MANUFACTURING TECHNOLOGY-II

MANUFACTURING TECHNOLOGY-II
UNIT-1 THEORY OF METAL CUTTING
Presented by
Prof.S.Sathishkumar
Assistant Professor
Department of Mechanical Engineering
Vel Tech (Engineering College)
Avadi-chennai-62
Email- sathishkumar@veltechengg.com
1

• 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
2

MANUFACTURING SYSTEM AND
PRODUCTION SYSTEM
3
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.

Production System - The Big Picture
4
Manufacturing System
People, Money, Equipment, Materials and Supplies, Markets, Management

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.
5

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.
6

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
7

Examples of Cutting Processes
8

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
9

Diagrammatic Representation of Material
Removal Operations
10

Cutting action involves shear deformation of work
material to form a chip.
As chip is removed, new surface is exposed.
Figure 21.2 (a) A cross-sectional view of the machining process, (b)
tool with negative rake angle; compare with positive rake angle in (a).
Machining

Mechanism of Chip formation
The form of the chips is an important index of machining
because it directly or indirectly indicates :
 Nature and behaviour 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.
13

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.
14

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
15

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
16

Piispanen model of Card Analogy
17

Piispanen model of Card Analogy
18

Four Basic Types of Chip in
Machining
1. Discontinuous chip
2. Continuous chip
3. Continuous chip with Built-up Edge (BUE)
4. Serrated chip
19

continuous chips are not always
desirable, particularly in
automated machine tools, it tends
to get tangled around the tool and
operation has to be stopped to
clear away the chips.
20
Continuous chips
Continuous chips are usually formed with ductile
materials at high rake angles and/or high cutting speeds.
A good surface finish is generally produced.

Continuous Chips
Continuous chips usually form under the following
conditions:
 Small chip thickness (fine feed)
 Small cutting edge
 Large rake angle
 High cutting speed
 Ductile work materials
 Less friction between chip tool interface through
efficient lubrication
21

Continuous Chips
• Deformation of the material takes place along a
narrow shear zone, primary shear zone.
• CCs may, because of friction, develop a secondary
shear zone at tool–chip interface. The secondary zone
becomes thicker as tool–chip friction increases.
• In CCs, deformation may also take place along a wide
primary shear zone with curved boundaries.
22

Discontinuous chips
Discontinuous chips consist of segments that may be
firmly or loosely attached to each other.
These chips occur when machining hard brittle
materials such as cast iron.
Brittle failure takes place along the shear plane before
any tangible plastic flow occurs.
Discontinuous chips will form in brittle materials at low
rake angles (large depths of cut).
23

Discontinuous Chips
DCs usually form under the following conditions:
1. Brittle work piece materials
2. Work piece materials that contain hard inclusions and
impurities, or have structures such as the graphite
flakes in gray cast iron.
3. Very low or very high cutting speeds.
4. Large depths of cut.
5. Low rake angles.
6. Lack of an effective cutting fluid.
7. Low stiffness of the machine tool.
24

Discontinuous Chips
Because of the discontinuous
nature of chip formation, forces
continually vary during cutting.
Hence, the stiffness or rigidity of
the cutting-tool holder, the Work
holding devices, and the machine
tool are important in cutting with
both DC and serrated-chip
formation.
25

Serrated chips
Serrated chips: semi-continuous chips with alternating
zones of high shear strain then low shear strain.
Metals with low thermal conductivity and strength that
decreases sharply with temperature, such as titanium,
exhibit this behavior.
26
The Semi-continuous chips have
a saw-tooth-like appearance.
Associated with difficult-to-
machine metals at high cutting
speeds.

