Theory of Metal Cuttingmechanics of Metal Cutting
Transcript of Theory of Metal Cuttingmechanics of Metal Cutting
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LECTURE-09THEORY OF METAL CUTTING
- Mechanics of Metal Cuttin
NI!HIL R" #HAR$ %h" #"DEPARTMENT OF INDUSTRIAL & PRODUCTION
ENGINEERING
BUET
Px
Py
Pz
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The force ##te$ in the genera ca#e of con*entiona turning "roce## i##ho'n in the foo'ing Fiu+e"
Px
Py
Pz
Pz
Px
Py Pxy
R
P0 3 fee fo+ce in the !irection of the too tra*eP 3 th+ust fo+ce in the !irection "er"en!icuar to the "ro!uce! #urface
P) 3 cuttin fo+ce or ,ain fo+ce acting in the !irection of the cutting *eocit%
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Pz
Px
PyPxyX
Y
Πo
φ
PxyR
ZXY
R
.......[2]..........cosPP
]........[1..........sinPP
xyy
xyx
ϕ
ϕ
=
=
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Se*era force# can -e !efine! reati*e to the orthogona cutting $o!e%Ba#e! on the#e force#. #hear #tre##. coefficient of friction. an! certain
other reation#hi"# can -e !efine!%
R
Ps
R2
Workpiece Tool
Chip
γ
β
Pz
Pn
Pxy
NF
R1
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Me+chant Ci+cle #ia+a, 3MC#4
The foo'ing reation#hi"# #ugge#t a circe re"re#entation of force# a#!one - Me+chant an! in!icate! in the foo'ing Fiu+e%
Pxy
Workpiece
PzPn
Ps
F
N R
γo
γo
η β
η-γo
Tool
Chip
.[7]....................cosPβsinPP
..[6]....................sinPβcosPP
]5[....................sin γPγcosP N
]4.[....................γcosPsin γPF
]3.......[xy
Pz
Pn
Ps
P NFR
xyzn
xyzs
oxyoz
oxyoz
β
β
+=
−=
−=
+=
+=+=+=
.....[8]tansinγPcosγP
cosγPsinγP
N
Fμ
[5]an[4]!"#ationF$o%
oxyoz
oxyozη =
−+
==
4here.
5 3 (inetic coefficient of friction
η & $ean ange of friction at the ra(e #urface
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Fro$ the geo$etr of force reation# of MCD circe
Pxy
Workpiece
PzPn
Ps
F
N R
γo
γo
η β
η-γo
Tool
Chip
]11[..........'γη(βcos
'γ(ηcosPP
[1)]an[*]!"#ationF$on
..[1)]'.........γηcos(βR P.......[*]'.........γcos(ηR P
o
)sz
)s
)z
−+
−=
−+= −=
Ba#e! on the #hear force. the #hear #tre##1+
s2 'hich act# aong the #hear "ane
-et'een the 'or( an! the chi" i#,
]12[..........t,
sinβP+
sinβ
t, -an/s0/a$t0/o a$/as0/$/
P+
o
ss
o
s
ss
=
===
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].......[14'γηcos(βsinβ
'γsin(ηt,+P
,i%ia$y
.[13]..........'γηcos(βsinβ
'γcos(ηt,+P
[12][11]an!"#ationF$o%
o
))sxy
o
))sz
−+
−=
−+−=
Pxy
Workpiece
PzPn
Ps
F
NR
γo
γo
η β
η-γo
Tool
Chip
In $eta cutting one of the $ain "ro-e$ i# toe*auate the cutting force# P) an! P0 fro$ the
gi*en cutting con!ition# an! initia "ro"ertie# of'or( $ateria an! it i# nece##ar to !eter$ine +s.
6 an! 7 - #uita-e reation#hi"#%
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Ea+nest-Me+chant Theo+6
Ern#t an! Merchant e0ten!e! their ana#i# an! #tu!ie! the reation#hi" -et'een the #hearange an! the cutting con!ition#% The #ugge#te! that the #hear ange a'a# ta(e# the *auethat re!uce# the tota energ con#u$e! in cutting to a $ini$u$% Becau#e the tota 'or( !onein cutting i# !e"en!ent u"on an! i# a !irect function of the co$"onent P) of the cutting force.
the !e*eo"e! an e0"re##ion for P) in ter$# of 6 an! the con#tant "ro"ertie# of the 'or("iece
$ateria% Con!ition for $a0i$u$ cutting force 1P)2 fro$ E+uation 89:;
{ }
...[16]..........cott,+2P
[15]an[13]!"#ationo%inin
]15........[..........
