ch13

Solutions for Fundamentals of Modern Manufacturing , 5e (published by Wiley)  MPGroover 2012

13 SHAPING PROCESSES FOR PLASTICS Review Questions 13.1

Wht re so!e so!e of of the resons resons "hy "hy plsti# plsti# shpin$ shpin$ pro#esses pro#esses re i!portn i!portnt% t% Answer. &he resons in#lude (1) !ny of the pro#esses re net shpe pro#esses' (2) in $enerl, less ener$y is e!ployed thn in !etl"orin$ pro#esses' (3) lo"er te!pertures re reuired to pro#ess  plsti#s  plsti#s thn thn !etls !etls or #er!i#s #er!i#s'' (*) there there is $ret fle+ibility fle+ibility in $eo!etry' $eo!etry' nd nd (5) pinti pintin$ n$ nd other finishin$ pro#esses re $enerlly not reuired.

13.2

dentify dentify the !in #te$ori #te$ories es of plsti plsti#s #s shpin$ shpin$ pro#esse pro#esses, s, s #lssif #lssified ied by the resultin resultin$ $ produ#t produ#t $eo!etry. Answer. &he #te$ories re (1) e+trusion, (2) !oldin$, (3) for!in$ of #ontinuous sheets nd fil!s, (*) fibers, (5) fo!ed produ#ts, nd (-) dis#rete for!ed sheets nd fil!s.

13.3

is#osity is#osity is n i!portnt i!portnt property property of  poly!er poly!er !elt in plsti#s plsti#s shpin$ shpin$ pro#esse pro#esses. s. /pon /pon "ht  pr!eters  pr!eters does does vis#osity vis#osity depend% depend% Answer. is#osity of  poly!er !elt depends on (1) te!perture nd (2) sher rte. lso, (3) the !ole#ulr "ei$ht of the poly!er ffe#ts vis#osity.

13.*

o" does does the the vis#osit vis#osity y of  poly!er poly!er !elt !elt differ differ fro! fro! !ost !ost fluids fluids tht re e"tonin e"tonin.. Answer.  poly!er !elt e+hibits pseudoplsti#ity, "hi#h !ens tht its vlue de#reses "ith in#resin$ sher rte.

13.5 13.5

Wht Wht does does vis#oel vis#oelst sti#i i#ity ty !en, !en, "hen "hen pplie pplied d to  poly!e poly!err !elt% !elt% Answer. is#oelsti#ity is  #o!bintion of vis#ous nd elsti# properties "hi#h #use the !elt to e+hibit !e!ory  the tenden#y to return to its previous shpe, s e+hibited by die s"ell in e+trusion.

13.13.-

4efin 4efinee die die s"el s"elll in in e+t e+tru rusi sion on.. Answer. 4ie s"ell is the tenden#y of the e+trudte to e+pnd in #rossse#tionl di!ensions i!!editely on e+itin$ the die orifi#e. t results fro! the vis#oelsti# properties of the poly!er !elt.

13. 13.

6riefly 6riefly des#ri des#ribe be the the pls plsti# ti# e+trusi e+trusion on pro#ess pro#ess.. Answer. n plsti# e+trusion,  poly!er !elt is #o!pressed to flo" throu$h  die orifi#e nd thus the #ontinuous len$th of the plsti# ssu!es  #rossse#tionl shpe tht is ppro+i!tely the s!e s tht of the orifi#e.

13.7

&he brrel brrel nd nd s#re" of n e+truder e+truder re $enerlly $enerlly divided divided into into three three se#tions' se#tions' identif identify y the se#tion se#tions. s. Answer. &he se#tions re (1) the feed se#tion, in "hi#h the feed sto# is fed fro! the hopper nd heted' (2) the #o!pression se#tion, in "hi#h the poly!er #hn$es to  vis#ous fluid' nd (3) the !eterin$ se#tion, in "hi#h pressure is developed to pu!p the plsti# throu$h the die orifi#e.

13.8

Wht re re the fun#tio fun#tions ns of the the s#reen s#reen p# p# nd breer breer plte t t the die end of the e+truder e+truder brrel% brrel% Answer. &he fun#tions re to (1) filter dirt nd lu!ps, (2) build pressure, (3) stri$hten the flo" nd re!ove !e!ory of the poly!er !elt.

13.10 Wht re re the vrious vrious for!s for!s of e+truded e+truded shpes shpes nd #orrespondin #orrespondin$ $ dies% dies% Answer. &he shpes re (1) solid profiles, su#h s rounds nd 9shpes' (2) hollo" profiles, su#h s tubes' (3) "ire nd #ble #otin$' (*) sheet nd fil!' nd (5) fil!ents (#ontinuous fibers). :+#erpts fro! this "or !y be reprodu#ed by instru#tors for distribution on  notforprofit bsis for testin$ or instru#tionl purposes only to reproduction or translation of this work work beyond that permitted students enrolled in #ourses for "hi#h the te+tboo hs been dopted.  Any other reproduction by Sections 107 or 108 of the 1976 United States Copyriht Act without the permission of the copyriht owner is unlawful!

