UNIVERSIDAD NACIONAL DEL CALLAO FACULT FACULTAD DE MECÁNICA Y DE ENERGIA ESCUELA PROFESIONAL DE INGENIERIA MECÁNICA Y ENERGIA
“LUBRICACIÓN INDUSTRIAL” HUAYLLACAYÁN CARRILLO JOSÉ LUIS CONCHA YANA KEVIN CLAUDIO CÁRDENAS GAMARRA EDWIN
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TABLA TABLA DE CONTENIDO C ONTENIDO TABLA DE CONTENIDO::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::+ TABLA TABLA DE ILUSTRACIONES:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: :::; INTRODUCCION::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::, RESUMEN::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::< LUBRICACION INDUSTRIAL:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::= 1.
Reseña histór tórica ica::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::=
2.
Lubricante.::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::=
3.
Tipos ipos de lub lubrica ricant nte. e.:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::>
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Prop Propie ieda dade des s de los los lub lubri rica cant ntes es..::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
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Clas Clasif ific icac ació ión n de de los los lubr lubric ican ante tes. s.::::::::::::::::::::::::::::::::::::::::::::::::::::::::::+?
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Tipos ipos de Lu Lubric bricac ació ión. n.::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::+>
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Re#( Re#()e )ene nes s de lubr lubric icac ació ión. n.:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::+
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CONCLUSIONES:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::)= BIBLIOGRAFIA:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::)> ANEOS:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: :::::::) A Sl$"/0'- (' %#'0/(a- 5& Ra/0(/ 9 B9(:::::::::::::::::::::::::::::::::::::::)
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TABLA DE ILUSTRACIONES FIGURA + R'la"/30 V/-"-/(a(T'5'&a#$&a:::::::::::::::::::::::::::::::::::::::::::::::::::+* FIGURA )M'(/"/30 (' la 1/-"-/(a( Sa9%l#:::::::::::::::::::::::::::::::::::::::::::::::::::::+; FIGURA ? F&/""/30:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::+, FIGURA ; D'-2a-#'::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::+= FIGURA , L$%&/"a"/30 5'&7'"#a:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::+> FIGURA < L$%&/"a"/30 /#a:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::+ FIGURA = L$%&/"a"/30 l//#':::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::+ FIGURA > C./0'#' H/(&-#4#/"::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::)* FIGURA C./0'#'- (' C0#a"#::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: :))
