metal cutting theory for mechanical engineers

8/11/2019 Metal Cutting Theory for Mechanical Engineers

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Simple common process of removal of un-wantedportion of material from a starting work-part orwork-piece or raw- material, so the remainingpart has the desired geometry

Machiningmaterial removal by a sharp cuttingtool, e.g., turning, milling, drilling etc.,

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

Nontraditional processes - various energy formsother than sharp cutting tool to remove materialexample. Electro Chemical Milling, EDM etc.,

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Cutting action involves sheardeformation of workmaterial to form a chip As chip is removed, new surface is exposed

(a) A cross-sectional view of the machining process, (b) tool with

negative rake angle; compare with positive rake angle in (a).

Machining

Dr M Varaprasada Rao


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

Variety of part shapes and special geometricfeatures possible, such as: Screw threads

Accurate round holes

Very straight edges and surfaces

Good dimensional accuracy and surfacefinish possible with machining operation.



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Produces Wasteful of material

Chips generated in machining are wastedmaterial, at least in the unit operation

More Time consuming Process

A machining operation generally takes more timeto shape a given part than alternative shapingprocesses, such as casting, powder metallurgy, orforming



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Generally performed after othermanufacturing processes, such as casting,forging, and bar drawing

Other processes create the general shapeof the starting work-part

Machining provides the final shape,dimensions, finish, and special geometricdetails that other processes cannot create



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Speedis the relative movement between tooland w/p, which producesa cut

Feedis the relative movement between tooland w/p, which spreadsthe cut



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Most Important Machining Operations: Turning

Drilling

Milling

Other Machining Operations: Shaping and Planning

Broaching Sawing



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Tool

Workpiece

Chip

Heat Generation Zones

(Dependent on sharpness

of tool)

(Dependent on m)

(Dependent on f

10%

30%

60%



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Tool Terminology

Side reliefangle

Side cuttingedge angle(SCEA)

Clearance or end

relief angle

BackRake(BR),+

Side Rake

(SR), +

End Cuttingedge angle

(ECEA)

Nose

Radius

TurningCuttingedge

FacingCuttingedge



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SINGLE POINT CUTTING TOOL TERMINOLOGY

ShankIt is main body of tool. The shank used to grippesd in toolholder.

FlankThe surface or surface below the adjacent of the cutting edge is

called flank of the tool. FaceIt is top surface of the tool along which the chips slides.

aseIt is actually a bearing surface of the tool when it is held in toolholder or clamped directly in a tool post.

HeelIt is the intersection of the flank & base of the tool. It is curved

portion at the bottom of the tool. NoseIt is the point where side cutting edge & base cutting edge

intersect.

Cutting edgeIt is the edge on face of the tool which removes thematerial from workpiece. The cutting edges are side cutting edge (majorcutting edge) & end cutting edge ( minor cutting edge)

Tool angles-Tool angles have great importance. The tool with properangle, reduce breaking of tool, cut metal more efficiently, generate lessheat.

Noise radiusIt provide long life & good surface finish sharp point onnose is highly stressed, & leaves grooves in the path of cut.Longer nose

radius produce chatter. 9/26/2014 17Dr M Varaprasada Rao


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MRR vfd

Roughing(R)

f 0.41.25mm /rev

d 2.5 20mm

Finishing(F)

f 0.125 0.4mm /rev

d 0.75 2.0mm

vR vF



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Cutting Models

ORTHOGONAL GEOMETRY OBLIQUE GEOMETRY

Tool

workpiece

Tool

workpiece



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Assumptions(Orthogonal Cutting Model)

The cutting edge is a straight line extending perpendicularto the direction of motion, and it generates a plane surface

as the work moves past it. The tool is perfectly sharp (no contact along the clearanceface).

The shearing surface is a plane extending upward fromthe cutting edge.

