production engineerng-M I

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1.1 MODULE-I THEORY OF METAL CUTTING Introduction to Manufacturing Process Manufacturing is the economical term for making goods and services available to satisfy human wants. Manufacturing proces ses are classified in to many ways. The principal types of manufacturing are: 1. Process type manufact uring- it involves a continues flow of materials through a series of process steps to obtain a finished product like chemicals.  2. Fabrication type manufacturing- it involves manufacturing of individual parts or components by a series of operations, such as rolling, machining and welding. Here the processes like Casting; Forming; Machining; Grinding and Finishing; Unconvent ional machining; joining; Heat treatment  3.  Assembly-t ype manufact uring in this type of manufacturing the parts or compone nts are put together to get a complete product such as machine. The manufacturing process are classified as I. Constant mass process: 1. Casting - a) sand casting, b) shell mould casting, c) Precision investment casting, d) Plaster mould casting, e) Permanent mould casting, f) Die casting, g) Centrifugal casting 2. Metal Forming Processes: a) Rolling b) Drop forging c) Press forging d) Upset forging e) Extrusion f) Wire Drawing g) Sheet metal Operations. 3. Powder Metallurgy processing 4. Heat treatment. II. Metal Removing processes: 1. Machining: a) Turning b) Drilling c) Milling d) Shaping and planning e) Sawing f) Broaching 2. Grinding and finishing 3. Unconventional machining III. Metal addition Processes: 1.  Welding and allied process: a) Gas welding b) Electric arc welding c) Electric resistance welding d) Thermit welding e) Cold welding f) Brazing g) Soldering. 2. Mechanical Joining: a) Bolting b) Riveting, etc.

Transcript of production engineerng-M I

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1.1

MODULE-I

THEORY OF METAL CUTTING

Introduction to Manufacturing Process

Manufacturing is the economical term for making goods and services available to satisfy 

human wants. Manufacturing processes are classified in to many ways.

The principal types of manufacturing are:

1.  Process type manufacturing- it involves a continues flow of materials through a seriesof process steps to obtain a finished product like chemicals. 

2.  Fabrication type manufacturing- it involves manufacturing of individual parts or components by a series of operations, such as rolling, machining and welding. Herethe processes like Casting; Forming; Machining; Grinding and Finishing;Unconventional machining; joining; Heat treatment  

3.   Assembly-type manufacturing – in this type of manufacturing the parts or components

are put together to get a complete product such as machine.

The manufacturing process are classified as

I. Constant mass process:1. Casting - a) sand casting, b) shell mould casting,

c) Precision investment casting, d) Plaster mould casting,e) Permanent mould casting, f) Die casting,g) Centrifugal casting

2. Metal Forming Processes:a) Rolling b) Drop forging c) Press forging

d) Upset forging e) Extrusion f) Wire Drawingg) Sheet metal Operations.

3. Powder Metallurgy processing4. Heat treatment.

II. Metal Removing processes:1.  Machining:

a) Turning b) Drilling c) Millingd) Shaping and planning e) Sawing f) Broaching

2. Grinding and finishing3. Unconventional machining

III. Metal addition Processes:

1. 

 Welding and allied process:a) Gas welding b) Electric arc weldingc) Electric resistance welding d) Thermit weldinge) Cold welding f) Brazingg) Soldering.

2. Mechanical Joining:a) Bolting b) Riveting, etc.

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1.2

Review of Deformation of metals

  When materials are subjected to external loads they are distorted or deformed. Thedeformation may be elastic, plastic or fracture. When the material returned to its originalconfiguration on removal of external loads, the deformation is elastic in nature but when itdoes not returns to its original configuration then the material is said to be deformedplastically. In case of fracture a part of the original body or material is completely separated

from the rest.

Ductility and Toughness

The term ductility is commonly used to describe the ability of a material to undergoplastic deformation before fracture. Similarly toughness is the ability to absorb energy inplastic deformation up to the point of fracture. Toughness therefore functions of both strengthand ductility. The limit of usual deformation is however function of total strain which can beimposed on a metal before necking occurs. In view of this a suitable measure of useful ductility is the total strain at the onset of necking. Similarly toughness can be defined in terms of thearea under the stress strain curve up to the point of necking.

Plane strain Deformation

Most metal working problems are analyzed in terms of plane strain deformation i.e. theplastic flow occurs entirely in one plane with no deformation in the direction perpendicular tothe plane. For example, let us consider the compression of a wide strip between two flat face asshown in figure below. The dies overlap the strip in its width direction (W1) narrow in breadth(W2). When W1>10W2, lateral strains are negligible and plane deformation is obtained.

