machining part i - cutting theory
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8/12/2019 Machining Part I - Cutting Theory
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8/12/2019 Machining Part I - Cutting Theory
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Computer Aided Manufacturing
Learning targets
Design chip removal
manufacturing processes.
Improve manufacturing
processes
Optimize costs in machining
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Computer Aided Manufacturing
Outline
Recall of material mechanical properties
Theory of metal cutting
Cutting forces
Cutting power
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Computer Aided Manufacturing
Machining processes
Goal: to remove material to transform the raw part
into the desired geometry.
In general they are the last processes performed
on the mechanical components.
If we compare them to casting or forming,
machining processes allow to obtain: Good tolerances
Good surface finish
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Computer Aided Manufacturing
Turning
Drilling
Milling
Grinding
Other
processes
Machining processes
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Computer Aided Manufacturing
Engineering stress-strain plot
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o A
P R
P : applied force
Ao: origi
nal area of test specimen
l : length at any point during elongation
l o: original gage length
E : modulus of elasticityo
o
l
l l e
= E e
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True stress-strain plot
7
1100-O aluminum
plotted on a log-log
scale
A
P
A: actual (instantaneous)area resisting the load
o
l
l
l
l l
l l
l
dl
o
ln)ln(0
nk
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Computer Aided Manufacturing
Loading & unloading
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Flow curve for various materials
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Elastic and perfectly plastic
Stiffness defined by E
Once Y reached, deforms
plastically at same stress
level Flow curve: K = Y , n = 0
Metals behave like this
when heated to
sufficiently hightemperatures (above
recrystallization)
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Computer Aided Manufacturing
Ductility
Ability of a material to plastically strain without fracture
Ductility measure = elongation EL
where EL: elongation; l f : specimen length at fracture; and l o: originalspecimen length
l f is measured as the distance between gage marks after two piecesof specimen are put back together.
o
o f
l
l l EL
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Elongation
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Toughness
Amount of energy per unit volume that the material
dissipates prior to fracture
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Computer Aided Manufacturing14
Y
Mechanical properties
Strength
DuctilityElastic Plastic
UTS
Toughness
Malleability
Stiffness
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Computer Aided Manufacturing
Mechanical properties
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Computer Aided Manufacturing
Recrystallization in Metals
● Most metals strain harden at room temperature
according to the flow curve (n > 0)
● But if heated to sufficiently high temperature
and deformed, strain hardening does not occur
o Instead, new grains are formed that are free of strain
o The metal behaves as a perfectly plastic material; that
is, n = 0
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n = 0
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Computer Aided Manufacturing
Temperature effect
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Most materials display
similar temperature
sensitivity for elastic
modulus, yield strength,
ultimate strength, and
ductility.
Increasing T
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Computer Aided Manufacturing
Strain rate effect
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The effect of strain rate on the
ultimate tensile strength of
aluminum.
Note that as temperatureincreases, the slope increases.
Thus, tensile strength becomes
more and more sensitive to
strain rate as temperature
increases. Source: After J. H.
Hollomon.
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Computer Aided Manufacturing
Machining processes
We will study:
“Orthogonal” cutting
A “simplified” process
Industrial processes
Cinematically more complex:
Turning
Drilling Milling
etc
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Computer Aided Manufacturing
Orthogonal cutting
Not much used in the real world, we study it
because:
● It is simple to describe from the cinematic
(motions) and dynamic (forces) points of
views.
● It allows us to understand the elementary
mechanism of chip formation.
● Many of the variables met in orthogonal
cutting are present in the industrial processes
(turning, milling, etc).
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Computer Aided Manufacturing
Orthogonal cutting
We have orthogonal cutting when the cinematic anddynamic variables belong to a plane.
