India aims to grow its manufacturing sector to further develop its economy. Manufacturing provides employment and supports agriculture and services. However, India's growth has relied on services while manufacturing and agriculture have faced challenges. Manufacturing processes can be classified into shaping, joining, removal, and regenerative methods. Mechanical properties like elasticity and plasticity determine how metals deform under forces. Dislocations allow plastic deformation at the atomic level. Tool geometry, such as rake and clearance angles, affect tool performance and machining characteristics like surface finish and forces. Maintaining proper tool geometry optimizes the machining process.

1. Mechanical Department SSET 2015
Page1
Production Engineering
Module I
Scenario of manufacturing process
India is one of the fastest growing economies in the world, and is seeing a steady growth, based
on strong fundamentals. But the Indian manufacturing sector is facing challenging times. It as
become imperative for India to breathe life and growth into its manufacturing sector.
Manufacturing sector is the backbone of economy of the country.
 It gives Employment ( capacity to absorb large labor force which increase income level)
 It is a Catalyst for agriculture and service sector growth (modernizing agriculture)
The economic growth in the country has been fueled by the service sector, but growth cannot
sustain without the support of the manufacturing and agriculture sector. Studies have estimated
that every job created in manufacturing has a multiplier effect, creating 2–3 jobs in the services
sector. India is held back by infrastructure, R&D, logistics, lack of clear and comprehensive
objectives, formulation of the Plan, focus on implementation, environmental sustainability,
regulations and Technology.
Classification of manufacturing process
Production or manufacturing can be simply defined as value addition processes by which raw
materials of low utility and value due to its inadequate material properties and poor or irregular
size, shape and finish are converted into high utility and valued products with definite
dimensions, forms and finish imparting some functional ability.
A simple example is shown below
Manufacturing processes can be broadly classified in four major groups as follows:
1. Shaping or forming Manufacturing a solid product of definite size and shape from a given
material taken in three possible states:
a. In solid state – e.g., forging rolling, extrusion, drawing etc.
b. In liquid or semi-liquid state – e.g., casting, injection moulding etc.
c. In powder form – e.g., powder metallurgical process.
2. Joining process (Welding, brazing, soldering etc).
3. Removal process (Machining, Grinding and Non-traditional machining etc).
4. Regenerative manufacturing(Production of solid products in layer by layer from raw
materials in different form)

2. Mechanical Department SSET 2015
Page2
Deformation of metal
Metal piece is subjected to a force, deformation occurs. Material deformation can be permanent
or temporary. Permanent deformation is irreversible (stays even after removal of the applied
forces) is called plastic deformation while the temporary (elastic) deformation disappears after
removal of the applied forces. Plastic deformation in metals is produced by movement of
dislocations or slips, which can be considered analogous to the distortion produced in a deck of
cards.
 Elastic deformation is reversible which
involves bond stretching.
 Plastic deformation is irreversible
which involves bond breaking and
slipping of atoms
Slip occurs when the shear stress exceeds a critical value. Slipping of atoms along crystal planes
(atomic planesis called deformation. A given point in the body is considered safe as long as the
maximum shear stress at that point is under the yield shear stress obtained from a uniaxial tensile
test.
The concept of slip (Dislocation) and plastic deformation
Plastic deformation(irreversible)for ductile material failure
Brittle material failure (without deformation)
Brittle material failure without deformation

3. Mechanical Department SSET 2015
Page3
Schimd law of shear stress **
Schmid's law defines the relationship between shear stress, the applied stress, and the orientation
of the slip system. Schmid's law can help to explain the differences in behavior of different
metals when subjected to a unidirectional force.
F unidirectional force
λ
angle defining slip direction relative to
the force
angle defining the normal to the slip
plane
Fr shear force
A area of slip plane
τr resolved shear stress in the slip direction
σ unidirectional or uniaxial stress
applied to the cylinder
„  ‟ is the angle between the slip direction and the applied force, and „ ‟ 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.
τr =
Fs
A
cosFFforceshear s 
A = A0 / cos 
Uniaxial stress σ =
F
A0
Shear stress, 

 coscos
coscos

oA
F
 coscos known as the Schmid Factor)
Slip process begins within the crystal when the shear stress on the slip plane in slip direction
reaches critical resolved shear stress τr against the uniaxial applied force

4. Mechanical Department SSET 2015
Page4
Machining process
Machining is a term used to describe a variety of material removal processes in which a cutting
tool removes unwanted material from a work-piece to produce the desired shape.
Machining: term applied to all material-removal processes
Machining is the most important of the manufacturing processes. Most machining has very low
set-up cost compared to forming, molding, and casting processes. However, machining is much
more expensive for high volumes. Machining is necessary where tight tolerances on dimensions
and finishes are required.
Metal cutting: material removal process using a sharp wedged tool
Various material removal processes
Metal cutting –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. Tool need not be harder than work is required.
Why Machining is Important
Good dimensional accuracy and surface finish
Fulfill functional requirements
Improved performance of machined part
Long service life of machined part
Variety of part shapes and special geometry features possible, such as: Screw threads,
accurate round holes, very straight edges and surfaces
Disadvantages with Machining
Wasteful of material
Chips generated in machining are wasted material
Time consuming or low material removal rate
A machining operation generally takes more time to shape a given part than
alternative shaping processes, such as casting, powder metallurgy, or forming
Performance and process parameters in metal cutting