Fig.1-1 plane strain deformation

Thus in plane strain deformation.a. The deformation is every where parallel to a given plane (x,y plane in the above fig.) b. The deformation is independent of z.

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1.3

METALCUTTING

This refers to only those processes where material removal is affected by the relativemotion between tool made of harder material and the work piece.

Principles of metal cutting

1. The cutting tool removes the material from the work piece therefore; the material of the toolis always harder than that of work piece.2. The tool should be strong enough and held rigidly on a proper support, so that it can withstand the heavy pressure during cutting.3. The shape of the tool should be designed in such a manner that its cutting edge produces themaximum cutting effect on the material of the job.4. For carrying out the process of cutting, the work piece and cutting tool must be movedrelative to each other for setting the depth of cut. Such a relative motion is produced by acombination of rotary and translatory movement either of the work piece or of the cutting toolor both. The nature of this relative motion between the tool, and the work piece varies fordifferent metal cutting processes like turning, shaping, planning, boring etc. as shown in the

table below.

Operation Motion of job Motion of cutting tool

TurningBoringDrillingPlaningMilling

Rotary Forward translationFixedTranslatory Translatory 

Forward translationRotationRotation as well as translatory feedIntermittent translationRotation

Nature of the relative motion for the various cutting operations

Factors affecting metal cutting1.   Work material2.  Cutting tool material3.  Cutting tool geometry 4.  Cutting speed5.  Feed rate6.  Depth of cut7.  Cutting fluid used.

•  Metal cutting operations are performed on machine tools using cuttingtools

•  In this process wastage of material in the form of chip occurs.

CUTTING TOOLS

Classification

The Cutting tools are classified broadly as1.  Single Point Cutting Tool

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1.5

iv)  End Relief Angle – It is the angle between the portion of the end flank immediately below the end cutting edge and a line perpendicular to the base of thetool, and measured at right angles to the end flank. This angle range from 5o to 15o for general turning.Small relief angles are necessary to give strength to cutting edge when machininghard and strong materials.Tools with increased values of relief angle penetrate and cut the work material more

efficiently and this reduces the cutting forces.Too large relief angles weaken the cutting edge and there is less mass to absorb andconduct the heat away from the cutting edge.

 v)  Back rake angle – It is the angle between the face of the tool and a line parallel tothe base of the tool measured in a plane (perpendicular) through the side cuttingedge.

-  This angle is positive, if the side cutting edge slopes downwards from thepoint towards the shank and is negative if the slope of the side cuttingedge is reverse.

 vi)  Side rake angle-It is the angle between tool face and a line parallel to the base of 

the tool and measured in a plane perpendicular to the base and side cutting edge.-  This angle gives the slope of the face of the tool from the cutting edge.-  The side rake is positive if the slope is away from the cutting edge and

negative if slope is towards the cutting edge.-  The rake angle specifies the ease with which a metal is cut.-  Higher the rake angle better is the cutting and lesser is the cutting forces.

There is a maximum value for the rake angle and this is generally of theorder of 15o for HSS cutting mild steel.

-  It is also possible zero rake angle. Used in case of highly brittle toolmaterials such as carbide, diamond etc.

 vii)  Clearance angle – Angle between the machined surface and under side of the tool

called the flank face.-  The clearance angle is provided such that the tool will not rub the

machined surface thus spoiling the surface and increasing the cuttingforces.

-   A very large clearance angle reduces strength of the tool tip, and hence anormal angle of 5o to 6o is used.

 viii)  Nose angle- It is the angle between side cutting edge and end cutting edge.

-  Nose radius is provided to remove the fragile corner of the tool; itincreases the tool life and improves surface finish. Too large nose radius will induce chatter. Recommended values of nose radius are as follows.

R = 0.4 mm for delicate components

1.5 mm for heavy depth of cut, interupted cuts and heavy cuts.

= 0.4 mm to1.2 mm for disposable carbide inserts for common use.

= 1.2 mm to 1.6 mm for heavy duty inserts.

 

Rake anglesThe rake angles serve the following functions:

a). it allows the chip to flow in convenient directions.

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1.7

 FIG 1-2a: Single Point Cutting Tool

FIG 1-2b : Single Point Cutting Tool

The seven important elements comprise the signature of the cutting tool and are always statedin the following order:

i)  Back rake angleii)  Side rake angle

iii) 

End relief angleiv)  Side relief angle v)  End cutting edge angle vi)  Side cutting edge angle vii)  Nose radius.