The chip does not flow to either side The depth of cut/chip thickness is constant uniform

relative velocity between work and tool Continuous chip, no built-up-edge (BUE)



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r to

tc

l

ssinf

lscos(f)

tanfrcos

1 rsin

AC

BDADDC

BDtan(f)cotf


T i F F O th l


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F t

FC

Fr

DIRECTION OF ROTATION

WORKPIECE

CUTTING TOOL

DIRECTION OF FEED

Velocity ofTool relative toworkpiece V

Longitudinal

'Thrust' Force (27%)

Radial

Force (6%)

Tangential 'Cutting' Force (67%)

Turning Forces For OrthogonalModel

End view section 'A'-'A'

Note: For the 2D Orthogonal MechanisticModel we will ignore the radial component

Ft

'A' 'A'

cF



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FL

FC

Fr

DIRECTION OF ROTATION

WORKPIECE

CUTTING TOOL

DIRECTION OF FEED

Velocity of

Tool relative toworkpiece V

Longitudinal Force

Radial Force

Thrust Force

Tangential Force

'Cutting' Force

Facing Forces For Orthogonal Model

End view

Note: For the 2D Orthogonal MechanisticModel we will ignore the Longitudinalcomponent



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Orthogonal Cutting Model(Simple 2D mechanistic model)

Mechanism: Chips produced by the shearing process along the shear plane

t 0

f

+

RakeAngle

Chip

Workpiece

Clearance AngleShear Angle

t c

depth of cut

Chip thickness

Tool

Velocity V

tool



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tool

Cutting Ratio(or chip thicknes ratio)

As Sinf =to

AB and Cosf-) =

tcAB

Chip thickness ratio (r) =t0

tc=

sinf

cos(f)

ftcto

f)

A

B

Chip

Workpiece



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Experimental Determination ofCutting Ratio

Shear angle fmay be obtainedeither from photo-micrographsor assume volume continuity

(no chip density change):

Since t0w0L0= tcwcLc and w0=wc(exp. evidence)

Cutting ratio , r =t 0tc

=L cL0

i.e. Measure length of chips (easier than thickness)

w

t

L0

0

0

wc

Lc

ct



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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 largelyreplaced by carbide or other inserts of various shapes and sizes, as shown in (b).



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Cutting processes remove material

from the surface of a workpiece by

producing chips.

Turning, in which the workpiece is

rotated and a cutting tool removes a

layer of material as the tool moves to the

left.Cutting off:in which the cutting tool

moves radially inward and separates the

right piece from the bulk of the blank.

Slab milling: in which a rotating cutting

tool removes a layer of material from thesurface of the workpiece.

End milling:in which a rotating cutter

travels along a certain depth in the work-

piece and produces a cavity.



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In the turning process, illustrated

the cutting tool is set at a certaindepth of cut (mm) and travels to

the left with a certain velocity as

the workpiece rotates. The feed, or

feed rate, is the distance the tooltravels horizontally per unit

revolution of the workpiece

(mm/rev). This movement of the

tool produces a chip, which moves

up the face of the tool.



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Figure : Schematic illustration of a two-dimensional cutting process, also called

orthogonal cutting: (a) Orthogonal cutting

with a well-defined shear plane, also

known as the Merchant Model. Note that

the tool shape, depth of cut, to, and the

cutting speed, V, are all independent

variables, (b) Orthogonal cutting without a

well-defined shear plane.



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Compare Figs.

Feed in turning is equivalent

to t0 Depth of cut in turning is

equivalent to width of cut(dimension perpendicular to

the page) in the idealized

model.

These relationships can bevisualized by rotating Fig.

20.3 CW by 90o.



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Independent variables in the cutting process:

Tool material, coatings and tool condition.

Tool shape, surface finish, and sharpness. Workpiece material, condition, and temperature.

Cutting parameters, such as speed, feed, and depth of cut.

Cutting fluids.

The characteristics of the machine tool, such as its stiffness anddamping.

Workholding and fixturing.

Dependent variables:

Type of chip produced.

Force and energy dissipated in the cutting process.

Temperature rise in the workpiece, the chip, and the tool.

Wear and failure of the tool.

Surface finish produced on the workpiece after machining.



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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 rakeangle of , and a

relief (clearance)

angle.

The shearing

process in chipformation is similar to

the motion of cards in

a deck sliding against

each other.



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

Chip thickness is always greater than the depth of cut

Chip compression ratio: reciprocal of r. It is a measure of how

thick the chip has become compared to the depth of cut.