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INTRODUCCION La l$%&/"a"/30 -' ('-a&&ll3 ('%/( a 6$' 5a' (' la '0'&2a %&/0(a(a a la 46$/0a -' ('-5'&(/"/a%a '0 7&a (' "al& 5&($"/( 5& 'l ('-2a-#' 9 &8a/'0#! '-#- 5&%l'a- '&a $0 /5a0#' &'# a 1'0"'&! '- 5& 'll 6$' -$ '-#$(/ '- (' 1al/-a /5a0"/a 9 '-' '- 'l 5&/0"/5al #/1 ('l ('-a&&ll (' '-#a 02&a7a 5&'-'0#a& al '-#$(/a0#' $0a /0#&($""/30 a la l$%&/"a"/30 6$' "0 $0 '-#$(/ 4- 5&7$0( -' 1$'l1' $0a /5a0#' '&&a/'0#a 5a&a 'l '.&a/'0# (' la '7/"/'0"/a (' a6$/0a&/a- $#/l/8a(a'0 la- /0($-#&/a-: S0 $"- l- a1a0"'- 6$' -' a0 l2&a( a-#a 'l (a (' 9! '-5'"/al'0#' "0 'l ('-a&&ll (' #'&a- 6$' '5l/"a0 (' a0'&a a#'4#/"a 'l "5a/'0# (' la- 5&5/'(a('- (' $0 l$%&/"a0#' a ('#'&/0a(a- "0(/"/0'-! l 6$' -' %$-"a '0 '-#a- #'&a- -0 l 6$' 0$0"a %#'0(&'-! $0a a6$/0a /('al:
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RESUMEN E0 '-#' #&a%a. -' ('7/0/&4 6$' '- $0 l$%&/"a0#' a- " l- #/5- (' l$%&/"a0#' 6$' '/-#'0! -$- 5&5/'(a('- 9 la- "a&a"#'&-#/"a- 6$' '-#4('%'0 #'0'& 5a&a $0 '.& a5&1'"a/'0#! -' 5&7$0(/8a&a 4- '0 la 1/-"-/(a(! 9a 6$' '- la 5&5/'(a( 4- /5a0#' !5&6$' '- "0 'lla 6$' -' "la-/7/"a a l- l$%&/"a0#'- '0 #&'- #/5-! #a%/@0 -' ('7/0/&4 a la 7&/""/30 9 a 'l ('-2a-#' 6$' -0 l- 7a"#&'- 6$' la l$%&/"a"/30 /0#'0#a &'($"/& !-' ('7/0/&4 "./0'#' 9 l- #/5- (' l$%&/"a"/30 6$' '/-#'0 6$/'0'- 1a&a0 ('5'0(/'0( ('l 2&-& ' l$%&/"a0#': F/0al'0#' -' ('-a&&lla&a l&'2'0'- (' l$%&/"a"/30! 6$' 1a&a0 ('5'0(/'0( a"$'&( a la 7$0"/30 9 la #a&'a '0 6$' -' '5l'a0 #'0'- a la l$%&/"a"/30 /(&-#4#/"a 6$' -' a5l/"a 5a&a 1//'0#- l'1'- 9 "a&2a- 5'-a(a-! " 5a&a l- #'l'-"5/- (' l- %-'&1a#&/- a-#&03/"- 9a 6$' %&/0(a $0a 2&a0 'a"#/#$( '0 'l 1//'0#! la l$%&/"a"/30 /(&(/04/"a 6$' '0 "a%/ &'6$/'&' (' 1//'0# 5a&a -$ 7$0"/0a/'0#! '/-#'0 46$/0a- 6$' '5l'a0 a%al$%&/"a"/0'-! 5&/'& la /(&-#4#/"a 5a&a (a& 1//'0# 9 ('-5$@-! "$a0( 9a -' 7&3 la 5'l"$la (' l$%&/"a0#' -' 5a-a a la l$%&/"a"/30 /(&(/04/"a:
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LUBRICACION INDUSTRIAL 1. Reseña histórica
L- l$%&/"a0#'- -0 $#/l/8a(- ('-(' /0/"/- (' la "/1/l/8a"/30! l- 5&/'&'0 $#/l/8a&l- 7$'&0 l- '2/5"/- 6$' &'"$&&a0 al '5l' (' 2&a-a-! 6$' '-#a%a0 'la%&a(a- (' $0a '8"la (' 2&a-a- a0/al'- -'%- "0 2&a-a(' &/2'0 1'2'#al 5a&a &'($"/& la 7a"/l/#a& 'l #&a-la( (' '0&'- %l6$'- (' 5/'(&a-: D$&a0#' la '(a( '(/a $% $0 ('-a&&ll "0#/0$ 5& la '.&a (' ll$%&/"a0#'-! 5'& 7$' a-#a la &'1l$"/30 /0($-#&/al (0(' Cl0'l W/ll/a D&a' ('-"$%&/3 'l a"'/#'! a&"a0( a- 'l "/'08 (' la '&a ('l 5'#&3l' 9 -$- ('&/1a(- 5& l 6$' -' "a%/3 'l '5l' (' 2&a-a- 5& a"'/#'/0'&al'- %&/6$'#a- 6$' 7$'&0 $9 ('-a&&lla(a 9 $#/l/8a(a- '0 la1a20'#a- 9 a6$/0a- /0($-#&/al'-: P'& 7$' ($&a0#' 'l -/2l ! "0 'l ('-a&&ll ('l #&! 1'"$l- 6$' -$&2/'&0 l- l$%&/"a0#'- 5&($"/(a- a %a-' (' .a%0'- '#4l/"-! "0 l "$al a%a 2&a0 1a&/'(a( (' l$%&/"a0#'- 9a 6$' "a(a 5&($"# '&a "&'a( 5a&a $0a 7$0"/30 '-5'"7/"a: A- " 'l $- (' a(/#/1- 'l "$al -' '-#$1 2'0'&al/8a0( 5a&a $0 '.& ('-'5' (' l- l$%&/"a0#'- '0 la &'($""/30 (' 7&/""/30 '0 la- a6$/0a&/a- 9 #&'-: Al 5&/0"/5/ $% $0a 0#&/a ('-"07/a08a '0 -$ $-! 5'& -' 1l1/3 'l 'l''0# 4- $#/l/8a( 5a&a &'($"/& la 7&/""/30! 5'& a-#a la a"#$al/(a( 'l l$%&/"a0#' 4- $#/l/8a( /0($-#&/al'0#' '- 'l (' 2&a-a (' l/#/: L- l$%&/"a0#'- /0'&al'- $#/l/8a(- '0 -$ a9&a -0 '#&a(- (' l9a"//'0#- 5'#&l'&- 4- 2&a0('- " l- ('l M'(/ O&/'0#': La l$%&/"a"/30 '- %4-/"a '0 la 5'&a"/30 (' la- a6$/0a&/a-! 5& l 6$' "0-#a0#''0#' '.&a 9 1a&a "0 la- 0$'1a- 0'"'-/(a('- 6$' 1a0 a5a&'"/'0(: Al#a/&a0! )**= 2. Lubricante.
