UNIVERSIDADE REGIONAL INTEGRADA DO ALTO URUGUAI E DAS MISSÕES DEPART DEPARTAMENTO AMENTO DE ENGENHARIAS ENGENHARI AS E CIÊNCIA DA COMPUTA COMPU TAÇÃO ÇÃO ENGENHARIA MECÂNICA
TREFILAÇÃO
Gilvan Blaski!i"# $%na&an 'av(&&% I)(i T(%i&in*% T(%i&in*% R%+(&% ,ania
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2
RESUMO
Os 5(%"ss%s / "%n6%(-a78% -"9ni"a al&(a- a :%-&(ia /% -a&(ial a&(av;s /as 6%(7a 6%(7ass a5li"a a5li"a/as /as 5%( 6((a6((a-n n&as &as a/<)a a/<)a/as /as -)/an -)/an/% /% a s)a :% :%-& -&(ia (ia44 N Ns& s& &(a+al*% a5(sn&a(-%s % 5(%"ss% / &(6ila78%. %n/ s &- )- 5(%=&% / )-a -><)ina 5a(a &(6ila( a 6(i% )-a +a((a / al)-?ni% @AA 2 "%- /i9-&(% ini"ial / 2 -- /i9-&(% 6inal / -C%-% s& ; )- 5(%"ss% (ali#a/% a 6(i% % -a&(ial 6i"a(> n"()a/%. as 5(%5(i/a/s -"9ni"as -"9ni"as /% -a&(ial -a&(ial &a-+;- s(8% al&(a/as. al&(a/as. a)-n&an/% a)-n&an/% s)a (sis&Fn"ia (sis&Fn"ia "%- )-a &ns8% / s"%a-n&% / sa?/a -ai%( /% <) a / n&(a/a. )-a v# <) % -a&(ial n8% s(> ("%#i/% a5s % l&i-% 5ass4
0
SUMÁRIO Sumário
INTRODUÇÃO......... INTRODUÇÃO.................... ..................... ..................... ..................... ..................... ......................................... ................................ ..4 4 1. PROCESSOS DE TREFILAÇÃO............. TREFILAÇÃO........................ ..................... ...................................... .............................. ..6 6 2. TIPOS DE TREFILAÇÃO.............. TREFILAÇÃO......................... ..................... ................................................. .......................................8 8 3. FIERAS DE TREFILAÇÃO............... TREFILAÇÃO......................... ..................... ...................... ..................... ..................... ................ .....9 9 4. TREFILAÇÃO DE TUBOS................. TUBOS............................ ..................... ..................... ..................... ...................... ............10 10 5. DEFEITOS NA TREFILAÇÃO............... TREFILAÇÃO.......................... ...................... ..................... ............................. ...................12 12 6. TRAT TRATAMENTOS TÉRMICOS................ TÉRMICOS........................... ..................... ..................... .............................. ...................13 13 7. SISTEMAS DE LUBRIFICAÇÃO............ UBRIFICAÇÃO....................... .................................................. ....................................... 