The cutting 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. 9/26/2014 54Dr M Varaprasada Rao


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The shear strain, , that the material undergoes can be express as:

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 = OC 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 workpiece material properties

and cutting process variables. 9/26/2014 55Dr M Varaprasada Rao


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Assuming that the shear angle adjusts itself to minimize the cutting force,

or that the shear plane is a plane of maximum shear stress.

is the friction angle and is related to the coefficient of friction, , at the tool

chip interface (rake face):

o From Eq above as the rake angle decreases

and / or the friction at the toolchip interface

increases, the shear angle decreases and thechip becomes thicker,

o Thicker chips mean more energy dissipation

because the shear strain is higher

o Because work done during cutting is converted

into heat, temperature rise is also higher. 9/26/2014 56Dr M Varaprasada Rao


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From Fig., since chip thickness is greater than the depth of cut, the velocity

of the chip, Vc, has to be lower than the cutting speed, V. Conservation of mass:

Vsis the velocity at which shearing

takes place in the shear plane.

From the velocity diagram we obtain the



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1. Continuous

2. Built-up Edge

3. Serrated or Segmented

4. Discontinuous

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. Thissurface has a jagged, rough appearance, which is caused by the

shearing mechanism shown in figure.



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Formed with ductilematerials at high cutting


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Basic types of chips produced in orthogonal metal cutting, their schematic representation, and

photomicrographs of the cutting zone: (a) continuous chip with narrow, straight, and primary shear

zone; (b) continuous chip with secondary shear zone at the chip-tool interface; (c) built-up edge; (d)

segmented or non-homogeneous chip; and (e) discontinuous chip.Source

: After M.C. Shaw, P.K. Wright,and S. Kalpakjian.

materials at high cutting

speeds and/or high rake

angles. a

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

toolchip interface .b

The secondary zone

becomes thicker as tool

chip friction increases.

In CCs, deformation may

also take place along a

wide primary shear zonewith curved boundaries (F



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The lower boundary is below the machined surface, subjectingthe machined surface to distortion, as depicted by the distorted

vertical lines.

This situation occurs particularly in machining soft metals at

low speeds and low rake angles. It can produce poor surface finish and induce residual surface

stresses.

Although they generally produce good surface finish, CCs are

not always desirable.



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BUE, consisting of layers of material from the workpiece that

are gradually deposited on the tool, may form at the tip of the

tool during cutting. D.

As it becomes larger, BUE becomes unstable and eventually

breads 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 aretaken to eliminate it.

Because of work hardening and deposition of successive layers

of material. BUE hardness increases significantly a.



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BUE is generally undesirable. 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.

The tendency for a BUE to form is reduced by any of the

following practices:

1. Increase the cutting speeds

2. Decreasing depth of cut

3. Increasing the rake angle

4. Using a sharp tool5. Using an effective cutting fluid

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

work-piece material.



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Serrated chips: semi-continuous chips with zones of low and

high shear strainfig e

Metals with low thermal conductivity and strength that

decreases sharply with temperature, such as titanium, exhibit

this behavior. The chips have a saw-tooth-like appearance.



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DCs consist of segments that may be firmly or loosely

attached to each other.

DCs usually form under the following conditions:

1. Brittle workpiece materials

2. Workpiece 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.

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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

Workholding devices, and the machine tool are important in

cutting with both DC and serrated-chip formation



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With soft workpiece materials such as pure aluminum orcopper, 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.



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Chip in Fig. 21.9a f lows

up the rake face of the toolat angle c (chip flow

angle), which is measured

in the plane of the tool

face.

Angle n, the normal rake

angle, is a basic geometric

property of the tool. This

is the angle between the

normal oz to the workpiece

surface and the line oa on

the tool face. The workpiece material

approaches the tool at a

velocity V and leaves the

surface (as a chip) with a

velocity Vc

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.



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Knowledge of the cutting forces and power involved inmachining 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 selectappropriate tool holders and work-holding devices.

b. The workpiece 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.



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Figure 21.11 (a) Forces acting on a cutting tool during two-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.



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

(21.11)

The coefficient of friction in metal cutting generally ranges

from about 0.5 to 2.

m

tan

tanfriction,oftCoefficien

tc

ct

FF

FF

N

F



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If the thrust force is too high or if the machine tool is notsufficiently 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 therake angle increases and/or friction at the rake face decreases,

this force can act upward.

This situation can be visualized by noting that when = 0

(that is, = 0), the resultant force, R, coincides with thenormal force, N.

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

upward.



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EXAMPLE : Relative Energies in Cutting

In an orthogonal cutting operation, to = 0.13 mm, V = 120 m/min,

= 10and the width of cut = 6 mm. It is observed that tc = 0.23

mm, Fc = 500 N and Ft = 200 N. Calculate the percentage of the

total energy that goes into overcoming friction at the tool-chipinterface.