S0 l- a#'&/al'- 6$' /0('5'0(/'0#''0#' (' -$ '-#a(! -' $#/l/8a 5a&a (/-/0$/& #&a#a& (' '1/#a& 'l &8a/'0# '0#&' (- -$5'&7/"/'- 6$' -' '0"$'0#&a0 '0 "0#a"#! (0(' a%a- -' '0"$'0#&a0 '0 1//'0# -l la (' a9& #aa Al#a/&a0! )**=: E-#' a#'&/al #a%/@0 '- $#/l/8a( '0 #&a- a5l/"a"/0'-! 5& '.'5l a"#$a& " $0 &'7&/2'&a0#' l/5/a& la- /5$&'8a- 6$' -0 -$- $#/l/(a('- 4"$0'-: 3. Tipos de lubricante.
?:+:M/0'&al =
E- %#'0/( 5& '(/ (' la ('-#/la"/30 &'7/0a"/30 ('l "&$( 0%&' "'&"/al “5'#&3l'”! '-#' l$%&/"a0#' '- 'l 4- %a&a# a 0/1'l $0(/al: S$ 2&a0 a%$0(a0"/a '0 'l '&"a( "'&"/al l a"' 'l 4- &'"0"/( 9 "'&"/al/8a( ('l $0(: Gal'&a ?:):S/0#@#/": S0 (' '.& &'0(//'0# 5&6$' -0 7a%&/"a(- $-a0( $0 5&"'- 6$/" 4- "-#- 6$' 'l '5l'a( '0 la %#'0"/30 (' l$%&/"a0#' /0'&al: Ta%/@0 -0 4- &'-/-#'0#'- al "al& 9 4- 74"/l'- (' 5&#'2'& '(/a0#' a0#//(a0#'-: A('4-! -0 '0- 1l4#/l'- 6$' l- l$%&/"a0#'/0'&al'-: Gal'&a P('- '0"0#&a& 1a&/- #/5- (' l$%&/"a0#'- -/0#@#/"- " 5& '.'5l ?:):+: H/(&"&a": E- $0 l$%&/"a0#' $9 "'&"/al/8a( '0 'l 4&'a la%&al 5'#&l'&a! 5& -$ %a. "-# 9 -$ 2&a0 a%$0(a0"/a '-#' /0'&al -' %#/'0' '(/a0#' $0 5&"'- (' ('-#/la"/30 llaa( /(&"&a"/02: ?:):): PAO: E- $0 "5$'-# (' %a-' -/0#@#/" $" 4- 'la%&a( 6$' 'l /(&"&a"! -' l' aa(' $0 a(/#/1 llaa( Pl/al7al'7/0a PAO! 5a&a 6$' %#'02a $0a 'l'1a(a &'-/-#'0"/a a la- #'5'&a#$&a- 9 $9 5"a 1la#/l/(a(: ?:):?: ESTER: E- $0 4"/( 2&a- "0 $0 al"l! -$ 7$'0#' 0 '- 'l 5'#&3l' !'- 'l l$%&/"a0#' 4- "-#- ('%/( a -$- $"- 5&"'-- 5a&a %#'0'&l! '-#' l$%&/"a0#' '- 5&/0"/5al'0#' $#/l/8a( '0 la a'&04$#/"a 5&6$' &'-/-#' #'5'&a#$&a- %a.a- (' <>C a-#a #'5'&a#$&a- 'l'1a(a- " ?),C: ?:?:O&240/": E-#- 0 -0 $-a(- "0'0#' '0 'l 4&'a la%&al (' la- /0($-#&/a"0 a6$/0a&/a-! ('%/( 5&/0"/5al'0#' a 6$' -' ('#'&/&a &45/(a'0#': 4. Propiedades de los lubricantes.
