Solutions for Fundamentals of Modern Manufacturing , 5e (published by Wiley) MPGroover 2012
19 SHEET METALWORKING Review Questions 19.1 19.1
dentify dentify the three three b!si" b!si" types types of of sheet sheet #et!l #et!l$or $or%in %in& & oper! oper!tio tions. ns. Answer. 'he three b!si" types of sheet #et!l$or%in& oper!tions !re (1) "uttin&, (2) bendin&, !nd () dr!$in&.
19.2
n "onventi "onvention!l on!l sheet #et!l$or%in& #et!l$or%in& oper!tions, oper!tions, (!) $h!t $h!t is the n!#e n!#e of the toolin& toolin& !nd (b) (b) $h!t $h!t is the n!#e of the #!"hine tool used in the oper!tions Answer. (!) 'he toolin& is "!lled ! pun"h*!nd*die. (b) 'he #!"hine tool is "!lled ! st!#pin& press.
19.
n bl!n%in& bl!n%in& of ! "ir"ul!r "ir"ul!r sheet*#et!l sheet*#et!l p!rt, is the the "le!r!n"e "le!r!n"e !pplied !pplied to the the pun"h pun"h di!#eter di!#eter or the die di!#eter Answer. 'he die di!#eter e+u!ls the bl!n% di!#eter, !nd the pun"h di!#eter is s#!ller by t$i"e the "le!r!n"e.
19. 19.
Wh!t Wh!t is the the differe differen"e n"e bet$ bet$een een ! "uto "utoff ff oper oper!ti !tion on !nd !nd ! p!rti p!rtin& n& oper!t oper!tion ion Answer. - "utoff oper!tion sep!r!tes p!rts fro# ! strip by she!rin& one ed&e of e!"h p!rt in se+uen"e. - p!rtin& oper!tion "uts ! slu& bet$een !d!"ent p!rts in the strip. See /i&ure 19..
19.5 19.5
Wh!t Wh!t is the the differe differen"e n"e bet$e bet$een en ! not"hi not"hin& n& oper!t oper!tion ion !nd !nd ! se#ino se#inot"h t"hin& in& oper oper!ti !tion on Answer. - not"hin& oper!tion "uts out ! portion of the sheet #et!l fro# the side of the sheet or strip, $hile ! se#inot"hin& oper!tion re#oves ! portion of the sheet #et!l fro# the interior of the sheet or strip.
19.
es"ribe es"ribe e!"h e!"h of of the t$o types of sheet*#e sheet*#et!l*be t!l*bendin& ndin& oper!tions3 oper!tions3 4*bendin& 4*bendin& !nd !nd ed&e ed&e bendin&. bendin&. Answer. n 4*bendin&, ! si#ple pun"h !nd die th!t e!"h h!ve the in"luded !n&le !re used to bend the p!rt. n ed&e bendin&, the pun"h for"es ! "!ntilevered sheet*#et!l se"tion over ! die ed&e to obt!in the desired bend !n&le. See /i&ure 19.12.
19. 19.
/or $h!t $h!t is is the the bend bend !llo !llo$!n $!n"e "e inte intende nded d to to "o#p "o#pens ens!te !te Answer. 'he bend !llo$!n"e is intended to "o#pens!te for stret"hin& of the sheet #et!l th!t o""urs in ! bendin& oper!tion $hen the bend r!dius is s#!ll rel!tive to the sto"% thi"%ness. n prin"iple the bend !llo$!n !llo$!n"e "e e+u!ls e+u!ls the len&th len&th of the bent #et!l #et!l !lon& !lon& its neutr!l neutr!l !6is. !6is.
19. 19.
Wh!t Wh!t is sprin sprin&b &b!"% !"% in shee sheet* t*#et #et!l !l bend bendin in& & Answer. Sprin&b!"% is the el!sti" re"overy of the sheet #et!l !fter bendin&7 it is usu!lly #e!sured !s the differen"e bet$een the fin!l in"luded !n&le of the bent p!rt !nd the !n&le of the toolin& used to #!%e the bend, divided by the !n&le of the toolin&.
19.9 19.9
efin efinee dr!$i dr!$in& n& in in the the "ont "onte6 e6tt of shee sheett #et!l #et!l$o $or% r%in in&. &. Answer. r!$in& is ! sheet #et!l$or%in& oper!tion used to produ"e "up*sh!ped or bo6*sh!ped, or other "o#ple6*"urved, hollo$ p!rts. r!$in& is !""o#plished by pl!"in& ! pie"e of sheet #et!l over ! die "!vity !nd then usin& ! pun"h to push the #et!l into the "!vity.
19.10
Wh!t !re so#e so#e of the the si#ple si#ple #e!sures #e!sures used to to !ssess !ssess the fe!sibili fe!sibility ty of ! proposed proposed "up*dr! "up*dr!$in& $in& oper!tion
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19*1
Solutions for Fundamentals of Modern Manufacturing , 5e (published by Wiley) MPGroover 2012
Answer. Me!sures of dr!$in& fe!sibility in"lude (1) dr!$in& r!tio "# "# " ":: " " p7 (2) redu"tion r ( " " * " p): "7 "7 !nd () thi"%ness*to*di!#eter r!tio, t : "7 "7 $here t sto"% thi"%ness, " thi"%ness, " bl!n% di!#eter, !nd " p pun"h di!#eter.
19.1 19.11
istin istin&ui &uish sh bet$e bet$een en redr!$ redr!$in& in& !nd !nd reverse reverse dr!$i dr!$in&. n&. Answer. n redr!$in&, the sh!pe "h!n&e is si&nifi"!nt enou&h (e.&., dr!$in& r!tio &re!ter th!n 2.0) th!t it #ust be "!rried out in t$o dr!$in& steps, prob!bly $ith !n !nne!lin& oper!tion bet$een the steps. n reverse dr!$in&, t$o dr!$s !re !""o#plished on the p!rt, one in one dire"tion, the se"ond in the opposite dire"tion.
19.12 19.12
Wh!t Wh!t !re so#e so#e possibl possiblee defe"ts defe"ts in dr!$n dr!$n sheet sheet*#et *#et!l !l p!rts p!rts Answer. r!$in& defe"ts in"lude (1) $rin%lin&, (2) te!rin&, () e!rin&, !nd () surf!"e s"r!t"hes, !s des"ribed in Se"tion 19...
19.1 19.1
Wh!t Wh!t is is !n e#bo e#boss ssin in& & oper! oper!ti tion on Answer. 8#bossin& is ! sheet #et!l$or%in& oper!tion used to "re!te indent!tions in the sheet, su"h !s r!ised letterin& or stren&thenin& ribs.
19.1 19.1
Wh!t Wh!t is stre stret" t"h h for# for#in in& & Answer. Stret"h for#in& of sheet #et!l "onsists of si#ult!neously stret"hin& !nd bendin& the sheet*#et!l $or% p!rt to !"hieve sh!pe "h!n&e.
