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

32 RAPID PROTOTYPING AND ADDITIVE MANUFACTURING Review Questions 32.1 32.1

Wht Wht is rpid rpid prototy prototypin pin!" !" Provi Provide de  defin definiti ition on of the the ter# ter#.. Answer. $pid prototypin! %onsists of  f#ily of fbri%tion pro%esses developed to #&e en!ineerin! prototypes in #ini#u# possible led ti#es bsed on  %o#puter'ided desi!n (*) #odel of the ite#.

32.2 32.2

Wht Wht re the three three types types of str strtin tin! ! #teri #terils ls in in rpid rpid prot prototy otypin pin!" !" Answer. +he three types of strtin! #terils in $P re (1) liuid, (2) solid, nd (3) po-ders.

32.3

esides the strtin! strtin! #teril #teril,, -ht -ht other other feture distin!uis distin!uishes hes the rpid rpid prototypin! prototypin! te%hnolo!ies te%hnolo!ies"" Answer. +he prt'build pro%ess lso distin!uishes the different $P te%hnolo!ies. So#e te%hniues use lsers to solidify the strtin! liuid, -hile others bond the solid lyers of sheet, nd still others bond the the po-ders po-ders to!ether to!ether..

32./

Wht is the the %o##on %o##on ppro% ppro%h h used used in ll of of the #teril #teril ddition ddition te%hnolo!i te%hnolo!ies es to prepre prepre the %ontrol instru%tions for the $P syste#" Answer. +he tet des%ribes the %o##on ppro%h s  three step pro%ess (1) Geo#etri% #odelin!, -hi%h %onsists of #odelin! the %o#ponent on  * syste# to define its en%losed volu#e (2) tesselltion of the !eo#etri% #odel, in -hi%h the * #odel is %onverted into  for#t tht pproi#tes its surf%es by f%ets (trin!les or poly!ons) nd (3) sli%in! of the #odel into lyers tht pproi#te the solid !eo#etry.

32.5 32.5

f ll of of the %urren %urrentt rpid rpid protot prototypi ypin! n! te%hn te%hnolo olo!ie !ies, s, -hi%h -hi%h one one is the #ost #ost -ide -idely ly used" used" Stereolitho!rphy. Answer. Stereolitho!rphy.

32.4 32.4

*es%ri *es%ribe be the $P te%hno te%hnolo! lo!y y %ll %lled ed solid solid !round !round %urin! %urin!.. Answer. Solid !round %urin! -or&s by %urin!  photosensitive poly#er lyer by lyer to %rete  solid #odel bsed on * !eo#etri% dt. nsted of usin!  s%nnin! lser be# to %%o#plish the %urin! of  !iven lyer, the entire lyer is eposed to n ultrviolet li!ht sour%e throu!h  #s& tht is positioned bove the surf%e of the liuid poly#er.

32.6 32.6

*es%ri *es%ribe be the the $P te%hno te%hnolo! lo!y y %lled %lled l#int l#inted' ed'ob7 ob7e%t e%t #nu #nuf% f%turi turin!. n!. Answer. 8#inted ob7e%t #nuf%turin! produ%es  solid physi%l #odel by st%&in! lyers of sheet sto%& tht re e%h %ut to n outline %orrespondin! to the %ross'se%tionl shpe of  * #odel tht hs been sli%ed into lyers. +he lyers re bonded one on top of the previous prior to %uttin!. fter %uttin!, the e%ess #teril in the lyer re#ins in pl%e to support the prt durin! buildin!. buildin!. Strtin! Strtin! #teril #teril in 8M 8M %n be be virtully virtully ny ny #teril #teril in sheet sto%& sto%& for#, for#, su%h su%h s pper, pper, plsti%, plsti%, %ellulose %ellulose,, #etls, #etls, or fiber're fiber'reinfor%e infor%ed d #terils. #terils. Sto%& Sto%& thi%&nes thi%&nesss is 0.05 0.05 to 0.50 ## (0.002 to 0.020 in).

32.9 32.9

Wht Wht is the strti strtin! n! #teri #teril l in in fuse fused'd d'depo eposit sition ion #od #odeli elin!" n!" Answer. +he strtin! #teril is  lon! fil#ent of - or poly#er.

Probe!s ns-ers to proble#s lbeled "A# re listed in n ppendi ppendi t the b%& of the boo&. :%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!