5. Mechanical Department SSET 2015
Page5
Dependent variable in metal cutting
Material removal rate
Surface finish
Tool wear rate/tool life performance characteristic of cutting
Dimensional accuracy
Power requirement
Temperature of cutting etc
Independent variables in metal cutting
Work material
Tool material
Tool geometry etc
Rigidity of machine
Cutting parameters Processes parameters
Cutting velocity
Feed
Depth of cut
Cutting fluid etc
Cutting speed refers to the speed at which the tool point of the cutter moves with respect to the
work measured in feet per minute.
In turning, it is given by the surface speed of the work piece,
V = π DoN in m/min
where Do is the diameter of the work piece in meter
N is the RPM of work or spindle speed
Feed – advancement of tool through the work piece in one rotation of spindle, (f mm/rev)
Depth of cut – distance by which tool penetrates in the work-piece (d, mm)
(Do-Df)/2
Df= dia of finished work piece
Cutting rate or MRR = volume / time
Volume of material removes = length * width * depth of the chip
In orthogonal cutting
Thickness of cut= feed
Width of cut= depth of cut
MRR = v f d
Where v = cutting speed;
f = feed;
d = depth of cut

6. Mechanical Department SSET 2015
Page6
Single point tool in metal cutting
Metal-cutting tools are classified as single point or multiple point. A cutting tool that uses a
single cutting edge to remove material is called single point tool. Multiple-point cutting tools
have two or more cutting edges.
• Single point: turning, shaping, planning, slotting tools etc
• Double point: drilling tools
• Multipoint: Milling, broaching, hobbing tools etc.
Tool signature/Geometry (Basic tool angles)
The numerical code that describes all the key angles of a given cutting tool is called tool
signature. Tool geometry is basically referred to some specific angles or slope of the salient
faces and edges of the tools at their cutting point. The tool signature defines the seven basic
angles of tool.
Back rack: It is defined as the angle between the face of the tool and a line parallel to the base
Side rake angle: It is the angle by which the face of the tool is inclined side ways.
Front clearance angle / End relief angles: The angle between front surface of the tool & line
normal to base of the tool is known as a front clearance angle. It avoid rubbing of work piece
against tool.

7. Mechanical Department SSET 2015
Page7
Side clearance /side relief angle: Angle formed by the side surface of the tool with a plane
normal to the base of the tool. It avoid rubbing between flank & work piece when tool is fed
longitudinally. It provides easy entering and leaving off from the work.
End cutting edge angle: This is the angle between end cutting edge & line normal to tool shank.
Large cutting angle weakens the tool. Large angle weakens the tool also.
Function – Provide clearance or relief to trailing end of cutting edge. It prevent rubbing or drag
between machined surface & the trailing port of cutting edge.
Side cutting edge angle (lead angle): It is the angle between side cutting edge & side of tool
flank. With lager side cutting edge angle the chips produced will be thinner & wider which
will distribute the cutting forces & heat produced more over cutting edge.
Increases of cutting angle provides
1. It increases the tool life as the cutting force is distributed over a wider area.
2. It diminishes the chip thickness for the same amount of feed and permits greater
cutting speed
3. It dissipates the heat quickly and improves performances
Too large cutting angle causes chatter.
Nose radius: It is curvature of the tool tip. It provides strengthening of the tool nose, tool life and
better surface finish (slight nose radius clears up the feed marks). Too large nose radius will
induce chatter (vibration) and causes more friction..
Effect of tool geometry angle on cutting performance characteristics
Tool geometry of the cutting tools play very important roles on their performances in achieving
performance, efficiency and overall economy of machining. Angles means inclination of some
faces with respect to some reference planes. Rake and clearance angles are most important.
Geometry of a cutting tool is determined by factors:
Properties of the tool material
Properties of the work piece
Processes parameters like feed, cutting speed and depth of cut, temperature etc
Performance like finish, MRR and accuracy and economy required
Rake angle: (α): It is the angle of the cutting face relative to the work. There are two rake angles,
namely the back rake angle and side rake angle, both of which help to guide chip flow.
Back rake angle: Defined as the angle between the face of the tool and a line parallel to the base.
Side Rake Angles: It is the angle by which the face of the tool is inclined sideways.
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. It affects the ability of the tool to
shear the work material and form chip.
Rake angle can also define as the inclination tool surface with the plane perpendicular to
reference plane. (The reference plane is plane perpendicular to cutting velocity vector.)

8. Mechanical Department SSET 2015
Page8
Rake angle functions
1. It allows the chip to flow in convenient direction and provide easy cutting.
2. It reduces the cutting force required to shear the metal and consequently helps to increase
the tool life and reduce the power consumption.
3. It improves the surface finish.
It can be positive or negative
Positive: reduce cutting forces and less deflection of work and machine
Negative: Negative rake is used to increase edge-strength and life of the tool but it
increases the cutting forces. Used to machine harder metals and heavy cuts which
requires strong cutting edge.
Zero rake to simplify the design and manufacture of the form tools.
Shaping process
Increase of rake angle:
1. Reduce strength of tool (reduce cutting edge strength)
2. Reduce the tool life - the capacity of the tool to conduct heat away from the cutting edge.
3. Reduce forces- helps reduce cutting force and thus cutting power requirement.
4. Reduce friction: Result thinner, less deformed and cooler chip.
5. Increase the surface finish and accuracy