19.15
dentify dentify the the prin"ip!l prin"ip!l "o#ponents "o#ponents of ! st!#pin& st!#pin& die die th!t th!t perfor#s perfor#s bl!n%in bl!n%in&. &. Answer. 'he prin"ip!l "o#ponents !re the pun"h !nd die, $hi"h perfor# the "uttin& oper!tion. 'hey !re !tt!"hed respe"tively to the pun"h holder (!.%.!. upper shoe) !nd die holder (!.%.!. lo$er shoe). -li&n#ent of the pun"h !nd die durin& the st!#pin& oper!tion is !"hieved by #e!ns of &uide pins !nd !nd bushin&s bushin&s in the pun"h holder holder !nd die die holder holder..
19.1
Wh!t !re !re the t$o t$o b!si" b!si" "!te&ories "!te&ories of stru"tur!l stru"tur!l fr!#es used used in st!#pin& st!#pin& presses presses Answer. '$o b!si" "!te&ories of press fr!#e !re (1) &!p fr!#e, !lso "!lled ;*fr!#e be"!use its profile profile is the the sh!pe of the letter letter <;=, !nd !nd (2) str!i&h str!i&ht*sided t*sided fr!#e, $hi"h $hi"h h!s h!s full full sides sides for &re!ter &re!ter stren&th !nd stiffness of the fr!#e.
19.1
Wh!t !re the the rel!tive rel!tive !dv!nt!&es !dv!nt!&es !nd dis!dv!n dis!dv!nt!&es t!&es of of #e"h!ni"!l #e"h!ni"!l presses presses versus versus hydr!uli" hydr!uli" presses presses in sheet #et!l$or%in& Answer. 'he #!in !dv!nt!&e of #e"h!ni"!l presses is f!ster "y"le r!tes. -dv!nt!&es of hydr!uli" presses presses !re lon&er lon&er r!# r!# stro%es stro%es !nd unifor# unifor# for"e throu&hout throu&hout stro%e. stro%e.
19.1 19.1
Wh!t Wh!t is the the Gue Gueri rin n pro pro"es "ess s Answer. 'he Guerin pro"ess is ! sheet*#et!l for#in& pro"ess th!t uses ! rubber die th!t fle6es to for"e the sheet #et!l to t!%e the sh!pe of ! for# blo"% (pun"h).
19.19 19.19
Wh!t Wh!t is ! #!or #!or te"hn te"hni"! i"!ll proble proble# # in tube tube bendi bendin& n& Answer. - #!or te"hni"!l proble# in tube bendin& is "oll!pse of the tube $!lls durin& the bendin& pro"ess. pro"ess.
19.20 19.20
istin istin&ui &uish sh bet$e bet$een en roll roll bendi bendin& n& !nd !nd roll roll for#in& for#in&.. Answer. >oll bendin& involves the for#in& of l!r&e sheet !nd pl!te #et!l se"tions into "urved for#s. >oll for#in& involves feedin& ! lone strip or "oil throu&h rot!tin& rolls so th!t the sh!pe of the rolls is i#p!rted to the strip.
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Solutions for Fundamentals of Modern Manufacturing , 5e (published by Wiley) MPGroover 2012
Probles -ns$ers to proble#s l!beled !A" !re listed in !n -ppendi6 -ppendi6 !t the b!"% of the boo%. #uttin$ O%er&tions
19.1
(S units) units) - po$er she!rs she!rs is is used to "ut soft "old*ro "old*rolled lled steel steel th!t th!t is .2 .2 ## thi"%. thi"%. -t $h!t $h!t "le!r!n"e "le!r!n"e should the she!rs be set to produ"e !n opti#u# "ut 19.1, Ac 0.00. Solution3 /ro# '!ble 19.1, A
19.2
'hus, c A Act 0.00(.2) '(19)
!A" (?S;S units) - bl!n%in& oper!tion is perfor#ed on :2*in*thi"% "old*rolled steel (h!lf h!rd). 'he p!rt is "ir"ul!r $ith di!#eter 2.500 in. eter#ine the !ppropri!te pun"h !nd die si@es for this oper!tion. Solution3 /ro# '!ble 19.1, A 19.1, Ac 0.05. 'hus, c 0.05(:2) 0.00 in Pun"h di!#eter " "b * 2c 2c 2.500 * 2(0.00) )(*+, in ie di!#eter " "b )(-'' in
19.
(S units) units) - "o#pound "o#pound die die is used to bl!n% bl!n% !nd !nd pun"h pun"h ! l!r&e $!sher $!sher out of 01S' 01S' !lu#inu# !lu#inu# !lloy !lloy sheet sto"% .2 ## thi"%. 'he outside di!#eter of the $!sher is 25.0 ##, !nd the inside di!#eter is 12.0 ##. eter#ine the pun"h !nd die si@es for (!) the bl!n%in& oper!tion, !nd (b) the pun"hin& oper!tion. Solution3 /ro# '!ble 19.1, A 19.1, Ac 0.00.
'hus, c 0.00(.2) 0.192 ##
(!) Al!n%in& pun"h di!#eter " "b * 2c 2c 25.0 * 2(0.192) )*(,) Al!n%in& die di!#eter " "b )-('' (b) Pun"hin& pun"h di!#eter " "h 1)('' Pun"hin& die di!#eter " "h B 2c 2c 12.0 B 2(0.192) 1)(.+ 19.
(S units) units) - bl!n%in& bl!n%in& die die #ust #ust be desi&ned desi&ned to bl!n% the p!rt p!rt outline outline sho$n sho$n in /i&ure P19.. 'he #!teri!l is *##*thi"% st!inless steel (h!lf h!rd). eter#ine the di#ensions of the bl!n%in& pun"h !nd the die openin&. Solution3 /ro# '!ble 19.1, A 19.1, Ac 0.05. 'hus, c 0.05(.0) 0.0 ## Al!n%in& die3 di#ensions !re the s!#e !s for the p!rt in /i&ure P19.. Al!n%in& pun"h3 5 ## len&th di#ension 5 * 2(0.) +*(* 50 ## $idth di#ension 50 * 2(0.) *9(* 'op !nd botto# 25 ## e6tension $idths 25 * 2(0.) )*(* 'he 25 ## inset di#ension re#!ins the s!#e.
19.5
!A" (?S;S units) eter#ine the bl!n%in& for"e re+uired in Proble# 19.2, if the she!r stren&th of the steel 0,000 lb:in 2 !nd the tensile stren&th is 55,000 lb:in 2. Solution3 $ St% t :2 in 0.095 in fro# Proble# 19.2. % % " " 2.5 .5 in $ St" St" 0,000(0.095)(.5) )9/*-. lb
19. 19.