2
cos)'γηβcos(βo$)'γηsin(βsinβ'γηcos(βcosβ
)γηcos(βsinβ
'γηsin(βsinβ'γηcos(βcosβ'γcos(ηt,+
)'γηcos(β
'γcos(η.
sinβ
t,+
β
β
Po$)
β
P
)sz
)))
2
)
))))s
o
))szz
β =
+−=
==−++=−+−−+
=
−+−+−−+−
=
−+
−
==
20γ
2
η
4
π
β
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Me+chant Theo+6
Merchant $o!ifie! the reation#hi" !eri*e! - Earne#t
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Co$-ining E+uation 89:; an! 8>?;
{ }
{ }
[ ]
[ ] ]23[..........β'tan(ccotβt)
,s
+z
P
[22]an[21]!"#ationF$o%
]22.......[....................)
85to)
8)c(9'1
cot)γη2β
9 ')
γηcot(2β
)')
γηsin(2β9 ')
γηcos(2β
)'sin(sin'cos(sin
'cos(sin'sin(cos
'sin(sin'cos(cos
'cos(
)'tan(1'cos(sin
'cos(o$)
β
zP
[21]!"#ation$o%(Pz'o$c/c#ttin%axi%#%o$onition
]21.....[..........'tan(1'cos(sin
'cos(
2
))
))
))
))
))
))
))
))
−+=
≅=−
=−+
=−+
=−+−−+
=−+−−+
−+−−+
−−+−−+
−
=−+−−+
−==
−+−−+−
=
γ η β β γ η β β
γ η β β γ η β β
γ η β β γ η β β
γ η τ
γ η β γ η β β
γ η τ
β β
γ η β γ η β β
γ η τ
k
k k t S or
k
t S
d
d
d
dP
k
t S
P
s
o z
o
z
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Lee an 8haffe+ Theo+6
Accor!ing to thi# theor the #hear occur# on a #inge "ane% So for acutting "roce## accor!ing to thi# theor. the foo'ing are #u""o#e! to
ho! goo!, The $ateria ahea! of the cutting too -eha*e! a# i!ea "a#tic $ateria
The chi" !oe# not get har!ene!
The chi" an! "arent 'or( $ateria are #e"arate! - a #hear "ane%
( )
( ) ..[25]..........1tanγ=t,+P
γtan=γcosγsin=
βtan1βcot
>0/$/
....[25]..........1βcott,+P
[24]an[13]!"#ationF$o%
..[24]....................4γηβ
))sz
o
o
o
)sz
)
+−=
−≅−==
+=
=−+
Lee an! Shaffer !eri*e! the foo'ing reation#hi" a#,
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The+,al As*ect of Chi* Fo+,ation
Machining i# inherent characteri)e! - generation of heat an! highcutting te$"erature% At #uch ee*ate! te$"erature the cutting too if
not enough hot har! $a o#e their for$ #ta-iit +uic( or 'ear outra"i! re#uting in increa#e! cutting force#. !i$en#iona inaccurac ofthe "ro!uct an! #horter too ife% The $agnitu!e of thi# cuttingte$"erature increa#e#. though in !ifferent !egree. 'ith the increa#e ofcutting *eocit. fee! an! !e"th of cut. a# a re#ut. high "ro!uction$achining i# con#traine! - ri#e in te$"erature% Thi# "ro-e$ increa#e#
further 'ith the increa#e in #trength an! har!ne## of the 'or( $ateria%@no'e!ge of the cutting te$"erature ri#e in cutting i# i$"ortant.-ecau#e increa#e# in te$"erature, a!*er#e affect the #trength. har!ne## an! 'ear re#i#tance of the cutting
too
cau#e !i$en#iona change# in the "art -eing $achine!. $a(ing contro of!i$en#iona accurac !ifficut an!
can in!uce ther$a !a$age to the $achine! #urface. a!*er#e affecting it#"ro"ertie# an! #er*ice ife%
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ariou# #tu!ie# ha*e -een $a!e of te$"erature# in cutting. -a#e! onheat tran#fer an! !i$en#iona ana#i#. u#ing e0"eri$enta !ata% A
#i$"e an! a""ro0i$ate e0"re##ion for the $ean te$"erature fororthogona cutting i#
333..)4.)
= K
t V
C
U T
c
ρ
thermal diffusivity (ratio of thermal conductivity to volumetric specific heat) of the
workpiece material (m2/sec).
=K
volumetric specific heat of the workpiece (J/mm2-C)=pC
depth of cut (mm)=t
cuttin velocity (m/sec)=!c
specific enery in the operation ("-m/mm#)=$
mean temperature rise at the tool-chip interface (oC)=%
where&
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E:e+cise
The !na$o$eter recor!e! the foo'ing. fee! force >?? (g. cutting force:?? (g% The ra(e ange of the too u#e! 'a# 9?o% The chi" thic(ne## ratio
?%:% Fin! Shear ange 162
Shear force 1P#2
Co??(g an! the fee! force i# (g% the ra(e ange of the too i# :o%Cacuate. Co
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During the $achining of AISI #tee. 'ith ?
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An6 ;uestions o+co,,ents