Built-Up Edges Chips
BUE, consisting of layers of material from the work piece
that are gradually deposited on the tool, may form at the
tip of the tool during cutting.
As it becomes larger, BUE becomes unstable and
eventually breaks up.
Part of BUE material is carried away by the tool side of
the chip; the rest is deposited randomly on the work piece
surface.
The process of BUE formation and destruction is
repeated continuously during the cutting operation,
unless measures are taken to eliminate it.
27

Built-up edges chips
1.Increase the cutting speeds
2.Decreasing depth of cut
3.Increasing the rake angle
4.Using a sharp tool
5.Using an effective cutting fluid
6.Use a cutting tool that has
lower chemical affinity for the
work piece material.
28
The tendency for a BUE to form is reduced by any of the
following practices:

Built-up edges chips
Because of work hardening and deposition of successive
layers of material. BUE hardness increases significantly.
BUE is generally undesirable as it results in poor surface
finish.
A thin, stable BUE is sometimes desirable because it
reduces wear by protecting the rake face of the tool.
As cutting speed increases the size of BUE decreases.
29

Types of Built-up edges
Fig. Different forms of built up edge
30

Effects of BUE formation
Formation of BUE causes several harmful effects, such
as:
 It unfavourably changes the rake angle at the tool tip
causing increase in cutting forces and power consumption
 Repeated formation and dislodgement of the BUE causes
fluctuation in cutting forces and thus induces vibration
which is harmful for the tool, job and the machine tool.
 Surface finish gets deteriorated
 May reduce tool life by accelerating tool-wear at its rake
surface by adhesion and flaking
 Occasionally, formation of thin flat type stable BUE may
reduce tool wear at the rake face.
31

Cutting Tool Classification
1. Single-Point Cutting Tools
– One dominant cutting edge
– Point is usually rounded to form a nose radius
– Eg: Turning uses single point tools
2. Multi-Point Cutting Tools
– More than one cutting edge
– Motion relative to work achieved by rotating
– Eg: Drilling and milling use rotating multiple cutting
edge tools
32

Figure: (a) A single-point tool showing rake face, flank, and tool point;
(b) A helical milling cutter, representative of tools with multiple
cutting edges.
Cutting Tool Classification
33

Right Hand Single Point Cutting Tool
34
FIGURE: (a) Schematic illustration of a right-hand cutting tool. Although these tools
have traditionally been produced from solid tool-steel bars, they have been largely
replaced by carbide or other inserts of various shapes and sizes, as shown in (b).

Right-hand Cutting Tool and Insert
35
Fig: (a) Schematic illustration of right-hand cutting tool. Although these tools have
been produced traditionally from solid tool-steel bars, they have been replaced largely
with (b) inserts made of carbides and other materials of various shapes and sizes.

Single Point Cutting Tool Geometry
36
Side rake angle
(αs)
End relief angle (ERA)
Nose Radius (NR)
End cutting edge angle (ECEA)
Side cutting edge angle (SCEA)
Side View
Front View
Top View
Lip angle
Back rake angle (αb)
Side relief angle (SRA)
Geometry of positive rake single point cutting tool

Geometry of negative rake single point cutting tool
Side rake angle (αs)
End relief angle (ERA)
Nose Radius (NR)
End cutting edge angle (ECEA)
Side cutting edge angle (SCEA)
Side View
Front View
Top View
Lip angle
Back rake angle (αb)
Side relief angle (SRA)
Single Point Cutting Tool Geometry
37

Back rake angle:
•The back rake angle is the angle between the face of the tool and a
line parallel to the base of the shank in a plane parallel to the side
cutting edge.
•The back rake angle affects the ability of the tool to shear the work
material and form chip.
Side Rake Angles:
•It is the angle by which the face of the tool is inclined side ways.
The Rake Angle:
• The side rake angle and the back rake angle combine to form the
effective rake angle. This is also called true rake angle or
resultant rake angle of the tool.
Cutting Tool Angles and Significance
38

39
The Rake Angle:
• The rake angle is always at the topside of the tool.
• The basic tool geometry is determined by the rake angle of the
tool.
• Rake angle has two major effects during the metal cutting
process.
• One major effect of rake angle is its influence on tool strength. A
tool with negative rake will withstand far more loading than a
tool with positive rake.
• The other major effect of rake angle is its influence on cutting
pressure. A tool with a positive rake angle reduces cutting forces
by allowing the chips to flow more freely across the rake surface.