(S units units)) eter#in eter#inee the #ini#u #ini#u# # for"e "!p!" "!p!"ity ity press press to perfo perfor# r# the bl!n% bl!n%in& in& !nd !nd pun"hin pun"hin& & oper!tion in Proble# 19. under the follo$in& "onditions3 (!) bl!n%in& !nd pun"hin& o""ur si#ult!neously !nd (b) the pun"hes !re st!&&ered so th!t pun"hin& o""urs first, then bl!n%in&. 'he !lu#inu# sheet #et!l h!s ! tensile stren&th 50 MP!. Solution3 (!) $ (!) $ 0.(&S 0.(&S )t% t .2 .2 ## fro# Proble# 19.. % 25 B 12 11.2 ##
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Solutions for Fundamentals of Modern Manufacturing , 5e (published by Wiley) MPGroover 2012
$ 0.(50)(.2)(11.2) 91/1'1 N (b) Con&est len&th $ill deter#ine the #ini#u# tonn!&e press re+uired, if pun"hin& !nd bl!n%in& !re perfor#ed sep!r!tely. /or the pun"hin& len&th of "ut, % % 12D, !nd for the bl!n%in& len&th of "ut, %25D %25D .5 ##. ?se the bl!n%in& oper!tion to deter#ine press "!p!"ity. $ 0.(50)(.2)(.5) ,1/-0- N 19.
(S units) units) eter#ine eter#ine the the tonn!&e tonn!&e re+uire#ent re+uire#ent for the the bl!n%in bl!n%in& & oper!tio oper!tion n in Proble# Proble# 19., 19., &iven &iven th!t th!t the st!inless steel h!s ! yield stren&th 25 MP!, she!r stren&th 50 MP!, !nd tensile stren&th 50 MP!. Solution3 $ St% t ## fro# Proble# 19.. % % 5 B 50 B 25 B 25 B 5 B 25 B 25 B 50 20 ## $ 50(.0)(20) -0,/''' N
19.
'he fore#!n fore#!n in the the press$o press$or%in& r%in& se"tion se"tion "o#es "o#es to to you you $ith $ith the the proble# proble# of ! bl!n%in& bl!n%in& oper!ti oper!tion on th!t is produ"in& p!rts $ith e6"essive burrs. (!) Wh!t !re the possible re!sons for the burrs, !nd (b) $h!t "!n be done to "orre"t the "ondition Solution3 (!) >e!sons for e6"essive burrs3 (1) "le!r!n"e bet$een pun"h !nd die is too l!r&e for the #!teri!l !nd sto"% thi"%ness7 !nd (2) pun"h !nd die "uttin& ed&es !re $orn (rounded) $hi"h h!s the s!#e effe"t !s e6"essive "le!r!n"e.
(b) 'o "orre"t the proble#3 (1) ;he"% the pun"h !nd die "uttin& ed&es to see if they !re $orn. f they !re, re&rind the f!"es to sh!rpen the "uttin& ed&es. (2) f the die is not $orn, #e!sure the pun"h !nd die "le!r!n"e to see if it e+u!ls the re"o##ended v!lue. f not, the die #!%er #ust ref!bri"!te the pun"h !nd:or die. en2in$
19.9
" old*rolled steel. 'he p!rt !A" (S units) - bendin& oper!tion is to be perfor#ed on 5.00 ## thi"% "old*rolled dr!$in& is sho$n in /i&ure P19.9. eter#ine the bl!n% si@e re+uired. Solution3 /ro# dr!$in&, E 0, # # .50 ## 10 * E 10 Ab 2( :0)( :0)( # B # B ' ' ba bat ) #(t (.5):(5.00) 1., $hi"h is less th!n 2.07 therefore, ' ba ba 0. Ab 2(10:0)(.5 B 0. 6 5.0) 2.0 ## i#ensions of st!rtin& bl!n%3 w .- / % % 5 B 2.0 B .5 1)9(.'
19.10 19.10
(S units units)) Solve Solve Proble Proble# # 19.9 e6"e e6"ept pt th!t th!t the the bend r!di r!dius us # # 10.5 ##. Solution3 /ro# dr!$in&, E 0, # # 11.5 ## 10 * E 10. Ab 2( :0)( :0)( # B # B ' ' ba bat ) #: #:t (10.5):(5.00) 2.17 therefore, ' therefore, ' ba ba 0.5 Ab 2(10:0)(10.5 B 0.5 6 5.00) 1. ## i#ensions of st!rtin& bl!n%3 w .- / % % 5 B 1. B .5 1.,(),
19.11 19.11
(?S;S units) units) -n !n&le !n&le br!"%et br!"%et is bent bent in ! 4*bendin& 4*bendin& oper!t oper!tion ion on ! press press br!%e br!%e fro# ! fl!t fl!t bl!n% bl!n% th!t is .0 in lon& by 1.5 in $ide by 5:2 in thi"%. 'he 90 bend is #!de in the #iddle of the *in len&th, so th!t the bend !6is is 1.5 in lon&. (!) eter#ine the di#ensions of the t$o e+u!l sides th!t $ill result !fter the bend, if the bend r!dius :1 in. 'he sides should be #e!sured to the be&innin& be&innin& of the bend bend r!dius. r!dius. (b) -lso, -lso, deter#ine deter#ine the len&th of the p!rtFs neutr!l neutr!l !6is !fter the the bend. bend.
86"erpts fro# this $or% #!y be reprodu"ed by instru"tors for distribution on ! not*for*profit b!sis for testin& or instru"tion!l purposes only to students enrolled in "ourses for $hi"h the te6tboo% h!s been !dopted. Any other reproduction reproduction or translation of this work work beyond that permitted by Sections 107 or 108 of the 1976 United States Copyriht Act without the permission of the copyriht owner is unlawful!