32'1


32.1

stereolitho!rphy. "A# (S units)  tube -ith  re%tn!ulr %ross se%tion is to be fbri%ted by stereolitho!rphy. utside di#ensions of the re%tn!le re /0 ## by 60 ##, nd the %orrespondin! inside di#ensions re 32 ## by 42 ## (-ll thi%&ness ; / ## # # e%ept t %orners). +he hei!ht of the tube ( " 'dire%tion) 'dire%tion) ; 50 ##. 8yer thi%&ness ; 0.10 ##, nd lser spot di#eter ; 0.25 ##. +he be# velo%ity %ross the the surf%e of the photopoly#er photopoly#er ; 650 ##9/ ; 914 ## 2 +i#e to %o#plete one lyer # i s#e for ll lyers. # i ; (914 ##2)<(0.25 ##)(650 ##
32.2 32.2

(S uni units) ts) Solv Solvee Proble Proble# # 32.1, 32.1, e%ep e%eptt tht tht the lye lyerr thi%&n thi%&ness ess ; 0.20 0.20 ##. $oution 8yer re Ai s#e for ll lyers. Ai ; /0(60) = 32(42) ; 2900 = 1>9/ ; 914 ## 2 +i#e to %o#plete one lyer # i s#e for ll lyers. # i ; (914 ##2)<(0.25 ##)(650 ##
32.3

(S units) units) +he prt prt in in Proble# Proble# 32.1 32.1 is is fbri%t fbri%ted ed usin! usin! fused fused depositio deposition n #odelin #odelin! ! insted insted of stereolitho!rphy stereolitho!rphy. 8yer thi%&ness ; 0.25 ##, nd the -idth of the etrudte deposited on the surf%e of the prt ; 0.65 ##. +he etruder -or& hed #oves in the $%y plne t  speed of 300 ##9/ ; 914 ## 2 +i#e to %o#plete one lyer # i s#e for ll lyers. # i ; (914 ##2)<(0.65 ##)(300 ##
32./

(S units) units) Solve Proble# Proble# 32.3, 32.3, e%ept e%ept the follo-i follo-in! n! dditi dditionl onl infor#ti infor#tion on is &no-n &no-n +he di#eter of the fil#ent fed into the etruder -or& hed is 1. 5 ##, nd the fil#ent is fed into the -or& hed fro# its spool t  rte of 31.65 ## of len!th per se%ond -hile the -or& hed is depositin! #teril. et-een lyers, the feed rte fro# the spool is Bero. $oution ross'se%tionl re of fil#ent ;  &29/ ; 914 ## 2 +i#e to %o#plete one lyer # i s#e for ll lyers. Prt volu#e ; prt %ross se%tionl re #ultiplied by hei!ht ; Aih Prt volu#e ' ; ; 914(50) ; /0,900 ##3 @u#ber of lyers nl ; ; (50 ##)<(0.25 ##
32.5

D150
:%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!

32'2


rte ; D30.00
32.4

(ASS units units)) 3* Print Printin! in! is is us used ed to fbri%te fbri%te  prototype prototype prt prt -hose -hose totl totl volu#e volu#e ; 1.16 in 3, hei!ht ; 1.22 in nd bse re ; 1.62 in 2. +he printin! hed is 5 in -ide nd s-eeps %ross the 10' in -or&tble in 3 se% for e%h lyer. $epositionin! $epositionin! the -or&tble hei!ht, re%otin! po-ders, nd returnin! the printin! hed for the net lyer t&e 13 se%. 8yer thi%&ness ; 0.005 in. o#pute n esti#te for the ti#e reuired to build the prt. !nore setup ti#e. $oution :%h s-eep of the printin! hed %o#pletes the lyer for#tion pro%ess for the prt. +he re of the bse lyer nd volu#e of the prt re irrelevnt. 8yer thi%&ness t ; ; 0.005 in @u#ber of lyers ni ; 1.22 in<(0.005 ##
32.6

(S units) units)  %one's %one'shped hped prt prt is to be fbri%te fbri%ted d usin! usin! stereoli stereolitho!r tho!rphy phy.. +he rdius rdius of of the %one %one t its bse ; /0 ##, nd its hei!ht ; /0 ##. +o #ini#iBe the stir%se effe%t, lyer thi%&ness ; 0.05 ##. +he di#eter of the lser be# ; 0.22 ##, nd the be# is #oved %ross the surf%e of the photopoly#er t  velo%ity velo%ity of 1000 ##
32.9

(S units) units) +he %one'sh %one'shped ped prt prt in Proble# Proble# 32.4 is built built usin! usin! l#inted' l#inted'ob7e ob7e%t %t #nuf%t #nuf%turin urin!. !. 8yer thi%&ness ; 0.20 ##. +he lser be# %n %ut the sheet sto%& t  velo%ity of 500 ##

