Theory of metal cutting-Module 1

THEORY OF METAL CUTTING

ME 010 803 PRODUCTION ENGINEERING

Module 1

• Definition of Manufacturing

• The word manufacturing is derived from Latin:

manus = hand, factus = made

• Manufacturing is the economic term for making goods and services available to satisfy human wants.

• Manufacturing implies creating value to a raw material by applying useful mental and physical labour. Manufacturing converts the raw materials to finished products to be used for some purpose.

• Whether from nature or industry materials cannot be used in their raw forms for any useful purpose.

• The materials are then shaped and formed into different useful components through different manufacturing processes to fulfil the needs of day-to-day work.

INTRODUCTION

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MANUFACTURING SYSTEM AND PRODUCTION SYSTEM

Manufacturing system:

• A collection of operations and processes used to obtain a desired product(s) or component(s) is called a manufacturing system.

• The manufacturing system is therefore the design or arrangement of the manufacturing processes..

Production system:

• A production system includes people, money, equipment, materials and supplies, markets, management and the manufacturing system.

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Production System - The Big Picture

Raw materials Manufacturi

ng Process Manufacturing Process

Finished product

Manufacturing System

People, Money, Equipment, Materials and Supplies, Markets, Management

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Material Removal ProcessesA family of shaping operations, the common feature of which is removal of material from a starting work part so the remaining part has the desired geometry.

Machining – material removal by a sharp cutting tool, e.g., turning, milling, drilling.

Abrasive processes – material removal by hard, abrasive particles, e.g., grinding.

Nontraditional processes - various energy forms other than sharp cutting tool to remove material.

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MACHININGMachining is a semi-finishing or finishing process essentially done to impart required or stipulated dimensional and form accuracy and surface finish to enable the product to

fulfill its basic functional requirements

provide better or improved performance

render long service life.

Machining is a process of gradual removal of excess material from the preformed blanks in the form of chips.

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Why Machining is Important

• Variety of work materials can be machined– Most frequently used to cut metals

• Variety of part shapes and special geometric features possible, such as:– Screw threads– Accurate round holes– Very straight edges and surfaces

• Good dimensional accuracy and surface finish

Examples of Cutting Processes

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Disadvantages with Machining

• Wasteful of material – Chips generated in machining are wasted material, at least

in the unit operation

• Time consuming – A machining operation generally takes more time to shape

a given part than alternative shaping processes, such as casting, powder metallurgy, or forming

Diagrammatic Representation of Material Removal Operations

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Cutting action involves shear deformation of work material to form a chip.

As chip is removed, new surface is exposed.

Figure 21.2 (a) A cross‑sectional view of the machining process, (b) tool with negative rake angle; compare with positive rake angle in (a).

Machining

Chip Formation

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Mechanism of Chip formationThe form of the chips is an important index of machining because it directly or indirectly indicates :

Nature and behaviour of the work material under machining condition

Specific energy requirement (amount of energy required to remove unit volume of work material) in machining work

Nature and degree of interaction at the chip-tool interfaces.

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Mechanism of Chip formationThe form of machined chips depend mainly upon :

Work material

Material and geometry of the cutting tool

Levels of cutting velocity and feed and also to some extent on depth of cut

Machining environment or cutting fluid that affects temperature and friction at the chip-tool and work-tool interfaces.

Knowledge of basic mechanisms of chip formation helps to understand the characteristics of chips and to attain favourable chip forms.

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A chip has two surfaces:

1. One that is in contact with the tool face (rake face). This surface is shiny, or burnished.

2. The other from the original surface of the work piece.

This surface does not come into contact with any solid body. It has a jagged, rough appearance, which is caused by the shearing mechanism.

Chip Formation

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Figure. More realistic view of chip formation, showing shear zone rather than shear plane. Also shown is the secondary shear zone

resulting from tool‑chip friction.

Primary & Secondary Shear Zone

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Piispanen model of Card Analogy

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Piispanen model of Card Analogy

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Four Basic Types of Chip in Machining

1. Discontinuous chip

2. Continuous chip

3. Continuous chip with Built-up Edge (BUE)

4. Serrated chip

continuous chips are not always desirable, particularly in automated machine tools, it tends to get tangled around the tool and operation has to be stopped to clear away the chips.

Continuous chips Continuous chips are usually formed with ductile materials at high rake angles and/or high cutting speeds.

A good surface finish is generally produced.

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Continuous chips usually form under the following conditions:

Small chip thickness (fine feed)

Small cutting edge

Large rake angle

High cutting speed

Ductile work materials

Less friction between chip tool interface through efficient lubrication

Continuous Chips

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Continuous Chips • Deformation of the material takes place along a

narrow shear zone, primary shear zone.

• CCs may, because of friction, develop a secondary shear zone at tool–chip interface. The secondary zone becomes thicker as tool–chip friction increases.

• In CCs, deformation may also take place along a wide primary shear zone with curved boundaries.

