Theory of Metal Cuttingmechanics of Metal Cutting

8/19/2019 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


2/18


3/18

&'(/#e*a+t,ent of Inust+ial . %+ouction Eninee+in

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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&'(#e*a+t,ent of Inust+ial . %+ouction Eninee+in

Pz

Px

PyPxyX

Y

Πo

φ

PxyR

ZXY

R

.......[2]..........cosPP

]........[1..........sinPP

xyy

xyx

ϕ

ϕ

=

=


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&'(1#e*a+t,ent of Inust+ial . %+ouction Eninee+in

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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&'('#e*a+t,ent of Inust+ial . %+ouction Eninee+in

].......[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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&'(&0#e*a+t,ent of Inust+ial . %+ouction Eninee+in

Me+chant Theo+6

Merchant $o!ifie! the reation#hi" !eri*e! - Earne#t


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&'(&e*a+t,ent of Inust+ial . %+ouction Eninee+in

Co$-ining E+uation 89:; an! 8>?;

{ }

{ }

[ ]

[ ] ]23[..........β'tan(ccotβt)

,s

+z

P


]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 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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&'(&)#e*a+t,ent of Inust+ial . %+ouction Eninee+in

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]....................4γηβ

))sz

o

o

o

)sz

)

+−=

−≅−==

+=

=−+

Lee an! Shaffer !eri*e! the foo'ing reation#hi" a#,


13/18

&'(&/#e*a+t,ent of Inust+ial . %+ouction Eninee+in

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&


16/18


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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&'(&'#e*a+t,ent of Inust+ial . %+ouction Eninee+in

An6 ;uestions o+co,,ents

Documents

Theory of Metal Cuttingmechanics of Metal Cutting