SolutionThe percentage of the energy can be expressed as:



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EXAMPLE: Relative Energies in Cutting



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The mean temperature in turning on a lathe is proportional to thecutting speed and feed:

Mean temperature Vafb

a and b are constants that depend on tool and workpiece

materials, V is the cutting speed, and f is the feed of the tool.

Max temperature is about halfway up the face of the tool.

As speed increases, the time for heat dissipation decreases

and temperature rises

Tool

Material

a B

Carbide 0.2 0.125HSS 0.5 0.375



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Figure : Typical temperature distribution inthe cutting zone. Note the severe

temperature gradients within the tool and

the chip, and that the workpiece is relatively

cool. Source: After G. Vieregge.

Figure : Proportion of the heat generated incutting transferred into the tool, workpiece, and

chip as a function of the cutting speed. Note

that the chip removes most of the heat.



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VTn

C

VTnd

xf

y C

Taylor Equation:



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Figure : Tool-life curves for a

variety of cutting-tool materials.

The negative inverse of the slope

of these curves is the exponent nin the Taylor tool-life equation andCis the cutting speed at T= 1

min, ranging from about 200 to

10,000 ft./min in this figure.



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(a) Schematic illustration of types of wear observed on various cutting tools. (b) Schematic illustrations

of catastrophic tool failures. A wide range of parameters influence these wear and failure patterns.



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Chipping: small fragments from the CE breaks away [sudden

loss of material] . Brittle CT like ceramic. Two main causes:

1. Mechanical shock: (i.e., impact due to interrupted cutting, as

in turning a splined shaft on a lathe).

2. Thermal fatigue: (i.e., cyclic variations in the temperature ofthe tool in interrupted cutting)

Thermal cracks normal to the cutting edge of the tool.

Chipping may occur in a region in the tool where a small crack

or defect already exists High +ve rake angles can contribute to chipping

Its possible for crater wear region to progress toward the tool

tip, weakening the tip and causing chipping



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Due to decreasing in yield strength from high temp during cutting, tools may

soften and undergo plastic deform

This type of deformation generally occurs when machining high-strength

metals and alloys.

Therefore, tools must be able to maintain their strength and hardness at

elevated temperature.

Wear groove or notch on cutting tools is due to:1. This region is the boundary where chip is no longer in contact with the

tool

2. This boundary known as DOC line, oscillates because of inherent

variations in the cutting operation and accelerates the wear process

3. This region is in contact with the machined surface from the previous cut

4. Since a machined surface may develop a thin work-hardened layer, this

contact could contribute to the formation of the wear groove

Light cuts should not be taken on rusted workpieces.



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B. Transducers are installed in original machine tools Continually monitor torque and forces during cutting

Signals are pre-amplified and microprocessor analyses and

interprets their content

The system is capable of differentiating the signals that comefrom tool breakage, tool wear, a missing tool, overloading of

the machine, or colliding machine comp

The system also auto compensate for tool wear and thus

improve dim accuracyC. Monitoring by tool-cycle time

In CNC expected tool life in entered into the machine control

unit, when it is reached, the operator makes the tool change.

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SF: geometric Features of surfaces SI: refers to properties such as fatigue life and corrosion

resistance.

Factors influencing SI:

1. temp2. residual stresses

3. metallurgical transformations

4. surface plastic deform, tearing and cracking

BUE has greatest influence on SF

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(a) (b)

Machined surfaces produced on steel (highly magnified),as observed with a scanning electron microscope: (a)

turned surface and (b) surface produced by shaping.

Source: Courtesy of J. T. Black and S. Ramalingam.

Rubbing generates heat

and induce residual stressescausing surface

damage

DOC should be greater

than the radius of thecutting edge.

the built-up edge has the

greatest influence on

surface finish. Figure 21.21

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Schematic illustration of a dull tool with respect to the depth of cut in

orthogonal machining (exaggerated). Note that the tool has a positive

rake angle, but as the depth of cut decreases, the rake angle effectively can

become negative. The tool then simply rides over the workpiece (without

cutting) and burnishes its surface; this action raises the workpiece

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Schematic illustration of feed marks on a

surface being turned (exaggerated).