It is usual to omit the symbols for degrees and mm, simply listing numerical value foreach component.

E.g. A typical tool signature is 0-10-6-6-8-90-1

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1.8

METHODS OF MACHINING

There are two methods of metal cutting depending on the arrangement of the cuttingedge with respect to the direction of relative work tool motion:

1.  Orthogonal Cutting or Two dimensional cutting

In this case the cutting edge of the tool is at right angles to the line of action orpath of the tool. In this method, the direction of chip flow velocity is normal to thecutting edge of the tool and the chip coils in a tight flat spiral. The cutting edge inorthogonal cutting is longer than width of cut. Cutting forces acts on a small area andtherefore, the life of the cutting tool is less. Orthogonal cutting is confined mainly tosuch operations as knife turning, broaching and slotting etc.

 When the tool is pushed in to the work piece, a layer of material is removed fromthe work piece and it slides over the front face of the tool called rake face. When thecutting edge of the wedge is perpendicular to the cutting velocity, the process iscalled orthogonal cutting. In this case the chip slides directly up to the tool face.

2.  Oblique Cutting or three dimensional cutting

In this case the cutting edge is inclined to the direction of tool feed or work feed.The chip flows sideways in a long curl. The direction of chip flow velocity is at anangle with the normal to the cutting edge of the tool. The cutting edge may or may not be longer than the width of cut. The depth of cut and feed is same in both cases, but the force which cuts and shears the metal cuts on longer area in case of obliquecutting. The heat developed per unit area is also less in oblique cutting. Because of these two reasons the tool will have a longer life. Secondly, the oblique tool willremove more metal in the same life as compared to orthogonal tool.

In most practical metal cutting processes, the cutting edge of the tool is notperpendicular to the cutting velocity but set at angle normal to the cutting velocity.Cutting in this case takes place in three dimensions (turning or milling) andrepresents the general case of oblique cutting. In oblique cutting a lateral direction of chip movement is obtained.

Fig 1.3(a)

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1.9

 Fig 1.3 (b)

Comparison between ‘Orthogonal Cutting’ & ‘Oblique Cutting’

S.

No.

  Aspects Orthogonal Cutting Oblique Cutting

1Inclination of thecutting edge of thetool.

Perpendicular to thedirection of tool travel

Inclined at an angle withthe normal to thedirection of tool travel.

2Clearance of the work piece width by thecutting edge.

The cutting edge clears the width of the work piece oneither ends.

The cutting edge may orMay not clear the width of the work piece.

3 The chip movement.

The chip flows over thetool face and direction of chip flow velocity isnormal to the cutting

edge. The chip coils in atight flat spiral.

The chip flows on the toolface making an angle withthe normal on the cutting

edge. The chip flowssideways in a long curl.

4.

Number of components of cutting force actingon the tool.

Only two components of the cutting force acting onthe tool. These twocomponents areperpendicular to eachother and can berepresented in a plane.

Three components of theforces (mutually perpendicular) act at thecutting edge.

5.

Maximum chip

thickness occurrence.

Maximum chip thickness

occurs at its middle

The maximum chipthickness may not occur at

middle.

6. Tool life. Less. More.

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1.10

Mechanism of Chip Formation

The cutting tool removes metal in the form of chips. As the tool advances material infront of the tool is compressed and when this compression exceeded, it is separated from the work piece and flows plastically in the form of chip.

The plastic flow takes place in the localized region called shear plane, which extendsfrom the cutting edge obliquely up to the uncut surface in front of the tool. The grains of the

metal in front of the cutting edge of the tool start elongating along the line LM and continue todo so until they are completely deformed along the line NP. Thus the deformation does notoccur sharply along a plane but it occurs along a narrow band shear zone at the order of 0.025mm. In figure the region between the lines LM and NP is called shear zone. After passing outthe shear zone, the deformed metal in the form of chip slides along the tool face due to velocity of tool. Actually the shear zone is wedge shaped which is thicker near the tool face at the rightthan at the left. This causes curling of the chip in the metal cutting. Again the owing to the nonuniform distribution of forces at the chip tool interface and on the shear plane, the shear planeis not straight but slightly curved concave downwards. This causes the chip curl away from thesurface of the tool.

FIG- 1-4; Chip Formation

Every machining operation involves the formation of chips, the nature of which depends

up on the operation, properties of the work piece material and cutting conditions.