14 8. DIMENSIONAMENTO DIMENSIONAMENTO E CLCULOS CLCULOS DO TREFILADOR............................ TREFILADOR............................15 15 CONCLUSÃO........ CONCLUSÃO................... ..................... ..................... ..................... ..................... ...................... ................................. ...................... 21 BIBLIO!RAFIA......... BIBLIO!RAFIA................... ..................... ...................... ..................... ..................... ..................... .............................. ....................22 22 ANE"OS.......... ANE"OS.................... ..................... ..................... ..................... ..................... ..................... ...................... ............................ ................. 23
INTRODUÇÃO A &(6ila78% ; )- 5(%"ss% / "%n6%(-a78% -)i&% an&i:%4 Os an&i:%s :?5"i%s. %s "*inss. %)&(%s 5%v%s /a an&i:)i/a/. "%n*"ia- a &;"ni"a / 6a+(i"a( 6i%s / -&ais 5("i%s%s -5(:a/%s na %)(ivsa(ia. na 5(%/)78% / =%ias a/%(n%s. ; % 5(%"ss% / 6a+(i"a78% / a(a- +a((as 6inas / -&al -&al.. a"a((&an/% a (/)78% /a s78% &(ansv(sal (s5"&iv% a)-n&% n% "%-5(i-n&% /% -a&(ial. 5%( -i% /a &(a78% /a 57a a&(av;s / )-a -a&(i# "*a-a/a 6i(ia. "%- 6%(-a / "anal "%nv(:n&4 "%nv(:n&4 O 5(%"ss% / &(6ila78% "%nsis& - 5)a( % -&al a&(av;s / )-a -a&(i#. 5%( -i% / )-a 6%(7a / &(a78% a l a5li"a/a na sa?/a /a -a&(i#4 A -ai%( 5a(& /% s"%a-n&% 5l>s&i"% ; "a)sa/a 5%( s6%(7%s / "%-5(ss8% (s)l&an&s /a (a78% /% -&al "%- a -a&(i#4 Eis&- -)i&as a5li"a7Js 5a(a a &(6ila:- "%-% na 5(%/)78% / 6i%s l;&(i"%s. "a+%s. "li5s / 5a5l. "%(/a 5a(a ins&()-n&%s -)si"ais (ai% 5a(a (%/as. /a (/)78% s)"ssiva / /i9-&(% / )-a ) -a +a((a -&>li"a -a"i7a 5%/- (s)l&a( +a((as. v(:al*Js a(a-s a(a-s44 A &(6ila78% 5%/ &a-+;- s( (ali#a/a - &)+%s &)+%s %"%s %"%s . ns& "as%. is&/iv(sas &;"ni"as -5(:a/as. "%- a )&ili#a78%. %) n8%. / )- -an/(il in&(n% a% &)+% <) 5(-i& 5(-i& )- -l*% -l*%(( "%n&( "%n&(%l %l /a s5s s5ss)( s)(aa 6inal. 6inal. :(al:(al-n& n& %s 5(%" 5(%"ss% ss%ss / &(6ila78% s8% (ali#a/%s K &-5(a&)(a a-+in& &%/avia. )-a v# <) as /6%(-a7Js nv%lvi/as s8% n%(-al-n& :(an/s. %"%(( )- a)-n&% "%nsi/(>vl / &-5(a&)(a /)(an& a %5(a78%. "%-% -%s&(a/% na 6i:)(a @24
Figura 1 P(%"ss% / La-ina78% 4
3
Al:)-as van&a:ns i-5%(&an&s 5a(a % 5(%"ss%
O -a&(ial 5%/ s( s&i(a/% (/)#i/% - s"78% &(ansv(sal -ais /% <) "%<)al<)( %)&(% 5(%"ss%
A 5("is8% /i-nsi%nal %+&i/a ; -ai%( /% <) - <)al<)( %)&(% 5(%"ss% "&% a la-ina78% a 6(i%. <) n8% ; a5li">vl Ks +i&%las "%-)ns / a(a-s
A s)5(6?"i 5(%/)#i/a ; )ni6%(--n& li-5a 5%li/a