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Solutions for Fundamentals of Modern Manufacturing , 5e (published by Wiley) MPGroover 2012
(") Where should the #!"hine oper!tor set the stop on the press br!%e rel!tive to the st!rtin& len&th of the p!rt (!) #::t (:1):(5:2) 1.2. 'herefore, ' 'herefore, ' ba Solution3 (!) # ba 0. Ab 2(90:0)(0.15 B 0. 6 0.1525) 0.5 in i#ensions (len&ths) of e!"h end 0.5(.0 * 0.5) 1(+1)) in (b) Sin"e the #et!l stret"hes durin& bendin&, its len&th $ill $ill be &re!ter !fter the bend th!n before. ts len&th before bendin& .000 in. 'he stret"hed len&th of the bend !lon& the neutr!l !6is $ill be3 Aent len&th 2 (90:0)(0.15 B 0.5 6 0.1525) 0.1 in 'herefore, the len&th of the neutr!l !6is of the p!rt $ill be 2(1.122) B 0.1 *('*10 in o$ever, o$ever, if stret"hin& o""urs !lon& the neutr!l !6is of the bend, then thinnin& of the stret"hed #et!l $ill !lso o""ur, !nd this $ill !ffe"t the pre"edin& "!l"ul!ted v!lue of the len&th of the bent se"tion. 'he !#ount of thinnin& $ill be inversely proportion!l to the !#ount of stret"hin& be"!use volu#e #ust re#!in "onst!nt, "onst!nt, before !nd !fter bendin&. bendin&. 'he sheet thi"%ness thi"%ness !fter bendin& (!ssu#in& unifor# unifor# stret"hin& !nd thinnin&) thinnin&) (0.5:0.1)(0.1525) (0.5:0.1)(0.1525) 0.10 0.10 in. Ho$ let us re"!l"ul!te the the len&th of the bent se"tion se"tion $ith this ne$ ne$ v!lue of t . 'he bend r!dius $ill re#!in the s!#e ( # # :1 0.15 in) be"!use it is lo"!ted !t the inside of the bend. Cen&th of neutr!l !6is !lon& the bend 2 (90:0)(0.15 B 0.5 6 0.10) 0.09 in. 'he ne$ fin!l len&th of the neutr!l !6is is % % 2(1.122) B 0.09 .029 in. 'he !#ount of stret"hin& is less th!n previously deter#ined, !nd so is the !#ount of thinnin&. -n iter!tive pro"edure #ust be used to !rrive !rrive !t the fin!l v!lues of of stret"hin& !nd thinnin&. thinnin&. >e"!l"ul!te the thi"%ness of the stret"hed sheet !s (0.5:0.09)(0.1525) 0.19 in, !nd re"!l"ul!tin& the len&th of the bent se"tion b!sed on this v!lue, $e h!ve the follo$in&3 Cen&th of neutr!l !6is !lon& the bend 2 (90:0)(0.15 B 0.5 6 0.19) 0.0 in 'he ne$ fin!l len&th of the neutr!l !6is is % % 2(1.122) B 0.0 .02 in. Ine #ore iter!tion3 'he thi"%ness of the stret"hed sheet is (0.5:0.0)(0.1525) (0.5:0.0)(0.1525) 0.1 in, !nd re"!l"ul!tin& the len&th of the bent se"tion b!sed on this v!lue, $e h!ve 2 (90:0)(0.15 B 0.5 6 0.1) 0.0 in. 'he ne$ fin!l len&th of the neutr!l !6is is % % 2(1.122) B 0.0 *('.1+ in. 'his is ! differen"e of only 0.0099 in fro# our previous v!lue of .01 in th!t i&nored thinnin& of the #et!l. (") 'he oper!tor should set the stop so th!t the tip of the 4*pun"h "ont!"ts the st!rtin& bl!n% !t ! dist!n"e 2.000 in fro# the end. 19.12
(S units) units) - bendin& bendin& oper!tion oper!tion is perfor#ed perfor#ed on .0*##*thi .0*##*thi"% "% "old*rolled "old*rolled steel steel sheet th!t th!t is 25 ## $ide !nd 100 ## lon&. 'he sheet is bent !lon& the 25 ## dire"tion, so th!t the bend !6is is 25 ## lon&. 'he resultin& sheet #et!l p!rt h!s !n !"ute !n&le of 0 !nd ! bend r!dius of ##. eter#ine (!) the bend !llo$!n"e, !nd (b) the len&th of the neutr!l !6is of the p!rt !fter the bend. .0 ## Solution3 (!) Given th!t E 0, # # .0 ##, !nd t 10 * E 150. Ab 2( :0)( :0)( # B # B ' ' ba bat ) #(t : 1.5, $hi"h is less th!n 2.07 therefore, ' ba ba 0. Ab 2(150:0)(.0 B 0. 6 .0) 19.1 ## (b) ue to stret"hin&, the neutr!l !6is of the fin!l p!rt $ill be &re!ter th!n 100.0 ##. 'he !#ount of stret"hin& $ill be the differen"e bet$een the bend !llo$!n"e !nd the len&th of the bent se"tion, $hi"h is "o#puted !s 2 (150:0)(.0 B 0.5 6 .0) 20.9. 'he differen"e 20.9 J 19.1 1.0 ## 'hus, the fin!l len&th of the neutr!l !6is $ill be % % 100 B 1. 1'1(0+'
86"erpts fro# this $or% #!y be reprodu"ed by instru"tors for distribution on ! not*for*profit b!sis for testin& or instru"tion!l purposes only to students enrolled in "ourses for $hi"h the te6tboo% h!s been !dopted. Any other reproduction reproduction or translation of this work work beyond that permitted by Sections 107 or 108 of the 1976 United States Copyriht Act without the permission of the copyriht owner is unlawful!
19*5
Solutions for Fundamentals of Modern Manufacturing , 5e (published by Wiley) MPGroover 2012
o$ever, o$ever, if stret"hin& o""urs !lon& the neutr!l !6is of the bend, then thinnin& of the stret"hed #et!l $ill !lso o""ur, !nd this $ill !ffe"t the pre"edin& "!l"ul!ted v!lue of the len&th of the bent se"tion. 'he !#ount of thinnin& $ill be inversely proportion!l to the !#ount of stret"hin& be"!use volu#e #ust re#!in "onst!nt, "onst!nt, before !nd !fter bendin&. bendin&. 'he sheet thi"%ness thi"%ness !fter bendin& (!ssu#in& unifor# unifor# stret"hin& !nd thinnin&) thinnin&) (19.1:20.9)(.0) (19.1:20.9)(.0) . ##. Ho$ let let us re"!l"ul!te the len&th of the bent se"tion $ith this ne$ v!lue of t . 'he bend r!dius $ill re#!in the s!#e ( # # .0 ##) be"!use it is lo"!ted !t the inside of the bend. Cen&th of neutr!l !6is !lon& the bend 2 (150:0)(.0 B 0.5 6 .) 20.99 ##. Ho$ the differen"e bet$een the len&th of the bent se"tion !nd the bend !llo$!n"e 20.99 J 19.1 1.5 ##. 'he ne$ fin!l len&th of the neutr!l !6is is % % 100 B 1.5 1'1(..- 'he !#ount of stret"hin& is less th!n previously deter#ined, !nd so is the !