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Discontinuous chips Discontinuous chips consist of segments that may be firmly or loosely attached to each other.

These chips occur when machining hard brittle materials such as cast iron.

Brittle failure takes place along the shear plane before any tangible plastic flow occurs.

Discontinuous chips will form in brittle materials at low rake angles (large depths of cut).

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Discontinuous Chips DCs usually form under the following conditions:

1. Brittle work piece materials

2. Work piece materials that contain hard inclusions and impurities, or have structures such as the graphite flakes in gray cast iron.

3. Very low or very high cutting speeds.

4. Large depths of cut.

5. Low rake angles.

6. Lack of an effective cutting fluid.

7. Low stiffness of the machine tool.

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Because of the discontinuous nature of chip formation, forces continually vary during cutting.

Hence, the stiffness or rigidity of the cutting-tool holder, the Work holding devices, and the machine tool are important in cutting with both DC and serrated-chip formation.

Discontinuous Chips

Serrated chips Serrated chips: semi-continuous chips with alternating zones of high shear strain then low shear strain.

Metals with low thermal conductivity and strength that decreases sharply with temperature, such as titanium, exhibit this behavior.

The Semi-continuous chips have a saw-tooth-like appearance.

Associated with difficult-to-machine metals at high cutting speeds.

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Built-Up Edges ChipsBUE, consisting of layers of material from the work piece that are gradually deposited on the tool, may form at the tip of the tool during cutting.

As it becomes larger, BUE becomes unstable and eventually breaks up.

Part of BUE material is carried away by the tool side of the chip; the rest is deposited randomly on the work piece surface.

The process of BUE formation and destruction is repeated continuously during the cutting operation, unless measures are taken to eliminate it.

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1. Increase the cutting speeds

2. Decreasing depth of cut

3. Increasing the rake angle

4. Using a sharp tool

5. Using an effective cutting fluid

6. Use a cutting tool that has lower chemical affinity for the work piece material.

Built-up edges chipsThe tendency for a BUE to form is reduced by any of the following practices:

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Built-up edges chipsBecause of work hardening and deposition of successive layers of material. BUE hardness increases significantly.

BUE is generally undesirable as it results in poor surface finish.

A thin, stable BUE is sometimes desirable because it reduces wear by protecting the rake face of the tool.

As cutting speed increases the size of BUE decreases.

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Fig. Different forms of built up edge

Types of Built-up edges

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Effects of BUE formation

Formation of BUE causes several harmful effects, such as:

It unfavourably changes the rake angle at the tool tip causing increase in cutting forces and power consumption

Repeated formation and dislodgement of the BUE causes fluctuation in cutting forces and thus induces vibration which is harmful for the tool, job and the machine tool.

Surface finish gets deteriorated

May reduce tool life by accelerating tool-wear at its rake surface by adhesion and flaking

Occasionally, formation of thin flat type stable BUE may reduce tool wear at the rake face.

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Cutting Tool Classification1. Single-Point Cutting Tools

– One dominant cutting edge– Point is usually rounded to form a nose radius– Eg: Turning uses single point tools

2. Multi-Point Cutting Tools– More than one cutting edge– Motion relative to work achieved by rotating – Eg: Drilling and milling use rotating multiple cutting

edge tools

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Figure: (a) A single‑point tool showing rake face, flank, and tool point;

(b) A helical milling cutter, representative of tools with multiple cutting edges.

Cutting Tool Classification

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Right Hand Single Point Cutting Tool

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

Right-hand Cutting Tool and Insert

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

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Single Point Cutting Tool Geometry

Side rake angle (αs)

End relief angle (ERA)

Nose Radius (NR)

End cutting edge angle (ECEA)

Side cutting edge angle (SCEA)

Side View

Front View

Top View

Lip angle

Back rake angle (αb)

Side relief angle (SRA)

Geometry of positive rake single point cutting tool

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Geometry of negative rake single point cutting tool

Side rake angle (αs)

End relief angle (ERA)

Nose Radius (NR)

End cutting edge angle (ECEA)

Side cutting edge angle (SCEA)

Side View

Front View

Top View

Lip angle

Back rake angle (αb)

Side relief angle (SRA)

Single Point Cutting Tool Geometry

Back rake angle:

•The back rake angle is the angle between the face of the tool and a line parallel to the base of the shank in a plane parallel to the side cutting edge.

•The back rake angle affects the ability of the tool to shear the work material and form chip.

Side Rake Angles:

•It is the angle by which the face of the tool is inclined side ways.

The Rake Angle:

• The side rake angle and the back rake angle combine to form the effective rake angle. This is also called true rake angle or resultant rake angle of the tool.

Cutting Tool Angles and Significance

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The Rake Angle:

• The rake angle is always at the topside of the tool.

• The basic tool geometry is determined by the rake angle of the tool.

• Rake angle has two major effects during the metal cutting process.

• One major effect of rake angle is its influence on tool strength. A tool with negative rake will withstand far more loading than a tool with positive rake.