9. Mechanical Department SSET 2015
Page9
Positive rake angles is recommended under the following conditions
 Machining low strength material
 Low power machine
 Long shaft of small diameter
 Set – up lacks strength and rigidity
 Low cutting speed
Negative rake angles is recommended under the following conditions
 Machining hard material which requires high cutting force
 High speed cutting and feed
The rake angle for a tool depends on the following factors
1. Type of the material being cut: A harder material requires low rake angle
2. Type of tool material: Negative rake angle is provided to increase the tool strength.
3. Cutting condition: high MRR, high feed and depth of cut requires high tool strength
4. Rigidity of tool holder and machine: low rigidity of machine requires low rake angle.
Clearance angle (γ) is essentially provided to avoid rubbing of the tool (flank) with the
machined surface which causes loss of energy and damages of both the tool and the job surface.
Clearance angle: Angle of inclination of clearance or flank surface from the finished surface.
Hence, clearance angle is a must and must be positive (3
o
~ 15
o
depending upon tool-work
materials and type of the machining operations like turning, drilling, boring etc). If clearance
angle increases, it reduces flank wear but weaken the cutting edge.
Side cutting edge angle
The following are the advantages of increasing this angle,
1. Provides gradual entering of tool to the work for smoothness of cut
2. Reduces the tool wear for the same depth of cut; as the cutting force is distributed on a
wider surface ( increases tool life )
3. It diminishes the chip thickness for the same amount of feed and permits greater cutting
speed.
4. It dissipates heat quickly for having wider cutting edge and increases tool life
5. Large side cutting edge angles cause the tool to chatter.
Nose radius
It is curvature of the tool tip. It provides strengthening of the tool nose and better surface
finish. Increase of nose radius increase the friction also which increases the cutting force.
Slight nose radius is usually provided to increase the surface finish. Too large nose radius
makes vibration/chatter.
Slight increases of nose radius
1. Improves surface finish
2. Higher tool life (Stronger edge)
3. Heavy feed rates and large depths of cut can be given

10. Mechanical Department SSET 2015
Page10
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.
Factors affecting Roughness
1. Cutting parameters
 High cutting speed
 Low feed improves the surface finish
 Low depth of cut
 Cutting fluid
2. Tool geometry
 Nose radius improves the surface finish
 rake angle – high rake angle improves the finish
 side cutting edge angle - high cutting angle decreases the finish
3. Tool and work material
Factors affecting Cutting forces
1. Tool geometry
 High positive rake angle
 Low nose radius
 Low side cutting angle
2. Cutting condition reduces forces
 Low feed
 Lowdepth of cut
 Use of cutting fluid
 Cutting forces is less depend on cutting speed
Role of surface roughness on crack initiation
Surface quality: Surface roughness can cause microscopic stress concentrations that lower the
fatigue strength. The fatigue life of a component can be expressed as the number of loading
cycles required to initiate a fatigue crack and to propagate the crack to critical size. The name
“fatigue” is based on the concept that a material becomes “tired” and fails at a stress level below
the nominal strength of the material. Failure from cyclic loading occurs when a fatigue crack has
grown large enough so that the remaining cross section cannot support the applied load.
Although a thorough understanding of fatigue crack initiation is lacking, experiments have
shown that surface roughness is one of the ingredients.
Surface roughness and surface damage imply that the free surface is no longer perfectly flat. As a
consequence, small sized stress concentrations along the material surface occur; it is still
significant for promoting cyclic slip and crack nucleation at the material surface. The effect of
surface roughness is very important in order to minimize the cost of machining and time of
machining and also to study the durability of materials.

11. Mechanical Department SSET 2015
Page11
System of description of tool geometry
Tool geometry is defined in different system followed in different countries for different
purposes.
Tool –in- hand system
Machine reference system also called ASA system (Machine configuration is taken as the
reference)
Tool reference system (cutting tool configuration is taken as reference)
Orthogonal rake system
Normal rake system
Work reference system (Configuration of work and tool together is taken as reference)
Machine reference system also called co-ordinate system
This system is also called ASA system (American Standards Association). In this System, the
three planes of reference and the coordinates are chosen based on the configuration and axes of
the machine tool concerned.
Reference plane (πR) is the plane perpendicular to the cutting velocity (Vc)
Machine longitudinal plane (πx) is the plane perpendicular to πR and taken in the direction
of feed (longitudinal feed).
Machine transverse plane (πy)is the plane perpendicular to both πR and πX or plane
perpendicular to πR and taken in the direction of cross feed.

12. Mechanical Department SSET 2015
Page12
Types of metal cutting
Principally there are two types of metal cutting:
Orthogonal cutting, and
Oblique cutting.
Orthogonal Cutting
This orthogonal cutting is also known as Two Dimensional (2-D) Cutting.
1. The cutting edge of the tool remains at 900
to the cutting velocity vector or feed
movement
2. The chip flows in a direction normal to the cutting edge of the tool (chip flow
orthogonally)
3. The tool life is lower than oblique cutting (for same conditions of cutting).
4. Orthogonal cutting involves only two forces so it is called two dimensional cutting
(cutting and feed force).
5. The shear force acts on a smaller area, so shear force per unit area is more.
6. Examples are facing a pipe, slot cuttings in lathe and straight broaching process etc.
Oblique Cutting
1. The cutting edge of the tool is inclined at an acute angle to the direction of feed or
velocity vector
2. The direction of the chip flow is not normal to the cutting edge. Rather it is at an angle to
the normal to the cutting edge.
3. It is three dimensional (3-D) cutting in nature.
4. The shear force acts on a larger area, hence the shear force per area is smaller
5. The tool life is higher than obtained in orthogonal cutting
In actual machining, majority of the cutting operations (turning, milling, etc.) are oblique cutting.

13. Mechanical Department SSET 2015
Page13
Mechanism of chip formation/cutting
Piispanen modeled the shear process of chip formation mechanism as a deck of cards where one
card at a time slides forward with cutting tool progresses as shown in figure shows down
Due to compression, shear stress develops, within that compressed region, in different
magnitude, in different directions and rapidly increases in magnitude. Whenever and wherever
the value of the shear stress reaches or exceeds the shear strength of that work material in the
deformation region, yielding or slip takes place resulting shear deformation in that region along
the plane of maximum shear stress. But the forces causing the shear stresses in the region of the
chip quickly diminishes and finally disappears while that region moves along the tool rake
surface towards and then goes beyond the point of chip-tool engagement. As a result the slip or
shear stops propagating long before total separation takes place. In the mean time the succeeding
portion of the chip starts undergoing compression followed by yielding and shear. This
phenomenon repeats rapidly resulting in formation and removal of chips in thin layer by layer.
Chip formation in brittle material
The stress ahead the cutting edge will increase with increasing applied load. When this stress
reaches a particular limit, a crack forms in front of the cutting edge. A further increase in the
applied load leads to the development of the crack, the fracture of the workpiece material takes
place. As such, separate, almost rectangular chip elements are produced.

