Chapter 21-Theory of Metal Machining.ppt

5/27/2018 Chapter 21-Theory of Metal Machining.ppt

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Chapter 21:

Theory of Metal Machining

Rizwan M. Gul

NWFP UET


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THEORY OF METAL MACHINING

Overview of Machining Technology

Theory of Chip Formation in Metal Machining

Force Relationships and the Merchant Equation Power and Energy Relationships in Machining

Cutting Temperature


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Material Removal Processes

A family of shaping operations, the common feature

of which is removal of material from a starting

workpart so the remaining part has the desired shape

Categories:

Machin ingmechanical material removal by a

sharp cutting tool, e.g., turning, milling, drilling

Ab rasive processesmechanical material

removal by hard, abrasive particles, e.g., grinding

Nontradi t ional processes- various energy forms

other than sharp cutting tool to remove material


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Machining A sharp cutting tool is used to cut away material to

leave the desired part shape Cutting action involves shear deformation of work

material to form a chip

As chip is removed, a 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)


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Why Machining is Important?

The industrial revolution and the growth of the manufacturingbased economies of the world can be traced to the

development of various machining operations

Variety of work materials can be machined

Most frequently applied to metals Variety of part shapes and special geometry features

possible, such as:

Screw threads

Accurate round holes Very straight edges and surfaces

Good dimensional accuracy (Tolerances 0.025 mm)

Excellent surface finish (Roughness less than 0.4 microns)


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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


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Machining in the Manufacturing Sequence

Generally performed after other manufacturing

processes, such as casting, forging, and bar drawing

Other processes create the general shape of the

starting workpart

Machining provides the final shape, dimensions,

finish, and special geometric details that other

processes cannot create


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Machining Technology

Machining is not just one process; it is group ofprocesses

All the processes use a cutting tool to form a chip thatis removed from the workpart

Relative motion is required between the tool andwork

This relative motion is achieved by means of aprimary motion called the speedand a secondarymotion called the feed

The shape of the tool and its penetration into thework surface, combined with these motions,produces the desired shape of the resulting worksurface


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Machining Operations

There are many kinds of machining operations, each

of which is capable of generating a certain part

geometry and surface texture

Most important machining operations: Turning

Drilling

Milling

Other machining operations: Shaping and planing

Broaching

Sawing


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Turning Single point cutting tool removes material from a

rotating workpiece to form a cylindrical shape The speed motion is provided by the rotating work

part and feed motion is given to the tool

Figure 21.3 (a) turning


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Drilling Used to create a round hole, usually by means of a

rotating tool (drill bit) that has two cutting edges

(b) drilling


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Milling

Rotating multiple-cutting-edge tool is moved slowly relative to

work to generate plane or straight surface

The speed motion is provided by the rotating cutter while the

direction of the feed motion is perpendicular to the tool axis of

rotation

Two forms: peripheral milling and face milling

Figure 21.3 - (c) peripheral milling, and (d) face milling


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Cutting Tool Classification

A cutting tool has one or more sharp cutting edges with

many angles e.g. rake angle, relief angle etc.The two basic types of cutting tools are:

1. Single-Point Tools

One cutting edge

Turninguses single point tools Point is usually rounded to form a nose radius

2. Multiple Cutting Edge Tools

More than one cutting edge

Motion relative to work usually achieved byrotating

Drillingand millinguse rotating multiple cuttingedge tools.


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Figure 21.4 - (a) A single-point tool showing rake face, flank, and tool

point; and (b) a helical milling cutter, representative of tools withmultiple cutting edges


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Cutting Conditions in Machining

Relative motion is required between tool and work toperform a machining operation

The three dimensions of a machining process:

Cutting speed vprimary motion

Feed fsecondary motion

Depth of cut dpenetration of tool below originalwork surface

V, f & d are collectively called as cut t ing condi t ions

For certain operations, material removal rate can be

found asMRR= v f d

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


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Cutting Conditions for Turning

Figure 21.5 - Cutting speed, feed, and depth of cut for a turning

operation


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Roughing vs. Finishing in Machining

Machining operations usually divide in two categories,

distinguished by purpose and cutting conditions

In production, several roughing cutsare usually

taken on the part, followed by one or two finishing

cuts

Roughing- removes large amounts of material from

the 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

Achieves final dimensions, tolerances, and finish

Low feeds and depths, high cutting speeds


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Machine Tools

A power-driven machine that performs a machining

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 Machine tools are operated by human operators or

numerical controls


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Orthogonal Cutting Model

A simplified 2-D model of machining that describes the

mechanics of machining fairly accurately

Although an actual machining process is three-dimensional,

the orthogonal model has only two dimensions that play

active role in the analysis


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Orthogonal Cutting Model (Contd.)