The rake angle has the following function:
• It allows the chip to flow in convenient direction.
• It reduces the cutting force required to shear the metal and
consequently helps to increase the tool life and reduce the power
consumption. It provides keenness to the cutting edge.
• It improves the surface finish.
40

41
Positive Rake:
• Positive rake or increased rake angle reduces compression, the
forces, and the friction, yielding a thinner, less deformed and
cooler chip.
• But increased rake angle reduces the strength of the tool
section, and heat conduction capacity.
• Some areas of cutting where positive rake may prove more
effective are, when cutting tough, alloyed materials that tend
to work-harden, such as certain stainless steels, when cutting
soft or gummy metals, or when low rigidity of work piece,
tooling, machine tool, or fixture allows chatter to occur.
• The shearing action and free cutting of positive rake tools will
often eliminate problems in these areas.

Negative Rake:
• To provide greater strength at the cutting edge and better heat conductivity,
zero or negative rake angles are employed on carbide, ceramic,
polycrystalline diamond, and polycrystalline cubic boron nitride cutting tools.
• These materials tend to be brittle, but their ability to hold their superior
hardness at high temperature results in their selection for high speed and
continuous machining operation.
• Negative rakes increases tool forces but this is necessary to provide added
support to the cutting edge. This is particularly important in making
intermittent cuts and in absorbing the impact during the initial engagement
of the tool and work.
• Negative rakes are recommended on tool which does not possess good
toughness (low transverse rupture strength). Thus negative rake (or small
rake) causes high compression, tool force, and friction, resulting in highly
deformed, hot chip.
42

The Rake Angle for a Tool Depends on the Following Factors:
• Type of material being cut:
A harder material like cast iron may be machined by smaller rake angle than
that required by soft material like mid steel or aluminum.
• Type of tool material:
Tool material like cemented carbide permits turning at very high speed. At high
speeds rake angle has little influence on cutting pressure. Under such condition
the rake angle can minimum or even negative rake angle is provided to increase
the tool strength.
• Depth of cut:
In rough turning, high depth of cut is given to remove maximum amount of
material. This means that the tool has to withstand severe cutting pressure. So
the rake angle should be decreased to increase the lip angle that provides the
strength to the cutting edge.
• Rigidity of the tool holder and machine:
An improperly supported tool on old or worn out machine cannot take up high
cutting pressure. So while machining under the above condition, the tool used
should have larger rake angle. 43

Relief Angles:
• Relief angles are provided to minimize physical interference or rubbing
contact with machined surface and the work piece.
• Relief angles are for the purpose of helping to eliminate tool breakage
and to increase tool life.
• If the relief angle is too large, the cutting tool may chip or break. If the
angle is too small, the tool will rub against the work piece and generate
excessive heat and this will in turn, cause premature dulling of the
cutting tool.
• Small relief angles are essential when machining hard and strong
materials and they should be increased for the weaker and softer
materials.
• A smaller angle should be used for interrupted cuts or heavy feeds, and
a larger angle for semi-finish and finish cuts.
44

Side relief angle:
• The Side relief angle prevents the side flank of the tool from rubbing
against the work when longitudinal feed is given.
• Larger feed will require greater side relief angle.
End relief angle:
• The End relief angle prevents the side flank of the tool from rubbing
against the work.
• A minimum relief angle is given to provide maximum support to the tool
cutting edge by increasing the lip angle.
• The front clearance angle should be increased for large diameter works.
End cutting edge angle:
• The function of end cutting edge angle is to prevent the trailing front
cutting edge of the tool from rubbing against the work. A large end
cutting edge angle unnecessarily weakens the tool.
• It varies from 8 to 15 degrees.
45

Side cutting edge angle:
The following are the advantages of increasing this angle:
•It increases tool life as, for the same depth of cut; the cutting
force is distributed on a wider surface.
•It diminishes the chip thickness for the same amount of feed and
permits greater cutting speed.
•It dissipates heat quickly for having wider cutting edge.
•The side cutting edge angle of the tool has practically no effect
on the value of cutting force or power consumed for a given
depth of cut & feed.
•Large side cutting edge angles are likely to cause the tool to
chatter.
46

Nose radius:
The nose of a tool is slightly rounded in all turning tools.
The function of nose radius is as follows:
• Greater nose radius clears up the feed marks caused by the previous
shearing action and provides better surface finish.
• All finish turning tool have greater nose radius than rough turning
tools.
• It increases the strength of the cutting edge, tends to minimize the
wear taking place in a sharp pointed tool with consequent increase in
tool life.
• Accumulation heat is less than that in a pointed tool which permits
higher cutting speeds.
47