#ount of thinnin&. -n iter!tive pro"edure #ust be used to !rrive !t the fin!l v!lues of stret"hin& !nd thinnin&. >e"!l"ul!te the thi"%ness of the stret"hed sheet !s (19.1:20.99)(.0) . ##, !nd re"!l"ul!tin& the len&th of the bent se"tion b!sed on this v!lue, $e h!ve the follo$in&3 Cen&th of neutr!l !6is !lon& the bend 2 (150:0)(.0 B 0.5 6 .) 20.0 ## 'he ne$ differen"e bet$een the len&th of the bent se"tion !nd the bend !llo$!n"e 20.0 J 19.1 1. ##, !nd the ne$ fin!l len&th of the neutr!l !6is is % % 100 B 1. 1'1(*** Ine #ore iter!tion3 'he thi"%ness of the stret"hed sheet is (19.1:20.0)(.0) .2 ##, !nd re"!l"ul!tin& the len&th of the bent se"tion b!sed on this v!lue, $e h!ve 2 (150:0)(.0 B 0.5 6 .2) 20.5 ##. 'he ne$ before !nd !fter differen"e 20.5 J 19.1 1.1 ##, !nd the ne$ fin!l len&th of the neutr!l !6is is % % 100 B 1.1 1'1(*1. . 'his is ! differen"e of 0. ## fro# our previous v!lue of 101.0 th!t i&nored thinnin& of the #et!l. 19.1
!A" (S units) eter#ine the bendin& for"e in Proble# 19.9 if the bend is perfor#ed in ! 4*die $ith ! die openin& di#ension 0 ##. 'he steel h!s ! tensile stren&th 50 MP! !nd she!r stren&th 250 MP!. Solution3 /or 4*bendin&, ' 4*bendin&, ' bf 1.. bf 2 $ ' ' bf " 1.(50)(5)(5.0) 2:0 1'/1+. N bf (&S )wt : "
19.1
(S units) units) Solve Solve Proble# Proble# 19.1 e6"ept e6"ept th!t th!t the oper!tio oper!tion n is perfor#ed perfor#ed usin& usin& ! $ipin& $ipin& die die $ith die die openin& di#ension 2 ##. die, ' bf 0.. Solution3 /or ed&e*bendin& in ! $ipin& die, ' bf 2 2 $ ' ' bf " 0.(50)(5)(5.0) :2 ./,'9 N bf (&S )wt : "
19.15
(?S;S units) units) eter#ine eter#ine the the bendin& bendin& for"e for"e re+uired re+uired in Proble# Proble# 19.11 19.11 if if the bend bend is perfor#ed perfor#ed in ! 4*die $ith ! die openin& di#ension 1.0 in. 'he #!teri!l h!s ! tensile stren&th 50,000 lb:in 2. Solution3 /or 4*bendin&, ' 4*bendin&, ' bf 1.. bf 2 $ ' ' bf " 1.(50,000)(1.5)(5:2) 2:1.0 )*.- lb bf (&S )wt : "
19.1
(?S;S units) units) Solve Solve Proble# Proble# 19.15, 19.15, e6"ept e6"ept th!t the the oper!tion oper!tion is perfor#ed perfor#ed usin& ! $ipin& $ipin& die $ith $ith die openin& di#ension 0.50 in. Solution3 /or ed&e*bendin& in ! $ipin& die, ' die, ' bf 0.. bf 2 2 $ ' ' bf ( &S ) wt : " " 0.(50,000)(1.5)(5:2) :0.50 1)'+ lb bf
19.1
(S units) units) - sheet*# sheet*#et!l et!l p!rt p!rt th!t is is .0 ## thi"%, thi"%, 5 ## lon&, lon&, !nd 20 ## $ide $ide is bent bent in ! 4*die 4*die to !n in"luded !n&le 0 !nd ! bend r!dius .5 ##. 'he bend is #!de in the #iddle of the 5 ## len&th, so th!t the bend !6is 20 ## lon&. 'he #et!l h!s ! yield stren&th 220 MP! !nd ! tensile stren&th 0 MP!. ;o#pute the for"e re+uired to bend the p!rt, &iven th!t the die openin& di#ension 12 ##.
86"erpts fro# this $or% #!y be reprodu"ed by instru"tors for distribution on ! not*for*profit b!sis for testin& or instru"tion!l purposes only to students enrolled in "ourses for $hi"h the te6tboo% h!s been !dopted. Any other reproduction reproduction or translation of this work work beyond that permitted by Sections 107 or 108 of the 1976 United States Copyriht Act without the permission of the copyriht owner is unlawful!
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Solutions for Fundamentals of Modern Manufacturing , 5e (published by Wiley) MPGroover 2012
Solution3 /or 4*bendin&, ' 4*bendin&, ' bf 1.. bf 2 $ ' ' bf " 1.(0)(20)() 2:12 1)/'-9 N bf (&S )wt : " 3r&win$ O%er&tions
19.1 19.1
erive erive !n e6pres e6pressio sion n for for the the redu"ti redu"tion on r in dr!$in& !s ! fun"tion of dr!$in& r!tio "#. "#. ( " "b * " * " p): " "b Solution3 >edu"tion r r!$in& r!tio "# r!tio "# " "b: " " p r "b: " "b * " * " p: " "b 1 * " * " p: " "b 1 * 1: "# "#
19.19
!A" (S units) - "ylindri"!l "up is produ"ed in ! deep de ep dr!$in& oper!tion. 'he "up hei&ht 5 ##, !nd its inside di!#eter 100 ##. Sheet*#et!l thi"%ness 2 ##. f the bl!n% di!#eter 225 ##, deter#ine (!) dr!$in& r!tio, (b) redu"tion, !nd (") thi"%ness*to*di!#eter r!tio. (d) s the oper!tion fe!sible Solution3 (!) "# (!) "# " "b: " " p 225:100 )()-
(b) r ( " "b * " * " p): " "b (225 * 100):225 0.555 --(-4 (") t : " "b 2:225 0.009 '(+94 (d) /e!sibility NoK "# is is too l!r&e (&re!ter th!n 50L), !nd t : " is "# is too l!r&e (&re!ter th!n 2.0), r is " is too s#!ll (less th!n 1L). 19.20
(S units) units) Solve Solve Proble# Proble# 19.19, 19.19, e6"ept e6"ept th!t th!t the st!rtin& st!rtin& bl!n% bl!n% si@e si@e di!#eter di!#eter 15 15 ##. (!) "# " "b: " " p 15:100 1(0Solution3 (!) "# (b) r ( " "b * " * " p): " "b (15 * 100):15 0.29 *)(94 (") t : " "b 2:15 0.011 1(1*4 (d) /e!sibility "# /e!sibility "# 2.0, r 50L, !nd t : " N " N 1L. o$ever, the oper!tion is not fe!sible be"!use the 15 ## di!#eter bl!n% si@e does not provide suffi"ient #et!l to dr!$ ! 5 ## "up hei&ht. 'he !"tu!l "up hei&ht possible $ith ! 15 ## di!#eter bl!n% "!n be deter#ined by "o#p!rin& surf!"e !re!s (one side only for "onvenien"e) bet$een the "up !nd the st!rtin& bl!n%. Al!n% !re! "2: 2 2 (15) : 2,05 ## . 'o "o#pute the "up surf!"e !re!, let us divide the "up into t$o se"tions3 (1) $!lls, !nd (2) b!se, !ssu#in& the "orner r!dius on the pun"h h!s ! ne&li&ible effe"t in our "!l"ul!tions !nd there is no e!rin& of the "up. 'hus, ;up !re! " ph B " p2: 100h B (100)2: 100h B 2500 1.1h 1.1h B 5. Set surf!"e !re! of "up surf!"e !re of st!rtin& bl!n%3 1.1h 1.1h B 5 2,05 1.1h 1.1h 1,199 h 51.5 ##. 'his is less th!n the spe"ified 5 ## hei&ht.