Orthogonal cutting uses a wedge-shaped tool in which thecutting edge is perpendicular to the direction of the cutting

speed

As tool is forced into the material, the chip is formed by

shear deformation along a plane called the shear plane,

which is oriented at an angle with the surface of thework

Along the shear plane the material is plastically deformed,

and at the sharp cutting edge of the tool failure of the

material occur, resulting in separation of the chip from theparent material

The tool in orthogonal cutting has only two elements of

geometry, rake angle () and clearance angle


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Chip Thickness Ratio

The position of the cutting tool below the original worksurface corresponds to the thickness of the chip prior

to the chip formation to

As the chip is formed along the shear plane, its

thickness is increased to tc

where r= chip thickness ratio or chip ratio;

to= thickness of the chip prior to chip formation;and tc = chip thickness after separation

Chip thickness after cut is always greater than before,

so chip ratio is always less than 1.0

c

o

t

tr


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Determining Shear Plane Angle

Based on the geometric parameters of the orthogonal

model, the shear plane angle can be determined

as:

where r= chip ratio, and = rake angle

sin

costan

r

r

1

)cos(

sin

s

s

l

lr


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Figure 21.7 - Shear strain during chip formation: (a) chip formationdepicted 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


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Shear Strain

Shear strain in machining can be computed from thefollowing equation, based on the preceding parallelplate model:

= tan(- ) + cot

where = shear strain,= shear plane angle, and= rake angle of cutting tool

BD

DCAD

BD

AC


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Figure 21.8 - More realistic view of chip formation, showing shear zone

rather than shear plane (the thickness is few thousands of an inch). Also

shown is the secondary shear zone resulting from tool-chip friction

Actual Chip Formation


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Four Basic Types of Chip in Machining

The formation of the chip depends on the type of

material being machined and the cutting conditions

of the operation. Four basic types of chip can be

distinguished:

1. Discontinuous chip

2. Continuous chip

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

4. Serrated chip


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Discontinuous Chip Brittle work materials

(e.g., cast irons)

Low cutting speeds

Large feed and depth ofcut

High tool-chip frictionand large feed and depthof cut promote itsformation

Figure 21.9 - Four types of chipformation in metal cutting:

(a) segmented


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Continuous Chip

Ductile work materials

(e.g., low carbon steel)

High cutting speeds

Small feeds and depths

Sharp cutting edge onthe tool

Low tool-chip friction

Figure 21.9 - Four types of chipformation in metal cutting:

(b) continuous


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Continuous with BUE

Ductile materials Low-to-medium cutting

speeds

Tool-chip friction causes

portions of chip to adhere torake face

BUE formation is cyclical; it

forms, then breaks off

Reduces tool life and causesrough surfaces

Figure 21.9 - Four types of chipformation in metal cutting: (c)

continuous with built-up edge


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Serrated Chip Semicontinuous - saw-

tooth appearance Cyclical chip formation

of alternating high shearstrain then low shearstrain

Most closely associatedwith difficult-to-machinemetals (titanium alloysand nickel based superalloys etc.) at highcutting speeds

Figure 21.9 - Four types of chipformation in metal cutting: (d)

serrated


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Forces in Metal Cutting

The forces applied against the chip by the tool can be

separated into two mutually perpendicular

components:

The friction force Fresisting the flow of the chip

along the rake face, and normal force to friction N

The resultant of forces F & N is Rand is oriented

at an angle called the friction angle

In addition, there are two force components applied

by the workpiece on the chip:

The shear force Rsis the force that causes shear

deformation to occur in the shear plane and

normal force to shear Fn

The resultant of Rs and Fnis R


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Forces Acting on Chip Friction forceF and Normal force to frictionN

Shear forceFsand Normal force to shearFn

Figure 21.10 -

Forces in metal

cutting: (a) forces

acting on the chip

in orthogonalcutting


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Resultant Forces

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

R' must be opposite in direction to R

R' must be collinear with R


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Coefficient of Friction

Coefficient of friction between tool and chip:

Friction angle related to coefficient of friction as

follows:

N

F

tan


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Shear Stress

Shear stress acting along the shear plane:

sin

wtA os

whereAs= area of the shear plane

Shear stress = shear strength of work material during

cutting

s

s

A

FS


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Cutting Force and Thrust Force Forces F, N, Fs, and Fncannot be directly measured

Forces acting on the tool that can be measured by adynamometer:

Cutting forceFcand Thrust forceF

t

The resultant is R

Figure 21.10 - Forcesin metal cutting: (b)

forces acting on the

tool that can be

measured


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Forces in Metal Cutting

Equations can be derived to relate the forces that

cannot be measured to the forces that can be

measured:

F = Fcsin + Ftcos

N = Fccos- Ftsin

Fs= Fccos- Ftsin

Fn= F

csin+ F

tcos

Based on these calculated force, shear stress and

coefficient of friction can be determined


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The Merchant Equation

Of all the possible angles at which shear deformation

could occur, the work material will select a shear

plane angle which minimizes energy, given by

Derived by Eugene Merchant

Based on orthogonal cutting, but validity extends to

3-D machining

Based on several assumptions so only provides an

approximate of the shear plane angle

2245


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What the Merchant Equation Tells Us

To increase shear plane angle Increase the rake angle

Reduce the friction angle (or coefficient of friction)

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The real value of the Merchant equation is that itdefines the general relationship between rake angle,

tool-chip friction, and shear plane angle


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

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

Figure 21.12 - Effect of shear plane angle: (a) higher with aresulting lower shear plane area; (b) smaller with a correspondinglarger shear plane area. Note that the rake angle is larger in (a), whichtends to increase shear angle according to the Merchant equation


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Power and Energy Relationships

A machining operation requires power The power to perform machining can be computed

from:

Pc= Fcv

where Pc= cutting power; Fc= cutting force; and v=cutting speed

In U.S. customary units, power is traditional

expressed as horsepower (dividing ft-lb/min by

33,000)

00033,

vFHP cc

where HPc= cutting horsepower, hp


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Power and Energy Relationships

The gross power required to operate the machinetool is greater than the power delivered to the cutting

process because of mechanical losses in the motor

and drive train in the machine

Gross power to operate the machine tool Pgor HPgisgiven by

or

where E= mechanical efficiency of machine tool

Typical Efor machine tools = 90%

E

PP cg

E

HPHP cg


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Unit Power and specific Energy in Machining

Useful to convert power into power per unit volumerate of metal cut

Called the unit power, Puor unit horsepower, HPu

or

where MRR= material removal rateMRR

P

P c

u MRR

HP

HP c

u

Unit power is also known as the specificenergyU

wt

F

wvt

vF

MRR

PPU

o

c

o

ccu

Units for specific energy are typically N-m/mm3 or J/mm3

(in-lb/in3)


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Specific Energy in Machining

Unit power and specific energy provides a useful

measure of how much power (or energy) is required

to remove one cubic inch of metal during machining

Table in the next slide presents listing of unithorsepower and specific energy values for selected

work materials based on two assumptions:

The cutting tool is sharp (dullness increases

required energy) The chip thickness before the cut is 0.25 mm

(smaller chip thickness increases required energy)


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Unit Horsepower and specific energy for selected work materials

EXAMPLE 21 1


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EXAMPLE 21.1:

In a machining operation that approximates orthogonal cutting, the cutting

tool has a rake angle =10o. The chip thickness before the cut to=0.50 mm

and the chip thickness after the cut tc=1.125 mm. Calculate the shear plane

angle and the shear strain in the operation

EXAMPLE 21.2:

Suppose in Ex 21.1that cutting force and thrust force are measured during

an orthogonal cutting operation with values: Fc=1559 N and Ft=1271 N.

The width of the orthogonal cutting operation w=3.0 mm. Based on these

data, determine the shear strength of the work material.

EXAMPLE 21.3:

Using the data and results from our previous examples, compute (a) the

friction angle using the Merchant equation, and (b) the coefficient of friction.

EXAMPLE 21.4:Continuing with our previous examples, let us determine cutting power and

specific energy required to perform the machining process if the cutting

speed =100 m/min. Summarizing data and results from previous examples,

to=0.50 mm, w=3.0 mm, Fc=1557 N.


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Cutting Temperature

Approximately 98% of the energy in machining is

converted into heat

This can cause temperatures to be very high at the

tool-chip (over 600oC)

The remaining energy (about 2%) is retained as

elastic energy in the chip


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Cutting Temperature

Several analytical methods to calculate cuttingtemperature

Method by N. Cook derived from dimensionalanalysis using experimental data for various work

materials

where T= temperature rise at tool-chip interface; U=

specific energy; v= cutting speed; to= chip thickness

before cut; C= volumetric specific heat of work

material; K = thermal diffusivity of the work material

333040

..

K

vt

C

UT o


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Cutting Temperature

Experimental methods can be used to measure

temperatures in machining

Most frequently used technique is the tool-chip

thermocouple

Using this method, K. Trigger determined the

speed-temperature relationship to be of the form:

T= K vm

where T= measured tool-chip interface temperature

The parameters Kand mdepend on cutting

conditions (other than v) and work material


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Cutting Temperature

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Chapter 21-Theory of Metal Machining.ppt