• The other major effect of rake angle is its influence on cutting pressure. A tool with a positive rake angle reduces cutting forces by allowing the chips to flow more freely across the rake surface.


The rake angle has the following function:• It allows the chip to flow in convenient direction. • It reduces the cutting force required to shear the metal and

consequently helps to increase the tool life and reduce the power consumption. It provides keenness to the cutting edge.

• It improves the surface finish.


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Positive Rake:

• Positive rake or increased rake angle reduces compression, the forces, and the friction, yielding a thinner, less deformed and cooler chip.

• But increased rake angle reduces the strength of the tool section, and heat conduction capacity.

• Some areas of cutting where positive rake may prove more effective are, when cutting tough, alloyed materials that tend to work-harden, such as certain stainless steels, when cutting soft or gummy metals, or when low rigidity of work piece, tooling, machine tool, or fixture allows chatter to occur.

• The shearing action and free cutting of positive rake tools will often eliminate problems in these areas.


Negative Rake:

• To provide greater strength at the cutting edge and better heat conductivity, zero or negative rake angles are employed on carbide, ceramic, polycrystalline diamond, and polycrystalline cubic boron nitride cutting tools.

• These materials tend to be brittle, but their ability to hold their superior hardness at high temperature results in their selection for high speed and continuous machining operation.

• Negative rakes increases tool forces but this is necessary to provide added support to the cutting edge. This is particularly important in making intermittent cuts and in absorbing the impact during the initial engagement of the tool and work.

• Negative rakes are recommended on tool which does not possess good toughness (low transverse rupture strength). Thus negative rake (or small rake) causes high compression, tool force, and friction, resulting in highly deformed, hot chip.


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The Rake Angle for a Tool Depends on the Following Factors:

• Type of material being cut:

A harder material like cast iron may be machined by smaller rake angle than that required by soft material like mid steel or aluminum.

• Type of tool material:

Tool material like cemented carbide permits turning at very high speed. At high speeds rake angle has little influence on cutting pressure. Under such condition the rake angle can minimum or even negative rake angle is provided to increase the tool strength.

• Depth of cut:

In rough turning, high depth of cut is given to remove maximum amount of material. This means that the tool has to withstand severe cutting pressure. So the rake angle should be decreased to increase the lip angle that provides the strength to the cutting edge.

• Rigidity of the tool holder and machine:

An improperly supported tool on old or worn out machine cannot take up high cutting pressure. So while machining under the above condition, the tool used should have larger rake angle. 43

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Relief Angles:

• Relief angles are provided to minimize physical interference or rubbing contact with machined surface and the work piece.

• Relief angles are for the purpose of helping to eliminate tool breakage and to increase tool life.

• If the relief angle is too large, the cutting tool may chip or break. If the angle is too small, the tool will rub against the work piece and generate excessive heat and this will in turn, cause premature dulling of the cutting tool.

• Small relief angles are essential when machining hard and strong materials and they should be increased for the weaker and softer materials.

• A smaller angle should be used for interrupted cuts or heavy feeds, and a larger angle for semi-finish and finish cuts.


Side relief angle:

• The Side relief angle prevents the side flank of the tool from rubbing against the work when longitudinal feed is given.

• Larger feed will require greater side relief angle.

End relief angle:

• The End relief angle prevents the side flank of the tool from rubbing against the work.

• A minimum relief angle is given to provide maximum support to the tool cutting edge by increasing the lip angle.

• The front clearance angle should be increased for large diameter works.

End cutting edge angle:

• The function of end cutting edge angle is to prevent the trailing front cutting edge of the tool from rubbing against the work. A large end cutting edge angle unnecessarily weakens the tool.

• It varies from 8 to 15 degrees.


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Side cutting edge angle:

The following are the advantages of increasing this angle:

• It increases tool life as, for the same depth of cut; the cutting force is distributed on a wider surface.

• It diminishes the chip thickness for the same amount of feed and permits greater cutting speed.

• It dissipates heat quickly for having wider cutting edge.

• The side cutting edge angle of the tool has practically no effect on the value of cutting force or power consumed for a given depth of cut & feed.

• Large side cutting edge angles are likely to cause the tool to chatter.


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Nose radius:

The nose of a tool is slightly rounded in all turning tools.

The function of nose radius is as follows:

• Greater nose radius clears up the feed marks caused by the previous shearing action and provides better surface finish.

• All finish turning tool have greater nose radius than rough turning tools.

• It increases the strength of the cutting edge, tends to minimize the wear taking place in a sharp pointed tool with consequent increase in tool life.

• Accumulation heat is less than that in a pointed tool which permits higher cutting speeds.


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Tool SignatureIt is the system of designating the principal angles of a single point cutting tool.

The signature is the sequence of numbers listing the various angles, in degrees, and the size of the nose radius.

There are several systems available like American standard system (ASA), Orthogonal rake system (ORS), Normal rake system (NRS), and Maximum rake system (MRS).

