Solutions for Fundamentals of Modern Manufacturing , 5e (published by Wiley) MPGroover 2012
10 FUNDAMENTALS OF METAL CASTING Review Questions 10.1 10.1
Identify Identify soe soe of the the ipo iport! rt!nt nt !dv!n !dv!nt!" t!"es es of of sh!pe#$ sh!pe#$!st !stin" in" pro$ess pro$esses. es. Answer. %dv!nt!"es in$lude (1) $ople& p!rt "eoetries !re possible' (2) soe $!stin" oper!tions !re net sh!pe pro$esses, e!nin" th!t no further !nuf!$turin" oper!tions !re needed to !$$oplish the fin!l p!rt "eoetry' () very l!r"e p!rts !re possible' () $!stin" is !ppli$!ble to !ny et!l th!t $!n be elted' !nd (5) soe $!stin" pro$esses !re suited to !ss produ$tion.
10.2 10.2
Wh!t Wh!t !re !re soe soe of of the the liit liit!tio !tions ns !nd !nd dis! dis!dv! dv!nt!" nt!"es es of of $!sti $!stin"* n"* Answer. +is!dv!nt!"es in$lude (1) liit!tions on e$h!ni$!l stren"th properties' (2) porosity' () poor diensi diension!l on!l !$$ur!$y !$$ur!$y'' () s!fety s!fety h!!rds h!!rds due to h!ndlin" h!ndlin" of of hot et!ls' et!ls' !nd !nd (5) environent! environent!ll probles. probles.
10. 10.
Wh!t Wh!t is ! f!$to f!$tory ry th!t th!t perfor perfors s $!sti $!stin" n" oper oper!ti !tions ons usu!ll usu!lly y $!lled $!lled** Answer. % foundry foundr y.
10. 10.
Wh!t Wh!t is the differe differen$e n$e bet-ee bet-een n !n open open old old !nd !nd ! $losed $losed old* old* Answer. %n open old is open to the !tosphere !t the top' it is !n open $ont!iner in the desired sh!pe -hi$h ust be fl!t !t the top. % $losed old h!s ! $!vity th!t is entirely en$losed by the old, -ith ! p!ss!"e-!y ($!lled the "!tin" syste) le!din" fro the the outside into the $!vity. $!vity. Molten et!l is poured into this "!tin" syste to fill the old.
10.5 10.5
!e the t-o b!si$ b!si$ old old types types th!t th!t distin distin"ui "uish sh $!st $!stin" in" pro$es pro$esses ses.. Answer. /he t-o old types !re (1) e&pend!ble olds !nd (2) per!nent olds.
10. 10.
Whi$h Whi$h $!stin $!stin" " pro$e pro$ess ss is the ost ost ipo iport! rt!nt nt $oer$ $oer$i!l i!lly* ly* Answer. S!nd $!stin" is the ost iport!nt $!stin" pro$ess.
10. 10.
Wh!t Wh!t is the differe differen$e n$e bet-ee bet-een n ! p!tt p!ttern ern !nd !nd ! $ore in s!nd s!nd oldin oldin"* "* Answer. /he p!ttern deterines the e&tern!l sh!pe of the $!st p!rt, -hile ! $ore deterines its intern!l "eoetry if the $!stin" in$ludes ! $!vity.
10. 10.
Wh!t Wh!t is e!n e!ntt by by the the ter ter sup super erhe he!t !t** Answer. Superhe!t is the teper!ture differen$e !bove the eltin" point !t -hi$h the olten et!l is poured. /he ter !lso refers to the !ount of he!t th!t is reoved fro the olten et!l bet-een pourin" pourin" !nd solidifi$!ti solidifi$!tion. on.
10.3 10.3
Why should should turb turbule ulent nt floflo- of of olten olten et!l et!l into into the the old old be be !voide !voided* d* Answer. /urbulen$e $!uses the follo-in" probles4 (1) it !$$eler!tes for!tion of o&ides in the solidified et!l, !nd (2) it $!uses old erosion or "r!du!l -e!rin" !-!y of the old due to ip!$t of olten et!l.
