Theory of Metal Cuttingmechanics of Metal Cutting(2)

8/13/2019 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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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


7/18


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"#%


9/18


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


11/18


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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%


14/18


15/18


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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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


17/18


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##


18/18

&'(&'#e*a+t,ent of In ust+ial . %+o uction En inee+in

An6 ;uestions o+co,,ents

Theory of Metal Cuttingmechanics of Metal Cutting(2)

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