O 5(%"ss% in6l)i nas 5(%5(i/a/s -"9ni"as /% -a&(ial. 5(-i&in/%. "%-+ina78% "%- )- &(a&a-n&% &;(-i"% a/<)a/%. a %+&n78% / )-a :a-a va(ia/a / 5(%5(i/a/s "%- a -s-a "%-5%si78% <)?-i"a4
1. PROC PROCES ESSO SOS S DE TRE TREFI FILA LAÇÃ ÇÃO O T(a&as / )- 5(%"ss% -"9ni"% <) "%n6( a% -a&(ial 5("is8% /i-nsi%nal -l*%(s 5(%5(i/a/s -"9ni"as4 A 6inali/a/ 6inali/a/ /% 5(%"ss% / &(6ila78% ; a %+&n78% / 6i%s / /i-nsJs. a"a+a-n&% s)5(6i"ial 5(%5(i/a/s -"9ni"as /6ini/as. %"%(( 5l% (a"i%na-n&% / )-a +a((a. 6i% %) &)+%4 Ds/ <) a s78% &(ansv(sal /a -a&(i# s=a s-5( -n%( <) a 57a &(a+al*a/a. % 5(%"ss% / &(6ila78% %"asi%na(> )-a (/)78% - >(a )- a)-n&% n% "%-5(i-n&%4 A -a&;(ia5(i-a 5a(a &(6ila78%. "%-)-n& /n%-ina/% 6i%-><)ina. ; % a(a- la-ina/% a <)n&4 P%( %)&(% la/%. a% l%n:% /as &a5as / &(6ila78% % -a&(ial ; n"()a/%. %) s=a. s)a (sis&Fn"ia -"9ni"a "(s "(s" " K -/i -/i/a /a <) <) a (/) (/)78 78%% / >(a >(a a)- a)-n& n&a4 a4 D Ds& s&aa 6%(6%(-a. a. - 6)n7 6)n78% 8% /as /as "a(a"&(?s&i"as /% 6i%-><)ina la-ina/% a <)n&. /as in6%(-a7Js 6inais /% 5(%/)&% %) /a n"ssi/a/ / )-a -ai%( (/)78% / >(a. 6a#s n"ss>(i% )- &(a&a-n&% &;(-i"% / ("%#i-n&%4 D)(a D) (an& n& a &(6 &(6ila ila78 78%. %. <) <) ; (al (ali# i#a/ a/%% a+ai a+ai% % /a &-5 &-5( (a& a&)( )(aa / ("(is&ali#a78%. % 6i% s%6( )- a)-n&% /a s)a (sis&Fn"ia -"9ni"a / (/)78% /a s)a /)"&ili/a/ /)"&ili/a/. . /vi/% /vi/% K /6%(-a78% /6%(-a78% 5l>s&i"a. 5l>s&i"a. "a(a"&(i# "a(a"&(i#an/% an/% % /n% /n%-ina/ -ina/%% 6i&% 6i&% / n"()a-n&%4 A"i-a / "(&% :(a) / n"()a-n&% n8% ; -ais 5%ss?vl &(a+al*a( % 6i%. sn/% n&8% n"ss>(ia. 5a(a % 5(%ss:)i-n&% /% 5(%"ss% / &(6ila78%. a a5li"a78% / )- &(a&a-n&% &;(-i"% 5a(a <) % "%n&(%l /as 5(%5(i/a/s -"9ni"as /% 6i% /)(an& % 5(%"ss% / &(6ila78% ; -)i&% i-5%(&an& 5a(a <) s& 5%ssa &( 5(%ss:)i-n&%. 5(%ss:)i-n&%. s()5&)(a /% 6i%. 5a(a <) % 6i%. a% 6inal /% 5(%"ss%. a5(sn& as "a(a"&(?s&i"as /i-nsi%nais. -"9ni"as -&al(:i"as i:i/as 5a(a s)a )&ili#a78%4 )&il i#a78%4 O &(a&a &(a&a- -n& n&%% &;(&;(-i" i"%% -n" -n"i% i%na na/% /% ; "%-) "%-)- -n& n& /n% /n%-i -ina na/% /% / ("%#i-n&%. <) 5%/ s( "%n&?n)% - 6%(n%s "%n&?n)%s %) s&a"i%n>(i%4 P%(&an&%. a /)"&ili/a/ ; 6a&%( 5(i-%(/ial. n% "as% /a &(6ila78%. 5%is ; a 5(%5(i/a/ <) in/i"a a "a5a"i/a/ /% -a&(ial s%6(( :(an/s /6%(-a7Js 5(-ann&s n)-a /&(-ina/a /i(78%. s- %"%((( ()5&)(a4 R5(sn&a a -ai%( %) -n%( 5%ssi+ili/a/ /% -a&(ial s( al%n:a/%4 N%(-al-n& % ("%#i-n&% />s - 6%(n%s / a&-%s6(a 5(%&&%(a isn&a i sn&a / %i:Fni% %) / %)&(%s :ass "%n&a-inan&s4
Figura 2 - Ban"a/a / T(6ila78%4 '%n& @BESCO. A(&*)( B4 01234