The system most commonly used is American Standard Association (ASA), which is:

Back rake angle, Side rake angle, End relief angle, Side relief angle, End cutting Edge angle, Side cutting Edge angle and Nose radius.

For example a tool may designated in the following sequence:

8-14-6-6-6-15-1

1. Back rake angle is 8

2. Side rake angle is 14

3. End relief angle is 6

4. Side relief angle is 6

5. End cutting Edge angle is 6

6. Side cutting Edge angle is 15

7. Nose radius is 1 mm49

Tool Signature

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Chip BreakersLong continuous chip are undesirable.

Chip breaker is a piece of metal clamped to the rake surface of the tool which bends the chip and breaks it.

Chips can also be broken by changing the tool geometry, thereby controlling the chip flow.

CBs increase the effective rake angle of the tool and, consequently, increase the shear angle.

Chips can also be broken by changing the tool geometry, thereby controlling chip flow, as in the turning operations.

Experience has indicated that the ideal chip is in the shape of the letter C or the number 9 and fits within a 25 mm square block.

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

Chip Breakers

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With soft work piece materials such as pure aluminum or copper, chip breaking by such means is generally not effective.

Common techniques used with such materials, include machining at small increments and then pausing (so that a chip is not generated) or reversing the feed by small increments.

In interrupted cutting operations, such as milling, chip breakers are generally not necessary, since the chips already have finite lengths because of the intermittent nature of the operation.

Chip Breakers

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

Oblique Cutting

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

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Orthogonal Cutting: The cutting edge of the tool remains

normal to the direction of tool feed or work feed.

The direction of the chip flow velocity is normal to the cutting edge of the tool.

Here only two components of forces are acting: Cutting Force and Thrust Force. So the metal cutting may be considered as a two dimensional cutting.

Oblique Cutting:• The cutting edge of the tool remains inclined at an

acute angle to the direction of tool feed or work feed.• The direction of the chip flow velocity is at an angle

with the normal to the cutting edge of the tool. The angle is known as chip flow angle.

• Here three components of forces are acting: Cutting Force, Radial force and Thrust Force or feed force. So the metal cutting may be considered as a three dimensional cutting.

The cutting edge being oblique, the shear force acts on a larger area and thus tool life is increased.

Feed

Tool

Work

Oblique cutting

Feed

Tool

Work

Orthogonal cutting

Orthogonal and Oblique Cutting

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Orthogonal metal cutting Oblique metal cuttingCutting edge of the tool is perpendicular

to the direction of tool travel.The cutting edge is inclined at an angle

less than 90o to the direction of tool travel.

The direction of chip flow is perpendicular to the cutting edge.

The chip flows on the tool face making an angle.

The chip coils in a tight flat spiral The chip flows side ways in a long curl.

For same feed and depth of cut the force which shears the metal acts on a smaller

areas. So the life of the tool is less.

The cutting force acts on larger area and so tool life is more.

Produces sharp corners. Produces a chamfer at the end of the cut

Smaller length of cutting edge is in contact with the work.

For the same depth of cut greater length of cutting edge is in contact with the

work.

Generally parting off in lathe, broaching and slotting operations are done in this

method.

This method of cutting is used in almost all machining operations.

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

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Assumptions in Orthogonal Cutting

No contact at the flank i.e. the tool is perfectly sharp.

No side flow of chips i.e. width of the chips remains constant.

Uniform cutting velocity.

A continuous chip is produced with no built up edge.

The chip is considered to be held in equilibrium by the action of the two equal and opposite resultant forces R and R’ and assume that the resultant is collinear.

The force system in general case of conventional turning process

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Forces acting on a cutting tool

The largest magnitude is the vertical force Ft which in turning is larger than feed force Fa, and Fa is larger than radial force Fr.

For orthogonal cutting system Fr is made zero by placing the face of cutting tool at 90 degree to the line of action of the tool.

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Two-Dimensional

Cutting Process

Fig: Schematic illustration of a 2-d cutting process, also called orthogonal cutting:

(a) Orthogonal cutting with a well defined shear plane, also known as the Merchant Model.

(b) Orthogonal cutting without a well-defined shear plane.

Note that the tool shape, depth of cut, to, and the cutting speed, V, are all independent variables.

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Mechanics of Orthogonal Metal Cutting During metal cutting, the metal is severely compressed in the

area in front of the cutting tool. This causes high temperature shear, and plastic flow if the metal is ductile.

When the stress in the work piece just ahead of the cutting tool reaches a value exceeding the ultimate strength of the metal, particles will shear to form a chip element, which moves up along the face of the work.

The outward or shearing movement of each successive element is arrested by work hardening and the movement transferred to the next element. The process is repetitive and a continuous chip is formed.

The plane along which the element shears, is called shear plane.