10.10
Wh!t is the $ontinui $ontinuity ty l!- !s !s it !pplies !pplies to to the floflo- of olten et!l in in $!stin"* $!stin"* Answer. /he $ontinuity l!-, or $ontinuity eu!tion, indi$!tes th!t the voluetri$ flo- r!te is $onst!nt throu"hout the liuid flo-. flo-.
10.11 10.11
Wh!t !re soe soe of the the f!$tors f!$tors th!t !ffe$t !ffe$t the fluidi fluidity ty of ! olten olten et!l et!l durin" durin" pourin" pourin" into into ! old $!vity*
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Solutions for Fundamentals of Modern Manufacturing , 5e (published by Wiley) MPGroover 2012
Answer. /he f!$tors in$lude (1) pourin" teper!ture !bove the eltin" point, (2) et!l !lloy $oposition, () vis$osity of the liuid et!l, !nd () he!t tr!nsfer to the surroundin"s.
10.12 10.12
Wh!t Wh!t does does he!t of fusion fusion e!n in $!stin $!stin"* "* Answer. 8e!t of fusion is the !ount of he!t ener"y reuired to tr!nsfor the et!l fro solid st!te to liuid st!te.
10.1
8o- does does solidifi$ solidifi$!tion !tion of of !lloys !lloys differ differ fro fro solidifi$!t solidifi$!tion ion of pure et!ls* et!ls* Answer. Pure et!ls solidify !t ! sin"le teper!ture eu!l to the eltin" point. Most !lloys (e&$eptions !re eute$ti$ !lloys) st!rt to solidify !t the liuidus !nd $oplete solidifi$!tion o$$urs !t the solidus, -here the liuidus is ! hi"her teper!ture th!n the solidus.
10.1 10.1
Wh!t Wh!t is ! eute eute$t $ti$ i$ !llo !lloy* y* Answer. % eute$ti$ !lloy is ! p!rti$ul!r $oposition in !n !lloy syste for -hi$h the solidus !nd liuidus teper!tures !re eu!l. /he teper!ture is $!lled the eute$ti$ teper!ture. 8en$e, solidifi$!tion o$$urs !t ! sin"le teper!ture, r!ther th!n over ! teper!ture r!n"e.
10.15
Wh!t is the the rel!tions rel!tionship hip 7no-n 7no-n !s 9hvorinov: 9hvorinov:ss rule rule in $!stin"* $!stin"* ; C m(# < A) A)2, -here " "S ; tot!l solidifi$!tion tie, C m ; Answer. 9hvorinov:s rule is su!ried4 " "S "S ; "S ; old $onst!nt, # ; ; volue of $!stin", !nd A !nd A ; ; surf!$e !re! of $!stin".
10.1
Identify Identify the the three three sour$es sour$es of of $ontr!$tion $ontr!$tion in ! et!l $!stin" $!stin" !fter !fter pourin". pourin". Answer. /he three $ontr!$tions o$$ur due to (1) $ontr!$tion of the olten et!l !fter pourin", (2) solidifi$!tion shrin7!"e durin" tr!nsfor!tion of st!te fro liuid to solid, !nd () ther!l $ontr!$tion in the solid st!te.
10.1 10.1
Wh!t Wh!t is ! $hi $hill ll in $!st $!stin in"* "* Answer. % $hill is ! he!t sin7 pl!$ed to en$our!"e r!pid freein" in $ert!in re"ions of the $!stin".