2. TIPO TIPOS S DE TREF TREFIL ILAÇ AÇÃO ÃO Eis&- al:)ns &i5%s i-5%(&an&s / 5(%"ss%s / &(6ila78%. "a/a )- s /v a% &i5% / -a&(ial )&ili#a/% s)as 5(%5(i/a/s -"9ni"as. % s"%a-n&% 5l>s&i"% ; 5(%/)#i/% 5la "%-+ina78% /a 6%(7a &(a"i%na/%(a "%- as 6%(7as "%-5(ssivas 5(%vnin&s /a (a78% /a -a&(i# -a&(i# s%+( % -a&(ial4 A &(6ila78% a 6(i%. ; )sa/a 5a(a -&ais / (/ C'C @C+i"% / 'a" Cn&(a/%4 O 6i% 6i% ; ; 5(5a(a/% / 6%(-a <) s 5(n/a na &a((a"*a /a &(6ila. sn/% n&8% Q5)a/%Q4 Q 5)a/%Q4 -/i/a <) % 6i% ; 5)a/% a&(av;s /a &a((a"*a. % s) v%l)- 5(-an" % -s-%. % /i9-&(% /i-in)i % s) "%-5(i-n&% a)-n&a4 N% 5(%"ss% / &(6ila78%. %"%(( % n"()a-n&% /% -a&(ial. %) s=a. %s :(8%s /% -a&(ial s8% al%n:a/%s "%- is&% s)a &ns8% / ()5&)(a a)-n&a4 A T(6ila78% a <)n& a5li"as a -&ais / (/ CCC @C+i"% / C%(5% Cn&(a/% (a(a-n& - -&ais / (/ HC @Ha:%nal C%-5a"&%4 P%( sss -&ais s(- 5%)"% -al>vis. ; n"ss>(i% a<)"Fl%s a&; )-a &-5(a&)(a a/<)a/a - <) %+&(8% -5a"%&a-n&% i:)al Ks (/s C'C. 5a(a 5%/(-. n&8%. s(- &(6ila/%s4 A5s (s6(ia-n&% (")5(a- s)a "a(a"&(?s&i"a %(i:inal4
Figura 3 - E-5l%s / -><)inas / T(6ila78% . '%n& @BESCO. A(&*)( B4 01234
3. FIER FIERAS AS DE TREF TREFIL ILAÇ AÇÃO ÃO As 6ii(as 5a(a a &(6ila:- %) &(6ilas. s8% "%-5%s&as / )-a "a("a7a / a7% )- n"l% 6i&% / -a&(ial +as&an& /)(%4 O n"l% ; :(al-n& 6i&% / "a(+&% / &)n:s&Fni% %) &)n:s&Fni% %) /ia-an& in/)s&(ial4 O /ia-an& sin&;&i"%. %) in/)s&(ial. ; )sa/% :(al-n& nas &a5as ini"iais / &(6ila:- n<)an&% <) as 6ii(as 6i&as / /ia-an& s8% )&ili#a/as nas &a5as 6inais4 Pa(a &(6ila( 6i%s -)i&% 6in%s )- "(is&al si-5ls / /ia-an& /ia-an& ; ; )&ili#a/%4 As 6ii(as / &(6il &(6ila7 a78% 8% s8% s8% "%ns "%ns&() &()?/ ?/as as - a7%s a7%s in/ in/6% 6%((->v >vi iss 5a(a 5a(a % &(a+ &(a+al al*% *% a 6(i% 6(i%.. a7%s a7%s in/ in/6% 6%((->v >vi iss 5a(a 5a(a % &(a+ &(a+al al*% *% a <)n <)n& &44 A 6a+( 6a+(i" i"a7 a78% 8%.. in"l in"l)in )in/% /% &(a& &(a&aa-n n&% &%ss &(-%-"9 &(-%-"9ni"% ni"%s. s. ; s%6is&i"a/ s%6is&i"a/aa i: i: "%nsi/(> "%nsi/(>vl vl s5"iali s5"iali#a78 #a78%% na "%-5&i&iva "%-5&i&iva in/s&(ia a&)al4 O 9n:)l% /a 6ii(a ; (6(n& a% 9n:)l% /% "%n / &(a+al*%. n% "ilin/(% / "ali+(a78% ; %n/ ; 6i&% % a=)s& /% /i9-&(% /% 6i%. a<)i s /v "%n&(%la( a al&)(a /% "ilin/(%. 5%is s s&a al&)(a 6%( 5<)na as %5(a7Js / (&i6i"a78% /as 6ii(as :as&as 5a(a a %+&n78% / )-a 6ii(a "%- )- /i9-&(% 6inal -ai%(4 O "%n / sa?/a /v 6a#( "%- <) a sa?/a /% 6i% s=a liv( n8% "a)s /an%s nas s)5(6?"is /a 6ii(a /% 6i%4 Os &i5%s -ais "%-)ns / 5(6is 5%/- s( vis&%s na 6i:)(a @34
Figura 4 - 'ii(a / T(6ila78% T(6ila78%.