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Chip Thickness Ratio

Where, r = chip thickness ratio;

to = thickness of the chip prior to chip formation; and

tc = chip thickness after separation

The ratio of to/tc is known as the cutting ratio, r, expressed as:

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Chip Thickness Ratio The outward flow of the metal causes the chip to be thicker after

the separation from the parent metal.

i.e. the chip produced is thicker than the depth of cut, so chip ratio always less than 1.0

Chip compression ratio: reciprocal of r. It is a measure of how thick the chip has become compared to the depth of cut.

The chip thickness ratio is an important and useful parameter for evaluating cutting conditions.

Since the undeformed chip thickness, to is a machine setting and is therefore known, the cutting ratio can be calculated easily by measuring the chip thickness with a micrometer.

)cos(

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s

c

o

l

l

t

tr

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Rearranging:

Chip Thickness Ratio

sin1

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r

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Determining Shear Plane AngleBased on the geometric parameters of the orthogonal model, the shear plane angle can be determined as:

where r = chip ratio, and = rake angle

sincos

tanr

r

1

When shear angle is smallThe plane of shear will be larger, chip is thicker and higher force required to remove the chip.

When shear angle is largeThe plane of shear will be shorter, chip is thinner and hence lesser force required to remove the chip.

The shear angle is determined from chip thickness ratio.

Figure: Shear strain during chip formation: (a) Chip formation depicted as a series of parallel plates sliding relative to each other, (b) One of the plates isolated to show shear strain, and (c) Shear strain triangle used to derive strain equation.

Shear Strain in Chip Formation

=

Shear strain in machining can be computed from the following equation, based on the parallel plate model:

Where,ε =Shear strain, = Shear plane angle and = Rake angle of cutting tool

Large shear strains are associated with low shear angles, or low or negative rake angles.

Shear strains of 5 or higher in actual cutting operations.

Deformation in cutting generally takes place within a very narrow deformation zone; that is, d = BD in Fig is very small. Therefore, the rate at which shearing takes place is high.

Shear angle influences force and power requirements, chip thickness, and temperature.

Consequently, much attention has been focused on determining the relationships between the shear angle and work piece material properties and cutting process variables.

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Shear Strain in Chip Formation

Velocity Relationship in Orthogonal Cutting

Figure (a) Schematic illustration of the basic mechanism of chip formation by shearing. (b) Velocity diagram showing angular relationships among the three speeds in the cutting zone.

The tool has a rake angle of α, and relief (clearance) angle. The shearing process in chip formation is similar to the motion of cards in a deck sliding against each other.

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Velocity Relationship

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Using sine rule,

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sc vvv

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sin

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rvvc

)-( Cos

Sin r

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0

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v

chip theup flowing material of Volume unit timeper material of Volume

Velocity Relationship

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Forces Acting on Chip

F, N, Fs, and Fn cannot be directly measured

Forces acting on the tool that can be measured:

– Cutting force Fc and Thrust force Ft

Fs = Shear Force, which acts along the shear plane, is the resistance to shear of the metal in forming the chip.

Fn = Force acting normal to the shear plane, is the backing up force on the chip provided by the work piece.

F = Frictional resistance of the tool acting against the motion of the chip as it moves upward along the tool

N = Normal to the chip force, is provided by the tool.

NS

/

FFR

FNR

It is assumed that the resultant forces R & R’ are equal and opposite in magnitude and direction. Also they are Collinear. Therefore for the purpose of analysis the chip is regarded as an independent body held in mechanical equilibrium by the action of two equal and opposite forces R, which the workpiece exerts upon the chip and R’ which the tool exerts upon the chip.

Forces acting on chip in Orthogonal cutting

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Resultant Forces

• Vector addition of F and N = resultant R

• Vector addition of Fs and Fn = resultant R '

• Forces acting on the chip must be in balance:

– R ' must be equal in magnitude to R

– R’ must be opposite in direction to R

– R’ must be collinear with R

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Cutting Forces

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

The following is a circle diagram. Known as Merchant’s circle diagram, which is convenient to determine the relation between the various forces and angles.

In the diagram two force triangles have been combined and R and R’ together have been replaced by R. the force R can be resolved into two components Fc and Ft.

Fc and Ft can be determined by force dynamometers. tc FFR

The rake angle (α) can be measured from the tool, and forces F and N can then be determined. The shear angle () can be obtained from it’s relation with chip reduction coefficient. Now Fs & Fn can also be determined.

Merchant’s Circle Diagram

∅

Work

ToolChip

Clearance Angle

Ft

Fc

F

N

Fn

Fs

α

α

β

(β - α)

R

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Merchant’s Circle Diagram

Work

ToolChip

Clearance Angle

Ft

Fc

F

N

Fn

Fs

α

α

β

∅

(β - α)

R

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Clearance Angle

The procedure to construct a Merchant’s circle diagram

Work

ToolChip

Ft

Fc

F

N

Fn

Fs

α

α

β

∅

R

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Set up x-y axis labeled with forces, and the origin in the centre of the page. The cutting force (Fc) is drawn horizontally, and the tangential force (Ft) is drawn vertically. (Draw in the resultant (R) of Fc and Ft.