32'3


32.>

(S units) units) Stereo Stereolith litho!rp o!rphy hy is to be used used to build build the prt in in Fi!ure Fi!ure 32.1 32.1 in the the tet. tet. *i#ensions *i#ensions of the prt re hei!ht ; 125 ##, outside di#eter ; 65 ##, inside di#eter ; 45 ##, hndle di#eter ; 12 ##, hndle distn%e fro# %up ; 60 ## #esured fro# %enter (is) of %up to %enter of hndle. +he hndle brs %onne%tin! the %up nd hndle t the top nd botto# of the prt hve  re%tn!ulr %ross se%tion nd re 10 ## thi%& nd 12 ## -ide. +he thi%&ness t the bse of the %up is 10 ##. +he lser be# di#eter ; 0.25 ##, nd the be# %n be #oved %ross the surf%e of the photopoly#er t ; 2000 ## ? 113.1 ? (3>0.0 = 54.5) ; /94/.5 ## 2 re (2) A2 ; (652 = 452)>.4 ? 113.1 ; 1212.6 ## 2 re (3) A3 ; (652 = 452)>.4 ?113.1 ? (3>0.0 = 54.5) ; 15/4.2 ## 2

@u#ber of lyers for e%h re (1) nl 1 ; (10 ##)<(0.1 ##.63 ? 30 ; 3>.63 s (2) # i2 ; (1212.6 ##2)<(0.25  2000) ? 30 ; 2./3 ? 30 ; 32./3 s (3) # i3 ; (15/4.2 ##2)<(0.25  2000) ? 30 ; 3.0> ? 30 ; 33.0> s +otl ti#e for ll lyers # c ; 100(3>.63) ? 1050(32./3) ? 100(33.0>) # c ; /%&33/ s ) (--+, !in ) %%+/- .r 32.10

stereolitho!rphy. +he prt is shped "A# (S units)  prototype of  prt is to be fbri%ted usin! stereolitho!rphy. li&e  ri!ht trin!le -hose bse ; 34 ##, hei!ht ; /9 ##, nd thi%&ness ; 25 ##. n ppli%tion, the prt -ill stnd on its bse, -hi%h is 34 ## by 30 ##. n the stereolitho!rphy pro%ess, the lyer thi%&ness thi%&ness ; 0.15 ##. *i#eter of the lser lser be# spot ; 0./0 ##, nd the be# is #oved %ross the surf%e of the photopoly#er t  velo%ity of 2200 ##
32.11 32.11

(ASS units) units) Fused Fused depositi deposition on #odelin! #odelin! is used used to fbri%te fbri%te  prt prt -hi%h -hi%h is  #odel of the the step pyr#id t S&&r in :!ypt :!ypt (built %ir% 2460 :). +he #odel hs si levels or steps, e%h -ith  thi%&ness of 0.16 in. +he botto# lyer ; 2.20 in on  side, nd su%%essive levels re 1.95, 1.50, 1.15, 0.90, nd 0./5 in on  side, respe%tively. respe%tively. ei!ht of the pyr#id ; 1.02 in. n the F*M pro%ess, lyer thi%&ness thi%&ness ; 0.010 in nd the -idth -idth of the etrudte deposited deposited on the surf%e ;


32'/


0.025 in. +he etruder hed #oves in the $%y plne t  speed of 10 in.50/ s 8evel 1 # 5 ; 16(0.4/<(0.025  10) ? 12) ; 2/9 s 8evel 1 # 4 ; 16(0.20<(0.025  10) ? 12) ; 219 s # c ; 35(40) ? 533 ? /36 ? 356 ? 2>/ ? 2/9 ? 219; /%-' s ) (,+'- !in ) %+%(3 .r