Tool Signature
It is the system of designating the principal angles of a single point
cutting tool.
The signature is the sequence of numbers listing the various angles,
in degrees, and the size of the nose radius.
There are several systems available like American standard system
(ASA), Orthogonal rake system (ORS), Normal rake system (NRS), and
Maximum rake system (MRS).
The system most commonly used is American Standard Association
(ASA), which is:
Back rake angle, Side rake angle, End relief angle, Side relief angle,
End cutting Edge angle, Side cutting Edge angle and Nose radius.
48

For example a tool may designated in the following sequence:
8-14-6-6-6-15-1
1. Back rake angle is 8
2. Side rake angle is 14
3. End relief angle is 6
4. Side relief angle is 6
5. End cutting Edge angle is 6
6. Side cutting Edge angle is 15
7. Nose radius is 1 mm
Tool Signature
49

Chip Breakers
Long continuous chip are undesirable.
Chip breaker is a piece of metal clamped to the rake surface of the
tool which bends the chip and breaks it.
Chips can also be broken by changing the tool geometry, thereby
controlling the chip flow.
CBs increase the effective rake angle of the tool and, consequently,
increase the shear angle.
Chips can also be broken by changing the tool geometry, thereby
controlling chip flow, as in the turning operations.
Experience has indicated that the ideal chip is in the shape of the
letter C or the number 9 and fits within a 25 mm square block.
50

Figure: (a) Schematic illustration of the action of a chip breaker. Note that the chip breaker
decreases the radius of curvature of the chip and eventually breaks it.
(b) Chip breaker clamped on the rake face of a cutting tool.
(c) Grooves in cutting tools acting as chip breakers. Most cutting tools used now are inserts
with built-in chip breaker features.
Chip Breakers
51

Chip Breakers
 With soft work piece materials such as pure aluminum or
copper, chip breaking by such means is generally not
effective.
 Common techniques used with such materials, include
machining at small increments and then pausing (so that a
chip is not generated) or reversing the feed by small
increments.
 In interrupted cutting operations, such as milling, chip
breakers are generally not necessary, since the chips
already have finite lengths because of the intermittent
nature of the operation.
52

Orthogonal and Oblique Cutting
The two basic methods of metal cutting using a single point tool are
the orthogonal (2D) and oblique (3D). Orthogonal cutting takes place
when the cutting face of the tool is 900 to the line of action of the
tool. If the cutting face is inclined at an angle less than 900 to the line
of action of the tool, the cutting action is known as oblique.

Oblique Cutting
54
FIGURE (a) Schematic illustration of cutting with an oblique tool. (b) Top view, showing
the inclination angle i. (c) Types of chips produced with different inclination angles

Orthogonal Cutting:
 The cutting edge of the tool remains
normal to the direction of tool feed or
work feed.
 The direction of the chip flow velocity is
normal to the cutting edge of the tool.
 Here only two components of forces are
acting: Cutting Force and Thrust Force.
So the metal cutting may be considered
as a two dimensional cutting.
Oblique Cutting:
• The cutting edge of the tool remains inclined at an
acute angle to the direction of tool feed or work
feed.
• The direction of the chip flow velocity is at an angle
with the normal to the cutting edge of the tool. The
angle is known as chip flow angle.
• Here three components of forces are acting: Cutting
Force, Radial force and Thrust Force or feed force. So
the metal cutting may be considered as a three
dimensional cutting.
 The cutting edge being oblique, the shear force acts
on a larger area and thus tool life is increased.
Feed
Tool
Work
Oblique cutting
Feed
Tool
Work
Orthogonal cutting
Orthogonal and Oblique Cutting
55

56
Orthogonal metal cutting Oblique metal cutting
Cutting edge of the tool is perpendicular
to the direction of tool travel.
The cutting edge is inclined at an angle
less than 90o to the direction of tool
travel.
The direction of chip flow is
perpendicular to the cutting edge.
The chip flows on the tool face making an
angle.
The chip coils in a tight flat spiral The chip flows side ways in a long curl.
For same feed and depth of cut the force
which shears the metal acts on a smaller
areas. So the life of the tool is less.
The cutting force acts on larger area and
so tool life is more.
Produces sharp corners. Produces a chamfer at the end of the cut
Smaller length of cutting edge is in
contact with the work.
For the same depth of cut greater length
of cutting edge is in contact with the
work.
Generally parting off in lathe, broaching
and slotting operations are done in this
method.
This method of cutting is used in almost
all machining operations.