Types of ChipsChips produced belong to following category 

1. Continuous chip2. Discontinuous chip3. Built-up chip.

Continues Chip

•  These are produced while machining more ductile material. This is mostdesirable

•  This is like a ribbon flows along the rake face.• 

Some ideal conditions that promote continues chips in metal are-  Small chip thickness (fine speed).-  Small cutting edge.-  Large rake angle.-  High cutting speed-  Less friction between chip tool interface though efficient lubrication.-  Ductile work materials.

 Advantages1.  These are most useful chips.

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1.11

2.  Surface finish obtained is good.3.  Cutting is smooth.4.  Higher tool life.5.  Lower power consumption.

Disadvantages1.  Due to large coil of chips, chip disposal is a problem.2.  Chip breakers are to be used to allow the chips to break.

Fig 1-5

Discontinues Chips

•  These are produced when cutting more brittle materials like grey cast iron, bronze andhard brass.

•  Chip produced is in the form of discontinues segments.•  Easier in the view of chip disposal.

•  But the cutting force becomes unstable due to variation coinciding with fracturing cycle.•  Discontinues chips are produced under the following conditions

-  low cutting speeds-  small rake angles-  higher depth of cut( large chip thickness)

Built Up Chip

  When machining ductile materials, conditions of high local temperature and extremepressure in the cutting zone and also high friction in the tool-chip interface may cause the work material to adhere or weld to the cutting edge of the tool forming the built up edge (BUE). Thiscauses the finished surface to be rough. However since the cutting is being carried by the BUE

and not the actual tool tip, the life of the cutting tool increases while cutting with BUE. That way BUE is not harmful in rough machining.

•  In general low cutting speed, high feed and small rake angle are conducive toBUE formation

•  Presence of BUE increases power transmission.

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1.12

CHIP CONTROL

The control and disposal of chips in high speed production turning, is important toprotect both the operator and the tools. The long and ribbon type continues chip that curls

round the cutting tool has sharp edges and can inflict deep, painful and dangerous cuts. Itshould never be handled with the bare hands. A swarf rake should be used to drag it away fromthe working zone of the machine.

The usual procedure to avoid the formation of continues chips is to break the chipintermittently with a chip breaker.

Fig (a) shows the schematic illustration of the action of the chip breaker. The chip  breaker decreases the radius of the curvature of this chip. Fig (b) shows the chip breakerclamped on the rake face of a cutting tool.

Chip BreakerFig 1-6

FORCE OF A SINGLE POINT TOOL [Ref: fig. 1.3 (a)]

The work material offers resistance to the cutting tool, during metal cutting. Thisresistance is overcome by the cutting force applied to the tool face. The work done by this forcein cutting is expended in shearing the chip from the work, deforming the chip and overcomingthe friction of the chip on the tool face and tool flank on the cutting surface.

The magnitude of the cutting force depends on the following factors;-   Work material-  Rate of feed-  Depth of cut-  Tool angles-  Cutting speed-  Coolant used, etc.

Orthogonal cutting: Resultant2 2

a t   R F F  = +  

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1.13

Oblique cutting: Resultant2 2 2

a r t   R F F F  = + +  

Ft is always largest of the three componentsFa due to feed motion is about 35 to55 % of Ft Fr which tends to pull back the work piece is about 25 to 30 % of Ft

MECHANISM OF METAL CUTTING

The basic mechanism by which chips are formed during the process of metal cutting isthat of deformation of the material, lying ahead of the cutting edge of the tool, because of theshearing action. Shear Zone, Shear Plane and Shear Angle

 When cutting tool is introduced in to the work material, plastic deformation takes placein a narrow region in the vicinity of the cutting edge. This region is called shear zone. (See fig1.7). The width of this zone is small and therefore chip formation is always described as aprocess of successive shears of thin layers of the work material along particular surfaces. Athigh speeds this zone can be assumed to be restricted to a plane called shear plane. Inclinationof this plane is called shear angle (ø). In fig-1.9 the sharp line LM separated the deformed andun deformed work material and indicates the projection of the shear plane.

The value of shear angle depends on work piece materials, cutting conditions, materialof tool, geometry of tool. When the shear angle is small the plane of shear will be larger, chip isthicker and therefore higher force is required to remove the chip. When shear angle is large,the plane of shear will be shorter, the chip is thinner and hence less force is required to removethe chip. The shear angle is determined from chip thickness ratio(r).

Fig- 1.7

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1.14

Fig-1.8

CHIP THICKNESS RATIO

The mach inability of the material is expressed by chip thickness ratio.