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Relevant Variables:
• v c = cutting speed
• b = cutting width
• hD = cutting thickness(Uncut chip thickness)
Section
plane
HKLM
Section
tool
hD
b
hD
vc
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Computer Aided Manufacturing
Orthogonal cutting
Uncut chip area:
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Chip thickness: hch
Chip transversal section: AD = hD b Cutting ratio:
Chip
transversal
section
ch
D
h
hr
tool
Section
plane
vc
b
hD
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Computer Aided Manufacturing
The tool
The tool is composed of:
● Rake face: surface
on which the chip
flows.● Flank face: surface
looking at the
machined surface.
● Cutting edge:intersection line
between rake face
and flank.
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Rake
Flank
Cuttingedge
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The tool
Cutting angles:
Rake angle g
Between the rake face and the
normal to the cutting direction:-15° < g < 30°
Clearance (or relief) angle
Between the flank and the
direction of the cutting direction:
2° < a < 15°
Solid angle
Between rake and flank faces:
a + b + g 90
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vc
g
b
chip
thickness
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Computer Aided Manufacturing
Cutting process
Part
Uncut chip
R e l a t i v e t o o
l - p a r t m o t i o n
Heat
Chip
Forces
Machined
surface
The chip removal mechanism
Associated to chip removal:
● Forces: The tool and the part
exchange the forces needed to
deform the working stock, separate
it from the part and transform it into
chip.
● Heat: Plastic deformation of theuncut chip plus the friction
between the tool and the chip
involve the generations of a large
heat amount.
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Tool
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t e m p e r a t u r e
s t r e s s e s
Stress and temperature
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Computer Aided Manufacturing
Temperature
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The chip removal mechanism
How does the machining allowancetransforms into chip ?
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The tool stresses the material until
this deforms plastically. With goodapproximation it can be said that the
area where the material is deformed
is a plane, called shear plane.
The deformation proceeds until the
separation between chip and part. Itis therefore the working stock that is
transformed into chip, that flows on
the tool.
Shear
plane
Chip
Shear stress
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Computer Aided Manufacturing
The chip removal mechanism
Comparison with reality
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Shear plane
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Computer Aided Manufacturing
Shear zone
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h D
h ch
v c g
b
Cutting edge
a
Shear plane Shear zone
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Computer Aided Manufacturing
The chip removal mechanism
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Source: After M.C. Shaw, P.K. Wright, and S.
Kalpakjian.
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Discontinuos chip
33
Source: After M.C. Shaw, P.K.
Wright, and S. Kalpakjian.
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Continuous chip
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Source: After M.C. Shaw, P.K.
Wright, and S. Kalpakjian.
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Computer Aided Manufacturing
Serrated (segmented) chip
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Source: After M.C. Shaw, P.K.
Wright, and S. Kalpakjian.
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Computer Aided Manufacturing
Built Up Edge
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Source: After M.C. Shaw, P.K.
Wright, and S. Kalpakjian.
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Computer Aided Manufacturing
Chip orientation
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(a) tightly curled chip
(b) chip hits workpiece and breaks
(c) continuous chip moving away from workpiece
(d) chip hits tool shank and breaks off
Source: G. Boothroyd, Fundamentals of Metal Machining and Machine Tools. Copyright ©1975; McGraw-Hill
Publishing Company.
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Computer Aided Manufacturing
Chip breakers
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Grooves as
chip breakers
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Computer Aided Manufacturing
Card deck model of chip formation
Mechanics of chip formation
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g ++ tancot
OC
OB
OC
AO
OC
ABShear strain
Shear Strain:
b
a
g
cos
sin
ch
D
h
hr Cutting ratio
g
g
a
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Mechanics of chip formation
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ch Dc hvhv g
Since hch > hD vg < v c
From the velocity diagram:
g g g
sincoscos
vvv shc
Where v sh is the velocity at which shearing takes place in the shear plane.
g
g
cos
sin
cc
ch
D
c vr vh
h
vv
Mass continuity
90+g
gg
90g
vc
vg
vsh
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Shear strain rate
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The shear strain rate is then the ratio of
v sh to the thickness a of the sheared
element (shear zone), or:
a
v
adt
dAB
OC
AB
dt
d
dt
d sh
1
Experimental evidence indicates that a is on the order of 10-2 to
10-3 mm. This means that, even at low cutting speed, the shear
strain rate is very high, on the order of 103 to 106 s-1.
g
g
a
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Shear strain rate
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vc
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Force circle
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b : friction angle b
Between the tool and the part a force F is developed that can be
subdivided in two components according to different directions:
● rake
● shear plane
● cutting direction
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F g and F gN
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F g : force tangential to the rake plane
● F g N : force normal to the rake plane
F g = F sen b F g N = F cos b
F g
F g N
b
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F c and F
f
Cutting force (F c ), parallel
to the cutting speed .