Orthogonal Cutting Model
A simplified 2-D model of machining that describes the mechanics
of machining fairly accurately.

Assumptions in Orthogonal Cutting
 No contact at the flank i.e. the tool is perfectly sharp.
 No side flow of chips i.e. width of the chips remains
constant.
 Uniform cutting velocity.
 A continuous chip is produced with no built up edge.
 The chip is considered to be held in equilibrium by the
action of the two equal and opposite resultant forces R
and R’ and assume that the resultant is collinear.
58

The force system in general case of
conventional turning process
59
Forces acting on a cutting tool

The largest magnitude is the vertical force Ft which in turning is
larger than feed force Fa, and Fa is larger than radial force Fr.
For orthogonal cutting system Fr is made zero by placing the face of
cutting tool at 90 degree to the line of action of the tool.
60

61

Two-
Dimensional
Cutting
Process
62
Fig: Schematic illustration of a 2-d
cutting process, also called
orthogonal cutting:
(a) Orthogonal cutting with a well
defined shear plane, also known as
the Merchant Model.
(b) Orthogonal cutting without a
well-defined shear plane.
Note that the tool shape, depth of
cut, to, and the cutting speed, V, are
all independent variables.

Mechanics of Orthogonal Metal Cutting
 During metal cutting, the metal is severely compressed in the
area in front of the cutting tool. This causes high temperature
shear, and plastic flow if the metal is ductile.
 When the stress in the work piece just ahead of the cutting tool
reaches a value exceeding the ultimate strength of the metal,
particles will shear to form a chip element, which moves up
along the face of the work.
 The outward or shearing movement of each successive element
is arrested by work hardening and the movement transferred to
the next element. The process is repetitive and a continuous chip
is formed.
 The plane along which the element shears, is called shear plane.
63

Chip Thickness Ratio
Where, r = chip thickness ratio;
to = thickness of the chip prior to chip formation; and
tc = chip thickness after separation
64
The ratio of to/tc is known as the cutting ratio, r, expressed as:

65
 The outward flow of the metal causes the chip to be thicker after
the separation from the parent metal.
 i.e. the chip produced is thicker than the depth of cut, so chip
ratio always less than 1.0
 Chip compression ratio: reciprocal of r. It is a measure of how
thick the chip has become compared to the depth of cut.
 The chip thickness ratio is an important and useful parameter for
evaluating cutting conditions.
 Since the undeformed chip thickness, to is a machine setting and
is therefore known, the cutting ratio can be calculated easily by
measuring the chip thickness with a micrometer.

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
s
s
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o
l
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t
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)cos(
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
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cos
tan
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r


9/12/2006

Determining Shear Plane Angle
Based on the geometric parameters of the orthogonal model, the
shear plane angle  can be determined as:
67
where r = chip ratio, and  = rake angle



sin
cos
tan
r
r


1
When shear angle is small
The plane of shear will be larger, chip is thicker and higher force
required to remove the chip.
When shear angle is large
The plane of shear will be shorter, chip is thinner and hence
lesser force required to remove the chip.
The shear angle is determined from chip thickness ratio.

Shear strain in machining can be computed from the following equation,
based on the parallel plate model:
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
𝜺 =
𝑨𝑪
𝑩𝑫
=
𝑨𝑫+𝑫𝑪
𝑩𝑫
= 𝐂𝐨𝐭 ∅ + 𝑻𝒂𝒏 (∅ −∝)
Where,
ε =Shear strain,  = Shear plane angle and  = Rake angle of cutting tool

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. 69
Shear Strain in Chip Formation

Velocity Relationship in Orthogonal Cutting
70
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.