4. TREF TREFIL ILAÇ AÇÃO ÃO DE TUBO TUBOS S Ta-+;Ta-+;- &- s a 5%ssi+li/a/ / &(6ila( &)+%s. al:)ns -5l%s (lvan&s 5a(a % 5(%"ss%4 C%- -an/(il. "%nsis&- n)-a +a((a l%n:a /)(a. <) s s&n/ 5%( &%/% % "%-5(i-n&% /% &)+%. % <)al ; 5)a/% "%- % &)+%. a&(av;s /a -a&(i#4 Ns& -;&%/% a 6%(7a ; &(ans-i&i/ &(ans-i&i/aa a% -&al. 5a("ial-n& 5a("ial-n& 5)a/a na s78% s78% / sa?/a 5las 5las 6%(7as 6%(7as / a&(i&% <) a&)a- a% l%n:% /a in&(6a" &)+%-an/(il4 A5s a &(6ila78%. % -an/(il ; (-%vi/% /% &)+% a&(av;s / )-a (&i6i"a/%(a. a <)al a)-n&a % /i9-&(% /% &)+% as &%l(9n"ias /i-nsi%nais4
Figura ! Man/(il Passan& . '%n& @BESCO. A(&*)( B4 01234
A &(6ila78% "%- 5l):) s&a"i%n>(i%. &an&% % /i9-&(% in&(n% <)an&% % &(n% s8% "%n&(%la/%s /)(an& % 5(%"ss%4 O 5l):) "%n&(%la % &a-an*% a 6%(-a /% /i9-&(% in&(n%4 A &(6ila78% "%- 5l):) 6l)&)an&. % 5l):) 6l)&)a na +%"a /a 6ii(a4 Esss 5l):)s 6l)&)an&s 5%/- 5(%5%("i%na( (/)78% /a >(a / a&; 3 . sn/% <) 5a(a )-a -s-a (/)78% as "a(:as / &(6ila78% s8% in6(i%(s as /% 5(%"ss% "%- 5l):) s&a"i%n>(i%4
21
Figura " - 'ii(a / T(6ila78% "%- +)"*a 6ia 6l)&)an& . '%n& @BESCO. A(&*)( B4 01234
Ns& "as%. -an/(il s- s)5%(& in&(n%. "%-% % in&(i%( /% &)+% n8% ; s)5%(&a/% a 5a(/ s &%(na li:i(a-n& -ais s5ssa a s)5(6?"i in&(na i((:)la(4
4 Figura # - 'ii(a / T(6ila78% s- s)5%(& in&(n% . '%n& @BESCO. A(&*)( B4 01234
22
. DEFE DEFEIT ITOS OS NA TREF TREFIL ILAÇ AÇÃO ÃO Os /6i&%s 5%/- s( (s)l&an&s / /6i&%s /a +a((a %(i:inal. 6iss)(as. las"as va#i%s. %) /% 5(%"ss% / /6%(-a78%4 O &i5% / /6i&% -ais "%-)- ; a 6n/a in&(na n% "n&(% /a +a((a %) &(in"a-n&% s&(ia/% %) "*v(%ns4 A 6(a&)(a s&(ia/a "n&(al %"%(((> 5a(a -a&(i#s "%9n:)l%s / in"lina78% 5<)n%s 5a(a (/)7Js 5<)nas. sn/% <). > -/i/a <) % 9n:)l% "(s" a (/)78% "(?&i"a 5a(a a a)sFn"ia /% /6i&% &a-+;- a)-n&a4
Figura $ ! D6i&%s na T(6ila78% T(6ila78%.