Locate the centre of R, and draw a circle that encloses vector R. If done correctly, the heads and tails of all 3 vectors will lie on this circle.

Draw in the cutting tool in the upper right hand quadrant, taking care to draw the correct rake angle (α) from the vertical axis.

Extend the line that is the cutting face of the tool (at the same rake angle) through the circle. This now gives the friction vector (F).


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A line can now be drawn from the head of the friction vector, to the head of the resultant vector (R). This gives the normal vector (N). Also add a friction angle (β) between vectors R and N. Therefore, mathematically, R = Fc+Ft = F + N.

Draw a feed thickness line parallel to the horizontal axis. Next draw a chip thickness line parallel to the tool cutting face.

Draw a vector from the origin (tool point) towards the intersection of the two chip lines, stopping at the circle. The result will be a shear force vector (Fs). Also measure the shear force angle between Fs and Fc.

Finally add the shear force normal (Fn) from the head of Fs to the head of R.

Use a scale and protractor to measure off all distances (forces) and angles.

sincos

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tC

FFN

GEODCDODABN

FFF

GBEDGBCGCBOAF

Frictional Force System

angle Friction WhereN

Ftan

friction of tcoefficien The

Relationship of various forces acting on the chip with the horizontal and vertical cutting force from Merchant circle diagram

Ft

Fc

F

N

α

α

β

(β - α)

R

αα

α

(90-α)

(90-α)

O

A

C

B

G

E

D

∅

Work

ToolChip

Clearance Angle

Ft

Fc

F

N

Fn

Fs

α

α

β

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R

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Shear Force System

cossin

(

sincos

tCN

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S

tCS

S

FFF

DEBCDEADAEF

RCosF

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CDOBABOBOAF

Also:

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Work

ToolChip

Clearance Angle

Ft

Fc

F

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Fn

Fs

α

α

β

(β - α)

R

∅

Ft

Fc

A

O

Fn

Fs

α

α

(β - α)

R

B

C

D

E

∅

∅

(90-∅)

(90-∅)

83

)tan(

cossin

sincos

sincos

cossin

SN

tCN

tCS

tC

tC

FF

FFF

FFF

FFN

FFF


∅

Work

ToolChip

Clearance Angle

Ft

Fc

F

N

Fn

Fs

α

α

β

(β - α)

R

84

Ft = R Sin (β-α)Fc = R Cos (β –α)

85

Knowledge of the cutting forces and power involved in machining operations is important for the following reasons:

a. Machine tools can be properly designed to minimize distortion of the machine components, maintain the desired dimensional accuracy of the machined part, and help select appropriate tool holders and work-holding devices.

b. The work piece is capable of withstanding these forces without excessive distortion.

c. Power requirements must be known in order to enable the selection of a machine tool with adequate electric power.

CUTTING FORCES and POWER

86

CUTTING FORCES and POWERCutting force, Fc, acts in the direction of cutting speed, V, and supplies energy required for cutting.

Thrust force, Ft , acts in a direction normal to cutting velocity, perpendicular to WP. The resultant force, R can be resolved into two components :

Friction force: F, along the tool-chip interface Normal force: N, perpendicular to it.

F = R sin β

N = R cos β

R is balanced by an equal and opposite force along the shear plane and is resolved into a shear force, Fs, and a normal force, Fn

Fs = Fc cos Ø – Ft sin Ø

Fn = Fc sin Ø + Ft cos Ø

87

Coefficient of FrictionCoefficient of friction between tool and chip:

Friction angle related to coefficient of friction as follows:

N

F

tanThe ratio of F to N is the coefficient of friction, μ, at the tool-chip interface, and the angle β is the friction angle.

The coefficient of friction in metal cutting generally ranges from about 0.5 to 2.

tan

tan friction, oft Coefficien

tc

ct

FF

FF

N

F

88

Shear StressShear stress acting along the shear plane:

sinwt

A os

where As = area of the shear plane,

Shear stress = shear strength of work material during cutting

sA

sF

89

CUTTING FORCES & POWERThrust Force

• If the thrust force is too high or if the machine tool is not sufficiently stiff, the tool will be pushed away from the surface being machined.

• This movement will, in turn, reduce the depth of cut, resulting in lack of dimensional accuracy in the machined part, As the rake angle increases and/or friction at the rake face decreases, this force can act upward.

• This situation can be visualized by noting that when μ = 0 (that is, β = 0), the resultant force, R, coincides with the normal force, N.

• In this case, R will have a thrust-force component that is upward.

The Power consumed/ work done per sec in cutting: vFP cC

The Power consumed/ work done per sec in shear: sss vFP

The Power consumed/ work done per sec in friction: cF vFP

The total Power required:

fsc PPPP

Power required in Metal cutting

90

Specific EnergySpecific Energy, ut ,is defined as the total energy per unit volume of material removed.