From fig Depth of cut, sint LM  φ =  

Chip thickness, cos( - )tc LM   φ α =  

Then chip thickness ratio,  /  cr t t =  

sin sin

cos( - ) cos cos sin sin

 LM r 

 LM 

φ φ 

φ α φ α φ α  = =

+  

1

cot cos sinr 

φ α α =

(cot cos sin ) 1r  φ α α + =  

1 sincot cos

α φ α 

−=  

cos. tan

1 sin

r ie

α φ 

α =

−  

1 costan

1 sin

α φ 

α 

−=

− 

the cutting ratio or chip thickness ratio is always less than unity, and can be measured by measuring depth of cut and chip thickness. But actually it is difficult to measure the chipthickness due to one side being rough.

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1.15

But , volume of metal removed = volume of chip

. . . . .c c c cb t l b t l ρ ρ =  

Where b, t, l, ρ are width, thickness or depth of cut, length and density of metal cut andc stands for chipIt is found that, width is same as that of metal and density also,

 / / c c

r t t l l= =  

lc – length of chip, l – length of uncut chip.

Cutting ratio is also defined as ratio of chip velocity V c to cutting speed V . the ratio V c /V can befound by finding the kinetic forces acting on the chip.

SHEAR ANGLE AND ITS RELEVANCE

Shear Zone

The chip formation in metal cutting is due to the plastic shear of the work material in a zoneknown as shear zone. Between the chip and the work material, there will be a transition zoneof plastic deformation. Within this zone the stress changes continuously as the movement of deformed material progresses. The plastic work flow of material around the tip of the cuttingtool can be observed in fig 1-11, the deformation process may be studied by grid technique andphoto micrographic methods. The results of such studies are schematically given in fig-1-12 because of the work hardening effect of the machined surface and friction between tool and work the outer layer of finished metal surface of the work immediately below the tool is alsosubjected to additional deformation. As the plastically deformed metal grains move from the

 boundary  oabc to boundary  od the shear strain increases. The upper boundary surface at which plastic strain occurs is subjected to continue plastic deformation is inclined at an angle øand is defined as shear plane angle. The grains elongated in the direction known as “directionof flow or crystal elongation” and are inclined at an angle ψ known as grain elongation angle.The angle ø will depend on the geometry of the cutting tool, the material being cut, thethickness of material removed and cutting speed. It is to be noted that the chip formation inmetal cutting is basically a large deformation process at very high strain rate.

Velocity Relationship In Orthogonal Cutting

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1.16

FIG- 1.9

Cutting velocity (V) = velocity of tool relative to the work piece  Velocity of chip (Vc) = velocity with which the chip moves over the rake face  Velocity of shear (Vs) = velocity with which the metal of the work piece shears along the

shear plane.The cutting velocity Vc and rake angle α are always known; the values of Vf and Vs can becalculated as follows:

Ref to fig, velocity diagram c sV V V→ → →

= +  

Using sin rule

sin sin sin

Vc Vs V  

  MSL MLS LMS= =

 

Simplifying

( ) {

[ ] {

sin sin 180 [(90 ) ]}sin 90 ( )

sin sin 90 sin 90 ( )}

sin cos cos( )

Vc Vs V  

Vc Vs V  

Vc Vs V  

φ φ φ α φ  φ φ α 

φ α φ α  

φ α φ α  

= =− − + − + − + −

= =− − −

= =−

 

sincos( )

cos

cos( )

V Vc

V Vs

φ φ α 

α 

φ α 

=−

=−

 

FORCES ON THE CHIP (Merchant’s Analysis)

There are usually two schools of thought

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1.17

1. Deformation zone is very thin and planar as shown in fig (a)2. The actual deformation zone is very thick with a fan shape assign fig(b)

The first, ie. The thin zone model is more useful for analytical purposes.The current analysis based on Merchant’s thin shear plane model which considers theminimum energy principle. This method is applicable at high cutting speeds which are

generally practiced in production.

 Assumptionsi)   Work moves with a uniform velocity.ii)  The surface where the shear occurs is a plane.iii)  The tool is perfectly sharp there is no contact along the clearance face.iv)  The cutting edge is a straight line which extends perpendicular to the direction of 

motion and generates plane surface as the work moves past it. v)   Width of the tool is greater than the width of the work. vi)  The stresses on the shear plane are uniformly distributed. vii)  Uncut chip thickness is constant.

 viii)   A continues chip is produced without any built up edge.ix)  The chip does not flow to either side, or there is no side spread.