● Feed force (F f ), normal to
the cutting speed.
These forces are not known,
but they can be measured orpredicted with mathematical
models.
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F c = F cos ( b g )
F f = F sen ( b g )F f
F c
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F sh
and F shN
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F sh = F cos ( + b g )
F shN = F sen ( + b g )
F sh: force in the shear plane
● F shN : force normal to the shear plane
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Computer Aided Manufacturing
Estimation of forces (theory)
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c
sh
D
cos sen
cos
F ( )
A ( )
b g
b g
+
γ f c f c
γN c f c f
cos sen tantan
cos sen tan
F F F F F
F F F F F
g g g b
g g g
+ +
Parameters:
• g is a property of the cutting tool
• b can be estimated:
g , b , , sh
g
g
g
g
g
g
)cos(
sen)(sensen)(sensen
D
c
DD
shNsh
g b
g b g b
+
+
A
F
A
F
A
F
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Computer Aided Manufacturing
Estimation of forces (theory)
48
F c = F cos ( b g )
F sh = F cos ( + b g ))cos(
sh
g b +
F
F
)cos(
)cos(shc
g b
g b
+
F
F
sen
D
shshshsh
A A F
)cos(
)cos(
sen
Dshc
g b
g b
+
A
F c
sh
D
cos sen
cos
F ( )
A ( )
b g
b g
+
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Computer Aided Manufacturing
Estimation of shear angle
49
Cutting ratio method
ch ch chD
c
ch D D D
b l l hr
h b l l
ch ch D ch DD
c
ch D D D
b l h b l hhr
h b l h M
c
c
costan
1 sen
r
r
g
g
Chip length
Chip mass
D D D ch ch chh b l h b l
Constant chip volume:
D chb b b
Orthogonal cutting:
c
ch
sin sin
cos cos
Dh A' B
r h A' B
g g
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Pijspanen model
• No strain hardening
• No Built Up Edge
• No friction on the flank
• Plastic deformation begins
when max = sh (elastic strain isnot considered)
• No friction between tool’s rake
and chip
Estimation of shear angle
Angle assumes a value that minimizes the shear strain g
2 2
1 1cot tan( ) 0
sen cos ( )
g g
g
+ +
24
g +
50
(g)
( -g)
a
(g)
( -g)
a
A’
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Estimation of shear angle
Ernst & Merchant model
• No strain hardening
• No Built Up Edge
• No friction on the flank
• Constant sh
• No friction between tool’s rake and chip
• Shear angle assumes the value that minimizes the energy
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Angle assumes a value that minimizes the energy of cutting
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Ernst & Merchant model
Estimation of shear angle
)cos(
)cos(
sen
Dshc
g b
g b
+
A
F
H A
H F U
+
)cos(
)cos(
sen
Dshcc
g b
g b
0c
U
224
b g +
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The cutting pressure kc is defined from the relationship:
def
c c D F k A
Cutting pressure method
kc depends on:
• AD
• Mechanical characteristics of the workpiece material
• Tool material and geometry (g in particular)
• vc
• lubrication conditions
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Kronenberg relationship:
y x bh
k k cs
c
where k cs is the specific cutting pressure to remove a chip
section of 1 mm2 with h = 1 mm and b = 1 mm
Typically, y 0, thus: cs
c
x
k k
h
• k cs related to the material to machine
• k c decreases as h increases
• x costant mainly related to the tool material
Cutting pressure
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Cutting with an oblique tool
In practice most of the cutting processes use oblique tools
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