Probe!s %ns-ers to probles l!beled "A# !re listed in !n %ppendi& %ppendi& !t the b!$7 of the boo7. $e%tin& %n' Pourin&
10.1 "A# (SI units) % dis7 0 $ in di!eter !nd 5 $ thi$7 is $!st of pure !luinu in !n open old $!stin" oper!tion. %luinu elts !t 0 9, but the pourin" teper!ture -ill be 00 9. /he !ount of !luinu he!ted -ill be 5= ore th!n -h!t is needed to fill the old $!vity. 9opute the !ount of he!t th!t ust be !dded to the et!l to he!t it to the pourin" teper!ture, st!rtin" fro ! roo teper!ture of 25 9. /he he!t of fusion of !luinu ; 3. ><". ?ther properties $!n be obt!ined fro /!bles .1 !nd .2. %ssue the spe$ifi$ he!t h!s the s!e v!lue for solid !nd olten !luinu. Soution4 @olue # ; ; $2h<; (0)2(5)< ; 2.2 $ @olue of !luinu to be he!ted ; 2.2(1 A 5=) ; 53. $ Bro /!ble .1 !nd .2, density ; ; 2.0 "<$ !nd spe$ifi$ he!t C ; ; 0.21 9!l<"# 9 ; 0. ><"# 9 8e!t reuired ; 2.0(53.)C0.(0#25) A 3. A 0.(00#0)D ; 1,12.1C55. A 3. A 12.2D ; 1()0*+),-. /
10.2 (ES9S units) units) Pure $opper $opper is he!ted he!ted to $!st ! l!r"e l!r"e re$t!n"ul! re$t!n"ul!rr pl!te in !n open open old. /he pl!teF pl!teFs len"th ; 20 in, -idth ; 10 in, !nd thi$7ness ; 2 in. 9opute the !ount of he!t th!t ust be !dded to the et!l to he!t it fro !bient teper!ture (5 B) to ! pourin" teper!ture of 2100 B. /he !ount of et!l he!ted -ill be 10= ore th!n -h!t is needed to fill the old $!vity. +ensity, eltin" point, !nd spe$ifi$ he!t of the solid et!l $!n be found in /!bles .1 !nd .2. /he spe$ifi$ he!t of $opper in the olten st!te ; 0.030 tu
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Solutions for Fundamentals of Modern Manufacturing , 5e (published by Wiley) MPGroover 2012
Soution4 @olue of re$t!n"ul!r pl!te # ; ; (20 & 10 & 2) ; 00.0 in @olue of $opper to be he!ted ; 00(1 A 10=) ; 0.0 in %ssuin" " o ; 5 B !nd usin" 6. (10.1), ; 0.2 & 0C0.032(131 # 5) A 0 A 0.030(2100 # 131)D ; 12.5C15.5 A 0 A 10.1D % ; H ,)(0 2tu
10. "A# (SI units) /he len"th of the do-nsprue le!din" into the runner of ! old ; 200 . /he $ross#se$tion!l !re! !t its b!se ; 00 2. @olue @olue of the old $!vity ; 0.0012 . +eterine (!) velo$ity of the olten et!l flo-in" throu"h the b!se of the do-nsprue, (b) volue r!te of flo-, !nd ($) tie reuired to fill the old $!vity. Soution4 (!) @elo$ity & ; (2 & 310 & 200) 0.5 ; (,32,000) 0.5 ; 1(*1 !!3s
(b) @olue flo- r!te ' ; &A ; &A ; 131 & 00 ; -(4)+, !!3s ($) /ie to fill $!vity " () ; ; # <' ; 1,200,000<53,2 1,200,000<53,2 ; +50+ s 10. (ES9S units) units) % old h!s ! do-nspru do-nspruee of len"th ; .0 in. /he $ross#se$t $ross#se$tion!l ion!l !re! !t the the botto botto of 2 the sprue is 0.5 in . /he sprue le!ds into ! horiont!l runner -hi$h feeds the old $!vity, -hose volue ; 5 in . +eterine (!) velo$ity of the olten et!l flo-in" throu"h the b!se of the do-nsprue, (b) volue r!te of flo-, !nd ($) tie reuired to fill the old $!vity. Soution4 (!) @elo$ity & ; (2 & 2.2 & 12 & .0)0.5 ; (.)0.5 ; .*51 in3se6