14. Mechanical Department SSET 2015
Page14
Shear zone (thick and thin)
During metal cutting the work material ahead of the too tip suffers plastic deformation and after
sliding on the rake face of the tool, goes to form chip. The zone of plastic deformation lies
between the chip and the un-deformed material. There are conflicting views on the shape of the
deformation or shear zone. Research study reveals that the size of zone varies with the cutting
condition. At high velocity it is found that shear plane is a narrow (thin) plane and at low
velocity metal cutting plane is thick.
So we say that at relatively low cutting speeds, the zone is large whereas at high speed it reduces
in size and approximates to a thin shear plane. So there are separate model of analysis for thin
and thick zone of deformation. In thin model, it is assumed that the work material shears across a
plane and there is no deformation on either side of shear plane (merchant, piispanen model).
Oxley and palmer model of analysis for thick model.
Two plastic deformation zones, namely the primary shear zone and the secondary shear zone
have been commonly accepted.
Primary shear zone- where shearing of chip from parent materials takes place.
Secondary shear zone- chip - tool interface deformation due to friction between tool and chip.
Shear plane:
As the tool is forced into the material, the chip is formed by shear deformation along a plane
called the shear plane, which is oriented at an angle Ф with the surface of the work. Shear plane
separates the deformed and undeformed work material.

15. Mechanical Department SSET 2015
Page15
Importance of shear angle
If all other factors remain the same, a higher shear angle results in a smaller shear plane area.
Since the shear strength is applied across this area, the shear force required to form the chip will
decrease when the shear plane area is decreased. This tends to make machining easier to
perform, and also lower cutting energy and cutting temperature.
To increase the shear plane angle
Increase the rake angle
Reduce the friction angle (or coefficient of friction)
Higher shear plane which means lower shear force which requires lower cutting forces, power,
temperature, all of which mean easier machining. The value of shear angle depends on
Work piece material
Cutting condition
Tool material
Tool geometry
When the shear angle is small, the plane of shear will be larger, chip is thick and therefore higher
cutting force is required to remove the chip and vice versa. The shear angle is determined from
the chip thickness ratio.
Chip thickness ratio

16. Mechanical Department SSET 2015
Page16
Derive expression for velocities in metal cutting (Velocity relationship in orthogonal cutting)

17. Mechanical Department SSET 2015
Page17
Forces acting in orthogonal cutting
Cutting is a process of extensive stresses and plastic deformations. The high compressive and
frictional contact stresses on the tool face result in a substantial cutting force F. The forces acting
during a metal cutting process are the following
1. Fs =shear force acting along the shear plane
2. Fn= force acting normal to shear plane
3. F= Frictional force acting against the chip flow acting along the tool
4. N= force normal to tool face (friction force)
anglefrictional
frictionofefficientco
N
F





 tan
Vector addition of F and N = R (resultant force that work exerts on chip)
Vector addition of Fs and Fn = R'(resultant force that tool exerts on chip)
For the chip to be in equilibrium, the resultant force R and R‟ should be equal in magnitude,
opposite in direction and collinear.
The resultant force R is due to the cutting force applying externally through the tool. Now these
resultant force components can be resolved horizontally and vertically called cutting forces.
Fc = cutting force acting along the cutting velocity
Ft = axial feed force or thrust force indirection of feed

18. Mechanical Department SSET 2015
Page18
Cutting forces in orthogonal cutting
2
22222
FtFcNFFsFR n 
The circle(s) drawn taking R or R1
as diameter is called merchant circle which contains all the
force components concerned as intercepts. The two circles with their forces are combined into
one circle having all the forces contained in that as shown by the diagram called Merchant‟s
Circle Diagram. Equations can be derived to relate the forces that cannot be measured to the
forces that can be measured.
Free body diagram of chip
Merchant represented various forces in a force circle diagram in which tool and reaction forces
have been assumed to be acting as concentrated at the tool point instead of their actual points of
application along the tool face and the shear plane. The horizontal cutting force Fc and vertical
force Ft can be measured in a machining operation by the use of a force dynamometer. Rake
angle of the tool can be measured and shear angle is calculated after found the chip ratio.
Several forces can be defined relative to the orthogonal cutting model. Based on these forces,
shear stress, coefficient of friction, and certain other relationships can be defined.

19. Mechanical Department SSET 2015
Page19
Following relation between the forces is obtained from merchant circle
Fc
Ft
 )tan( 
Known factors of orthogonal cutting
1. Cutting speed, feed, depth of cut
2. Rake angle of tool
3. Chip thickness after machining
4. Cutting forces measured Ft and feed force Fc using dynamometer
Factors to be determined
1. Friction force and Shear force
2. Friction angle  (Normal force to friction force)
3. Normal force to shear force
4. Cutting power determination
Knowledge of the cutting forces is essential for the following reasons:
1. Estimation of cutting power consumption,
2. Structural design of the machine – fixture – tool system
3. Evaluation of role of the various machining parameters (cutting speed, feed, tool
geometry, cutting fluid etc) on cutting forces
4. Study of behaviour and machinability characterisation of the work materials
5. Condition monitoring of the cutting tools and machine tools.
Advantages of Merchant’s diagram
 Easy, quick and reasonably accurate determination of several other forces from a
few known forces
 Friction at chip tool interface and dynamic yield shear strength can be easily
determined
 Equations relating the different forces can be easily derived.