20
". TRAT TRATAMENTO MENTOS S T%RMICO T%RMICOS S Al:)ns &(a&a-n&%s &;(-i"%s s8% i-5%(&an&s /5%is /a &(6ila78%. %s a(a-s s8% s)+-&i/%s a &(a&a-n&%s &;(-i"%s 5a(a al?vi% / &nsJs %) %+&n78% / 5(%5(i/a/s -"9ni"as /s=a/as4 A+ai%. A+ai%. %s 5(in"i5ais &(a&a-n&%s )&ili#a/%s4
R"%#i-n&% ; % &(a&a-n&% -ais i-5%(&an& 5la (&%-a/a /a -a"i# <) 5(-i& n%vas /6%(-a7Js a 6(i%4 O"%((- /%is 6n-n%s /is&in&%s sisi-)l&9 )l&9n n%s %s % al?v al?vi% i% / &ns &nsJ Jss => a +ai +aias as &-5 &-5( (a& a&)( )(as as.. a ("(is&ali#a78% "%- a n)"la78% "(s"i-n&% / n%v%s :(8%s4
T-5(a (vni/% s8% &(a&a-n&%s -n%s i-5%(&an&s 5a(a a &(6ila78% - si4 S8% (ali#a/%s s%-n& n% 6inal /% 5(%"ss%. - si&)a7Js -)i&% s5"iais / a5li"a78% -"9ni"a. "%-% - -%las4 O si-5ls. /)5l% %) a&; -s-% &(i5l% (vni-n&% s(v 5a(a li-ina( a "ssiva 6(a:ili/a/ / &F-5(a. a)-n&an/% a &na"i/a/4
Pa&n&a-n&% ; )- &(a&a-n&% &;(-i"% "l)siv% - a(a-s4 P%( -i% /% 5(%"ss%. 5(%")(as 6%(-a( )-a 5(li&a 6in?ssi-a "*a-a/a s%(+i&a. 5a(a /5%is n"()>la 5%( &(6ila78% 6inal a 6(i%. :an*an/%s (sis&Fn"ia -"9ni"a -)i&% lva/a. "%- +%a &na"i/a/4
2
#. SIST SISTEM EMAS AS DE LUB LUBRIF RIFICA ICAÇÃ ÇÃO O As -><)inas / &(6ila( 5%/- s( "lassi6i"a/as &a-+;- / a"%(/% "%- % s) sis&-a / l)+(i6i"a78%. <) 5%/- s( M><)inas "%- sis&-a / i-(s8% %n/ a 6ii(a %s an;is 6i"a- i-(s%s n% li<)i/% (6(i:(an& l)+(i6i"an& M><)inas "%- sis&-a / as5(s8% %n/ a 6i(a ("+ )- =a&% / li<)i/% (6(i:(an& l)+(i6i"an&
23
$. DIM DIMENS ENSION IONAME AMENT NTO O E CÁLCULOS CÁLCULOS DO TREF TREFILA ILADOR DOR $.1. D&'i(i)*+ ,a Fi&ira N%s ">l")l%s 6%(a- )&ili#a/as 3 "asas "asas a5s a v?(:)la. v?(:)la. a((/%n/an/% a((/%n/an/% a l&i-a4 Pa(a in?"i% / ">l")l%s 6%(a- a/-i&i/%s a ->i-a /6%(-a78% a"i&a 5l% al)-?ni% "%-% 3. WX1.3. % 'a&%( / a&(i&%. YX1.14 '%i "al")la/a ini"ial-n& a /6%(-a78% &%&al 5la E<4 24
ϕ total
= ln
D f 0 D10
E0
= ln
2B 0
= −1.SP21 @2
%n/ % W&%&al ; a /6%(-a78% &%&al na &(6ila78%. D 1 % /i9-&(% ini"ial /a 6ii(a - -- D6 ; ; % /i9-&(% 6inal /a 6ii(a 6 ii(a - --4 O n-(% / 5asss ; "al")la/% 5la E<4 04
N =
ϕ total ϕ máx
=
1.SP21 1.S3
= 2.1B @0
C%-% N X2.1 X2.1 ; -ai%( <) 2. a((/%n/as % n-(% / 5asss 5a(a )- n-(% -ai%(4 N% "as% s(> a/%&a/% N X0 X0 5asss. assi- "al")las % W 5ass na E<4 4
ϕ passe
=
ϕ total
N
=
1.SP21 0
= −1.3ECC @
Assi-. "al")las % D1 5la E<4 34
√
− 0,4855
D 1= e
2
∗13 =10,2 mm
@3
A5s. 6%i "al")la/% % 9n:)l% &i-% /a 6ii(a 5la E<4 4 2
α ot
=
1.EP4u4
A1 − A2 A2
=