131

Solutions for Fundamentals of Modern Manufacturing , 5e (published by Wiley)  MPGroover 2012

13.11 13.11 Wht is is the distin distin#tion #tion bet"een bet"een plsti# plsti# sheet sheet nd fil!% Answer. &he distin#tion is bsed on thi#ness. Sheet sto# hs  thi#ness $reter thn 0.5 !! (0.020 in), "hile fil! sto# is less thn 0.5 !! (0.020 in) thi#.

13.12 Wht is is the blo"nfi blo"nfil! l! pro#ess pro#ess for produ#i produ#in$ n$ fil! fil! sto#% sto#% Answer. &he blo"nfil! pro#ess is  "idely used pro#ess for !in$ thin polyethylene fil! for  p#$in$.  p#$in$. t #o!bines #o!bines e+trusion e+trusion nd blo"in$ blo"in$ to produ#e produ#e  tube of of thin fil!. &he pro#ess pro#ess be$ins be$ins "ith the e+trusion of  tube tht is i!!editely dr"n up"rd "hile still !olten nd si!ultneously e+pnded in si;e by ir inflted into it throu$h the die !ndrel.

13.13 13.13 4es#rib 4es#ribee the #lend #lenderi erin$ n$ pro#es pro#ess. s. Answer. <lenderin$ is  pro#ess for produ#in$ sheet nd fil! sto# out of rubber or rubbery ther!oplsti#s su#h s plsti#i;ed P<. n the pro#ess, the initil feedsto# is pssed throu$h  series of rolls to "or the !teril nd redu#e its thi#ness to the desired $$e.

13.1* Poly!er Poly!er fibers nd fil!ents fil!ents re used in severl severl ppli#tio ppli#tions' ns' "ht is the !ost !ost i!portnt i!portnt #o!!er#il #o!!er#il ppli#tion% Answer. &e+tiles.

13.15 Wht is is the te#hni# te#hni#l l differen#e differen#e bet"een bet"een  fiber fiber nd  fil!ent% fil!ent% Answer.  fiber is  lon$, thin strnd of !teril "hose len$th is t lest 100 ti!es its di!eter'  fil!ent is  fiber of #ontinuous len$th.

13.1- !on$ the the syntheti# syntheti# fiber fiber !terils, !terils, "hi#h "hi#h re the !ost !ost i!portnt% i!portnt% Answer. Polyester is the !ost i!portnt #o!!er#illy, follo"ed by nylon, #ryli#s, nd ryon.

13.1 6riefly des#ribe des#ribe the the in=e#tio in=e#tion n !oldin$ !oldin$ pro#ess. pro#ess. Answer. n=e#tion !oldin$ is  pro#ess in "hi#h  poly!er is heted to  hi$hly plsti# stte nd for#ed to flo" under hi$h pressure into  !old #vity, "here it solidifies. &he !oldin$ is then re!oved fro! the #vity.

13.17 n in=e#tion!o in=e#tion!oldin$ ldin$ !#hine !#hine is divided divided into t"o prin#ipl prin#ipl #o!ponen #o!ponents. ts. !e the!. Answer. &he #o!ponents of n in=e#tion!oldin$ !#hine re (1) the in=e#tion unit nd (2) the #l!pin$ unit.

13.18 Wht re the the t"o bsi# types of #l!pin$ #l!pin$ units% units% to$$le #l!p nd (2) hydruli#. n ddition, there Answer. &he #l!pin$ units re> (1) !e#hni#l to$$le re hydro!e#hni#l units "hi#h #o!bine hydruli# nd !e#hni#l #tutions. 13.20 Wht is is the fun#ti fun#tion on of $tes $tes in in=e#tion in=e#tion !olds% !olds% Answer. &he fun#tion of $tes in n in=e#tion !old is to #onstri#t the flo" of !olten plsti# into the #vity, "hi#h in#reses the sher rte nd redu#es the vis#osity of the poly!er !elt.

13.21 Wht re the the dvnt$es dvnt$es of  threeplte threeplte !old over over  t"oplte t"oplte !old in in=e#tio in=e#tion n !oldin$% !oldin$% Answer. s the !old opens, the threeplte !old uto!ti#lly seprtes the !olded prt(s) fro! the runner syste!.

13.22 4is#uss 4is#uss so!e of the the defe#ts tht tht #n o##ur in in plsti# plsti# in=e#tion in=e#tion !oldin$. !oldin$. Answer. &he defe#ts in#lude (1) short shots, in "hi#h the poly!er !elt solidifies before fillin$ the #vity' (2) flshin$, in "hi#h the poly!er !elt is suee;ed into the prtin$ surf#es bet"een the !old hlves nd round e=e#tion pins' (3) sin !rs, in "hi#h the surf#e is dr"n into the !oldin$ :+#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 reproduction or translation of this work work beyond that permitted students enrolled in #ourses for "hi#h the te+tboo hs been dopted.  Any other reproduction by Sections 107 or 108 of the 1976 United States Copyriht Act without the permission of the copyriht owner is unlawful!