FIG- 1.10

Ft – Tangential or cutting forceFf – Feed force

-   forces acting on the tool and measured by dynamometer 

Fc- Compressive force on the shear planeFs – Shear force on the shear plane

-   Forces exerted by the work piece on the chip.

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1.18

F – Frictional force along the rake face of toolN – Normal force at the rake face of tool

- Forces exerted by the tool on the chipRef fig – (b)α – tool rake angle, ø – shear plane angle, β – angle of friction

cos sin

cos sin

cos sin

cos

tan

tan ,tan

 f t 

 f t 

t f 

 f t 

t f 

  Now F PW WL

F F F 

  N MP UW UQ

F F F 

  N F F  

  Dividing by we get 

F F F F 

but coefficient of friction  N F F N  

Where F and N are the components of resultat tool force R

α α 

α α 

α α 

α 

α 

 β µ α 

= +

= +

= = −

+=

+

= = =−

 

, cos sin

cos sin

cos( )

sin( )

cos( ) cos( )

s t f 

 f t 

 f 

  Now F F F  

Fc F F  

F R

F R

Fs R or R

φ φ 

φ φ 

 β α 

 β α 

  β α φ φ β α  

= −

= +

= −

= −

= − + + −

 

,From the above equaions  

c o s( )

co s ( )

c o s ( )

co s( )

s

t s

F R

F R

F F 

 β α 

φ β α 

 β α 

φ β α 

−=

+ −

  −= + −  

 

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1.19

STRESS AND STRAIN ON THE CHIP

Geometry of Chip formationFig-1.11

Since the chips are formed due to the plastic deformation of the work piece material,they experience stress and strain.

 As – area of shear plane,

  A = (b x t) = cross sectional area of un cut chip= As sin ø

 b – width of cut, t – un cut chip thickness.Mean normal stress (σ) :

s i n

 / s i n

[ c o s s i n ] s i n

c c c

s

 f t 

F F F 

  A A A

F F 

 A

φ σ 

φ 

φ φ φ σ 

×= = =

+ ×=

 

s s

s

s

F F ×sinMean shear stress, τ = =

A A

τ.b.tF =sin

φ 

φ  

But we have, s t f F = F cos -F sinφ φ   

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1.20

s t f t f  

s

F F cos F sin (F cos F sin ) sin

As

 A A

φ φ φ φ φ  τ 

− −= = =  

SHEAR STRAIN

To evaluate the shear strains, let us take the help of Piispanen’s model as shown in fig. (He

considered un deformed metal as a stack of cards which would slide over one another as wedgeshaped tools moved under these cards. Though this idea is an oversimplified one, it accountsfor a number of features that are found in practice. A practical example is when paraffin iscut; a block wise slip is clearly evident .

cot tan ( )

s BA BD DAShear strain

  y CD CDε 

ε φ φ α  

∆ += = =

= + − 

cos sin( )

sin cos( )

cos .cos( ) sin .sin( )

sin .cos( )

cos[ ( )]

sin .cos( )

cos:

cos( )

s Vs V  strain rate is given by

  y t y y

φ φ α 

φ φ α 

φ φ α φ φ α  

φ φ α 

φ φ α 

φ φ α 

α ε 

φ α 

−= +

− + −=

− −=

∆= = = ×

∆ × ∆ ∆ − ∆

 

 Where ∆y – thickness of deformation zonet- time to achieve final value of strain

 Work Done During Metal Cutting and Specific Cutting Energy 

Most of the energy consumed in metal cutting is utilized for plastic deformation.

Total work done in cutting, W = Ft x V   Work done in shear Ws = Fs x Vs  Work done in friction, Wf = F x VcThus, W = Ft x V = Fs Vs + F.Vc

Fs – shear force on the shear plane,F – Frictional force along the rake face of the tool, V- Cutting velocity  Vs- Velocity of shear

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 Vc – velocity with which the chip moves over the rake face of the cutting tool.

In order to get better picture of the efficiency of the metal cutting operation it isnecessary to have a new parameter which does not depend on the cutting processparameters. The specific cutting energy “Esp” is such a parameter which can be obtained by dividing the total work done with the material removal rate (MRR).

Metal Removal rate (MRR)

Metal removal rate is defined as the volume of metal removed in unit time. It is used tocalculate time required to remove specified quantity of material from the work piece.If t- depth of cut in mm, f- feed in mm/rev and V- cutting speed in mm/s,Then,Metal removal rate = V x f x t mm3/s

If metal removal rate is optimum we ca reduce the machining cost. To achieve this, thecutting tool material should be proper, cutting tool should be properly ground and itshould support rigidly so that no case of vibration.