Where wt0vc is the MRR

Units for specific energy are typically N‑m/mm3

Therefore is simply the cutting force to the projected area of cut.

If uf and us be specific energy for friction and specific energy for shearing, then

As the rake angle increases, the frictional specific energy remains more or less constant, where as the shear specific energy rapidly reduced.

00 wt

F

vwt

vFu CC

t

vwt

vF

wt

Fr

vwt

vF

vwt

Fvuuu ssssc

sft0000

91

Approximate Specific-Energy Requirements in Cutting Operations

MATERIAL SPECIFIC ENERGY*

W-s/mm3 hp-min/in3 Aluminum alloys Cast irons Copper alloys High-temperature alloys Magnesium alloys Nickel alloys Refractory alloys Stainless steels Steels Titanium alloys

0.4-1.1 1.6-5.5 1.4-3.3 3.3-8.5 0.4-0.6 4.9-6.8 3.8-9.6 3.0-5.2 2.7-9.3 3.0-4.1

0.15-0.4 0.6-2.0 0.5-1.2 1.2-3.1

0.15-0.2 1.8-2.5 1.1-3.5 1.1-1.9 1.0-3.4 1.1-1.5

* At drive motor, corrected for 80% efficiency; multiply the energy by 1.25 for dull tools.

92

93

The Merchant Equation Of all the possible angles at which shear deformation can occur, the work material will select a shear plane angle that minimizes energy, given by

Derived by Eugene Merchant.

Based on orthogonal cutting, but validity extends to 3-D machining.

2245

94

Assuming that the shear angle adjusts itself to minimize the cutting force, or that the shear plane is a plane of maximum shear stress.

(21.3)

β is the friction angle and is related to the coefficient of friction, μ, at the tool – chip interface (rake face):

From Eq (21.3), as the rake angle decreases and/or the friction at the tool–chip interface increases, the shear angle decreases and the chip becomes thicker,Thicker chips mean more energy dissipation because the shear strain is higher. As work done during cutting is converted into heat, temperature rise is also higher.

The Merchant Equation

Ernest and Merchant gave the relation

)(2

1

4

Theory of Ernst and Merchant (1944)

Assumptions of the theory:• Tool edge is sharp.• The work material undergoes deformation across a thin shear

plane.• There is uniform distribution of normal and shear stress on the

shear plane.• The work material is rigid and perfectly plastic.• The shear angle adjusts itself to give minimum work.∅• The friction angle β remains constant and is independent of .∅• The chip width remains constant.

M. Eugene Merchant

95

96

What the Merchant Equation Tells Us

• To increase shear plane angle – Increase the rake angle – Reduce the friction angle (or coefficient of friction)

2245

97

Higher shear plane angle means smaller shear plane which means lower shear force

Result: lower cutting forces, power, temperature, all of which mean easier machining

Figure - Effect of shear plane angle φ: (a) higher φ with a resulting lower shear plane area; (b) smaller φ with a corresponding larger shear plane area. Note that the rake angle is larger in (a), which tends to increase shear angle according to the Merchant equation

Effect of Higher Shear Plane Angle

98

Lee and Shaffer theory

99

Schmid’s Law As we know plastic deformation by slip is due to shear stresses.

Even if we apply a tensile force on the specimen the shear stress resolved onto the slip plane is responsible for slip.

When the Resolved Shear Stress (RSS) reaches a critical value → Critical Resolved Shear Stress (CRSS) → plastic deformation starts (The actual Schmid’s law)

τs = σ cos ψ cos θ Schmid's Law

Schmid's law defines the relationship between shear stress, the applied stress, and the orientation of the slip system. It is an equation for finding the stress in the slip plane given an axial force and the angle of the slip plane.

Schmid's law helps to explain the differences in behavior of different metals when subjected to a unidirectional force.

100

Schmid’s Law

θ = angle defining slip direction relative to the force F = unidirectional force Ψ = angle defining the normal to the slip plane Fs = Shear force

τs = Resolved shear stress in the slip direction A = area of slip plane

σ = unidirectional stress applied to the cylinder

101

Schmid’s LawThe slip plane and slip direction to the applied force can be oriented by defining the angles θ and ψ. θ is the angle between the slip direction and the applied force, and ψ is the angle between the normal to the slip plane and the applied force.

In order for the dislocation to move in its slip system, a shear force acting in the slip direction must be produced by the applied force. This resolved shear force Fs is given by:

Fs = F Cos θ

If the equation is divided by the area of the slip plane, A = A0/Cos ψ, Schmid's law is obtained:

τs = σ cos ψ cos θ

where:

τs =Fs /A & σ =F/A0

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

Question: Who sketched this figure?

Friction Force

Leonardo Da Vinci (1452-1519) showed that the friction force is independent of the geometrical area of contact.

The paradox: Intuitively one would expect the friction force to scale proportionally to the contact area.