132

Solutions for Fundamentals of Modern Manufacturing , 5e (published by Wiley)  MPGroover 2012

 by #ontr#tio #ontr#tion n of intern internll !teril' !teril' nd nd (*) "eld "eld lines lines "here "here the the !elt hs hs flo"ed flo"ed round round  #ore #ore or other #onve+ detil in the !old #vity nd !et fro! opposite dire#tions, thus resultin$ in !e#hni#l  properties  properties tht tht re inferior inferior to those those in in the rest rest of the prt. prt. 13.23 13.23 4es#rib 4es#ribee stru#tur stru#turlfo lfo! ! !oldin$ !oldin$.. Answer. Stru#turlfo! !oldin$ is n in=e#tion !oldin$ pro#ess in "hi#h  $s or $sprodu#in$ in$redient is !i+ed "ith the poly!er !elt prior to in=e#tion into the !old #vity' this results in the  prt hvin$ hvin$  tou$h tou$h outer outer sin surrounded surrounded by by  fo! fo! #ore.

13.2* Wht re the si$nifi#nt si$nifi#nt differen#e differen#ess in the euip!ent nd opertin$ opertin$ pro#edures pro#edures bet"een bet"een in=e#tion in=e#tion !oldin$ of ther!oplsti#s nd in=e#tion !oldin$ of ther!osets% Answer. &he differen#es in in=e#tion !oldin$ of ther!osets re (1) shorter brrel len$th, (2) lo"er te!pertures in the brrel, these first t"o resons to prevent pre!ture #urin$' nd (3) use of  heted !old to #use #rosslinin$ of the &S poly!er.

13.25 13.25 Wht Wht is re#tio re#tion n in=e#ti in=e#tion on !oldin !oldin$% $% Answer. ?e#tion in=e#tion !oldin$ involves the !i+in$ of t"o hi$hly re#tive liuid in$redients nd i!!editely in=e#tin$ the !i+ture into  !old #vity "here #he!i#l re#tions ledin$ to solidifi#tion o##ur. &he t"o in$redients for! the #o!ponents used in #tlyst#tivted or !i+in$#tivted ther!oset syste!s.

13.2- Wht inds inds of produ#ts produ#ts re re produ#ed produ#ed by by blo" !oldin$% !oldin$% Answer. 6lo" !oldin$ is used to produ#e hollo", se!less #ontiners, su#h s bottles.

13.2 Wht is is the for! for! of the strtin$ strtin$ !teril !teril in ther!ofor ther!ofor!in$% !in$% Answer. &her!ofor!in$ strts "ith  ther!oplsti# sheet or fil!.

13.27 Wht is the the differen#e differen#e bet"een bet"een  positive positive !old nd nd  ne$tive ne$tive !old in ther!ofor ther!ofor!in$% !in$% Answer.  positive !old hs  #onve+ shpe'  ne$tive !old hs  #on#ve #vity.

13.28 Why re the !olds !olds $enerlly $enerlly !ore #ostly #ostly in !e#hni#l !e#hni#l ther!ofor!in$ ther!ofor!in$ thn thn in pressure pressure or v#uu! ther!ofor!in$% Answer. n !e#hni#l ther!ofor!in$, !t#hin$ !old hlves re reuired' "hile in other ther!ofor!in$ pro#esses, only one !old for! is reuired.

13.30 Wht re re the pro#esse pro#essess by "hi#h "hi#h poly!er poly!er fo!s fo!s re produ#ed produ#ed%% Answer. &here re severl fo!in$ pro#esses> (1) !e#hni#l $ittion  !i+in$  liuid resin "ith ir, then hrdenin$ the poly!er by !ens of het or #he!i#l re#tion' (2) !i+in$  physi#l  blo"in$  blo"in$ $ent $ent "ith "ith the poly!er poly!er   $s su#h s nitro$en nitro$en (2) or pentne (< 512) "hi#h #n be dissolved in the poly!er !elt under pressure, so tht the $s #o!es out of solution nd e+pnds "hen the pressure is subseuently redu#ed' nd (3) !i+in$ the poly!er "ith #he!i#l #o!pounds, #lled #he!i#l blo"in$ $ents, tht de#o!pose t elevted te!pertures to liberte $ses su#h s <@2 or 2 "ithin the !elt.