If b- the width of the chip, it can be taken

MRR = V.b.t

t

. . .

1 co s( )b y u sin g th e eq u a tio n fo r F

. c o s( )

1 co s( ).. co s( )

1 . co s ( ).

. s in co s( )

t t sp

s

F V F  E 

V b t b t  

F sb t 

 Ab t 

b t 

b t 

 β α 

φ β α 

 β α τ φ β α 

 β α τ 

φ φ β α  

×= =

−= ×

+ −

−= × + −

−=

+ −

 

[Since As = A/ sinø = b.t/ sinø]

cos( )sin .cos( )

sp E  τ β α φ φ β α  

−=

+ −  

THEORIES ON MECHANICS OF METAL CUTTING

1) Ernst – Merchant Theory 

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It is based on the following assumptions:

i)  The shear stress is maximum at the shear plane and it remainsconstant.

ii)  The expenditure is minimum in this process, ie. Shears will takesplace in a direction in which energy required for shearing isminimum.

In Merchant’s theory 

Ft = R cos (ß- )

F s = R c os (ø+ ß - )

α 

α   

cos( )

cos( )

. .

sin

. . cos( )

sin cos( )

t s

F F 

b t Fs

b t F 

 β α 

φ β α 

τ 

φ τ β α 

φ φ β α  

−=

+ −

=

−= ×

+ −

 

Differentiating the above eq. w.r.t ø and equating to zero to find the valueof shear angle, ø for which Ft is minimum, i.e.:

0

, cos .cos( ) sin .sin( ) 0

cos( ) 0

cos(2 ) cos( / 2)

2 / 2

 / 4 / 2 / 2

dFt 

We get 

or 

Shear angle

φ 

φ φ β α φ φ β α  

φ φ β α  

φ β α π  

φ β α π  

φ π α β  

=

+ − − + − =

+ + − =

+ − =

+ − =

= + −

 

2. Merchant theory 

Merchant found that the above theory agreed well with experimental results obtained when cutting synthetic plastics but agreed poorly with experimental results obtained for steelmachined with sintered carbide tool.

Merchant modified his theory by assuming that shear stress ‘ τ’ along the shear plane varies linearly with normal stress, ie.,

0 k τ τ σ = +  

 Where k is a constant. (τ0 is the value of  τ when σ =0)

This assumption agreed with the work of Bridgman, where in experiments on poly crystalline metals, the shear strength was shown to be dependent on the normal stress on theplane of shear. Merchant then derived,

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2 C φ β α + − =  

 Where, C = machining constant; its value varies from 70o to 80o for various steels.Most recent experimental work indicates that τ remains constant for a given material over a wide range of cutting conditions and therefore k would be expected to be zero.

3) Stabler Theory 

He modified Ernst-Merchant eq: as= π /4 - β + α / 2φ   

3) Lee and Shaffer Theory  

Solution to the problem of the mechanics of orthogonal cutting is obtained by using theslip line field theory . According to this theory shear occurs on a single plane. In thisanalytical model it is assumed that the material being cut behaves as an ideal plastic material, which means that the elastic strain is negligible during chip formation.

Fig shows a slip line field using shear plane model. It is assumed that there must be a

stress field within the chip to transmit the cutting forces from the shear plane to the tool face.They represent a slip line field in which no deformation occurs although it is stressed up to the yield point. This shows the Mohr’s circle for the stresses at the boundaries of the stressed zone, which results in the equation:

= π /4 ( β)

= π /4 - + - considering built up edge Also

φ α 

φ β α θ  

+ −

 

FIG-1.12

EFFECT OF CERTAIN ANGLES ON CUTTING FORCE AND SURFACE FINISH

Rake Angle

The rake face controls the directions of he resultant force on the tool and chip flow. Withzero inclination angles or zero back rake angle chip will flow parallel to the work surface andmay cause removal problem. With appropriate inclination or back rake angle the chip can bemade to flow away from the work piece and strikes a suitable chip breaker, curl and break in tosmall fragments for easy disposal. The rake angle influences the cutting forces, power andsurface finish. The larger the rake angle the lower are the cutting forces and power and better isthe surface finish. Large rake however decreases the cutting angle between the rake andprincipal flank faces and less metal is available to support the tool and conduct the heatgenerated due to plastic deformation and friction. Further the angle chosen could be positive or

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negative depending up on the tool strength. A positive back rake angle moves away the chipfrom the work surface. A negative rake angle result in a stronger cutting edge. As the rake angleis decreased the shear plane angle will be decreased, resulting in a thicker chip. But at higherspeeds the cutting force decreases and a negative rake is recommended for machining highstrength alloys, for interrupted cuts and for carbide and ceramic tools.