20. Mechanical Department SSET 2015
Page20
Limitations of use of Merchant’s Circle diagram
 MCD is valid only for orthogonal cutting
 It is based on single shear plane theory
 It gives apparent (not actual) coefficient of friction.
Assumptions in merchant circle analysis
Merchant established relationship between various forces acting on the chip during orthogonal
metal cutting with following assumptions
 Thin shear zone
 Continuous chip is formed
 Orthogonal cutting (edge perpendicular to cutting velocity)
 Perfectly sharp cutting edge
 Shearing in a plane
Theories in metal cutting
Several investigators such as Ernst and Merchant, Merchant, Stabler, Lee and Shaffer, Palmer
and Oxley have carried out lot of work to establish relationship between rake, shear and friction
angles and proposed their own theories.
Merchant Theory
Merchant‟s hypothesis is that the shear plane is located to minimize the cutting force, or where
the shear stress is maximum. Of all the possible angles at which shear deformation could occur,
the work material will select a shear plane angle  which minimizes energy. Merchant‟s
relationship between shear angle, rake angle, and friction angle can be derived as below from the
merchant circle diagram.
Assumption in mechant analysis
 Thin shear zone
 Shearing in a plane
 Continuous chip is formed
 Orthogonal cutting (edge perpendicular to cutting velocity)
 Perfectly sharp cutting edge

21. Mechanical Department SSET 2015
Page21
Finding the maximum of the shear stress where the shearing taking place
s
s
A
F
areashear
forceshear
stressshear
cutofthicknesst
cutofwidthb
cuttingbeforechipofareationcrosstbA
planeshearofareaAs






)sec(*
From the merchant diagram


sin
sincos
A
A
FtFF
s
cs



A
FtFc  sin)sincos( 
From merchant diagram, we have
tan
Fc
Ft
 )( 
Apply Ft in terms of Fc
Take derivative of the shear stress with respect to the shear angle and setting the derivative to
zero, then we get Merchant Equation:
0




angleshaer
anglefriction
anglerake
equationmechant









22
45

The Merchant equation defines the general relationship between rake angle, tool-chip friction,
and shear plane angle.
Conclusions of merchant equation analysis
Rake angle increases, shear angle increases;
Friction decreases, shear angle increases

22. Mechanical Department SSET 2015
Page22
Lee Shaffer theory in metal cutting (Slip line theory)
Slip line field theory is a technique often used to analyze the stresses and forces involved in the
major deformation of metals. A line, which generally (curved, tangential) along its length to the
maximum shear stress is called a slip-line. A complete set of slip-lines in a plastic region forms a
slip-line field. Lee and Shaffer‟s work was the first contribution of the slip-line field models of
chip formation
Slip-line field solution for shear angle Ø was derived based on two assumptions:
The material cut behaves as an ideal plastic solid which does not strain-hardened.
The shear plane represents the direction of the maximum stress.
Slip lines consist of a set of two types of lines that intersect orthogonally. The shear plane AB is
the one set of slip-lines because the maximum shear stress must occur along the shear plane. The
directions of maximum shear therefore lie at 45° to σ1 and σ2. These are slip lines along which
plastic flow occurs.
The plane AC is stress free and slip lines meet AC at 450.
AB is the shear plane and set of
parallel AB and another set perpendicular to AB is inclined at an angle (450
-β) with the tool face.

23. Mechanical Department SSET 2015
Page23
Work done during metal cutting
We are giving cutting force and feed force
toolthefeedforpowercuttingforpowerrequiredpowertotal 
Power required for cutting = cutting force * cutting velocity + feed force (thrust force) * feed
velocity (negligible compared with cutting power)
VFp
velocityFeedFVFP
c
tc
*
**


Cutting force Fc is in the direction of primary motion. This cutting force constitutes about 70~80
% of the total force.
Power supplied = power required for shearing + power required for the chip flow along the tool
face (friction power)
shearofvelocityVs
forcefrictionalF
forceshearFs
flowchipofvelocityVc
VFPf
VFPs
PPP
c
ss
fs







*
*

24. Mechanical Department SSET 2015
Page24
Specific Cutting Energy
The energy consumed in removing a unit volume of material is called the specific cutting energy,
and it is also called unit power.
twlchipofthicknesswidthlengthmaterialofvolume
removedmaterialofvolume
consumedenergy
energyspecific
**** 

Volume of material removed/sec (MRR) also called cutting rate (m3
/sec)
dwftcutorthogonalin
fdVie
twVMRR
cudofvelocitychipoflength




,
**
**
*sec/
fsp
f
s
p
UUUenergyspecifictotal
MRR
powerFrictional
Upowerfrictionalspecific
fdV
VsFs
MRR
powerShear
Uenergyshearspecific
fd
Fc
fdV
VFc
MRR
VFc
Uenergycuttingspecific




**
*
***
**
Cutting forces in oblique cutting
zPyPxPRtresulcuttingobilqueIn 222
tan 
In oblique cutting, resultant force R=
Px = feed force in the direction of the tool travel
Py=thrust force in the direction perpendicular to the produced surface
Pz=cutting force or main force acting in the direction of the cutting velocity.