13.31 Wht re so!e of the $enerl $enerl #onsiderti #onsidertions ons tht produ#t produ#t desi$ners desi$ners !ust !ust eep in !ind "hen desi$nin$ #o!ponents out of plsti#s% Answer. So!e of the $enerl #onsidertions re the follo"in$> (1) Plsti#s re not s stron$ or stiff s !etls nd should not be used in ppli#tions "here hi$h stresses "ill be en#ountered. (2) !p#t resistn#e of plsti#s is $enerl $ood, better thn !ny #er!i#s. (3) Servi#e te!pertures of plsti#s re li!ited reltive to en$ineerin$ !etls nd #er!i#s. (*) &her!l e+pnsion is $reter for plsti#s thn !etls' so di!ensionl #hn$es due to te!perture vritions re !u#h !ore si$nifi#nt thn for !etls. (5) Mny types of plsti#s de$rde fro! sunli$ht nd #ertin other for!s of rdition. :+#erpts fro! this "or !y be reprodu#ed by instru#tors for distribution on  notforprofit bsis for testin$ or instru#tionl purposes only to reproduction or translation of this work work beyond that permitted students enrolled in #ourses for "hi#h the te+tboo hs been dopted.  Any other reproduction by Sections 107 or 108 of the 1976 United States Copyriht Act without the permission of the copyriht owner is unlawful!

133

Solutions for Fundamentals of Modern Manufacturing , 5e (published by Wiley)  MPGroover 2012

lso, so!e plsti#s de$rde in o+y$en nd o;one t!ospheres. Ainlly, plsti#s re soluble in !ny #o!!on solvents.

Problems ns"ers to proble!s lbeled A! re listed in n ppendi+ ppendi+ t the b# of the boo. E"trusion

13.1

A! (S units) &he di!eter of n e+truder brrel B 75 !! nd its len$th B 2.00 !. &he s#re" rottes t 55 revC!in, its #hnnel depth B 7.0 !!, nd its fli$ht n$le B 17 . ed pressure t the die end of the brrel B 10.0 + 10 - P. is#osity of the poly!er !elt B 100 Ps. Aind the volu!e flo" rte of  plsti#  plsti# t the the die end end of the the brrel. brrel.

 B 0.5# 2 $2 % d c sin A #os A B 0.52(75+103)2(55C-0)(7+10 3)sin 17 #os 17 Solution> "d  B B 2-1,*-2 + 10 8(0.3080)(0.8510) B -.73 + 10 - !3Cs  p B 10.0 + 10 - P B 10 + 10 - C!2 "b B p#$d c3sin2 AC(12&') B (10 + 10-)(75+103)(7+103)3(sin 17)2C12(100)(2.00) B 5*.*0(10 -) !3Cs " ( B -.73 + 10 - !3Cs  5*.*0 + 10 - !3Cs B ##$%3 " 1&'( m3)s 13.2

(/S
13.3

A! (/S
 B 0.5# 2 $2 % d c sin A#os A B 0.5 2(3.0)2(1)(0.25)sin 1.5 #os 1.5 Solution> "d  B B 11.103(0.300)(0.853) B 3.17* in 3Cse# (700)(3.0)(0.25) 3(sin 1.5)2C12(130 +10*)(0) B 0.85 in 3Cse# "b B  (700)(3.0)(0.25) " ( B 3.17*  0.85 B #$#&- in3)se, 13.*

(S units) units) &he &he di!eter di!eter of n e+truder e+truder brrel brrel B 100 !! nd its its len$th len$th B 2.2.- !. S#re" S#re" #hnnel #hnnel depth depth B .0 !!, nd its pit#h B 85 !!. &he vis#osity of the poly!er !elt B 105 Ps, nd hed pressure in the brrel B *.0 MP. Wht rottionl speed of the s#re" is reuired to #hieve  volu!etri# flo" rte of 80 #! 3Cs%  pC(#$)) B tn1(85C100 ) B 1-.7 Solution> A B tn1( p  B 0.5# 2 $2 % d c sin A#os A B 0.52(0.100)2( % )(.0 )(.0 + 103)sin 1-.7 #os 1-.7 B 85.  %  +  + 10- !3Cs "d  B (*+10-)(0.100)(+10 3)3(sin 1-.7)2C12(105)(2.-) B 11.02 + 10 - !3Cs "b B p#$d c3sin2 AC(12&') B  (*+10   "b B 85. %  +  + 10  F 11.02 + 10 - B 80 + 10- !3Cs " ( B "d   85. %  B  B 80.0  11.02 B 101.02  B 101.02C85. B 1$&.( rev)s / (3$3 rev)min  %  B

13.5

(/S
:+#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 reproduction or translation of this work work beyond that permitted students enrolled in #ourses for "hi#h the te+tboo hs been dopted.  Any other reproduction by Sections 107 or 108 of the 1976 United States Copyriht Act without the permission of the copyriht owner is unlawful!

13*

Solutions for Fundamentals of Modern Manufacturing , 5e (published by Wiley)  MPGroover 2012

 B 0.5# 2 $2 %d c sin A #os A B 0.5# 2(3.52)(55C-0)(0.25)sin 20 #os 20 B *.*5 in 3Cse# Solution* "d  B "b B "d  F  F " ( B *.*5 F 2.50 B 1.85 in 3Cse# (3.5)(0.253)sin2(20)C(12(1.85)()(12)) B &$&&. lb's)in# & B p#$d c3 in2 AC(12 "b '  ') B 500# (3.5)(0.25 13.13.-

4ete 4eter! r!in inee the the heli heli+ + n$ n$le le A t "hi#h the s#re" pit#h  p is eul to the s#re" di!eter  $. &his is #lled the HsureH n$le in plsti#s e+trusion  the n$le tht provides  fli$ht dvn#e eul to one di!eter for e#h rottion of the s#re". Solution> ssu!e fli$ht lnd B ;ero. Aro! :. (15.*), tn A B pit#hC  $ f pit#h B $, then A B tn1(1C ) / 10$((

13.