Using sine rule,
)90sin(sin))(90sin(  


sc vvv
 cossin)cos(
sc vvv


)cos(
sin




v
vc
rvvc 







)-(Cos
Sin
r


)cos(
cos




v
vs
c
c
cc
t
t
rvv
wtvwt
0
0
rAs,
v
chiptheupflowingmaterialofVolumeunit timepermaterialofVolume



Velocity Relationship
72

Forces Acting on Chip
73
F, N, Fs, and Fn cannot be directly measured
Forces acting on the tool that can be measured:
– Cutting force Fc and Thrust force Ft

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
74

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
75

Cutting Forces
76
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.

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 () 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
77

Merchant’s Circle Diagram
78
Work
Tool
Chip
Clearance Angle
Ft
Fc
F
N
Fn
Fs
α
α
β
∅
(β - α)
R

Clearance Angle
The procedure to construct a Merchant’s
circle diagram
79
Work
Tool
Chip
Ft
Fc
F
N
Fn
Fs
α
α
β
∅
R

circle diagram
 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).
80

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.
81



sincos
cossin
tC
tC
FFN
GEODCDODABN
FFF
GBEDGBCGCBOAF




Frictional Force System
angleFrictionWhere
N
F
tan
frictionoftcoefficienThe




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
82

Shear Force System



cossin
(
sincos
tCN
N
S
tCS
S
FFF
DEBCDEADAEF
RCosF
FFF
CDOBABOBOAF




 Also:
)tan(   SN FF
∅
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-∅)
83

)tan(
cossin
sincos
sincos
cossin










SN
tCN
tCS
tC
tC
FF
FFF
FFF
FFN
FFF
∅
Work
Tool
Chip
Clearance Angle
Ft
Fc
F
N
Fn
Fs
α
α
β
(β - α)
R
84
Ft = R Sin (β-α)
Fc = R Cos (β –α)

CUTTING FORCES and POWER
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.
85

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
86

Coefficient of Friction
Coefficient of friction between tool and chip:
87
Friction angle related to coefficient of friction as follows:
N
F

 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.



tan
tan
friction,oftCoefficien
tc
ct
FF
FF
N
F




Shear Stress
Shear stress acting along the shear plane:
88
sin
wt
A o
s 
where As = area of the shear plane,
Shear stress = shear strength of work material during
cutting
s
A
s
F


CUTTING FORCES & POWER
Thrust Force
• If the thrust force is too high or if the machine tool is not
sufficiently stiff, the tool will be pushed away from the surface
being machined.
• This movement will, in turn, reduce the depth of cut, resulting in
lack of dimensional accuracy in the machined part, As the rake
angle increases and/or friction at the rake face decreases, this
force can act upward.
• This situation can be visualized by noting that when μ = 0 (that is,
β = 0), the resultant force, R, coincides with the normal force, N.
• In this case, R will have a thrust-force component that is upward.
89

The Power consumed/ work done per sec in cutting: vFP cC 
The Power consumed/ work done per sec in shear: sss vFP 
The Power consumed/ work done per sec in friction: cF vFP 
The total Power required:
fsc PPPP 
Power required in Metal cutting
90

Specific Energy
91
Specific Energy, ut ,is defined as the total energy per unit volume of
material removed.
Where wt0vc is the MRR
Units for specific energy are typically N-m/mm3
Therefore is simply the cutting force to the projected area of cut.
If uf and us be specific energy for friction and specific energy for
shearing, then
As the rake angle increases, the frictional specific energy remains
more or less constant, where as the shear specific energy rapidly
reduced.
00 wt
F
vwt
vF
u CC
t 
vwt
vF
wt
Fr
vwt
vF
vwt
Fv
uuu ssssc
sft
0000


Approximate Specific-Energy Requirements
in Cutting Operations
92
MATERIAL SPECIFIC ENERGY*
W-s/mm3
hp-min/in3
Aluminum alloys
Cast irons
Copper alloys
High-temperature alloys
Magnesium alloys
Nickel alloys
Refractory alloys
Stainless steels
Steels
Titanium alloys
0.4-1.1
1.6-5.5
1.4-3.3
3.3-8.5
0.4-0.6
4.9-6.8
3.8-9.6
3.0-5.2
2.7-9.3
3.0-4.1
0.15-0.4
0.6-2.0
0.5-1.2
1.2-3.1
0.15-0.2
1.8-2.5
1.1-3.5
1.1-1.9
1.0-3.4
1.1-1.5
* At drive motor, corrected for 80% efficiency; multiply the energy
by 1.25 for dull tools.