19.21
(?S;S units) units) - deep dr!$in& dr!$in& oper!tion oper!tion is perfor#ed perfor#ed in in $hi"h the the inside inside of the "ylindri"!l "ylindri"!l "up "up h!s ! di!#eter .25 in !nd ! hei&ht 2.5 in. Sto"% thi"%ness :1 in, !nd bl!n% di!#eter . in. Pun"h !nd die r!dii 5:2 in. 'he #et!l h!s ! tensile stren&th 5,000 lb:in 2, ! yield stren&th 2,000 lb:in 2, !nd ! she!r stren&th of 0,000 lb:in 2. eter#ine (!) dr!$in& r!tio, (b) redu"tion, (") dr!$in& for"e, !nd (d) bl!n%holder for"e. Solution3 (!) "# (!) "# .:.25 1(+1
(b) r ( " "b J " J " p): " "b (. J .25):. .5:.0 0. **(+4 (") $ (") $ " pt (&S )( )( " "b: " " p * 0.) (.25)(0.15)(5,000)(.:.25 * 0.) 1+'/9'' lb (d) $ (d) $ h 0.015) 0.015) ( " "b2 * ( " " p B 2.2t 2.2t B B 2 #d )2) $ h 0.015(2,000) (.2 * (.25 B 2.2 6 0.15 B 2 6 0.1525) 2) 0.015(2,000) (.2 * .952) 86"erpts fro# this $or% #!y be reprodu"ed by instru"tors for distribution on ! not*for*profit b!sis for testin& or instru"tion!l purposes only to students enrolled in "ourses for $hi"h the te6tboo% h!s been !dopted. Any other reproduction reproduction or translation of this work work beyond that permitted by Sections 107 or 108 of the 1976 United States Copyriht Act without the permission of the copyriht owner is unlawful!
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Solutions for Fundamentals of Modern Manufacturing , 5e (published by Wiley) MPGroover 2012
F h 5 -)/1'' lb
19.22
!A" (S units) - "up*dr!$in& oper!tion is perfor#ed in $hi"h the "upEs inside di!#eter 0 ## !nd its hei&ht 50 ##. Sto"% thi"%ness .0 ##, !nd bl!n% di!#eter 150 ##. Pun"h !nd die r!dii ##. 'ensile stren&th 00 MP! !nd yield stren&th 10 MP! for this sheet #et!l. eter#ine (!) dr!$in& r!tio, (b) redu"tion, (") dr!$in& for"e, !nd (d) bl!n%holder for"e. Solution3 (!) "# (!) "# 150:0 1(+0-
(b) r ( " "b * " * " p): " "b (150 J 0):150 0:150 '(*, (") $ (") $ " pt (&S )( )( " "b: " " p * 0.) (0)()(00)(150:0 * 0.) .-*/*1+ N (d) $ (d) $ h 0.015) 0.015) ( " "b2 * ( " " p B 2.2t 2.2t B B 2 #d )2) $ h 0.015(10) (1502 * (0 B 2.2 6 B 2 6 ) 2) 0.015(10) (1502 * 9.2) F h 5 11*/9*) N 19.2
(?S;S units) units) - deep dr!$in& dr!$in& oper!tion oper!tion is perfor#ed perfor#ed on on ! sheet*#et!l sheet*#et!l bl!n% bl!n% th!t is 1: 1: in thi"%. thi"%. 'he hei&ht of the "up . in !nd its di!#eter 5.0 in (both inside di#ensions). (!) -ssu#in& the pun"h r!dius r!dius 0, "o#pute "o#pute the the st!rtin& st!rtin& di!#eter di!#eter of the bl!n% to "o#plete "o#plete the the oper!tion oper!tion $ith no no #!teri!l left in the fl!n&e. (b) s the oper!tion fe!sible (i&norin& the f!"t th!t the pun"h r!dius is too s#!ll) re#!ins "onst!nt. Solution3 (!) ?se surf!"e !re! to "o#pute bl!n% di!#eter, !ssu#in& thi"%ness t re#!ins 2 2 ;up !re! $!ll !re! B b!se !re! " ph B " p : 5(.) B 0.25 (5) 25.25 in2 Al!n% !re! "b2: 0.25 "b2 Settin& bl!n% !re! "up !re!3 0.25 "b2 25.25 "b2 25.25:0.25 101.0 Db 5 1'('-' in (b) 'est for fe!sibility3 fe!sibility3 "# "# " "b: " " p 10.050:5.0 )('1( Ae"!use "# Ae"!use "# N N 2.0, this oper!tion #!y not be fe!sible. fe!sible. If If "ourse, "ourse, the @ero pun"h pun"h r!dius r!dius #!%es #!%es this oper!tion oper!tion infe!sibl infe!siblee !ny$!y !ny$!y.. With With ! rounded pun"h r!dius, the bl!n% si@e $ould be sli&htly s#!ller, $hi"h $ould redu"e "#. "#.
19.2
(?S;S units) units) Solve Proble# Proble# 19.2, 19.2, e6"ept e6"ept use use ! pun"h pun"h r!dius r!dius 0.5 0.5 in. in. Solution3 ?se surf!"e !re! "o#put!tion, !ssu#in& thi"%ness t re#!ins "onst!nt. 'he surf!"e !re! of the "up $ill be divided into three se"tions3 (1) str!i&ht $!lls, $hose hei&ht .0 * 0.5 .25 in, (2) +u!rter toroid for#ed by the 0.5 r!dius !t the b!se of the "up, !nd () b!se, $hi"h h!s ! di!#eter 5.0 * 2 6 0.5 .25 in A1 " ph (5.0)(.25) 5.0 in 2 A2 len&th of the +u!rter "ir"le !t the b!se #ultiplied by the "ir"u#feren"e of the "ir"le des"ribed by the "entroid "entroid (P!ppus*Gu (P!ppus*Guldin ldin 'heore#)3 'heore#)3 len&th len&th of +u!rter +u!rter "ir"le ": ": 0.25 (2 6 0.5) 0.59 in. 'he "entroid is lo"!ted !t the "enter of the !r", $hi"h is 0.5 sin 5 0.25 beyond the "enter of the 0.5 in r!dius. 'hus, the di!#eter of the "ir"le des"ribed by the "entroid is .25 .25 B 2 6 0.25 .0 in A2 .(0.59) . in 2 A (.25)2: 1.1 in 2 'ot!l !re! of "up 5.0 B . B 1.1 .2 in 2 Al!n% !re! "b2: 0.55 "b2 Settin& bl!n% !re! "up !re!3 0.55 " 0.55 "b2 .2 "b2 .2:0.55 9.25 Db 5 9(+9' in
'est for fe!sibility3 "# fe!sibility3 "# " "b: " " p 9.9:5.0 1(90+, $hi"h is less th!n the li#itin& r!tio of 2.0. 'he thi"%ness to di!#eter r!tio t : " "b 0.125:9.9 0.012 1.2L, $hi"h is !bove the v!lue of 1L 86"erpts fro# this $or% #!y be reprodu"ed by instru"tors for distribution on ! not*for*profit b!sis for testin& or instru"tion!l purposes only to students enrolled in "ourses for $hi"h the te6tboo% h!s been !dopted. Any other reproduction reproduction or translation of this work work beyond that permitted by Sections 107 or 108 of the 1976 United States Copyriht Act without the permission of the copyriht owner is unlawful!