(S units) units) n e+truder e+truder brrel brrel hs hs di!eter di!eter B 70 70 !! nd nd len$th len$th B 2.0 !. ts s#re" s#re" hs hs  #hnnel #hnnel depth B - !!, fli$ht n$le B 17 de$rees, nd it rottes t 1 revCse#. &he plsti# !elt hs  vis#osity B 150 Ps. 4eter!ine the e+truder #hr#teristi# by #o!putin$ "!+ nd p!+ nd then findin$ the liner eution definin$ the stri$ht line bet"een the!.  B 0.5# 2 $2 % d c sin A#os A B 0.52(0.07)2(1)(- +103)sin 17 #os 17 Solution> "ma( B "d  B B 0.1785 + 10 3(0.3080)(0.8510) B 55. + 10 - !3Cs  pma( B - $%'& #ot ACd c2 B -(0.07)(1)(2)(150)(#ot 17)C(-+10 3)2 B *52.*(3.0)C3-+10 - B 37.- + 10 - P B 37.- MP " ( B 55. + 10-  (55. +10 -C37.-) p Q x  /  / ..$0 " 1&'( ' 1$%% " 1&'( p, "here p hs units of MP nd " ( hs units of ! 3Cs

13.7

A! (/S A B tn1(pit#hC   $) B tn1(*.7C*.5 ) B 17.5  B 0.5# 2 $2 %d c sin A #os A B 0.52(*.5)2(1)(0.25)sin 17.5 #os 17.5 "d  B B 2*.87(0.321*)(0.8*-8) B .-02 in 3Cse# B *5-.1 in 3C!in   "b B *5-.1  "d  B  B 15 " ( B "d   "b B *5-.1  15 B 271.1 in 3C!in B *.-7- in 3Cse#  ' B *.5(22) B 88 in "b B p#$d c3sin2 AC(12&') B   p(*.5)(0.25) 3(sin 17.5) 2C(12(50+10*)(88)) B *.-70.0037*2 p B *.-7 p /  p / 1##& lb)in#

13.8

(/S "d  B B 1-.*5(0.25-)(0.8-13) B *.357 in 3Cse# (350)(*)(.25) 3(sin 1-) 2C(12(70+10*)(120)) B 0.*53 in 3Cse# "b B p#$d c3sin2 AC(12&') B  (350)(*)(.25) " ( B *.357  0.*53 B 3.805 in 3Cse#.  A ( B 0.25(22  1.2) B 0.72 in 2 ) ( B 3.805C0.72 B %$%0+ in)se, / ##$3- t)min

13.10 (/S
135

Solutions for Fundamentals of Modern Manufacturing , 5e (published by Wiley)  MPGroover 2012

nd len$th B 10 ft. &he s#re" rottes t -0 revC!in' it hs  #hnnel depth B 0.30 in nd fli$ht n$le B 1-. &he hed pressure hs  vlue of 00 lbCin 2 nd the vis#osity of the poly!er !elt is 80 + 10 * lbse#Cin 2.  die s"ell rtio of 1.20 is observed in the e+trudte. /nder these #onditions, deter!ine () the outside nd inside di!eters of the finl tubin$ nd (b) the produ#tion rte in len$th of tubeC!in. Solution> () 4ie s"ell rtio B 1.2, *$ B 2.5(1.2) B 3.0 in nd  +$ B 2.0(1.2) B 2.* in