The rake angle for a single point HSS tools generally varies between 5 to 15 degreesdepending up on the work material, higher values being used for softer material like

aluminum. In general harder is the material lower is the rake angle.

Cutting Edge AngleSide cutting edge angle influence the direction of chip flow. When the principle cutting

edge is perpendicular to the axis of rotation of the work i.e. when the lead angle is zero, the fulldepth of cut will be in contact with the work suddenly as the tool enters into the full depthgradually. Increasing the side cutting edge angle decreases the thickness of the chip andincreases the width of the chip for the same feed rate. Thus, for the same depth of cut the crosssectional area of the chip will be spread over a longer cutting edge, and will permit increasedfeeds. But an excessive side cutting edge angle will cause chatter and is to be avoided. Forgeneral machining 15 to 30o is recommended.

The purpose of end cutting edge angle is to prevent rubbing of the cutting edge and thefinished surface of the work piece. An excessive angle weakens the cutting edge. At largeprinciple cutting edge angles, the force component which is trying to separate the tool from the work piece increases and promotes chatter. With very small angles excessive pressure normalto the work surface are produced, causing chatter and larger tool surface contact with difficulty for tool penetration in to the work. 4 to 15o are recommended for general cutting conditions.

Relief AngleEnd relief and side relief angles are provided to prevent rubbing of the tool on the flank 

faces, i.e. below the cutting edge. Increased relief angles reduce the strength of the cuttingedge. Also, increased relief angles reduce the force required for tool penetration in to the work.

But this disadvantage is recommended for low strength materials only.

Nose Radius A cornered pointed edge with a zero nose radius is not good for a cutting tool. Having a

curved nose radius reduces the heat concentration, improve the surface finish and strengthenthe tool point. A larger nose will permit for heavy depth of cut, higher feed and interruptedcuts. But there is a limit for larger size of the nose radius and will cause chatter because of longer contact with work. Thus in general, the nose radius increases the forces and the toolchatter. In single point tools, a nose radius in the range of 0.5 to 3 mm has been found to bequite satisfactory.

FRICTION IN METAL CUTTINGIn Chip Formation, the friction occurring between the chip and the tool face is acontrolling influence.

The actual contact of two sliding surfaces through the high spots can be seen under amicroscope; this is called asperities.

 When a normal load is applied, yielding occurs at the tips of the contacting asperitiesand the real area of contact (A r) increases until it is capable of supporting the applied load. Thisreal area of contact A r is only a small fraction of apparent contact area (A a) for the vast majority of engineering applications.

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FIG-1.13 Micro view of asperities in contact

r

y

NA =

σWhere N – normal force and  y

σ  – mean yield stress of the asperities.

It has been seen that under the influence of normal and tangential load very hightemperature are developed at the contacting asperities and the metallic bonding of thecontacting high spots can occur. Thus, sliding of one surface relating to the other must be

accompanied by shearing of the welding asperities. When plastic deformation takes place at the contacting surfaces, then the mechanism of 

friction is different because the real area of contact approaches that of the apparent area of contact. Under these conditions the friction force is independent of normal force.

Further it has been observed that coefficient of friction increases with an increase in therake angle. Normally, it is expected that with an increase in the rake angle, the metal cuttingforces decrease and should normally be associated with a decrease in friction. However inactual practice the coefficient of friction increases. This happens because the influence of therake angle is no the same on the different components of the cutting force. The normal force onthe rake face decreases a great extent compared to the friction force. Thus, although there is anoverall decrease in the forces friction coefficient increases. That is why it is called apparent

coefficient of friction.In metal cutting we have sliding situations of high normal load and with a metal surface

 which is chemically clean; the clean metal surface explains the high value of friction coefficient(µ) and the high normal load and the departure from the usual laws of friction. Thus, thefriction along the rake face of a cutting tool can be considered as partially sticking and partially sliding.In the ‘sticking zone ‘ the shear stress constantly approaches the yield stress of the work material, while in the ‘sliding zone’, the normal Coulomb’s laws of friction hold good.

FIG-1.14 Fig-Chip Tool Friction