The Merchant Equation
Of all the possible angles at which shear deformation can
occur, the work material will select a shear plane angle 
that minimizes energy, given by
Derived by Eugene Merchant.
Based on orthogonal cutting, but validity extends to 3-D
machining.
93
22
45

 

Assuming that the shear angle adjusts itself to minimize the cutting force, or
that the shear plane is a plane of maximum shear stress.
(21.3)
β is the friction angle and is related to the coefficient of friction, μ, at the tool
– chip interface (rake face):
From Eq (21.3), as the rake angle decreases
and/or the friction at the tool–chip interface
increases, the shear angle decreases and the
chip becomes thicker,
Thicker chips mean more energy dissipation
because the shear strain is higher. As work
done during cutting is converted into heat,
temperature rise is also higher. 94
The Merchant Equation

Ernest and Merchant gave the relation
)(
2
1
4


 
Theory of Ernst and Merchant (1944)
Assumptions of the theory:
• Tool edge is sharp.
• The work material undergoes deformation across a thin shear
plane.
• There is uniform distribution of normal and shear stress on the
shear plane.
• The work material is rigid and perfectly plastic.
• The shear angle ∅ adjusts itself to give minimum work.
• The friction angle β remains constant and is independent of ∅.
• The chip width remains constant.
M. Eugene Merchant
95

What the Merchant Equation Tells Us
• To increase shear plane angle
– Increase the rake angle
– Reduce the friction angle (or coefficient of friction)
96
22
45

 

Higher shear plane angle means smaller shear plane which means
lower shear force
Result: lower cutting forces, power, temperature, all of which mean
easier machining
Figure - Effect of shear plane angle φ: (a) higher φ with a resulting lower shear plane area;
(b) smaller φ with a corresponding larger shear plane area. Note that the rake angle is
larger in (a), which tends to increase shear angle according to the Merchant equation
97
Effect of Higher Shear Plane Angle

Schmid’s Law
99
 As we know plastic deformation by slip is due to shear stresses.
 Even if we apply a tensile force on the specimen  the shear stress
resolved onto the slip plane is responsible for slip.
 When the Resolved Shear Stress (RSS) reaches a critical value →
Critical Resolved Shear Stress (CRSS) → plastic deformation starts
(The actual Schmid’s law)
τs = σ cos ψ cos θ Schmid's Law
Schmid's law defines the relationship between shear stress, the
applied stress, and the orientation of the slip system. It is an equation
for finding the stress in the slip plane given an axial force and the angle
of the slip plane.
Schmid's law helps to explain the differences in behavior of different
metals when subjected to a unidirectional force.

Schmid’s Law
100
θ = angle defining slip direction relative to the force F = unidirectional force
Ψ = angle defining the normal to the slip plane Fs = Shear force
τs = Resolved shear stress in the slip direction A = area of slip plane
σ = unidirectional stress applied to the cylinder

Schmid’s Law
101
The slip plane and slip direction to the applied force can be oriented by
defining the angles θ and ψ. θ is the angle between the slip direction and
the applied force, and ψ is the angle between the normal to the slip plane
and the applied force.
In order for the dislocation to move in its slip system, a shear force acting in
the slip direction must be produced by the applied force. This resolved
shear force Fs is given by:
Fs = F Cos θ
If the equation is divided by the area of the slip plane, A = A0/Cos ψ,
Schmid's law is obtained:
τs = σ cos ψ cos θ
where:
τs =Fs /A & σ =F/A0

Question: Given that all objects shown below are of equal mass and
identical shape, in which case the frictional force is greater?
Question: Who sketched this figure?
Friction Force

Leonardo Da Vinci (1452-1519) showed that the friction force is
independent of the geometrical area of contact.
The paradox: Intuitively one would expect the friction force to
scale proportionally to the contact area.
Da Vinci law and the Paradox
Amontons' first law: The force of friction is directly proportional to
the applied load. Friction, FS is proportional to the normal force, FN
Amontons' second law: The frictional force is independent of the
geometrical contact area.
NS FF 
Amontons’ laws