25. Mechanical Department SSET 2015
Page25
Types of chips produced during the metal cutting
There are three different types of chips
1. Continuous chips,
2. Discontinuous chips
3. Continuous chips with built up edge
Types of chip formation depends on
a. Work material (ductile, brittle)
b. Tool material
c. Cutting tool geometry (rake angle, cutting angle etc.)
d. Cutting condition (velocity and feed rate, depth, cutting fluid etc).
Continuous chip: when machining ductile materials at high speeds and relatively small feeds
and depths, long continuous chips are formed. A continuous chip may damage the finished
surface
Favorable factors for continuous chip formation
1. ductile work materials
2. large rake angle,
3. high cutting speed,
4. sharp cutting edge,
5. Less friction between chip tool interface through efficient lubrication.
Continuous chip Discontinuous chip Continuous chips with BUE
Discontinuous chips:
Discontinuous chip: when machining relatively brittle materials at low cutting speeds, the chips
often form into separated segments. Discontinuous chip formation may cause vibration, surface
roughness and reduced tool life.
Factors favourable for discontinuous chip
1. work material – brittle like grey cast iron
2. feed – large
3. tool rake – negative
4. cutting fluid – absent or inadequate

26. Mechanical Department SSET 2015
Page26
Continuous chips with BUE:
 When machining ductile materials due to conditions of high local temperature and
extreme pressure the cutting zone and also high friction in the tool chip interface, there
are possibilities of work material to weld to the cutting edge of tool and thus forming
built up edges (BUE).
 Successive layers are added to the build up edge. When this edge becomes large and
unstable it is broken and part of it is carried up the face of the tool along with chip while
remaining is left in the surface being machined. Thus contributing to the roughness of
surface. Built up edge protects the cutting edge of tool, thus changing the geometry of the
cutting tool.
Factors favourable to form BUE
1. work material – ductile
2. cutting velocity – medium
3. feed – medium or large
4. Cutting fluid – inadequate or absent.
Effects of BUE formation
 Harmful effect
 It unfavourably changes the rake angle at the tool tip causing increase if cutting force
i.e. power consumption.
 Repeated formation and dislodgement of the BUE causes fluctuation in cutting forces
and thus induce vibration.
 Poor surface finish.
 Good effect: BUE protects the cutting edge of the tool i. e. increases tool life.
Reduction or Elimination of BUE by
Increase
1. Cutting speed
2. Rake angle
Reduce
1. Feed
2. Depth of cut
3. Use of
Cutting fluid
Change cutting tool material
Chip breakers:
Continuous machining of ductile metals produces continuous chips, which leads to their handling
and disposal problems. The problems become acute when ductile but strong metals like steels are
machined at high cutting velocity for high MRR.
1. becomes dangerous to the operator and the other people working in the vicinity
2. may cause damage to workpiece surface and machine tool
3. creates difficulties in easy collection and disposal of chips

27. Mechanical Department SSET 2015
Page27
There are three principle methods to produce the favourable discontinuous chip:
1. proper selection of cutting conditions
2. use of chip breakers
3. change in the work material properties
The chip should be broken into small pieces for easy removal, safety and to prevent damage to
machine and work. The function of chip breakers is to reduce the radius of curvature of chips and
thus break it.
The principles and methods of chip breaking are generally classified as follows :
1. Self breaking
This is accomplished without using a separate chip-breaker either as an
attachment or an additional geometrical modification of the tool.
2. Forced chip breaking by additional tool geometrical features or devices:
Self breaking
1. By natural fracturing of the strain hardened outgoing chip after sufficient cooling and spring
back in fig 7.1 (a)
2. By striking against the cutting surface of the job, as shown in Fig. 7.1 (b), mostly under pure
orthogonal cutting
3. By striking against the tool flank after each half to full turn as indicated in Fig. 7.1 (c).
Clamped chip breaker
Forced chip breaker
1. In-built type
2. Clamped or attachment type
In-built breakers are in the form of step or groove at the rake surface near the cutting edges of the
tools. Clamped chip breaker is also used as shown in figure to reduce the radius of curvature and
made to break.

28. Mechanical Department SSET 2015
Page28
Friction in metal cutting
In metal cutting, it has been observed that co-efficient of friction has properties that are quite
different from the properties of ordinary sliding friction obeying laws of friction.
The Laws of Friction:
1. Amontons' 1st Law: The force of friction is directly proportional to the applied load
2. Amontons' 2nd Law: The force of friction is independent of the apparent area of contact. The
frictional force depends upon the nature of the surfaces in contact.
Coulomb's Law of Friction: Kinetic friction is independent of the sliding velocity.
Bowden and Tabor -adhesion theory of friction. It states that friction is a result of the true contact
area between the solids
If normal force (N) increases, then frictional force also (F) increases and  is constant, so we can
say that co-efficient of friction (not frictional force) is independent of normal load and area of
contact which is a constant for given pair of material surfaces in contact.
NF
N
F
  ,
Real area and apparent area of contact
When two objects touch, a certain portion of their surface areas will be in contact with each
other. Contact area is the fraction of this area that consists of the atoms of one object in contact
with the atoms of the other object. Because objects are never perfectly flat due to asperities, the
actual contact area (on a microscopic scale) is usually much less than the contact area apparent
on a macroscopic scale. Contact area may depend on the normal force between the two objects
due to deformation.
In the cases where the real area contact (Ar) is very less compared with apparent area (Aa)
contact as shown in figure and general friction laws can be used.
1
0


areaapparent
areareal
ie
validnotisfrictionoflawthehighveryisloadnormaltheasarearealtoequalisareaapparentwhen
validisfrictionoflaws
areaapparent
areareal