(b) "d  B  B 0.5# 2 $2 %d c sin A #os A B 0.5 2(5)2(-0C-0)(0.3)sin 1- #os 1B 3.0(0.25-)(0.8-13) B 8.705 in 3Cse# (00)(5)(0.3) 3(sin 1-) 2C(12(80 +10*)(120)) B 1.*0 in 3Cse# "b B p#$d c3sin2 AC(12&') B  (00)(5)(0.3) " ( B 8.705  1.*0 B 7.0-5 in 3Cse#  A ( B 0.25(3.02  2.*2) B 2.5*5 in 2 ) ( B 7.0-5C2.5*5 B 3$1(- in)se, / 1.$+% t)min 13.11 A! (S units) n e+truder hs  brrel di!eter nd len$th of 100 !! nd 2.7 !, respe#tively. &he s#re" rottes t 50 revC!in, its #hnnel depth B .5 !!, nd its fli$ht n$le B 1 . &he plsti# !elt hs  sher vis#osity B 15 Ps. 4eter!ine () the e+truder #hr#teristi#, (b) the shpe f#tor  ,  s for  #ir#ulr die openin$ "ith di!eter B 3.0 !! nd len$th B 12.0 !!, nd (#) the opertin$ point ( " nd p).  B 0.5 2(.1)2(50C-0)(.5+10 3) sin 1 #os 1 B 307.* + 10 -(0.282*)(0.85-3) Solution> () "ma( B "d  B B 7-.2 + 10- !3Cs (.1)(50C-0)(2.7)(15)(#ot 1)C(.5+10 3)2 B **.5 + 10 - P B**.5 MP  pma( B - (.1)(50C-0)(2.7)(15)(#ot Q x  /  / +($# " 1&'( ' 1$-#( " 1&'1# p, "here p hs units of P (b) Given> $d  B  B 3 !!, 'd  B  B 12 !!. *  B (3 + 103)*C(127(15)(12 + 10 3)) B &$-%(0 " 1&'1# m.)Ns  ,  s B  $d  C127&'d  B (#) 0.8*- + 1012 p B 7-.2 + 10 -  1.82- + 1012 p 2.72 + 1012 p B 7-.2 + 10 p B 3&$& " 1&( P2 B 3& P2 " ( B 0.8*- + 1012 (30 + 10-) B #+$% " 1&'( m3)s  "ith e+truder #hr#teristi#> " ( B 7-.2 + 10-  1.82- + 1012 (30 + 10-) B 27.* + 10 - !3Cs C4e,5  "ith 13.12 (/S () "ma( B 0.52(*.5)2(1)(0.35)sin 20 #os 20 B 3*.85(0.3*2)(0.838) B 11.2* in 3Cse#  pma( B -(*.5)(1)(132)(0.0125)(#ot 20)C(0.35) 2 B 313- lb)in#

(b) Given> $d  B  B 0.312 in, 'd  B  B 0.5 in *  B  (0.312) (0.312)*C127(0.0125)(0.5) B  &$&#%+&+ in.)lb'se,  ,  s B  $d  C127&'d  B (#) Aro! (), " ( B "ma(  ("ma(C p  pma() p  p B 11.2*  0.003571 p Aro! (b), " ( B 0.02*707 p
13-

Solutions for Fundamentals of Modern Manufacturing , 5e (published by Wiley)  MPGroover 2012

sher vis#osity B 100 + 10 * lbse#Cin 2. Aind () the e+truder #hr#teristi#, (b) the vlues of " nd p t the opertin$ point if the die #hr#teristi# is " ( B 0.00150 p. Solution> () "ma( B 0.5 2(5)2(50C-0)(0.3)sin 1. #os 1. B 30.7*(0.30*0)(0.852) B 7.83 in 3Cse# (5)(50C-0)(1**)(0.01)(#ot 1.)C(0.3) 2 B 383.- lbCin 2  pma( B - (5)(50C-0)(1**)(0.01)(#ot " ( B "ma(  ("ma(C p  pma() p  p B +$-3 ' &$&&##(+ p

(b) Given die #hr#teristi# defined by " ( B 0.0015 p " ( B 7.83  0.0022-7 p B 0.0015 p 0.003 p B 7.83  p B #30& lb)in# " ( B 7.83  0.0022-7(230) B  3$.. in3)se, 13.1* (/S &he uthorIs spredsheet #o!puttions returned n opti!u! vlue of 13.5 .

13.15 (/S () "ma( B 0.5# 2 $2 %d c sin A #os A B 0.5 2(*.0)2(5C-0)(0.2-)sin 20 #os 20 B 18.*(0.3*20)(.838) B -.3** in 3Cse# (*.0)(5C-0)(7*)(0.00-5)(#ot 20)C(0.2-) 2 B 3535 lbCin 2  pma( B -#$%'& #ot ACd c2 B- (*.0)(5C-0)(7*)(0.00-5)(#ot " ( B "ma(  ("ma(C p  pma() p  p B -.3** F (-.3**C3535) p BQ x  =  = ($3%% ' &$&&10-. p &$&&10-. p, "here p hs units of 2 3 lbCin  nd " ( hs units of in Cse#

(b) Given /shped #ross se#tion e+truded t 0.1* lbCse# 4ensity of poly!er    B  B spe#ifi# $rvity of poly!er +  -water B1.2(-2.* lbCft 3) B 5 lbCft 3  -B 5 lbCft 3C(123 in3Cft3) B 0.0*33 lbCin 3 " ( B 0.11C0.0*33 B 2.5*0 in 3Cse# 2.5*0 B -.3**  0.00185  p 0. 00185 p B -.3** F 2.5*0 B 3.70*  p /  p / #11- lb)in # (#) " ( B ,  s p  ,  s B " (C p  p B 2.5*0C2118 B 0.0012 Q x  /  / &$&&1# p &$&&1# p In6e,tion ol7in8

13.1- A! (S units) @ne of the di!ensions spe#ified for n in=e#tion !olded prt !de of ylon-,- B 150.00 !!. S  B  $c B 150.00  150.00(0.00-)  150.00(0.00-) 2 B 150.00  3.00  0.0- B 1.3$&( mm 13.1 (/S
13

Solutions for Fundamentals of Modern Manufacturing , 5e (published by Wiley)  MPGroover 2012

