Theory of Metal Cuttingmechanics of Metal Cutting(2)
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Transcript of Theory of Metal Cuttingmechanics of Metal Cutting(2)
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LECTURE-09THEORY OF METAL CUTTING
- Mechanics of Metal Cuttin
NI!HIL R" #HAR$ %h" #"DEPARTMENT OF INDUSTRIAL & PRODUCTIONENGINEERING
BUET
P x
P y
P z
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&'()#e*a+t,ent of In ust+ial . %+o uction En inee+in
Mechanics of Metal Cuttin
The force acting on a cutting too !uring the "roce## of $etacutting are the fun!a$enta i$"ortance in the !e#ign of cuttingtoo #% The !eter$ination of cutting force# nece##ar for!efor$ation the 'or( $ateria at the #hear )one i# e##entia for#e*era i$"ortant re+uire$ent#,
to e#ti$ate the "o'er re+uire$ent# of a $achine too
to e#ti$ate the #training action# that $u#t -e re#i#te! - the$achine too co$"onent#. -earing#. /ig# an! fi0ture#to e*a uate the ro e of *ariou# "ara$eter# in cutting force#to e*a uate the "erfor$ance of an ne' 'or( $ateria . too$ateria . en*iron$ent. techni+ue# etc% 'ith re#"ect to $achina-i it1cutting force#2
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&'(/#e*a+t,ent of In ust+ial . %+o uction En inee+in
The force # #te$ in the genera ca#e of con*entiona turning "roce## i##ho'n in the fo o'ing Fi u+e"
P x
P yP z
P z
Px
P y P xy
R
P0 3 fee fo+ce in the !irection of the too tra*eP 3 th+ust fo+ce in the !irection "er"en!icu ar to the "ro!uce! #urface
P ) 3 cuttin fo+ce or ,ain fo+ce acting in the !irection of the cutting *e ocit %
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&'(#e*a+t,ent of In ust+ial . %+o uction En inee+in
P z
P x
P yP xyX
Y
o
P xyR
ZXY
R
.......[2]..........cosPP
]........[1..........sinPP
xyy
xyx
==
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&'(1#e*a+t,ent of In ust+ial . %+o uction En inee+in
Se*era force# can -e !efine! re ati*e to the orthogona cutting $o!e %Ba#e! on the#e force#. #hear #tre##. coefficient of friction. an! certainother re ation#hi"# can -e !efine!%
R
P s
R 2
Workpiece Tool
Chip
P z
P n
P xy
NF
R 1
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&'(2#e*a+t,ent of In ust+ial . %+o uction En inee+in
Me+chant Ci+cle #ia +a, 3MC#4
The fo o'ing re ation#hi"# #ugge#t a circ e re"re#entation of force# a#!one - Me+chant an! in!icate! in the fo o'ing Fi u+e %
P xy
Workpiece
P zP n
P sF
N R
o
o
- o
Tool
Chip
.[7]....................cosPsinPP
..[6]....................sinPcosPP
]5[....................sin PcosP N
]4.[....................cosPsin PF
]3.......[xyPzPnPsP NFR
xyzn
xyzs
oxyoz
oxyoz
+===
+=
+=+=+=
.....[8]tansinPcosP
cosPsinP
NF
[5]an[4]!"#ationF$o%
oxyoz
oxyoz =+==
4here.5 3 (inetic coefficient of friction & $ean ang e of friction at the ra(e #urface
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&'(5#e*a+t,ent of In ust+ial . %+o uction En inee+in
Fro$ the geo$etr of force re ation# of MCD circ e
P xy
Workpiece
P zP n
P sF
N R
o
o
- o
Tool
Chip
]11[..........'(cos
'(cosPP
[1)]an[*]!"#ationF$on
..[1)]'.........cos(R P.......[*]'.........cos(R P
o
)sz
)s
)z
+=
+= =
Ba#e! on the #hear force. the #hear #tre##1+s2 'hich act# a ong the #hear " ane-et'een the 'or( an! the chi" i#,
]12[..........t,
sinP+
sint,
- an/s0/a$t0/o a$/as0/$/P
+
o
ss
o
s
ss
=
===
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&'('#e*a+t,ent of In ust+ial . %+o uction En inee+in
].......[14'cos(sin'sin(
t,+P
,i%i a$ y
.[13]..........'cos(sin
'cos(t,+P
[12][11]an!"#ationF$o%
o
))sxy
o
))sz
+
=
+=
P xy
Workpiece
P zP n
P sF
NR
o
o
- o
Tool
Chip
In $eta cutting one of the $ain "ro- e$ i# toe*a uate the cutting force# P ) an! P 0 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 re ation#hi"#%
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&'(9#e*a+t,ent of In ust+ial . %+o uction En inee+in
Ea+nest-Me+chant Theo+6
Ern#t an! Merchant e0ten!e! their ana #i# an! #tu!ie! the re ation#hi" -et'een the #hearang e an! the cutting con!ition#% The #ugge#te! that the #hear ang e a 'a # ta(e# the *a uethat 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*e o"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........[..........