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Solutions for Fundamentals of Modern Manufacturing , 5e (published by Wiley) MPGroover 2012
used !s ! "riterion of fe!sibility in "up dr!$in&. dr!$in&. Where!s the oper!tion in Proble# 19.2 $!s not fe!sible, the oper!tion in the present proble# see#s fe!sible. 19.25
!A" (S units) - dr!$in& oper!tion is perfor#ed on .2 ## sto"%. 'he p!rt is ! "ylindri"!l "up $ith inside hei&ht 0 ## !nd inside di!#eter 0 ##. -ssu#e the "orner r!dius on the pun"h is @ero. (!) /ind the re+uired st!rtin& bl!n% si@e "b. (b) s the dr!$in& oper!tion fe!sible Solution3 (!) ?se surf!"e !re! "o#put!tion, !ssu#in& thi"%ness t re#!ins "onst!nt. ;up !re! $!ll !re! B b!se !re! " ph B " p2: (0)(0) B 0.25 (0)2 10, ## 2 Al!n% !re! "b2: 0.55 "b2 Settin& bl!n% !re! "up !re!3 0.55 " 0.55 "b2 10, "b2 10,:0.55 1,19 Db 5 11*(9
(b) 'est for fe!sibility3 fe!sibility3 "# "# " "b: " " p 11.9:0 1(91-6 t : " "b .2:11.9 0.029 )(094( 'hese "riteri! v!lues indi"!te th!t the oper!tion is fe!sible7 ho$ever, $ith ! pun"h r!dius # p 0, this sh!pe $ould be diffi"ult to dr!$ be"!use the dr!$in& pun"h $ould !"t on the #et!l li%e ! bl!n%in& pun"h. 19.2 19.2
(S units units)) Solve Solve Proble Proble# # 19.25, 19.25, e6"ept e6"ept th!t th!t the the hei&ht hei&ht 50 50 ##. Solution3 ;up !re! $!ll !re! B b!se !re! ;up !re! " ph B " p2: (0)(50) B 0.25 (0)2 12,252 ## 2 Al!n% !re! "b2: 0.55 "b2 Settin& bl!n% !re! "up !re!3 0.55 " 0.55 "b2 12,252 "b2 12,252:0.55 15,59 Db 5 1)*(9
'est for fe!sibility3 "# fe!sibility3 "# " "b: " " p 12.9:0 )('+6 t : " "b .2:12.9 0.025 )(-,4. Sin"e "# Sin"e "# is is &re!ter th!n 2.0, this oper!tion is prob!bly infe!sible. -lso, !s in the previous proble#, the pun"h r!dius # r!dius # p 0 $ould render this oper!tion diffi"ult if not infe!sible. 19.2
(S units) units) Solve Solve Proble# Proble# 19.25, 19.25, e6"ept e6"ept th!t th!t the "orner r!dius on the pun"h 10 ##. Solution3 ?se surf!"e !re! "o#put!tion, !ssu#in& thi"%ness t re#!ins re#!ins "onst!nt. 'he surf!"e !re! of the "up $ill be divided into three se"tions3 (1) str!i&ht $!lls, $hose hei&ht 0 * 10 0 ##, (2) +u!rter toroid for#ed by the 10 ## r!dius !t the b!se of the "up, !nd () b!se, $hi"h h!s ! di!#eter 0 * 2 6 10 0 ##. A1 " ph (0)(0) 5,55 ## 2 A2 len&th of the +u!rter "ir"le !t the b!se #ultiplied by the "ir"u#feren"e of the "ir"le des"ribed by the "entroid "entroid (P!ppus*Gu (P!ppus*Guldin ldin 'heore#)3 'heore#)3 len&th len&th of +u!rter +u!rter "ir"le 2 # p: 0.25(2 6 10) 15.1 ##. 'he "entroid is lo"!ted !t the "enter of the !r", $hi"h is 10 sin 5 .01 beyond the "enter of the 10 ## r!dius. 'hus, the di!#eter of the "ir"le des"ribed by the "entroid is 0 B 2 6 .01 5.12 ##. A2 5.12 (15.1) 22 ## 2 A (0)2: 125 ## 2 'ot!l !re! of "up 555 B 22 B 125 9,5 ## 2 Al!n% !re! "b2: 0.55 "b2 Settin& bl!n% !re! "up !re!3 0.55 " 0.55 "b2 9,5 "b2 9,5:0.55 12,20 Db 5 11'(-
'ests for fe!sibility3 "# fe!sibility3 "# " "b: " " p 110.5:0 1(+*. t : " "b .2:110.5 0.029 )(94. Sin"e "# Sin"e "# is is less th!n 2.0 !nd t : " "b is &re!ter th!n 1L, this oper!tion is "onsidered fe!sible.
86"erpts fro# this $or% #!y be reprodu"ed by instru"tors for distribution on ! not*for*profit b!sis for testin& or instru"tion!l purposes only to students enrolled in "ourses for $hi"h the te6tboo% h!s been !dopted. Any other reproduction reproduction or translation of this work work beyond that permitted by Sections 107 or 108 of the 1976 United States Copyriht Act without the permission of the copyriht owner is unlawful!
19*9
Solutions for Fundamentals of Modern Manufacturing , 5e (published by Wiley) MPGroover 2012
19.2
'he fore#!n fore#!n in the the dr!$in& dr!$in& se"tion se"tion of the shop sho$s sho$s you you sever!l sever!l s!#ples s!#ples of p!rts p!rts th!t h!ve h!ve been deep dr!$n in the shop. 'he s!#ples h!ve v!rious defe"ts. Ine h!s e!rs, !nother h!s $rin%les, !nd ! third h!s torn se"tions !t its b!se. Wh!t !re the "!uses of e!"h defe"t !nd $h!t re#edies $ould you propose Solution3 (1) Ears !re "!used by sheet #et!l th!t h!s dire"tion!l properties. 'he #!teri!l is !nisotropi". Ine re#edy is to !nne!l the #et!l to redu"e the dire"tion!lity of the properties.