1.EP41.1E4
2B
0
− 21.0 0
21.0
0
= 1.01E3 rad = 22.S3° @
Pa(a "al")la( % :(a) / s6%(7%. )sas a E<4 4
ϕ A. máx
tga 1.PC tg 22.3S 1.PC = −1.A1SB 4 ln 42 − = 4 ln 42 − = µ 1.1E tg α tg 22.3S 2 + 2 + 1 . 1E µ
@
"%-% WA.-> Z W 5ass @1.1 Z 1.3. %s val%(s a"i-a "al")la/%s 5%/- s( )&ili#a/%s. 5%is a /6%(-a78% /6%(-a78% n"ss>(ia ; -n%( <) a /6%(-a78% /6%(-a78% <) % -a&(ial a:)n&a4 C%- s&s val%(s (ali#%)s %s s+%7%s /as 6ii(as 2 0. il)s&(a/%s nas 6i:)(as @ @214
Figura ! 'ii(a /% 5(i-i(% 5ass4
2
Figura 1 ! 'ii(a /% s:)n/% 5ass4
S(8% (ali#a/%s 0 5asss "%- )- ("%#i-n&% in&(-/i>(i% "%/6%(-a78% / 3. 9n:)l% /a 6ii(a / 22.3[4 Os /i9-&(%s s(8%. (s5"&iva-n&. D0 X 2 --. D1 = 21.0 -- D0 X --4
$.2. C/0u0+ ,a F+r)a Cal")lan/%s as &nsJs / s"%a-n&% / n&(a/a sa?/a 5las E
e
σ e
= 31 \ ϕ \ n = 31 \ 1.110 \1.B = A.2SSPkgf U mm 0 @
S
σ e
kg f U mm 0 = 31 \ ϕ \ n = 31 \ 1.3ECC \ 1.B = B0.013Ckgf
@
%n/ %n/ σ ee ; a &ns8% &ns8% / s"%as"%a-n& n&%% ini"ia ini"iall - kgf/mm² . φ ; a /6% /6%((-a7 a78% 8% n ; % "%6i"in& / n"()a-n&% σ se ; a &ns8% / s"%a-n&% 6inal - kgf/mm² 4 C%- iss%. a &ns8% / s"%a-n&% -;/ia ; /a/a 5la E<4 @4
2
e
σ σ´ e =
s
σ e +σ e 2
=
6,1997 + 32,2045 2
2
=19,2021 kgf / mm
@
C%- s& val%(. 5%/- s( "al")la/as as 6%(7as 5a(a % 5(i-i(% s:)n/% 5asss. 5las 5las E
A2 tg tg α F 2 = A2σ e 2 + 42 − A µ 1
µ α
1 . 1E 0 tg 21.0 22.S3 tg 22.S3 = E2.P20E ] 2S.0102 ] 2 + = SCE.AAC1kgf 42 − 0 1 . 1E 2B
F 0
tg α = A0σ e 2 + µ
A0 tg 42 − A2
µ α 0
@21
1 . 1E 0 tg tg 22.S3 E 22.S3 = C1.0ACC ] 2S.0102 ] 2 + 4 2 − 0 1.1E 21.0
= CS1.303Ck gf @22
Pa(a v(i6i"a( s *av(> /6i&%s n% -a&(ial. "%-% % "*a5;) "*inFs. )&ili#a-s as E
σ 2
=
F 2 A 2
= SCE.AAC1 = 22.PB02kgf U mm 0 E2.P20E
a=
σ 1 σ σ´ e
=
11,7321 19,2021
=0,61
@20
@2
2
O val%( %+&i/%s 5a(a % :(a) / s6%(7%. "%- a1X 1.2 ; in6(i%( a 1. <) ; % val%( s&a+l"i/% "%-% )- li-i& 5a(a vi&a( % s)(:i-n&% / /6i&%s in&(n%s4
$.3. C/0u0+ ,a &0+i,a,& & P+5(ia
'%i a&(i+)?/% % val%( / "%-5(i-n&% ini"ial 5a(a a +a((a sn/% / 0 m. Assi-. 5a(a "al")la( %s "%-5(i-n&%s "%-5(i-n&%s / sa?/a. sa?/a. )&ili#%)s a E<4 E<4 @234
π ∗0,013
4
2 2
m ∗2 m =
0,010 2 π ∗0,010
2 2
m ∗ L1=
4
π ∗0,008
4
2 2
m ∗ L2
@23
O+&n/%s %s val%(s / 1 X 0.03 m 0 X .02 m4 U&ili#an/% a vl%"i/a/ 6inal 6inal / sa?/a /a 6ii(a 6ii(a / ! " X 1. m/s. 5%/-%s "al")la( a vl%"i/a/ / sa?/a na 5(i-i(a 6ii(a. "%- a E<4 E<4 @24
0,008 π ∗0,008 V 1=
A 2∗V 2 A 1
=
2
4
2
m ∗0,5 m / s
0,0102 π ∗0,0102 4