Ra

f2

8R

where

f feed

R tool - nose radius

Surface roughness:

the higher the feed, and thesmaller the tool-nose radius, R,

the more prominent these marks

will be.

Vibration and chatter adversely

affect surface finish because a

vibrating tool periodically changes

the dimensions of the cut.

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Machinability of a material is defined in terms of 4 factors:

1. SF and SI of the machined part

2. tool life

3. force and power req

4. chip control

Tool life and SF: most important factors in machinability

Machinability ratings

based on a tool life, T = 60min

standard material is AISI 1112 steel (resulfurized), given arating of 100

for a tool life of 60 min, this steel should be machined at speed

of 100 ft/min

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FIGURE : Terminology used in a turning operation on a lathe, where f is the feed (in./rev or

mm/rev) and d is the depth of cut. Note that feed in turning is equivalent to the depth of cut in

orthogonal cutting and the depth of cut in turning is equivalent to the turning is equivalent tothe width of cut in orthogonal cutting.

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FIGURE (a) Crater wear and (b) flank wear on acarbide tool. Source: J. C, Keefe, LehighUniversity.

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FIGURE : Construction of polycrystalline cubic-boron-nitride or

diamond layer on a tungsten-carbide insert.

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FIGURE (a) Schematic illustration of a turning operationshowing depth of cut, d, and feed, f. cutting speed is thesurface speed of the work-piece at the tool tip. (b) Forcesacting on a cutting tool in turning. F

c

is the cutting force;Ftis the thrust or feed force (in the direction of feed); andFris the radial force that tends to push the tool away fromthe workpiece being machined. Compare this figure with atwo-dimensional cutting operation.

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Shear Plane Length


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and Angle f

Shear plane length AB =t0

sinf

Shear plane angl e (f) =Tan -1 rcos1-rsin

or make an assumption, such as fadjusts to minimize

cutting force: f = 450

+ /2 -/2 (Merchant)

f

tcto

f)

A

B

Chip

tool

Workpiece

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VelocitiesV = Chip Velocity(Chip relative to tool)

c


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(2D Orthogonal

Model)

Velocity Diagram

From mass continuity: Vt o= Vctc

From the Velocity diagram:

V s=V cos

cos(f)

V c=Vr and V c=V sinf

cos(f)

(Chip relative

to workpiece)

(Chip relative to tool)

Tool

Workpiece

Chip

V

s V = Cutting Velocity

(Tool relative to

workpiece)

Shear Velocity

f

90 f

f

Vs

V c

V

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Cutting Forces


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g(2D Orthogonal Cutting)

Free Body Diagram

Generally we know:Tool geometry & typeWorkpiece material

and we wish to know:F = Cutting ForceF = Thrust ForceF = Friction Force

N = Normal ForceF = Shear Force

F = Force Normal

to Shear

c

t

s

n

Tool

Workpiece

Chip

Dynamometer

R

R

R

R

FcF

t

f sF

Fn

N

F

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Force Circle Diagram


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g(Merchants Circle)

R

Ft

Fc

Tool

F

N

Fs

f

f

Fn

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Forces on the Cutting Tool


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and the workpiece

Importance: Stiffness of tool holder, stiffness of machine, andstiffness of workpiece must be sufficient to avoid significantdeflections (dimensional accuracy and surface finish)

Primary cause: Friction force of chip up rake face + Shearingforce along shear plane

Cutting speed does not effect tool forces much (friction forcesdecrease slightly as velocity increases; static friction is thegreatest)

The greater the depth of cut the greater the forces on the tool

Using a coolant reduces the forces slightly but greatlyincreases tool life

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Stresses


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On the Shear plane:

Normal Stress=s=Normal Force/Area = Fn

AB w = Fnsinf

tow

Shear Stress=s=Shear Force/Area =Fs

AB w =

Fssinf

tow

On the tool rake face:

= Normal Force / Area=

N

tc w (often assume tc = contact length)

= Shear Force/ Area= Ftc w

Note:s= y= yield strength of the material in shear

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Power (or energy consumed per unit time) is the producof force and velocity. Power at the cutting spindle:

Power is dissipated mainly in the shear zone and on therake face:

Actual Motor Power requirements will depend on machiefficiency E (%):

Cutting Power Pc = FcV

Power for Shearing Ps = FsVs

Friction Power Pf= FV

Motor Power Required =PcE

x100

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Material Removal Rate (MRR)