(b) @olue flo- r!te ' ; &A ; &A ; .1 & 0.5 ; 450- in3se6 ($) /ie to fill $!vity " () ; ; # <' ; 5.0<.05 ; +5+ se6 10.5 (SI units) units) /he flo- r!te r!te of liuid liuid et!l into into the do-nsprue do-nsprue of of ! old ; 0. H
10. "A# (ES9S units) /he volue flo- r!te of olten et!l into the do-nsprue fro the pourin" $up is 5 in
10. (SI units) units) Molten Molten et!l is is poured into the the pourin" pourin" $up of of ! s!nd old old !t ! ste!dy ste!dy r!te r!te of 500 $
10. (ES9S units) units) Molten Molten et!l is poured poured into into the do-nsprue do-nsprue !t ! $onst!nt $onst!nt floflo- r!te durin" durin" the tie tie it t!7es to fill the old. %t the end of pourin" the sprue is filled !nd there is ne"li"ible et!l in the pourin" pourin" $up. $up. /he do-nsprue do-nsprue is .0 in lon", its $ross#se$ti $ross#se$tion!l on!l !re! !re! !t the the top ; 0. in 2, !nd !t the b!se ; 0. in2. /he $ross#se$tion!l !re! of the runner le!din" fro the sprue !lso ; 0. in 2, !nd it is .0 in lon" before le!din" into the old $!vity, -hose volue ; 5 in . /he volue of the riser lo$!ted 6&$erpts fro this -or7 !y be reprodu$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 te&tboo7 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
!lon" the runner ne!r the old $!vity ; 25 in . It t!7es ! tot!l of .0 se$ to fill the entire old (in$ludin" $!vity, riser, runner, !nd sprue. /his is ore th!n the theoreti$!l tie reuired, indi$!tin" ! loss of velo$ity due to fri$tion in the sprue !nd runner. +eterine (!) the theoreti$!l velo$ity !nd flor!te !t the b!se of the do-nsprue' (b) tot!l volue of the old, in$ludin" do-nsprue, runner, !nd riser' ($) !$tu!l velo$ity !nd flo- r!te !t the b!se of the sprue' !nd (d) loss of he!d in the "!tin" syste due to fri$tion. Soution4 (!) @elo$ity & ; (2 & 2.2 & 12 & .0)0.5 ; .*51 in3se6 Blo- r!te ' ; .1 & 0.0 ; 405* in3se6
(b) /ot!l # ; ; 5.0 A 25.0 A 0.5(0. A 0.)(.0) A 0.(.0) ; ((50 in ($) %$tu!l flo- r!te ' ; 33.0< ; 50 in3se6 %$tu!l velo$ity & ; .0<0. ; --50 in3se6 (d) & ; (2 & 2.2 & 12 & h)0.5 ; 2. h0.5 ; 55.0 in
10.3 (ES9S units) units) +eterine +eterine the the shrin7 shrin7 rule to to be used by p!ttern p!ttern !7ers !7ers for !"nesiu !"nesiu. . Esin" the shrin7!"e v!lue in /!ble 10.1, e&press your !ns-er in ters of de$i!l fr!$tion in$hes of elon"!tion per foot foot of len"th len"th $op!re $op!red d to ! st!nd!rd st!nd!rd one#foot one#foot s$!le. s$!le. Soution4 Bor -hite $!st iron, shrin7!"e 2.1= fro /!ble 10.1. /hus, line!r $ontr!$tion ; 1.0 0.021 ; 0.33. Shrin7 rule elon"!tion ; (0.33) #1 ; 1.0215 Bor ! 12#in$h rule, * rule, * ; ; 1.0215(12) ; 12.25 in 6lon"!tion per foot of len"th ; 05+-, in
10.10 "A# (SI units) +eterine the shrin7 rule to be used by old !7ers for die $!stin" of in$. Esin" the shrin7!"e v!lue in /!ble 10.1, e&press your !ns-er in ters of de$i!l of elon"!tion per 00 of len"th $op!red to ! st!nd!rd 00# s$!le. Soution4 Bor in$, shrin7!"e 2.= fro /!ble 10.1. /hus, line!r $ontr!$tion ; 1.0 0.02 ; 0.3. Shrin7 rule elon"!tion ; (0.3) #1 ; 1.02 Bor ! 00# rule, * rule, * ; ; 1.02(00) ; 0.00 6lon"!tion per 00 of len"th ; *500* !!