Da Vinci law and the Paradox

Amontons' first law: The force of friction is directly proportional to the applied load. Friction, FS is proportional to the normal force, FN

Amontons' second law: The frictional force is independent of the geometrical contact area.

NS FF

Amontons’ laws

A way out of Da Vinci’s paradox has been suggested by Bowden and Tabor, who distinguished between the real contact area and the geometric contact area. The real contact area is only a small fraction of the geometrical contact area.

Bowden and Tabor (1950, 1964)

Figure from: Scholz, 1990

105

Adhesion theory of frictionThe understanding of friction between solids was made clearer after the development of the junction growth theory by Bowden and Tabor (1950).

This is also known as the adhesion theory of friction.

It states that friction is a result of the true contact area between the solids.

The true area of contact is far less in comparison to the apparent contact area. True area of contact is a sum of the all micro-contacts at the asperities of the two solids and will be dependent on the yield strength of the materials.

A soft material such as rubber would give near complete contact meaning true area of contact will be equal to the apparent area of contact.

106

Ploughing in FrictionAll contacting surfaces are directly affected by surface friction. Surface friction allows control of all forms of motion. factors affecting the coefficient of surface friction includes Ploughing

It is the Ploughing of one surface by the asperities on the other surface.

107

Coulomb's Law of FrictionKinetic friction is independent of the sliding velocity.

Dry friction resists relative motion of two solid surfaces in contact. The two regimes of dry friction are static friction, between non-moving surfaces, and kinetic friction (sliding friction or dynamic friction) between moving surfaces.

Coulomb friction, named after Charles-Augustin de Coulomb, is an approximate model used to calculate the force of dry friction. It is governed by the model:

Where,

Ff = friction force exerted by each surface on the other. It is parallel to the surface, in a direction opposite to the net applied force.

μ = coefficient of friction, (an empirical property of the materials in contact)

Fn is the normal force exerted by each surface on the other, directed perpendicular (normal) to the surface.

108

An experiment, in the style of Coulomb

109

Coulomb’s observations

110

The Coulomb friction may take any value from zero up to , and the direction of the frictional force against a surface is opposite to the motion that surface would experience in the absence of friction.

Thus, in the static case, the frictional force is exactly what it must be in order to prevent motion between the surfaces; it balances the net force tending to cause such motion.

The force of friction is always exerted in a direction that opposes movement (for kinetic friction) or potential movement (for static friction) between the two surfaces.

For an example of potential movement, the drive wheels of an accelerating car experience a frictional force pointing forward; if they did not, the wheels would spin, and the rubber would slide backwards along the pavement. Note that it is not the direction of movement of the vehicle they oppose, it is the direction of (potential) sliding between tire and road.

Coulomb's Law of Friction

111

Friction in Metal Cutting

112

THE MECHANICS OF OBLIQUE CUTTING

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

Chip flows up the rake face of the tool at angle αc (chip flow angle), which is measured in the plane of the tool face.

Angle αn , the normal rake angle, is a basic geometric property of the tool. This is the angle between the normal OZ to the work piece surface and the line OA on the tool face.

The work piece material approaches the tool at a velocity V and leaves the surface (as a chip) with a velocity Vc

Effective rake angle αe is calculated in the plane of these two velocities. Assuming that the chip flow angle αc is equal to the inclination angle i, the effective rake angle αe is

As i increases, the effective rake angle increases and the chip becomes thinner and longer.

THE MECHANICS OF OBLIQUE CUTTING

113

Cutting forces in Oblique Cutting

76

References1. Kalpakjian, Schmid, Manufacturing Processes for Engineering Materials, 4th

edition,, Prentice Hall 2003 2. DeGarmo, E. P., J. T. Black, and R. A. Kohser, Materials and processes in

Manufacturing, PHI.3. P.N. Rao, Manufacturing Technology – Metal Cutting and Machine Tools, TMH.4. George Schneider,Jr. CMfgE, Cutting Tool Applications5. Amstead, B. H., P. F. Ostwald, and M. L. Begeman, Manufacturing Processes, 8th

ed., Wiley, New York, 1988.6. Amitabha Battacharya , Metal Cutting Theory and Practice7. Shaw, M. C., Metal Cutting Principles, Oxford University Press, Oxford, 1984.8. Schey, J.A., Introduction to Manufacturing Processes, McGraw-Hill, NewYork, 1977.9. Lindberg, R. A., Processes and Materials of Manufacture,10.William J Patton, Machine tool Operations, Reston publishing company11.O W Boston, Metal Processing, 2nd edition 1951, John Wiley and Sons12.B.S.Raghuwanshi, A course in Workshop Technology-Dhanpat Rai & Sons.13.Hajra Choudhury, Elements of Workshop Technology–Vol.-II, Media Promoters

and Publishers.14.O P Khanna, Production Technology-(Vol. II)15.R K Jain, Production Technology16.HMT, Production Technology, HMT

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Theory of metal cutting-Module 1