(2) Wrinkles !re "!used by "o#pressive bu"%lin& of the fl!n&e !s it is dr!$n in$!rd to for# the "up. 'here !re sever!l possible re#edies3 (!) in"re!se the t : " "b r!tio by usin& ! thi"%er &!&e sheet #et!l. 'his #!y not be possible sin"e ! desi&n "h!n&e is re+uired. (b) n"re!se the bl!n%holder pressure pressure !&!inst !&!inst the the $or% durin& durin& dr!$in&. dr!$in&. () Tearing o""urs due to hi&h tensile stresses in the $!lls of the "up ne!r the b!se. - re#edy $ould be to provide provide ! l!r&er l!r&er pun"h pun"h r!dius. r!dius. 'e!rin& 'e!rin& "!n !lso !lso o""ur o""ur due to to ! die "orner r!dius r!dius th!t is is too s#!ll. 19.29
(?S;S units) units) - "up*sh!ped "up*sh!ped p!rt is dr!$n dr!$n $ithout $ithout ! bl!n%holde bl!n%holderr fro# sheet #et!l #et!l $hose $hose thi"%ness thi"%ness 0.25 in. 'he inside di!#eter of the "up 2.5 in, its hei&ht 1.5 in, !nd the "orner r!dius !t the b!se 0.5 in. (!) Wh!t is the #ini#u# st!rtin& bl!n% di!#eter th!t "!n be used (b) oes this bl!n% di!#eter provide suffi"ient #!teri!l to "o#plete the "up (19.1), "b * " * " p 5t 5t Solution3 (!) -""ordin& to 8+. (19.1), " "b 5t 5t B " B " p 5(0.25) B 2.5 .(0- in (b) Ae"!use the sheet #et!l is r!ther thi"%, let us use volu#e r!ther th!n !re! to deter#ine $hether there is suffi"ient #et!l in ! .5 in bl!n% di!#eter. 'he dr!$n "up "onsists of three se"tions3 (1) "up $!lls, (2) toroid !t b!se, !nd () b!se. * 1 (1.5 * 0.5) O(2.5 B 2 6 0.25) 2 * (2.5)2): 1.125 (2.5): 2.0 in * 2 ("ross*se"tion of +u!rter toroid) 6 ("ir"le #!de by s$eep of "entroid) ;ross*se"tion of +u!rter toroid 0.25 O(0.5 B 0.25) 2 * (0.5) 2 0.19 in 2 ;ir"le #!de by "entroid s$eep h!s di!#eter (2.5 * 2 6 0.25) B 2(0.5 B 0.25:2)sin 5 2.5 in * 2 2.5 (0.19) 1.51 in * (2.5 * 2 6 0.5) 2(0.25): 0.01 in 'ot!l * * 1 B * 2 B * 2.0 B 1.51 B 0.01 .5 in 4olu#e of bl!n% "b2t: (0.25) "b2: 0.19 "b2 Settin& bl!n% volu#e "up volu#e3 0.19 " 0.19 "b2 .5 "b2 .5:0.19 2.1 "b *(+1 in( 'he di!#eter of .5 in "o#puted in (!) does not provide suffi"ient #et!l to "o#plete the dr!$in&. 'his oper!tion is not fe!sible.
Ot7er O%er&tions
19.0
(?S;S units) units) - 20*in*lon& 20*in*lon& sheet*#et sheet*#et!l !l $or%pie"e $or%pie"e is stret"hed stret"hed in ! stret"h stret"h for#in& for#in& oper!tio oper!tion n to the di#ensions sho$n in /i&ure P19.0. 'hi"%ness of the be&innin& sto"% :1 in !nd $idth .5 in. 'he #et!l h!s ! flo$ "urve defined by ! stren&th "oeffi"ient 5,000 lb:in 2 !nd ! str!in h!rdenin& e6ponent 0.20. 'he yield stren&th of the #!teri!l 0,000 lb:in 2. (!) /ind the stret"hin& for"e $ for"e $ re+uired ne!r the be&innin& of the oper!tion $hen yieldin& first o""urs. eter#ine (b) true str!in e6perien"ed by the #et!l, (") stret"hin& for"e $ , !nd (d) die for"e $ for"e $ die die !t the very end $hen the p!rt is for#ed !s indi"!ted in /i&ure P19.0(b). Solution3 (!) ?se 0.002 !s st!rt of yieldin&. $ %t) %t) f ) f 5,000(0.002) 0.20 21,00 lb:in 2 $ (.5)(0.15)(21,00) .*/-'' lb
86"erpts fro# this $or% #!y be reprodu"ed by instru"tors for distribution on ! not*for*profit b!sis for testin& or instru"tion!l purposes only to students enrolled in "ourses for $hi"h the te6tboo% h!s been !dopted. Any other reproduction reproduction or translation of this work work beyond that permitted by Sections 107 or 108 of the 1976 United States Copyriht Act without the permission of the copyriht owner is unlawful!
19*10
Solutions for Fundamentals of Modern Manufacturing , 5e (published by Wiley) MPGroover 2012
(b) -fter stret"hin&, the len&th of the pie"e is in"re!sed fro# 20.0 in to 2(10 2 B 52)0.5 22.1 in ln(22.1:20) ln 1.11 '(111, (") -t the fin!l len&th of 22.1 in, the thi"%ness of the sheet #et!l h!s been redu"ed to #!int!in "onst!nt volu#e, !ssu#in& $idth % $idth % .5 in re#!ins the s!#e durin& stret"hin&. t f 0.15(20:22.1) 0.1 in ) f 5,000(0.111) 0.20 ,00 lb:in 2 $ .5(0.1)(,00) ,9/''' lb (d) $ (d) $ die $ sin sin die 2 *1 A A t!n (5:10) 2.5 $ die die 2(9,000) sin 2.5 ,1/0'' lb 19.1
!A" (S units) eter#ine the st!rtin& dis% di!#eter re+uired to spin the p!rt in /i&ure P19.1 usin& ! "onvention!l spinnin& oper!tion. 'he st!rtin& thi"%ness 2. ##. Solution3 /ro# p!rt dr!$in&, r!dius 25 B (100 * 25):sin 0 25 B 5:0.5 15 ## St!rtin& di!#eter " di!#eter " 2(15) .-'
19.2
(S units) units) f the p!rt p!rt illustr!t illustr!ted ed in /i&ure /i&ure P19.1 P19.1 $ere #!de #!de by she!r she!r spinnin& spinnin&,, deter#ine deter#ine (!) the the $!ll thi"%ness !lon& the "one*sh!ped portion, !nd (b) the spinnin& redu"tion r . Solution3 (!) t f t sin sin (2.)sin 0 2.(0.5) 1()
(b) r (t (t * * t f ):t ):t (2. J 1.2):2. '(-' 5 -'4 19.
eter#ine eter#ine the the she!r she!r str!in str!in e6perien"e e6perien"ed d by the #et!l #et!l in Proble# Proble# 19.2. 19.2. Solution3 A!sed on side$ise displ!"e#ent of #et!l throu&h ! she!r !n&le of 0 , She!r str!in "ot 0 1(0.)(
19.
(S units) units) - 5*## 5*## di!#eter di!#eter tube tube is bent bent into ! r!ther r!ther "o#ple6 "o#ple6 sh!pe sh!pe $ith ! series of of si#ple si#ple tube bendin& bendin& oper!tions oper!tions.. 'he $!ll thi"%ne thi"%ness ss on the tube tube .5 .5 ##. 'he tubes tubes !re used to to deliver deliver fluids fluids in ! "he#i"!l pl!nt. n one of the bends $here the bend r!dius is 125 ##, the $!lls of the tube !re fl!ttenin& b!dly. Wh!t "!n be done to "orre"t the "ondition Solution3 Possible solutions3 (1) ?se ! #!ndrel to prevent "oll!psin& of tube $!ll. (2) >e+uest the desi&ner to in"re!se the bend r!dius to " " 225 ##. () P!"% s!nd into the tube. 'he s!nd $ill !"t !s !n intern!l fle6ible #!ndrel to support the tube $!ll.
86"erpts fro# this $or% #!y be reprodu"ed by instru"tors for distribution on ! not*for*profit b!sis for testin& or instru"tion!l purposes only to students enrolled in "ourses for $hi"h the te6tboo% h!s been !dopted. Any other reproduction reproduction or translation of this work work beyond that permitted by Sections 107 or 108 of the 1976 United States Copyriht Act without the permission of the copyriht owner is unlawful!
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