A lathe of pre WWII Material removal processes · PDF fileLab groups fixed, and thank you....
Transcript of A lathe of pre WWII Material removal processes · PDF fileLab groups fixed, and thank you....
Today, February 25th 2.008 Design & Manufacturing
� HW#2 due before the class, #3 out on II the web after the class. � Math Formulae, handoutSpring 2004
� Lab groups fixed, and thank you. � group report!!!
Metal Cutting I � Metal cutting demo � Cutting physics
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Material removal processes
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A lathe of pre WWII
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Expensive $100 -$10,000
Quality: Very h
Flexibility: Any shape under the
Rate: Slow
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Machined Surface
µ inch
1000 ium 500
125
Fine 32 Very fine 16
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Surface roughness by machining
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Rough MedAvg.Better than Avg. 63
Extremely fine
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ss VF ⋅:shearingfor Power
cc VF ⋅:input
cVF ⋅:friction viadissipatedPower
VtwVFu
o
sss ⋅⋅
⋅=:shearingfor energy Specific
VtwVFuo
cf ⋅⋅
⋅=:frictionfor energy Specific
VtwVF
VtwVFuu
o
ss
o
cfs ⋅⋅
⋅+
⋅⋅⋅
=+:energyspecificTotal
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Cutting processes
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� Product quality: surface, tolerance � Productivity: MRR , Tool wear
� Physics of cutting � Mechanics � Force, power
� Tool materials � i
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Cutting Tools
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Why do we study cutting physics?
Des gn for manufacturing
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Cutting process modeling
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� What are the forces involved? �
� How do the above relate to power
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Orthogonal cutting in a lathe
Rake angle
To
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Methods: Modeling and Experiments
Key issues How does cutting work?
What affect does material properties have?
requirements, MRR, wear, surface?
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Shear angle
: depth of cut
Shear plane
Assume a hollow shaft
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Cutting tool and workpiece..
Power
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Varying rake angle α:
- α α = 0
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Primary shear zone
Secondary shear zone
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Basic cutting geometry
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( ) ( )cos
φsin r
ct ot
V cV
− ===
ctcVo ⋅
r <1
V
Vc
tcto
Continuity
to
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Velocity diagram in cutting zone
( ) ( ) ( )φsin cV
αcos sV
cos V
== −
( ) ( )cos
φsin r
ct ot
V cV
− ===
( ) ( )cos
φVsin cV
− =
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We will use the orthogonal model
Shear angle
α φ
t V = ⋅
Cutting ratio:
: chip thickness : depth of cut
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α φ
α φ
α φ
Law of sines
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Forces and power
� FBD at the tool-workpiece contact � What are the forces involved
� Thrust force, Ft � Cutting force, Fc � Resultant force, R � Friction force, F � Normal Force, N � Shear Force, Fs, Fn
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ian
Fc
α
φ
R
Ft
Fc
Fn
Fs
F
N α
β
Ft β−α
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E. Merchant’s cutting diagram
Source: Kalpajk
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( ) ( ) α )βRcos(φφsintFφcoscFsF =⋅−⋅=
( ) ( )φcostFφsincFnF ⋅+⋅=
( )βF ⋅=
( )βN ⋅= ( )βtanµ =
β =
FBD of Forces
( ) ( )αtantFcF
αtancFtF
N F
µ ⋅+
==
( )α-βsinRFt ⋅=
( )α-βcosRFc ⋅=
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� What does this mean: �
� Merchantto minimize cutting force or max. shear stress
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22 45 βαφ = o
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− +
sin R cos R
Angle Friction
2 µ 0.5 :Typcially < <
⋅ −
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Analysis of shear strain
Low shear angle = large shear strain ’s assumption: Shear angle adjusts
Can derive: − +
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Shear angle
( ) α βcosRFc
( ) ( ) α)βRcos(φφsintFφcoscFsF =⋅=
α)βcos(φ/α)cos(βFscF −=
As.σssF =
α)βcos(φ/α)cos(βφsin A
σcF s −=
0dFc/dφ =
2245 βαφ = o
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� ion increases �
�
� ion via shear �
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2 β
2 α
45φ o
−+=
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⋅ =
− + ⋅ −
− +
strength) shear plane. shear of (area
− +
− +
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Things to think about
As rake angle decreases or frictShear angle decreases Chip becomes thicker Thicker chip = more energy dissipatMore shear = more heat generation Temperature increase!!!
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Power
ss VF ⋅
VF c ⋅
c ⋅
V VF u
o
ss s ⋅ ⋅
⋅ =
Vu
o
c f ⋅ ⋅
⋅ =
V VF
Vuu
o
ss
o
c fs ⋅ ⋅
⋅ +
⋅ ⋅ ⋅
=+
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imate)
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: shearing for Power
: input Power
V F : friction via dissipated Power
t w : shearing for energy Specific
t w V F : friction for energy Specific
t w t w V F : energy specific Total
MRR
=> shearing + friction
Experimantal data 2.008-spr ng-2004 S.Kim Kalpak an
Specific energy (rough est
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Example � i�
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2.0
1.01.25
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Cutting zone pictures BUE
serrated di
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Consider the turning with a rod, from 1.25 nch diameter to 1.0. to; depth of cut, 0.005 inch f; feed rate, 0.025 inch/rev
; spindle speed, 1000 rpm uf;spec c energy for fr ct on us;specific energy for shear, 0.35 hp min/in1 hp = 550 ft. bf/s
How many passes? Tools speed? Time to make this part? V c max? Max power needed? Initial cutting force?
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continuous secondary shear
scontinuous
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