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Material Removal Rate (MRR)

Material Removal Rate(MRR) = Volume RemovedTime

Volume Removed = Lwto

Time to move a distance L = L/V

Therefore,MRR=LwtoL/V

= Vwto

MRR = Cutting velocity x width of cut x depth of cu

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Specific Cutting Energy( U it P )


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(or Unit Power)

Energy required to remove a unit volume of material (often quoted asa function of workpiece material, tool and process:

Ut = Energy

Volume Removed

= Energy per unit time

Volume Removed per unit time

Specific Energy for shearing Us= FsVsVwto

Specific Energy for friction Uf=FVc

Vwto=

Frwto

Ut =Cutting Power(Pc)

Material Removal Rate(MRR)=

FcV

Vwto=

Fcwto

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Specific Cutting Energy


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Decomposition

1. Shear Energy/unit volume (Us)(required for deformation in shear zone)

2. Friction Energy/unit volume (Uf)(expended as chip slides along rake face)

3. Chip curl energy/unit volume (Uc)(expended in curling the chip)

4. Kinetic Energy/unit volume (Um)

(required to accelerate chip)

Ut = Us+ Uf+Uc +U

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Specific Cutting EnergyRelationship to Shear strength of M ater ial


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Relationship to Shear strength of M ater ial

SHEAR ENERGY / UNIT VOLUMESpecific Energy for shearing Us=

FsVsVwto

FRICTION ENERGY / UNIT VOLUME

Specific Energy for friction Uf=FVc

Vwto=

Frwto

= Fwtc

=

APPROXIMATE TOTAL SPECIFIC CUTTING ENERGY

Ut = Us + Uf= s + y1+ )

U s=scos

sinf cos(f)

=s.

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During this process three basic types of chipsare formed namely: Discontinuous

Continuous

Continuous with a Built-Up Edge (BUE)

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Typically associated with brittle metals like CastIron

As tool contacts work, some compression takesplace

As the chip starts up the chip-tool interferencezone, increased stress occurs until the metalreaches a saturation point and fractures off thework piece.

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Conditions which favorthis type of chip Brittle work material

Small rake angles on cutting

tools Coarse machining feeds

Low cutting speeds

Major disadvantagecouldresult in poor surface finish

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Continuous ribbon of metal that flows upthe chip/tool zone.

Usually considered the ideal condition forefficient cutting action.

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Conditions which favor this type of chip: Ductile work

Fine feeds

Sharp cutting tools

Larger rake angles

High cutting speeds

Proper coolants

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Same process as continuous, but as themetal begins to flow up the chip-tool zone,small particles of the metal begin to adhere

or weld themselves to the edge of thecutting tool.

As the particles continue to weld to the toolit affects the cutting action of the tool.

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This type of chip iscommon in softer non-ferrous metals and lowcarbon steels.

Problems Welded edges break off and

can become embedded inworkpiece

Decreases tool life Can result in poor surface

finishes

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In metal cutting the power input into theprocess in largely converted to heat.

This elevates the temperature of the chips,work-piece and tool.

These elements along with the coolant act asheat sinks.

So lets look at coolants

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Cutting fluids are used extensively in metalremoval processes and they Act as a coolant, lubricant, and assist in removal of

chips.

Primary mission of cutting fluids is to extend tool lifeby keeping keep temperatures down.

Most effective coolant is water

However, it is hardly ever used by itself.

Typically mixed with a water soluble oil to add

corrosion resistance and add lubrication capabilities.

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Environmental Concerns Machine systems and Maintenance

Operators Safety

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Machining Operations can be classified intotwo major categories: Single point = Turning on a Lathe

Multiple tooth cutters = pocket milling on a verticalmilling machine

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Inputs Work material

Type of Cut

Part Geometry and Size

Lot size Machinability data

Quality needed

Past experience of the decision maker

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Manufacturing Practice Machine Condition

Finish part Requirements

Work holding devices/Gigs

Required Process Time

Outputs

Selected Tools Cutting parameters

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High Hardness

Resistance to Abrasion and Wear

Strength to resist bulk deformation

Adequate thermal properties

Consistent Tool life Correct Geometry

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Wide variety of materials and compositionsare available to choose from when selecting acutting tool

We covered these in the previous chapter

9/26/2014145Dr M Varaprasada Rao


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The geometry of a cutting tool is determinedby three factors: Properties of the Tool material

Properties of the Work piece

Type of Cut



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The most important geometrys to consideron a cutting tool are Back Rake Angles

End Relief Angles

Side Relief Angles



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149/194

Back-Allows the tool to shear the work andform the chip.