10.11 (SI units) % fl!t pl!te is to be $!st in !n open old -hose botto h!s ! su!re sh!pe th!t th!t is 200 by 200 . /he /he old is 0 deep. deep. % tot!l of 1,000,000 1,000,000 of olten !luinu is poured into the old. Solidifi$!tion shrin7!"e is 7no-n to be .0=, -hi$h is ! voluetri$ $ontr!$tion, not ! line!r $ontr!$tion. /!ble 10.1 lists the line!r shrin7!"e due to ther!l $ontr!$tion !fter solidifi$!tion. If the !v!il!bility of olten et!l in the old !llo-s the su!re sh!pe of the $!st pl!te to !int!in its 200 by 200 diensions until solidifi$!tion is $opleted, deterine the fin!l diensions of the pl!te. Soution4 /he initi!l volue of liuid et!l ; 1,000,000 . When poured into the old it t!7es the sh!pe of the open old, -hi$h is 200 by 200 su!re, or 0,000 2. /he st!rtin" hei"ht of the olten et!l is 1,000,000 < 0,000 ; 25 . @oluetri$ solidifi$!tion shrin7!"e is =, so -hen the !luinu solidifies its volue ; 1,000,000(0.3) ; 30,000 . e$!use its b!se still e!sures 200 by 200 due to the flo- of liuid et!l before solidifi$!tion, its hei"ht h!s been redu$ed to 30,000 < 0,000 ; 2.5 . /her!l $ontr!$tion $!uses ! further shrin7!"e of 1.=.
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Solutions for Fundamentals of Modern Manufacturing , 5e (published by Wiley) MPGroover 2012
/hus the fin!l diensions of the pl!te !re 200(0.3) by 200(0.3) by 2.5(0.3) ; 1(,540 !! b9 1(,540 !! b9 +51(- !!. Soi'i:i6%tion Ti!e %n' Riser Desi&n
10.12 (SI units) units) When $!stin" $!stin" lo- $!rbon $!rbon steel under under $ert!in old $onditi $onditions, ons, the old $onst!nt $onst!nt in 2 9hvorinov:s rule ; .0 in<$ . +eterine ho- lon" solidifi$!tion -ill t!7e for ! re$t!n"ul!r $!stin" -hose len"th ; 0 $, -idth ; 15 $, !nd thi$7ness ; 20 . Soution4 @olue # ; ; 0 & 15 & 2 ; 300 $ %re! A %re! A ; ; 2(0 & 15 A 0 & 2 A 15 & 2) ; 100 $ 2 9hvorinovFs rule4 " "S ; C m (# (# < A) A)2 ; (300<100) 2 ; +541 !in "S ;
10.1 (SI units) units) In the previous previous proble solve solve for tot!l solidifi solidifi$!tion $!tion tie tie only usin" usin" !n e&ponent e&ponent v!lue of 1.3 in 9hvorinov:s rule inste!d of 2.0. Wh!t !dJustent ust be !de in the units of the old $onst!nt* ; C m (# (# < A) A)1.3 ; (300<100)1.3 ; +54,- !in Soution4 9hvorinovFs rule4 " "S "S ; /he units for C m be$oe in
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Solutions for Fundamentals of Modern Manufacturing , 5e (published by Wiley) MPGroover 2012
@olue # ; ; $2 *< *< ; ( $) $)2(1.0 $)< $)< ; 1.0335 $ 1.0335 $ $ ; (2.25 in )<1.0335 ; .2 in $ ; $ ; (.2)0. ; 5,4 in * ; * ; 1.0(.) ; 45,+4 in (b) /o /o find the solidifi$!tion solidifi$!tion tie, first deterine the old $onst!nt in 9hvorinovFs 9hvorinovFs rule. 2 2 %re! of l!r"er $!stin" A $!stin" A ; ; 2 $ < A $* ; $* ; 2 () () < A ()(5.0) ()(5.0) ; 35.50 in 2 (#+A) #+A) ; 0.2<35.50 ; 0. C m ; .0<(0.) 2 ; 11.05 in