A way out of Da Vinci’s paradox has been suggested by Bowden
and Tabor, who distinguished between the real contact area
and the geometric contact area. The real contact area is only a
small fraction of the geometrical contact area.
Bowden and Tabor (1950, 1964)
Figure from: Scholz, 1990

Adhesion theory of friction
The understanding of friction between solids was made
clearer after the development of the junction growth theory
by Bowden and Tabor (1950).
This is also known as the adhesion theory of friction.
It states that friction is a result of the true contact area
between the solids.
The true area of contact is far less in comparison to the
apparent contact area. True area of contact is a sum of the all
micro-contacts at the asperities of the two solids and will be
dependent on the yield strength of the materials.
A soft material such as rubber would give near complete
contact meaning true area of contact will be equal to the
apparent area of contact. 105

Ploughing in Friction
106
All contacting surfaces are directly affected by surface friction. Surface
friction allows control of all forms of motion. factors affecting the
coefficient of surface friction includes Ploughing
It is the Ploughing of one surface by the asperities on the other
surface.

Coulomb's Law of Friction
Kinetic friction is independent of the sliding velocity.
Dry friction resists relative motion of two solid surfaces in contact. The two
regimes of dry friction are static friction, between non-moving surfaces,
and kinetic friction (sliding friction or dynamic friction) between moving
surfaces.
Coulomb friction, named after Charles-Augustin de Coulomb, is an
approximate model used to calculate the force of dry friction. It is governed
by the model:
Where,
Ff = friction force exerted by each surface on the other. It is parallel to the
surface, in a direction opposite to the net applied force.
μ = coefficient of friction, (an empirical property of the materials in contact)
Fn is the normal force exerted by each surface on the other, directed
perpendicular (normal) to the surface.
107

An experiment, in the style of
Coulomb
108

Coulomb's Law of Friction
The Coulomb friction may take any value from zero up to , and the
direction of the frictional force against a surface is opposite to the
motion that surface would experience in the absence of friction.
Thus, in the static case, the frictional force is exactly what it must be
in order to prevent motion between the surfaces; it balances the net
force tending to cause such motion.
The force of friction is always exerted in a direction that opposes
movement (for kinetic friction) or potential movement (for static
friction) between the two surfaces.
For an example of potential movement, the drive wheels of an
accelerating car experience a frictional force pointing forward; if
they did not, the wheels would spin, and the rubber would slide
backwards along the pavement. Note that it is not the direction of
movement of the vehicle they oppose, it is the direction of (potential)
sliding between tire and road. 110

THE MECHANICS OF OBLIQUE
CUTTING
112
Figure
(a) Schematic illustration of cutting with an oblique tool. (Note the direction of chip movement)
(b) Top view, showing the inclination angle, i,.
(c) Types of chips produced with tools at increasing inclination angles.

THE MECHANICS OF OBLIQUE
CUTTING
Chip flows up the rake face of the tool at angle αc (chip flow angle),
which is measured in the plane of the tool face.
Angle αn , the normal rake angle, is a basic geometric property of the
tool. This is the angle between the normal OZ to the work piece
surface and the line OA on the tool face.
The work piece material approaches the tool at a velocity V and
leaves the surface (as a chip) with a velocity Vc
Effective rake angle αe is calculated in the plane of these two
velocities. Assuming that the chip flow angle αc is equal to the
inclination angle i, the effective rake angle αe is
As i increases, the effective rake angle increases and the chip
becomes thinner and longer.
113

Cutting forces in Oblique Cutting
76

References
98
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
11.O W Boston, Metal Processing, 2nd edition 1951, John Wiley and Sons
12.B.S.Raghuwanshi, A course in Workshop Technology-Dhanpat Rai & Sons.
13.Hajra Choudhury, Elements of Workshop Technology–Vol.-II, Media Promoters and
Publishers.
14.O P Khanna, Production Technology-(Vol. II)
15.R K Jain, Production Technology
16.HMT, Production Technology, HMT

MANUFACTURING TECHNOLOGY-II

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