearance Angle
Ft
Fc
F
N
Fn
Fs
α
α
β
(β - α)
R
Ft = R Sin (β-α)
Fc = R Cos (β –α)

35. Knowledge of the cutting forces and power involved in
machining operations is important for the following
reasons:
a. Machine tools can be properly designed to minimize
distortion of the machine components, maintain the
desired dimensional accuracy of the machined part,
and help select appropriate tool holders and work-
holding devices.
b. The work piece is capable of withstanding these
forces without excessive distortion.
c. Power requirements must be known in order to
enable the selection of a machine tool with adequate
electric power.
CUTTING FORCES and POWER

36. CUTTING FORCES and POWER
Cutting force, Fc, acts in the direction of cutting speed, V, and
supplies energy required for cutting.
Thrust force, Ft , acts in a direction normal to cutting velocity,
perpendicular to WP. The resultant force, R can be resolved
into two components :
 Friction force: F, along the tool-chip interface
 Normal force: N, perpendicular to it.
F = R sin β
N = R cos β
R is balanced by an equal and opposite force along the shear
plane and is resolved into a shear force, Fs, and a normal
force, Fn
Fs = Fc cos Ø – Ft sin Ø
Fn = Fc sin Ø + Ft cos Ø

37. Coefficient of Friction
Coefficient of friction between tool and chip:
Friction angle related to coefficient of friction as follows:
N
F
=µ
βµ tan=
The ratio of F to N is the coefficient of friction, μ, at the tool-chip
interface, and the angle β is the friction angle.
The coefficient of friction in metal cutting generally ranges from about
0.5 to 2.
α
α
µ
tan
tan
friction,oftCoefficien
tc
ct
FF
FF
N
F
−
+
==

38. Shear Stress
Shear stress acting along the shear plane:
φsin
wt
A o
s =
where As = area of the shear plane,
Shear stress = shear strength of work material during
cutting
s
A
s
F
=τ

39. References
1. Kalpakjian, Schmid, Manufacturing Processes for Engineering Materials, 4th
edition,, Prentice Hall 2003
2. DeGarmo, E. P., J. T. Black, and R. A. Kohser, Materials and processes in
Manufacturing, PHI.
3. P.N. Rao, Manufacturing Technology – Metal Cutting and Machine Tools,TMH.
4. George Schneider,Jr. CMfgE, Cutting Tool Applications
5. Amstead, B. H., P. F. Ostwald, and M. L. Begeman, Manufacturing
Processes, 8th ed.,Wiley, New York, 1988.
6. Amitabha Battacharya , Metal Cutting Theory and Practice
7. Shaw, M. C., Metal Cutting Principles, Oxford University Press, Oxford, 1984.
8. Schey, J.A., Introduction to Manufacturing Processes, McGraw-Hill, NewYork,
1977.
9. Lindberg, R.A., Processes and Materials of Manufacture,
10.William J Patton, Machine tool Operations, Reston publishing company
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