(!) 9hvorinovFs rule4 " "S ; C m(#+A) #+A)2 "S ; (1) Sphere volue # ; ; $< ; (1) (1)< ; < < d Sphere surf!$e !re! A !re! A ; ; $2 ; (1) (1)2 ; d d2 #+A ; #+A ; ( <)< <)< ; ; 1< ; 0.1 d 9hvorinovFs rule " "S ; (0.1) 2C m ; 050+,,*C 050+,,*C m "S ; (2) 9ylinder volue # ; ; $2 % < < ; (1) (1)2(1)< ; < < ; 0.25 d d 9ylinder !re! A !re! A ; ; 2 $2< A $* ; $* ; 2 (1) (1)2< A (1)(1) (1)(1) ; <2 <2 A ; ; 1.5 d d2 #+A ; #+A ; 0.25 <1.5 <1.5 ; ; 0.1 d 050+,,*C m 9hvorinovFs rule " "S ; (0.1) 2C m ; 050+,,*C "S ; () 9ube4 # ; * ; * ; (1) ; 1.0 d 9ube !re! ; *2 ; (1)2 ; .0 d2 #+A ; #+A ; 1.0<.0 ; 0.1 d 050+,,*C m 9hvorinovFs rule " "S ; (0.1) 2C m ; 050+,,*C "S ; (b) %ll three sh!pes !re euiv!lent !s risers. ($) If C m ; .5 in<$ 2 ; 50 in
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Solutions for Fundamentals of Modern Manufacturing , 5e (published by Wiley) MPGroover 2012
(1) Sphere volue # ; ; $< ; 1.0 d . $ ; < ; ; 1.310 d . $ ; $ ; (1.310) 0. ; 1.21 d Sphere !re! A !re! A ; ; $2 ; (1.21) (1.21)2 ; . d2 #+A ; #+A ; 1.0<. ; 0.20 d 9hvorinovFs rule " "S ; (0.20) 2C m ; 0504+*C 0504+*C m "S ; (2) 9ylinder volue # ; ; $2 % < < ; $< ; 1.0 d . $ ; < ; ; 1.2 d 0. /herefore, $ /herefore, $ ; ; % % ; ; (1.2) ; 1.0 d 9ylinder !re! A !re! A ; ; 2 $2< A $* ; $* ; 2 (1.0) (1.0)2< A (1.0)(1.0) (1.0)(1.0) ; 5.5 d 2 #+A ; #+A ; 1.0<5.5 ; 0.10 d 050+.C m 9hvorinovFs rule " "S ; (0.10) 2C m ; 050+.C "S ; () 9ube4 # ; * ; * ;1.0 d. * ; * ; 1.0 d 2 2 9ube !re! ; * ; (1) ; .0 d2 #+A ; #+A ; 1.0<.0 ; 0.1 d 050+,,*C m 9hvorinovFs rule " "S ; (0.1) 2C m ; 050+,,*C "S ; (b) Sphere -ould be the best riser, sin$e # < A r!tio A r!tio is "re!test. ($) Given th!t C m ; .5 in<$ 2 ; 50 in
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Solutions for Fundamentals of Modern Manufacturing , 5e (published by Wiley) MPGroover 2012
10.21 (ES9S units) units) % $ylindri$!l $ylindri$!l riser riser is to be desi"ned for for ! s!nd $!stin" old. old. /he len"th len"th of the $ylinder $ylinder is to be 1.25 ties its di!eter. /he $!stin" is ! su!re pl!te, e!$h side ; 10 in !nd thi$7ness ; 0.5 in. If the et!l is $!st iron, !nd the old $onst!nt ; 1.0 in
10.22 (ES9S units) units) % $ylindri$!l $ylindri$!l riser riser -ith di!eter#to#len di!eter#to#len"th "th r!tio ; 1.0 is to be desi"ned desi"ned for ! s!nd $!stin" old. /he $!stin" "eoetry is illustr!ted in Bi"ure P10.22, in -hi$h the units !re in$hes. If the old $onst!nt in 9hvorinov:s rule ; 13.5 in
6&$erpts fro this -or7 !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 te&tboo7 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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