=0,3076 m / s
2
m
2
@2
C%- %s val%(s /as vl%"i/a/s 5%/-%s "al")la( as 5%&Fn"ias n"ss>(ias 5a(a a &(6ila78% n% 5(i-i(% 5ass. E<4 @2. n% s:)n/%. E<4 @24 2
F 1∗V 1 958,6650 ∗0,3076 P1= = =3,9318 CV
75
75
F 2∗V 2 590,4245∗0,5 P2= = =3,9362 CV 75 75
@2
@2
S(8% S(8% n"ss> n"ss>(i% (i%ss 0 -%&%( -%&%(ss / #!s 5a(a (ali#a( a &(6ila78% "%-5l&a /% a(a-4
$.4. R&u0a,+
A5s &%/%s %s ">l")l%s / /i-nsi%na-n&% 6inali#a/%s 5a(a &(6ila( )-a +a((a / al)-?ni% AA2 "%- /i9-&(% / 2 --. "%n"l)i)s <) % 5(%"ss% /v(> &( /%is 5asss / &(6ila78% &(6ila78% 5a(a "*:a( a% /i9-&(% /i9-&(% /s=a/% / --. "%- /6%(-a78% 5%( 5ass / 3.. a5sa( / % al)-?ni% &( )-a ->i-a /6%(-a78% a"i&>vl / 34
Ta6&0a 1 ! P(in"i5ais /a/%s ">l")la/%s 5a(a % 5(%"ss%4 N-(% / 5asss 5asss σ´ e Tns8% / s"%a-n&% -;/ia σ
W 5ass D1 L1 D2 L2 D0 L0 ^%&
0 2.0102 kgf/mm² 1.3 2 mm 0111 mm 21.0 mm 03. mm mm 02. mm 22.3% 01
'%(7a 2 '%(7a 0 Vl%"i/a/ 2 Vl%"i/a/ 0 P%&Fn"ia 2 P%&Fn"ia 0 P%&Fn"ia T%&al
.1 kgf 1.303 kgf 1.1 m/s 1. m/s .2 #! .0 #! . #!
CONCLUSÃO C%- a (ali#a78% /s& &(a+al*% 5("+)s a i-5%(&9n"ia /% 5(%"ss% / &(6ila78% 5a(a a in/s&(ia. sn/% <) v>(i%s 5(%/)&%s <) )&ili#a-%s - n%ss% /ia a /ia s8% 5(%vnin& /s&a %5(a78%4 Al;- /% -ais. % 5(%"ss% / &(6ila78% &- v>(ias van&a:ns. 5%is % -a&(ial 5%/ s( s&i(a/% (/)#i/% - s"78% &(ansv(sal "%- &i-a 5("is8% /i-nsi%nal. % a"a+a-n&% s)5(6i"ial /ia/% n% a(a- ; )ni6%(--n& li-5% 5%li/%. % 5(%"ss% &a-+;- in6l)i nas 5(%5(i/a/s -"9ni"as /% -a&(ial. 5(-i&in/%. - "%-+ina78% "%- )- &(a&a-n&% &;(-i"% a/<)a/%. a %+&n78% / /i6(n&s 5(%5(i/a/s (sis&Fn"ias a% 6inal /% 5(%"ss%. "%-% 5%( -5l%. )a)-n&% /a s)a (sis&Fn"ia ( sis&Fn"ia -"9ni"a. /vi/% K /6%(-a78% 5l>s&i"a4 A&(av;s / ">l")l%s / /i-nsi%na-n&%. "%ns:)i)s 5(%=&a( a 6ii(a <) 5%ssi+ili&a a &(6ila78% /% a(a- i-5%s&% 5a(a % 5(%=&%. "al")lan/%s 5(%=&an/%s "a/a &a5a /% 5(%"ss%4
02
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Pr+&+ ,& C+('+r8a)*+. E- !!!4"i--4"%-4+(. a"ssa/% 0210114
Pr+&+ ,& Fa6ria)*+. V%l)- I4 A5%s&ila /% C)(s% T;"ni"% - M"9ni"a4 Tl")(s% 01114 CETLIN. P4 R4 HELMAN. H4 Fu(,a8&(+ ,a C+('+r8a)*+. S8% Pa)l% A(&li+( E/i&%(a. 0114 Pa"*"%. L)i# $4Bsk%!. A(*&)( B4 P(%"ss%s / C%n6%(-a78%. P%(&% Al:(. =)l*% 011. 5>: 0 324 DIETER. G4E4 M"*ani"al M&all)(:b. 2. SI M&(i" E/i&i%n. M"G(a!Hill4 B//%s. $4 an/ Bi++lb M4$4 P(in"i5ls %6 -&al -an)6a"&)(in: 5(%"ss. 2. A(n%l/4 A(n%l/4
00
ANE9OS
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