2cos)'cos(o$)'sin(sin'cos(cos
)cos(sin
'sin(sin'cos(cos'cos(t,+
)'cos(
'cos(.
sint,+
P
o$)P
)sz
)))
2)
))))s
o
))szz
=
+=
==++=++
=+ ++
=+==
20
2
4
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&'(&0#e*a+t,ent of In ust+ial . %+o uction En inee+in
Me+chant Theo+6
Merchant $o!ifie! the re ation#hi" !eri*e! - Earne#t
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&'(&)#e*a+t,ent of In ust+ial . %+o uction En inee+in
Lee an 8haffe+ Theo+6
Accor!ing to thi# theor the #hear occur# on a #ing e " ane% So for acutting "roce## accor!ing to thi# theor . the fo o'ing are #u""o#e! toho ! goo!,
The $ateria ahea! of the cutting too -eha*e! a# i!ea " a#tic $ateriaThe chi" !oe# not get har!ene!The chi" an! "arent 'or( $ateria are #e"arate! - a #hear " ane%
( )
( ) ..[25]..........1tan=t,+P
tan=cos
sin=tan
1cot
>0/$/
....[25]..........1cott,+P
[24]an[13]!"#ationF$o%
..[24]....................4
))sz
oo
o
)sz
)
+=
==
+=
=+
Lee an! Shaffer !eri*e! the fo o'ing re ation#hi" a#,
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&'(&/#e*a+t,ent of In ust+ial . %+o uction En inee+in
The+,al As*ect of Chi* Fo+,ation
Machining i# inherent characteri)e! - generation of heat an! highcutting te$"erature% At #uch e e*ate! te$"erature the cutting too ifnot enough hot har! $a o#e their for$ #ta-i it +uic( or 'ear outra"i! re#u ting 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 *e ocit . fee! an! !e"th of cut. a# a re#u t. 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 cuttingtoocau#e !i$en#iona change# in the "art -eing $achine!. $a(ing contro of!i$en#iona accurac !ifficu t 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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&'(&1#e*a+t,ent of In ust+ial . %+o uction En inee+in
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
thermal diffusivity (ratio of thermal conductivity to volumetric specific heat) of theworkpiece material (m 2/sec).
=K
volumetric specific heat of the workpiece (J/mm 2-C)=pC
depth of cut (mm)=t
cuttin velocity (m/sec)=! c
specific ener y in the operation ("-m/mm #)=$
mean temperature rise at the tool-chip interface ( oC)=%
where&
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&'(&2#e*a+t,ent of In ust+ial . %+o uction En inee+in
E:e+cise
The ! na$o$eter recor!e! the fo o'ing. fee! force >?? (g. cutting force:?? (g% The ra(e ang e of the too u#e! 'a# 9? o% The chi" thic(ne## ratio
?%: % Fin!Shear ang e 162Shear force 1P #2
Co??(g an! the fee! force i# (g% the ra(e ang e of the too i# : o%Ca cu ate.
Co
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&'(&5#e*a+t,ent of In ust+ial . %+o uction En inee+in
During the $achining of AISI #tee . 'ith ?%? $$Cutting #"ee! 3 ? $ $inThe #hear ang e 3 >? o
The "o'er con#u$e! 'hi e $achining3 :(4The "o'er con#u$e! 'hi e running i! e 3 ?% ? (4
Ca cu ate,The #hear forceChi" thic(ne## ratioNor$a "re##ure on the chi"Chi" thic(ne##
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&'(&'#e*a+t,ent of In ust+ial . %+o uction En inee+in
An6 ;uestions o+co,,ents