It can be positive or negative Positive = reduced cutting forces, limited deflection

of work, tool holder and machine Negative = typically used to machine harder

metals-heavy cuts

The side and back rake angle combine to

from the true rake angle



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Larger positive rakeangles Reduce compression

and less chance of a

discontinuous chip Reduce forces

Reduce friction

Result = A thinner, lessdeformed, and cooler

chip.



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Typical tool materials which utilize negativerakes are:

Carbide

Diamonds

Ceramics

These materials tend to be much more brittlethan HSS but they hold superior hardness athigh temperatures.

The negative rake angles transfer the cutting

forces to the tool which help to provide addedsupport to the cutting edge.



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Positive rake angles Reduced cutting forces

Smaller deflection of work, tool holder, andmachine

Considered by some to be the most efficient way to

cut metal Creates large shear angle, reduced friction and heat

Allows chip to move freely up the chip-tool zone

Generally used for continuous cuts on ductile

materials which are not to hard or brittle



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Negative rake angles Initial shock of work to tool is on the face of the

tool and not on the point or edge. This prolongsthe life of the tool.

Higher cutting speeds/feeds can be employed



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Factors to consider for tool angles The hardness of the metal

Type of cutting operation

Material and shape of the cutting tool

The strength of the cutting edge



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A.N.S.I. Insert Identification

System

ANSI - B212 4-1986

M1-Fine

M2-Medium

M3-S.S

M4-Castiron

M5-General

Purpose



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Turning


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Single point cutting tool removes material from

a rotating workpiece to form a cylindrical shape

Three most common machining processes: (a) turning,


Used to create a ro nd hole s all b means

Drilling


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Used to create a round hole, usually by meansof a rotating tool (drill bit) with two cuttingedges


l l d l d

Milling


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Rotating multiple-cutting-edge tool is movedacross work to cut a plane or straight surface

Two forms: peripheral side) milling and faceend) milling

(c) peripheral milling, and (d) face milling.



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1. Single-Point Tools

One dominant cutting edge

Point is usually rounded to form a nose radius

Turning uses single point tools

2.

Multiple Cutting Edge Tools

More than one cutting edge

Motion relative to work achieved by rotating

Drilling and milling use rotating multiple

cutting edge tools


Cutting Tools


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(a) A single-point tool showing rake face, flank, and tool point; and (b)

a helical milling cutter, representative of tools with multiple cuttingedges.



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Three dimensions of a machining

process: Cutting speed vprimary motion

Feed fsecondary motion

Depth of cut dpenetration of tool

below original work surface

For certain operations, materialremoval rate can be computed as

R

MR

= v f d

where v= cutting speed; f= feed; d= depth of cut


Cutting Conditions for Turning


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Speed, feed, and depth of cut in turning.



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In production, several roughing cuts areusually taken on the part, followed by one ortwo finishing cuts

Roughing- removes large amounts ofmaterial from starting workpart Creates shape close to desired geometry, but

leaves some material for finish cutting High feeds and depths, low speeds

Finishing- completes part geometry

Final dimensions, tolerances, and finish Low feeds and depths, high cutting speeds



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A power-driven machine that performs amachining operation, including grinding

Functions in machining: Holds workpart

Positions tool relative to work Provides power at speed, feed, and depth that

have been set

The term is also applied to machines that

perform metal forming operations


t


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where r= chip thickness ratio; to

=thickness of the chip prior to chipformation; and t

c

= chip thickness afterseparation

Chip thickness after cut is alwaysgreater than before, so chip ratioalways less than 1.0

c

o

t

tr



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totc


d h


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Based on the geometric

parameters of the orthogonalmodel, the shear plane angle fcan be determined as:

where r= chip ratio, and = rake angle

f

sin

costan

r

r

1


Shear Strain in Chip Formation


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Figure 21.7 Shear strain during chip formation: (a) chipformation depicted as a series of parallel plates sliding relativeto each other, (b) one of the plates isolated to show shearstrain, and (c) shear strain triangle used to derive strainequation.



