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:
◦ Machining – material removal by a sharp cutting tool,
e.g., turning, milling, drilling
◦ Abrasive processes – material removal by hard, abrasive
particles, e.g., grinding
◦ Nontraditional processes - various energy forms other
than sharp cutting tool to remove material

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 Machining
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
 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 and surface
finish
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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 Operations
 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

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

Figure 21.3 - The three most

common types of machining
process: (b) drilling

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 Milling
Rotating multiple-cutting-edge tool is moved slowly
relative to work to generate plane or straight
surface
 Two forms: peripheral milling and face milling

Figure 21.3 - (c) peripheral milling, and

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(d) face milling
Cutting Tool Classification
1. Single-Point Tools
◦ One cutting edge
◦ Turning uses 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 by
rotating
◦ Drilling and milling use rotating multiple
cutting edge 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 with
multiple cutting edges

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Cutting Conditions in Machining
 The three dimensions of a machining process:
◦ Cutting speed v – primary motion
◦ Feed f – secondary motion
◦ Depth of cut d – penetration of tool below original
work surface
 For certain operations, material removal rate
can be found as
MRR = 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
In production, several roughing cuts are 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
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 Orthogonal Cutting Model
A simplified 2-D model of machining that describes
the mechanics of machining fairly accurately

Figure 21.6 - Orthogonal cutting: (a) as a three-dimensional process

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 Chip Thickness Ratio

to
r =
tc
where r = chip thickness 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

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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:
r cos 
tan  =
1 − r sin

where r = chip ratio, and  = rake angle

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

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 Shear Strain
Shear strain in machining can be computed
from the following equation, based on the
preceding parallel plate model:
 = tan( - ) + cot 
where  = shear strain,  = shear plane angle,
and  = rake angle of cutting tool

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Figure 21.8 - More realistic view of chip formation, showing shear
zone rather than shear plane. Also shown is the secondary shear
zone resulting from tool-chip friction

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Four Basic Types of Chip in
Machining
1. Discontinuous chip
2. Continuous chip
3. Continuous chip with Built-up Edge
(BUE)
4. Serrated chip

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 Segmented Chip
 Brittle work materials
(e.g., cast irons)
 Low cutting speeds
 Large feed and depth
of cut
 High tool-chip
friction

Figure 21.9 - Four types of chip

formation 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 on
the tool
 Low tool-chip friction

Figure 21.9 - Four types of chip formation

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
to rake face
 BUE formation is cyclical;
it forms, then breaks off

Figure 21.9 - Four types of chip

formation 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 shear
strain then low shear
strain
 Most closely associated
with difficult-to-
machine metals at high
cutting speeds

Figure 21.9 - Four types of chip

formation in metal cutting: (d)
serrated

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 Forces Acting on Chip
 Friction force F and Normal force to friction N
 Shear force Fs and Normal force to shear Fn

Figure 21.10 -
Forces in metal
cutting: (a) forces
acting on the chip
in orthogonal
cutting

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Resultant Forces
 Vector addition of F and N = resultant R
 Vector addition of Fs and Fn = resultant R'
 Forces acting on the chip must be in
balance:
◦ R' must be equal in magnitude to R
◦ R’ must be opposite in direction to R
◦ R’ must be collinear with R

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 Coefficient of Friction

Coefficient of friction between tool and chip:

F
=
N

Friction angle related to coefficient of friction as follows:

 = tan 

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 Shear Stress

Shear stress acting along the shear plane:

Fs
S=
As
where As = area of the shear plane

t ow
As =
sin 
Shear stress = shear strength of work material during cutting

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 Cutting Force and Thrust Force
 Forces F, N, Fs, and Fn cannot be directly measured
 Forces acting on the tool that can be measured:
◦ Cutting force Fc and Thrust force Ft

Figure 21.10 - Forces

in 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 = Fc sin + Ft cos
N = Fc cos - Ft sin
Fs = Fc cos - Ft sin
Fn = Fc sin + Ft cos
 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
 
 = 45 + −
2 2
 Derived by Eugene Merchant
 Based on orthogonal cutting, but validity extends to
3-D machining

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 What the Merchant Equation Tells
Us

 
 = 45 + −
2 2

 To increase shear plane angle

◦ Increase the rake angle
◦ Reduce the friction angle (or coefficient of
friction)

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 Higher shear plane angle means smaller shear plane
which means lower shear force
 Result: lower cutting forces, power, temperature, all
of which mean easier machining

Figure 21.12 - Effect of shear plane angle : (a) higher  with a

resulting lower shear plane area; (b) smaller  with a corresponding
larger shear plane area. Note that the rake angle is larger in (a), which
tends to increase shear angle according to the Merchant equation

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TMC 40
Power and Energy Relationships
A machining operation requires power
The power to perform machining can be
computed from:
Pc = Fc v
where Pc = cutting power; Fc = cutting
force; and v = cutting speed

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 Power and Energy Relationships

In U.S. customary units, power is traditional expressed as

horsepower (dividing ft-lb/min by 33,000)

Fcv
HPc =
33,000
where HPc = cutting horsepower, hp

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 Power and Energy Relationships

Gross power to operate the machine tool Pg or

HPg is given by
Pc HPc
Pg = or HPg =
E E
where E = mechanical efficiency of machine tool
• Typical E for machine tools =  90%

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 Unit Power in Machining

 Useful to convert power into power per unit

volume rate of metal cut
 Called the unit power, Pu or unit horsepower, HPu

Pc HPc
Pu = or HPu =
MRR MRR
where MRR = material removal rate

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 Specific Energy in Machining

Unit power is also known as the specific energy U

Pc Fcv Fc
U = Pu = = =
MRR vt ow t ow

Units for specific energy are typically N-m/mm3 or J/mm3 (in-lb/in3)

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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
 The remaining energy (about 2%) is
retained as elastic energy in the chip

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 Cutting Temperature
 Several analytical methods to calculate cutting
temperature
 Method by N. Cook derived from dimensional
analysis using experimental data for various work
materials
0.333
0.4U  vt o 
T =  
C  K 
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

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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
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Metal Cutting theory
 Plastically deform a material using a hard
tool in order to obtain desired physical
shape and properties
 Very complex phenomena
 Essential for high precision; high
performance products