29. Mechanical Department SSET 2015
Page29
Theories of friction(causes)
When two surfaces are loaded together they can adhere over some part of the contact and this
adhesion is therefore one form of surface interaction causing friction.
We can consider two types of interaction
1. Adhesion theory of friction
2. Ploughing theory of friction-interlocking of asperities
Adhesion Theory of Friction
When two surfaces are loaded together they can adhere over some part of the contact and this
adhesion is therefore one form of surface interaction causing friction. Because the real contact
area is small the pressure over the contacting asperities is assumed high enough to cause them to
deform plastically. This plastic flow of the contacts causes an increase in the area of contact until
the real area of contact is just sufficient to support the load. Real area of contact is a sum of the
all micro-contacts at the asperities of the two solids. Motion cannot take place without
deformation of the welded asperities.
Friction due to Plowing Effect
Plowing is caused by asperities of a hard metal penetrating into a softer metal and plowing out a
groove by plastic flow in the softer material. This is a major component of friction during
abrasion processes and also it is probably important in cases where the adhesion term is small.
Hard sphere „A‟ (figure) loaded against a softer „B‟ causes displacement of material B during
motion. Ploughing of surface asperities by the harder material on the softer material while sliding
Ploughing of A onto B(Mechanical interlocking)
Friction in metal cutting
In metal cutting due to very high normal stress, the real area is almost equal to apparent area
where a law of friction is not valid. It has been observed that these classical laws of friction
cannot be applied to metal cutting process. In metal cutting, high values of coefficient of friction
and change of this co-efficient with respect of cutting parameters is noticed.
Variation of normal and shear stress in metal cutting
The region close to the tool cutting edge having very high normal stress was called the “Sticking
zone” which is varied from tool edge. At this area due to very high normal load and temperature
apparent and real area of contact becomes same and total adhesion will take place. The shear
stress remained constant for half of the tool chip contact length from the tool tip. Eventually, it
decreased to zero in the second half. The zone where both normal and the shear stress varied
was known as the “Sliding zone”. In metal cutting the normal force and shear force is variation is
shown in the figure.

30. Mechanical Department SSET 2015
Page30
From merchant analysis of orthogonal cutting, it is found that co-efficient of friction is not
constant, but it varies with tool angle and cutting forces.
It has been observed that co-efficient of friction increases with the increase in rake angle.
If friction increases between the tool chip face, then cutting force required for metal cutting
increases. Friction conditions at the tool chip interface strongly influence the tool chip contact
length.The stresses and temperatures at tool-chip interface and around the cutting edge can be
critically high in some cutting conditions and can cause excessive tool wear or even premature
tool failure. The contact regions and the friction parameters between the chip and the tool are
influenced by factors such as cutting speed, feed rate, rake angle, etc. Also it affects the tool
wear, dimensional accuracy, vibration, build up edge formation and temperature rise etc.
***********************************************

31. Mechanical Department SSET 2015
Page31
Questions (Module I)
1. What is shear angle? Discuss its importance.
2. What is meant by shear zone in metal cutting?
3. What is the relationship between chip velocity and cutting velocity in orthogonal
cutting?**
4. Derive an expression to show-the relationship between chip thickness ratio, shear angle
and rake angle.**
********************************************************************
5. Explain the mechanism of chip formation in metal cutting.*****
6. What are the factors that influence the type of chip produced in a metal cutting process?
7. What are the conditions which will favour the formation of continuous chip
8. Name the different types of chips formed in metal cutting. Describe each type with the
help of neat sketches.********
9. Briefly explain different types of chip breakers.*
10. Why are chip breakers necessary? Explain in the common methods of chip breaking?*
11. What do you mean by "built up edge”? Explain why it is undesirable.
12. Discuss the mechanism and formation of BUE and how do they affect the cutting
operation.******
13. If there any advantage in having a built-up edge? Explain.
*****************************************************************
14. Define "too1 signature? **
15. Name two system of tool designation.
16. Explain with the help of neat sketch the complex geometry of a single point out cutting
tool.*****
17. With-the help of a neat sketch indicate various tool angles. Also explain their importance.
18. Draw the tool having the tool signature 7 -16-6-8- 18-16-2 mm.**
19. Explain the American system of single point cutting tool nomenclature.
20. What is meant by tool geometry? Explain the tool geometry of a twist drill.
21. How are cutting tools designated? - Describe an orthogonal Rake system.
22. Compare the Co-ordinate system with orthogonal system of tool nomenclature with
23. Explain the tool geometry of a single point tool in ISO system.
***********************************
24. Discuss in detail, the effect of side cutting edge angle and nose radius on cutting
characteristics? **
25. Bring out the effect of rake angle and nose radius on cutting force and surface finish.
26. Discuss the effect of tool angles in metal cutting.
27. Discuss the effect of cutting angle on cutting force.
28. What is the effect of rake angle, cutting angle and nose radius on cutting force and
surface finish '?
29. What is the effect of rake angle on cutting force?
30. Give the significance of providing nose radius on tool tip.**

32. Mechanical Department SSET 2015
Page32
31. Define Rake angle, Cutting angle and Nose radius.
32. Differentiate between positive and negative rake angles. (4 marks)
*****************************************************************
33. Differentiate oblique and orthogonal cutting.*****
34. Describe orthogonal and oblique cutting.**
35. Differentiate Two-dimensional and Three dimensional cutting
36. What are the advantages of orthogonal cutting?
*************************************************************
37. Explain Merchants circle diagram in an orthogonal metal cutting process and express the
shearing force, frictional resistance and normal force in terms of cutting force and feed
force.
38. Draw and explain the Merchants circle diagram by showing the various forces acting on
the chip tool interface.***
39. Sketch Merchants circle diagram and explain the different quantities involved.****
40. Write a brief note on Merchants circle diagram**
41. With a neat sketch, explain various force components in orthogonal cutting***
42. What are the three components of cutting force in turning a cylindrical job**
43. What do you understand by specific cutting force?
44. Describe how power for machining in a lathe is arrived at.
45. What assumptions were made by Merchant in arriving at Merchant theory?
46. Define cutting rate.
****************************************************************
47. Define friction and explain the effect of friction in metal cutting.***
48. What is the function of friction in metal cutting? How do you calculate the coefficient of
friction?
49. Discuss the effect of increasing normal load on apparent to real area of contact with
suitable sketches. **
Ans: When normal load increases, the real area increases and may become same as
apparent area. This happens in sticking area of metal chip when normal load is very high.
Then frictional force is independent of normal load and general law of friction cannot be
used
50. Discuss the nature of friction at the tool chip and tool work interfaces. How does friction
affects the cutting process and tool wear? Explain how friction conditions can be
modified at the above interfaces.
*****************************************************************
51. In an orthogonal turning operation, the following data were obtained:
Chip thickness = 0.45 mm
Width of cut = 2.5mm
Feed = 0.25 mm/rev
Cutting force = 113 kgf

