extrusion - me.iitb.ac.inramesh/courses/ME649/extrusion.pdf · – direct extrusion – indirect...
Transcript of extrusion - me.iitb.ac.inramesh/courses/ME649/extrusion.pdf · – direct extrusion – indirect...
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
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ver. 1
Extrusion
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
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Overview
• Equipment• Characteristics• Mechanical Analysis
– direct extrusion– indirect extrusion
• Redundant work• Defects
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
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Geometry (90o die)
D1
D2
p
dead zone45o angle
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
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Equipment
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
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Extrusion
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
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Equipment
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
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Extrusions
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
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Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
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Characteristics
• Similar to closed die forging• Forging
– slug (bulk) is forging– flash (extrusion) is waste
• Extrusion– extrusion (flash) is part– billet (bulk) is waste
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
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Types
• Direct• Indirect• Tubular• Hydrostatic• Cold Impact
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
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Types
1 – direct2 – indirect3 – heading (forging also)
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
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Flow types• “Laminar”• “Turbulent”
– redundant work– can bring outside of billet into
center– leaving the skin keeps outside
scale out of final extrusion
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
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Steel extrusion• Tprocessing = 2100 to 2400oF (1150 – 1315oC) • Tmelting = 2500 - 2800oF (1370 – 1540oC)• Die ≈ 400oF (205oC)• Obviously “Hot”
– above recyrstallization point• Lubricants
– glass (viscous lube ) 0.001” thick– MoS2
– graphite
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
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Mechanical Analysis
D1
D2
p
dead zone45o angle
externalfriction
internalfriction
x
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
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Assumptions
• Metal deforms uniformly– D1 to D2
• No redundant work• Can’t use slab analysis
– die angles too great– friction too high
• Dead zone sets up at 45 degrees
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
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p τfriction
Upper bound analysis• Work input by external forces
= plastic work expended
friction external
compress work toplastic
friction internalpressure
W
W
W W
&
&
&&
+
+
=
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
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Rate of work = Power
• Work rate = Power• Work rate = Area • stress • velocity
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
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Pressure work input• Power = A • p • v
– ram moves at velocity, vram
ramp vpDW ⋅⋅=4
21π&
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
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Internal “frictional” work input• Work determined by integrating rate of
frictional work dissipation at each cross section from D2 to D1 – τfriction = τflow– vi is in x-direction
DD + dD
dx
dL=dD/√245o
⋅= ∫
1
2
D
Diflowf DdLvW πτ&
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
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• Volumetric flow rate
– where D, Ai, vi are instantaneous
Internal “frictional” work input
iiram vAvAQ == 1
rami vDDv
21
=
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
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2
121 ln
2 DDDv
W flowramf ⋅=
τπ&
Internal “frictional” work input
∫=1
22
21D
D
flowramf D
dDDvW
τπ&
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
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Plastic work to compress input• Power = up x Area x velocity
• hence
ετεεσ flowfp YduvolumeEnergy 2/ ==== ∫
2
1ln2DD
=ε
ramflowpw vDDDW ⋅
⋅
⋅=∴
4ln4
21
2
1 πτ&
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
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Total work input (without external friction)
• reducing2
121
2
121
21
ln2
44
ln444
DDvD
DDvDvpD
flowram
flowramram
⋅⋅⋅+
⋅⋅⋅=⋅⋅
τπ
τππ
2
1ln414.32 D
Dpflow
⋅=τ
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
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Extrusion ratio (re)
• Reduction in area (RA) is large– it is not sensitive for classification
• Use re instead
RADDre −
=
=
11
2
2
1
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Extrusion pressure (without external friction)
2
2
1
2
1 ln707.1ln414.32
⋅=⋅=
DD
DDp
flowτ
eflow
rp ln707.12
⋅=τ
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
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Billet - wall friction
• Assume limiting case:friction stress = shear flow stress
τf = τflow
τflow
τflow
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
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Additional pressure due to billet - wall friction
xDDp flow ⋅⋅⋅=⋅
⋅∆ 1
21
4πτπ
1
22 D
xpflow
=∆τ
τflow
τflow
x
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Direct extrusion pressure
1
22222 D
xppppflowflowflowflow
x +=∆
+=ττττ
1
12
1
2ln707.12
2ln414.32
Dxrp
Dx
DDp
eflow
x
flow
x
+⋅=
+⋅=
τ
τ
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
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12
+===nKY
n
flowflowεστ
Strain hardening (cold – below recrystallization point)• Not plane strain (Tresca)
average flow stress:due to shape of element
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
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Example – 1-1
• You are forward, cold extruding Al-1100 (K = 140 MPa, n = 0.25), 10-cm diameter billet to a diameter of 5-cm at 1 m/min. The billet is initially 25 cm long
• The ram is made of a high-strength steel with a yield stress of 1.5 GPa.
• Determine the extrusion force and power.• Determine the safety factor for indenting the
ram.
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
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Example – 1-2
• The equations we use are:
12
1 2ln414.32 D
xDDp
flow
x +⋅=τ
12
+==nKY
n
flowετ
=
2
1ln2DDε
1+=== ∫ ∫ nKdKdu n
pεεεεσ
because
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
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Example – 1-3• We need to determine the dead-zone length to
subtract from the initial billet length.
• so X = 0.25 – 0.025 = 22.5 cm45°
2.5 cm5 cm2.5 cm
2.5 cm
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Example – 1-4• Substituting values
39.15
10ln2ln22
1 =
=
=
DDε
( ) MPanKY
n
flow 6.121125.0
39.11401
225.0
=+
×=
+==
ετ
+⋅×=
12
1 2ln414.32Dx
DDp flowx τ
MPaPextrusion 83410
5.2225
10ln414.36.121max, =
×
+⋅×=
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
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Example – 1-5
• Safety factor against indenting the ram– to determine the “press-fit” failure, we would
need the dimensions of the extrusion die and its material
8.1834.05.1
max,
===GPaGPan
extrusion
y
σσ
( ) MNAreaPF extrusionextrusion 6.61.04
10834 26 =××=×=π
kWmMNspeedFPower 110sec60min/min/16.6 =××=×=
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
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Redundant work
• ∆ = dm/L• dm = (D1 + D2) / 2• p = Qr σflow
p
D1
D2L (contact length)
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Redundant work factor (Backofen)(frictionless)
Qr =
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Defects• Surface materials drawn
into center– pipe, tail pipe
• Surface materials extruded– eliminate by leaving
skin
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
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Chevron Cracking
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Chevron cracking defect
• Hydrostatic tension– outer layer in compression– inner layer in tension, if
entire part is not plastic• eliminate by using a fluid
– hydrostatic compression– reduces friction
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
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Defects
• Surface speed cracking– high friction– temperature– speed
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Summary• Equipment• Characteristics• Mechanical Analysis
– direct extrusion• Redundant work• Defects