(b) Colu#e of pyr#id ' ; ; 0.16(/.9/ ? 3./2 ? 2.25 ? 1.32 ? 0.4/ ? 0.20) ; 2.15/ in 3 Wei!ht of pyr#id ) ; ; 0.039(2.15/) ; 0.092 lb Mteril %ost ; >.50(0.092) ; D0.69
(ASS units) units) Given Given the dt dt in Proble# Proble# 32.11 32.11 in -hi%h -hi%h fused deposi deposition tion #odeli #odelin! n! is dditive dditive #nuf%turin! pro%ess,  totl of nine pyr#id #odels -ill be fbri%ted in one build %y%le to redu%e the %ost per pie%e. @ote tht the 12'se% dely for repositionin! pplies for e%h lyer, not e%h prt. +i#e lost to #ove the etrusion hed bet-een prts in e%h lyer is ne!li!ible. () o#pute n esti#te for the ti#e reuired to build the nine prts. Setup ti#e ; 35 #in for the bt%h. !nore post'pro%essin! post'pro%essin! ti#e. (b) *eter#ine the the %ost per pyr#id. $oution () First, %o#pute the re of e%h level of the pyr#id, 1 throu!h 4. re of botto# level ; A1 ; (2.20)2 ; /.9/ in2 re of level 2 ; A2 ; (1.95) 2 ; 3./2 in 2 re of level 3 ; A3 ; (1.50) 2 ; 2.25 in 2 re of level / ; A/ ; (1.15) 2 ; 1.32 in 2 re of level 5 ; A5 ; (0.90) 2 ; 0.4/ in 2 re of level 4 ; A4 ; (0./5) 2 ; 0.20 in 2 e%use lyer thi%&ness ; 0.010 in nd e%h level is 0.16 in thi%&, the nu#ber of lyers nl ; ; 0.16<0.010 ; 16 lyers per level. o#pute the pro%essin! ti#e for e%h level 8evel 1 # 1 ; 16(>(/.9/)<(0.025  10) ? 12) ; 3144 s 8evel 1 # 2 ; 16(>(3./2)<(0.025  10) ? 12) ; 22>6 s 8evel 1 # 3 ; 16(>(2.25)<(0.025  10) ? 12) ; 1591 s 8evel 1 # / ; 16(>(1.32)<(0.025  10) ? 12) ; 1012 s 8evel 1 # 5 ; 16(>(0.4/)<(0.025  10) ? 12) ; 302 s 8evel 1 # 4 ; 16(>(0.20)<(0.025  10) ? 12) ; 235 s


32'5


# c ; 35(40) ? 3144 ? 22>6 ? 1591 ? 1012 ? 302 ? 235; -0,3 s ) %/3+%' !in ) 2+3-' .r

(b) Colu#e of e%h pyr#id ' ; ; 0.16(/.9/ ? 3./2 ? 2.25 ? 1.32 ? 0.4/ ? 0.20) ; 2.15/ in 3 Wei!ht of e%h pyr#id ) ; ; 0.039(2.15/) ; 0.092 lb Mteril %ost of e%h pyr#id ; >.50(0.092) ; D0.69 ; 1(+*-4 32.13

(ASS units) units)  plst plsti% i% prt tht tht %onsists %onsists of  sphere sphere sittin! sittin! in the the #iddle #iddle of  sure sure bse is to be fbri%ted by fused deposition #odelin!. +he sphere di#eter ; 1.25 in. +he bse is 1.5 in on  side nd 0.365 in thi%&. +he sphere is i#bedded in the bse  depth of 0.0>3 in. +he prt -ill be built fro# the bse up. up. +otl +otl hei!ht ; 1.532 in. in. n the F*M pro%ess, lyer thi%&ness thi%&ness ; 0.005 in nd -idth of etrudte deposited on the surf%e ; 0.010 in. +he etruder hed #oves in the $%y plne t  speed of 12 in3 ; 1.532 in 2 2 3 Colu#e of the bse ' base base ; * h (1.5) (0.365) ; 0.9// in Colu#e of sphere ' sphere ; H &3<4 ; H(1.25) 3<4 ; 1.023 in3 e%use the sphere is i#bedded in the bse  distn%e ; 0.0>3 in, the spheri%l se!#ent tht %onstitutes the overlp #ust be subtr%ted fro# the volu#e. Colu#e Colu#e of spheri%l se!#ent ; Hh2(1.5 & = h)<3 ; H(0.0>3)2(1.5(1.25) = 0.0>3)<3 ; 0.014 in 3 ' sement ; +otl volu#e of prt ' pc ; 0.9// ? 1.023 = 0.014 ; 1.951 in 3 Colu#e of support stru%ture ' ss ; (1.5)2(1.532) = 1.951 ; 3.//6 = 1.951 ; 1.5>4 in 3 @u#ber of lyers ; 1.532<0.005 1.532<0.005 ; 304./ round do-n do-n to 304 lyers Asin! :. (32.9), # c ; 20(40) ? 1.951<(0.005  12  0.010) ? 1.5>4<(0.005  12  0.010) ? 304(10) ; %*&**0 se4 ) %((+'0 !in ) 2+'', .r

he%& e%use the t-o etruder heds operte -ith the s#e speed nd -idth of deposit, the %y%le ti#e %ould hve been deter#ined si#ply by usin! the totl %ube volu#e insted of distin!uishin! distin!uishin! bet-een the prt nd the support stru%ture. +hus # c ; 20(40) ? 3.//6<(0.005  12  0.010) ? 304(10) ; %*&**0 se4 ) %((+'0 !in ) 2+'', .r


32'4

ch32

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