 B 0.00 for poly#rbonte fro! &ble 13.1. Solution> S  B  $c B *.00  *.00(0.00)  *.00(0.00) 2 B *.00  0.027  0.0002 B %$&#+# in 13.17 (S units) units) &he fore!n in the the in=e#tion in=e#tion !oldin$ !oldin$ deprt!ent deprt!ent sys tht tht  polyethylene polyethylene prt produ#ed produ#ed in one of the opertions hs $reter shrin$e thn the #l#ultions indi#te it should hve. &he i!portnt di!ension of the prt is spe#ified s 112.5 0.25 !!. o"ever, the #tul !olded prt !esures 112.02 !!. () s  first step, the #orrespondin$ !old #vity di!ension should be #he#ed. () Given> S  B (b) d=ust!ents to redu#e shrin$e in#lude> (1) in#rese in=e#tion pressure, (2) in#rese #o!p#tion ti!e, nd (3) in#rese !oldin$ te!pertures. 13.18 (/S Aor polyethylene the shrin$e B 0.025 inCin fro! &ble 2 4ie <vity B  $c B $ p  $ pS     $ pS   B 3.000  3.000 (0.025)  3.000 (0.025) 2 B 3.0 in Aor polystyrene, polystyrene, the shrin$e is 0.00* inCin Prt di!ension B  $cC(1  S     S 2) B 3.0C(1  0.00*  0.00* 2) B 3$&(. in 13.20 (/S Aor polyethylene the density B 0.033 lbCin 3 fro! &ble *.1 olu!e of e#h prt plus pportioned sprue nd runner B 0.57  0.*0C* B 0.-7 in 3 Wei$ht of e#h prt plus pportioned sprue nd runner B 0.-7(0.033) B 0.022** lb
13.21 n in=e#tion in=e#tion !oldin$ !oldin$ opertion opertion is produ#in$ produ#in$ prts prts "ith flshin$. flshin$. n ddition, ddition, so!e of the prt di!ensions re oversi;ed, indi#tin$ tht either the #orrespondin$ !old di!ensions re too lr$e or  prt shrin shrin$e $e is less less thn thn nti#ipted nti#ipted.. 6t#hes 6t#hes of this this prt hve been been produ#ed produ#ed severl severl ti!es before before "ithout these ulity proble!s, so the !old !ust be #orre#tly si;ed. Me so!e re#o!!endtions tht !i$ht llevite the proble!s. Solution> Alsh on plsti# !oldin$s #n be #used by vents nd #lern#es in the !old tht re too lr$e. o"ever, be#use the prts hve been produ#ed before "ithout these proble!s, this possible #use #n be ruled out. @ther possible resons for flsh in#lude (1) hi$h in=e#tion pressure #o!pred to #l!pin$ for#e, (2) !elt te!pertures tht re too hi$h, nd (3) e+#essive !ount of  poly!er !elt in=e#ted into into the !old #vity. #vity. &hus, re#o!!endtions re#o!!endtions in#lude (1) redu#e in=e#tion in=e#tion  pressure or in#rese #l!pin$ #l!pin$ for#e, or both, (2) redu#e !elt te!pertures te!pertures in brrel, nd (3) redu#e :+#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 reproduction or translation of this work work beyond that permitted students enrolled in #ourses for "hi#h the te+tboo hs been dopted.  Any other reproduction by Sections 107 or 108 of the 1976 United States Copyriht Act without the permission of the copyriht owner is unlawful!

137

Solutions for Fundamentals of Modern Manufacturing , 5e (published by Wiley)  MPGroover 2012

shot si;e per #y#le. &hese #hn$es should lso brin$ the shrin$e of the prt #loser to the nti#ipted vlue. Ot4er ol7in8 O9er2tions 2n7 T4ermoormin8