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Shear strain in machining can be

computed from the followingequation, based on the precedingparallel plate model:

= tan(f- ) + cot f

where = shear strain,f= shearplane angle, and= rake angle ofcutting tool



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Vector addition of F and N = resultant R


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Vector addition of Fand N= resultant R

Vector addition of Fsand Fn= resultant R' Forces acting on the chip must be in balance:

R' must be equal in magnitude to R Rmust be opposite in direction to R R

must be collinear with R


F N F and F cannot be directly measured

Cutting Force and Thrust Force


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F, N, Fs, and Fncannot be directly measured

Forces acting on the tool that can bemeasured: Cutting force Fcand Thrust force Ft


Figure 21.10 Forces

in metal cutting: (b)

forces acting on the

tool that can be

measured

9/26/2014177

C ffi i f f i i b l d hi


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Coefficient of friction between tool and chip:

Friction angle related to coefficient of friction as follows:

N

Fm

m tan


Fs


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F

F

N

Fn

R



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F

F

N

R



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F

F

N

R

Ft

Fc



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F

F

N

R

Ft

Fc

F = Fc sin + Ftcos

N = Fc cos - Ftsin


Fs


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F

F

N

Fn

R


Fs


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F

Fn

R


Fs


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F

Fn

R

Fc

Ft


Fs

Fs= Fc cos f- Ftsin f


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F

Fn

R

Fc

Ft

Fn= Fc sin f+ Ftcos f9/26/2014


Th i b d i d l h


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Thus equations can be derived to relate the

forces that cannot be measured to the forcesthat can be measured:

F = Fcsin + Ftcos

N = Fc

cos- Ft

sin

Fs= Fccosf- Ftsinf

Fn= Fcsinf+ Ftcosf

Based on these calculated force, shear stress

and coefficient of friction can be determined



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Shear stress acting along the shear plane:


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Shear stress acting along the shear plane:

fsin

wtA o

s

whereAs= area of the shear plane

Shear stress = shear strength of work material during cutting

s

s

A

FS


Cutting forces given shear strength


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Letting S = shear strength, we can derive the following

equations for the cutting and thrust forces*:

Fs= S As

Fc= Fs cos ( /[cos ( f ]

Ft= Fs sin ( /[cos ( f ]

* The other forces can be determined from the equations on the previous

slide.


Machining example


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In orthogonal machining the tool has rake angle 10, chip thickness before

cut is to= 0.02 in, and chip thickness after cut is tc= 0.045 in. The cutting

and thrust forces are measured at Fc= 350 lb and Ft= 285 lb while at a

cutting speed of 200 ft/min. Determine the machining shear strain, shear

stress, and cutting horsepower.

Solution (shear strain):

Determine r = 0.02/0.045 = 0.444

Determine shear plane angle from tan f = r cos/[1r sin]

tanf

= 0.444 cos10

/[10.444 sin10

] =>f

= 25.4

Now calculate shear strain from = tan(f -) + cot f

= tan(25.4 - 10) + cot 25.4 = 2.386 in/in answer!


Machining example (cont.)


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Solution (shear stress):

Determine shear force from Fs= Fc cos f- Ftsin f

Fs= 350 cos 25.4 - 285 sin 25.4 = 194 lb

Determine shear plane area from As= tow/sinf

As= (0.02) (0.125)/sin25.4= 0.00583 in2

The shear stress is

= 194/0.00583 = 33,276 lb/in2 answer!9/26/2014192Dr M Varaprasada Rao

Machining example (cont.)


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Solution (cutting horsepower):

Determine cutting hp from hpc= Fc v/33,000

hpc= (350) (200)/33,000 = 2.12 hp answer!


Shear Plane Angle = tan-1[(r cos )/(1 r sin )]

Shear Strain = tan(f- ) + cot f

Forces in Cutting:


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Forces in Cutting:

F = Fc sin + Ft cosN = Fc cos- Ft sin

Fs = Fc cosf- Ft sinf

Fn = Fc sinf+ Ft cosf

Forces Fc and Ft in terms of Fs:

Fc= Fs cos ( )/[cos ( f )]

Ft= Fs sin ( )/[cos ( f )] Merchant Relation:

f 45 /2/2

Shear Stress:

= Fs/As

where As= tow/sinf

metal cutting theory for mechanical engineers

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