33. Mechanical Department SSET 2015
Page33
Thrust force = 29.5 kgf
The cutting speed was 150 m/min and the rake angle was +100
Calculate (a) Chip thickness ratio (b) Shear angle (c) Velocity of chip along tool face
(d) Friction angle (e) Coefficient of friction
52. Determine the power required to cut a brass bar on a lathe when the cutting speed is 18
meters per minute, feed is 0.06 mm. per revolution and depth of cut is 0.058 cm. Assume
that the power lost in friction is 30% (K = 12,000 for brass).
53. Calculate the power-consumed during cutting of a low carbon steel bar 40 mm diameters,
if cutting force is 150 kg at 200 rpm.
*****************************************************************
54. Name two popular metal cutting theories and describe them in brief
55. Explain the force system in milling and derive an expression for cutting power
requirement.
56. Explain the significance of shear angle theories in metal cutting
57. Present with a neat sketch the shear angle theories of merchant and Lee & Shaffer, clearly
stating its assumptions. Discuss the validity of this theory.
**************************************************************
 What are the advantages of providing side cutting angle?
It decreases chip thickness. Small chip thickness means less cutting force and tool wear. It
also helps the gradual engagement of tool into the work which reduces chatter and bending
etc
 What is the operating parameter to increase the material removal rate feed or depth of cut.
Material removal rate can be increased either by increasing the feed or depth of cut
For the increase the depth of cut, speed has to be reduced for the same tool life. Also support
and strength of work-piece should be enough. So less preferable
Increased feed rate will increase the material removal rate only with slight decrease in tool
life. So increase feed is the best method within the allowable finish. Increased feed will
reduce the surface finish.

34. Mechanical Department SSET 2015
Page34
Problems

35. Mechanical Department SSET 2015
Page35

36. Mechanical Department SSET 2015
Page36

37. Mechanical Department SSET 2015
Page37

38. Mechanical Department SSET 2015
Page38

39. Mechanical Department SSET 2015
Page39

40. Mechanical Department SSET 2015
Page40

41. Mechanical Department SSET 2015
Page41

42. Mechanical Department SSET 2015
Page42
Additional notes
Tool reference system (Orthogonal Rake System (ORS))
Planes are selected in relation with cutting edges which are mutually perpendicular to each other.
The references from which the tool angles are specified are the
Reference plane (πR) perpendicular to the cutting velocity vector
Cutting plane (πc) -plane perpendicular to πR and containing the principal cutting edge
Orthogonal plane (πo ) is the plane perpendicular to πR and πc
The axes;
Xo long the line of intersection of πR and πO
Yo along the line of intersection of πR and πC
Zo along the velocity vector, ( normal to both
Xo and Yo axes).
ASA system has limited advantage and use like convenience of inspection. But ORS is
advantageously used for analysis and research in machining and tool performance. But ORS
does not reveal the true picture of the tool geometry when the cutting edges are inclined from
the reference plane, i.e., λ≠0. Besides, sharpening or re-sharpening, if necessary, of the tool
by grinding in ORS requires some additional calculations for correction of angles.

43. Mechanical Department SSET 2015
Page43
Normal rake system (NRS)
The basic difference between ORS and NRS is the fact that in ORS, rake and clearance
angles are visualized in the orthogonal plane, πo, whereas in NRS those angles are visualized
in another plane called Normal plane, πN. The orthogonal plane, πo is simply normal to πR
and πC irrespective of the inclination of the cutting edges, i.e., λ, but πN (and πN‟ for
auxiliary cutting edge) is always normal to the cutting edge. The limitations of ORS are
overcome by using NRS for description and use of tool geometry.
πRN = Normal reference plane
πC = Cutting plane
πN = Plane to to the cutting edge
Rake angles
γn = normal rake: angle of inclination angle of the rake surface from πR and measured on
normal plane, πN
αn = normal clearance: angle of inclination of the principal flank from πC and measured on
πN
αn‟= auxiliary clearance angle: normal clearance of the auxiliary flank (measured on πN‟ –
plane normal to the auxiliary cutting edge.
The cutting angles, φ and φ1 and nose radius, r (mm) are same in ORS and NRS.

44. Mechanical Department SSET 2015
Page44
Shear strain

45. Mechanical Department SSET 2015
Page45
Shear zone analysis
There is conflicting evidence about the nature of the deformation zone in metal cutting.
This has led to two basis schools of thought in the approach to analysis. Many workers,
such as Piispaneu, Merchant, Kobayashi and Thomsen, have favored the thin-plane (or
thin-zone) model.
The available experimental evidence indicates that the thick-zone model may describe the
cutting process at very low speeds, but at higher speeds most
evidence indicates that a thin shear plane is approached. Thus it seems that the thin-zone model
is likely to be the most useful for practical cutting conditions. In addition, it leads to far simpler
mathematical treatment than does the thick-zone model. For these two reasons the analysis of
the thin zone has received far more attention and is more complete than that of the thick zone.
******************************************************************