13.22 A! (S units) &he e+trusion die for  polyethylene prison used in blo" !oldin$ hs  !en di!eter of 20.0 !!. &he si;e of the rin$ openin$ in the die B 2.0 !!. &he !en di!eter of the  prison  prison is observed observed to s"ell s"ell to  si;e of of 23.0 !! fter e+itin$ e+itin$ the die orifi#e. orifi#e. f f the di!eter di!eter of the  blo"!olded  blo"!olded #ontiner #ontiner B 125 125 !!, deter!in deter!inee () the the #orrespond #orrespondin$ in$ "ll "ll thi#ness thi#ness of the finl #ontiner nd (b) the inside di!eter of the prison.  B 23C20 B 1.15 Solution> () r  s B $ pC $  $d  B t m B t  p $ pC $  $m B r  s t d d  $  $ pC $  $m B (1.15)(2.0)(23)C125 B  &$%#3 mm (b) t  p B r  s t d d  B  B (1.15)(2.0) B 2.3 !! Men di!eter of the prison B 23.0 !!, so !en rdius  +. B 23.0C2 B 11.5 !! nside rdius B !en rdius !inus onehlf "ll thi#ness B 11.5 F 2.3C2 B 10.35 !! Prison +$ B 2( +.  +.) B 2(10.35) B #&$0 mm 13.23 (S units) units)  prison prison is e+truded e+truded fro!  die "ith outside outside di!eter di!eter B 11.5 !! nd inside inside di!eter di!eter B .5 !!. &he observed die s"ell B 1.25. &he prison is used to blo" !old  bever$e #ontiner "hose outside di!eter B 112 !! ( stndrd si;e 2liter sod bottle). () Wht is the #orrespondin$ "ll thi#ness of the #ontiner% (b) @btin n e!pty 2liter plsti# sod bottle nd (#refully) #ut it #ross its di!eter. /sin$  !i#ro!eter, !esure the "ll thi#ness to #o!pre "ith your ns"er in ().  B (11.5  .5)C2 B 8.5 !!, nd t d d  B  B (11.5  .5)C2 B 2.0 !! Solution> () $d  B 2 t m B (1.25) (2.0)(8.5)C112 B  &$#(. mm / &$&1& in! (b) Mesured vlue should be #lose to #l#ulted vlue. So!e "ll thi#nesses re less. 13.2* (/S
(b) $d  B  B $ pCr  s B 0.778C1.22 B &$0#- in 13.25 (S units) units) n e+trusion e+trusion opertio opertion n produ#es produ#es  prison "hose "hose !en di!eter di!eter B 25 !!. &he inside nd outside di!eters of the e+trusion die re 17 !! nd 22 !!, respe#tively. f the !ini!u! "ll thi#ness of the blo"!olded #ontiner is to be 0.*0 !!, "ht is the !+i!u! possible di!eter of  the blo" !old%  B (22  17)C2 B 20 !!, nd t d d B Solution> $d  B   B (22  17)C2 B 2 !! r  s B 25C20 B 1.25 2 ?errn$in$ :. (13.22) in te+t,  $m B r  sd 2t d d $   d Ct m B (1.25) (2)(20)C(0.*0) B 1.($#. mm 13.2- (S units) units) n in=e#tion in=e#tion !oldin$ !oldin$ opertion opertion produ#es produ#es  prison prison "hose "hose outside di!eter di!eter B 20 !! nd "ll thi#ness B *.0 !!. &he #orrespondin$ di!ensions of the !old #vity re the s!e. f the di!eter of the blo" !old #vity B 150 !!, "ht is the "ll thi#ness of the blo"!olded #ontiner% Solution> E $ pt  p B E $mt m so $ pt  p B $mt m ?errn$in$, t m B $ pt  pC $  $m B 20(*.0)C150 B &$.33 mm

13.2 (/S
138

Solutions for Fundamentals of Modern Manufacturing , 5e (published by Wiley)  MPGroover 2012

PP !oldin$ #o!pound should be loded into the !old in order to !eet these spe#ifi#tions% &he spe#ifi# $rvity of the PP $rde B 0.80 (the density of "ter B -2.* lbCft 3).  B spe#ifi# $rvity of poly!er +  -water B 0.80(-2.* lbCft 3) B 5-.2 lbCft 3 Solution> 4ensity    B  - B 5-.2 lbCft 3C(127 in3Cft3) B 0.0325 lbCin 3 olu!e B  ( $ K(1.00 + 12) 3C- (1.00 +12  2C7) 3L B 55.37 in 3  $o3  $i3)C- B  K(1.00 Wei$ht /  B  B (55.37)(0.0325) B 1$+& lb 13.27 &he proble! proble! in  ther!ofor!in$ ther!ofor!in$ opertion opertion is tht tht there is too !u#h thinnin$ thinnin$ in the the "lls of the lr$e lr$e #upshped prt. &he opertion is #onventionl pressure ther!ofor!in$ usin$  positive !old, nd the plsti# is n 6S sheet "ith n initil thi#ness of 3.2 !!. () Why is thinnin$ o##urrin$ in the "lls of the #up% (b) Wht #hn$es #ould be !de in the opertion to #orre#t the proble!% Solution> () s the strtin$ flt sheet is drped over the #onve+ #upshped !old, the portion #ont#tin$ the bse of the #up e+perien#es little stret#hin$. o"ever, the re!inin$ portions of the sheet !ust be stret#hed si$nifi#ntly to #onfor! to the sides of the #up. en#e, thinnin$ in these sides results.

(b) &he proble! #ould be solved by either (1) fbri#tin$  ne$tive !old to repl#e the #urrent  positive  positive !old, !old, sin#e sin#e  ne$tive ne$tive !old "ill "ill distribu distribute te the !teril !teril !ore unifor!ly unifor!ly nd result in ppro+i!tely eul thinnin$ throu$hout the sheet' or (2) prestret#h the sheet s in Ai$ure 13.37 in the te+t.

:+#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 reproduction or translation of this work work beyond that permitted students enrolled in #ourses for "hi#h the te+tboo hs been dopted.  Any other reproduction by Sections 107 or 108 of the 1976 United States Copyriht Act without the permission of the copyriht owner is unlawful!

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