theory of metal cutting mg university(s8 production notes)

Mechanical Department SSET 2015

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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)


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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


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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,

coscoscoscos

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

http://www.engineeringarchives.com/les_physics_force.html

http://www.engineeringarchives.com/ref_genref_grl.html

http://www.engineeringarchives.com/les_matsci_slipslipdirectionslipplane.html

http://www.engineeringarchives.com/glos_physics.html#normal




http://www.engineeringarchives.com/les_mom_shearstress.html




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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


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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


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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.


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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.)


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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


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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 (3o

~ 15o

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


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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.


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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.


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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.


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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.


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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.


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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


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Derive expression for velocities in metal cutting (Velocity relationship in orthogonal cutting)


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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


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Cutting forces in orthogonal cutting

2

22222FtFcNFFsFR 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.


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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.


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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


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Finding the maximum of the shear stress where the shearing taking place

s

s

A

F

areashear

forceshearstressshear

cutofthicknesst

cutofwidthb

cuttingbeforechipofareationcrosstbA

planeshearofareaAs

)sec(*

From the merchant diagram

sin

sincos

AA

FtFF

s

cs

A

FtFc sin)sincos(

From merchant diagram, we have

tanFc

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

2245

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


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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 45

0. 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.

http://en.wikipedia.org/wiki/Stress_(mechanics)

http://en.wikipedia.org/wiki/Deformation_(engineering)

http://en.wikipedia.org/wiki/Metal


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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

*

*


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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

consumedenergyenergyspecific

****

Volume of material removed/sec (MRR) also called cutting rate (m3/sec)

dwftcutorthogonalin

fdVie

twVMRR

cudofvelocitychipoflength

,

**

**

*sec/

fsp

f

s

p

UUUenergyspecifictotal

MRR

powerFrictionalUpowerfrictionalspecific

fdV

VsFs

MRR

powerShearUenergyshearspecific

fd

Fc

fdV

VFc

MRR

VFcUenergycuttingspecific

**

*

***

**

Cutting forces in oblique cutting

zPyPxPRtresulcuttingobilqueIn 222tan

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.


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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


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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


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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.


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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.

NFN

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

arearealie

validnotisfrictionoflawthehighveryisloadnormaltheasarearealtoequalisareaapparentwhen

validisfrictionoflawsareaapparent

areareal

http://en.wikipedia.org/wiki/Physical_body

http://en.wikipedia.org/wiki/Atom

http://en.wikipedia.org/wiki/Asperity_(material_science)

http://en.wikipedia.org/wiki/Microscopic

http://en.wikipedia.org/wiki/Macroscopic

http://en.wikipedia.org/wiki/Normal_force

http://en.wikipedia.org/wiki/Deformation_(engineering)


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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.


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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.

***********************************************


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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.**


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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


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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.


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Problems


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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.


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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.


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Shear strain


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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.

******************************************************************

theory of metal cutting mg university(s8 production notes)

Engineering

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