Pa&a $0 '.& '-#$(/ (' la- 5&5/'(a('- (' l- l$%&/"a0#'- -' (/1/(/&40 '0 5&5/'(a('- 7-/"a- 9 5&5/'(a('- 6$/"a-: ;:+:P&5/'(a('- F-/"a-: ;:+:+: V/-"-/(a(:
>
La 1/-"-/(a( -' ('7/0' " la &'-/-#'0"/a /0#'&0a (' la- -$-#a0"/a- a 7l$/&! -$ $0/(a( '- 'l 5/-': E-#a 5&5/'(a( '- $#/l/8a(a 5a&a la "la-/7/"a"/30 (' l- l$%&/"a0#'-! 5& 'll '- /5a0#' -$ '-#$(/: T(a- la- -$-#a0"/a-! #a0# -3l/(-! l6$/(- 9 2a-'--! 5&'-'0#a0 '-#a 5&5/'(a(! 5'& la /0#'0-/(a( (' '-#a 5&5/'(a( 1a&a (' a"$'&( al '-#a( '0 la 6$' -' '0"$'0#&'0: E0 l- -3l/(- la 1/-"-/(a( '- $9 'l'1a(a! '0 "a%/ '0 l- l6$/(- al /2$al 6$' l- 2a-'- la 1/-"-/(a( 0 '- #a0 0#&/a: P'& 0 '- -l 'l '-#a( 'l 7a"#& ('l "$al ('5'0(' la 1/-"-/(a(! #a%/@0 ('5'0(' (' la #'5'&a#$&a a la "$al -' '0"$@0#&'la -$-#a0"/a! -/ -' '0"$'0#&a a $0a %a.a #'5'&a#$&a -$ 1/-"-/(a( -' 'l'1aQ '0 "a%/! -/ -' '0"$'0#&a a $0a 'l'1a(a #'5'&a#$&a -$ 1/-"-/(a( -' &'($"' 0#&/a'0#': L$'2 -' 5$'(' "0"l$/& 6$' la &'la"/30 '0#&' la 1/-"-/(a( 9 la #'5'&a#$&a '- /01'&-a: E0 la 7/2$&a + -' $'-#&a la &'la"/30 '0#&' la 1/-"-/(a( 9 la #'5'&a#$&a! " 9a -' '5l/"3! '-#a '- /01'&-a:
*+,R- 1 Relación /iscosidad0Te)peratura.
Fuente: Universidad Nebrija, Lubricación, (enero de 2010), recuperado el 12 de setiembre, 2015 de: ##5:0'%&/.a:'-al5'8&L$%&/"a"/0:5(7
O#& 7a"#& ('l "$al ('5'0(' la 1/-"-/(a( '- la 5&'-/30! 6$' a (/7'&'0"/a (' la #'5'&a#$&a la &'la"/30 P&'-/30V/-"-/(a( '- (' a0'&a (/&'"#a! '- ('"/& 6$' a a9& 5&'-/30! a9& 1/-"-/(a( 9 a '0& 5&'-/30! '0& 1/-"-/(a(: ;:+:): 0(/"' (' 1/-"-/(a(: C -' '0"/03 a0#'&/&'0#' la 1/-"-/(a( ('5'0(' (' la #'5'&a#$&a! 9 '- ll'1a a 6$' -'a +*
$9 5'&.$(/"/al #&a%a.a& "0
l$%&/"a0#'-! ('%/( a 6$' la 7&/""/30 6$' -' 5&($"' '0#&' la- 5/'8a- 'l "al& 2'0'&a( 5& 'l 7$0"/0a/'0# (' la a6$/0a&/a 'l'1a0 la #'5'&a#$&a 9 '-# a7'"#a a la '7/"/'0"/a ('l l$%&/"a0#': Pa&a 'll -' /0#&($. 'l #@&/0 (' 0(/"' (' 1/-"-/(a(! 6$' '- $0a "a0#/(a( 0$@&/"a 6$' &'5&'-'0#a la &'-/-#'0"/a ('l "a%/ (' 1/-"-/(a( "0 la #'5'&a#$&a '0 $0 l$%&/"a0#': E0#&' a9& -'a 'l 0(/"' (' 1/-"-/(a( a9& -'&4 la &'-/-#'0"/a al "a%/ (' 1/-"-/(a(: L /('al -'&a 6$' $0 l$%&/"a0#' #'02a la /-a 1/-"-/(a( a (/7'&'0#'#'5'&a#$&a-! 5a&a 'll -' -$/0/-#&a0 a(/#/1- 6$' a$'0#a0 'l 0(/"' (' 1/-"-/(a( '0 l- l$%&/"a0#'-: L- a(/#/1- -0 -$-#a0"/a- 6$' a$'0#a0 -$ -l$%/l/(a( a '(/a 6$' a$'0#a la #'5'&a#$&a: A %a.a- #'5'&a#$&a- la 5a/"/5a"/30 ('l a(/#/1 0 '- a5&'"/a%l'! 5'& a '(/a 6$' la #'5'&a#$&a a$'0#a! la a2/#a"/30 l'"$la& 5&($"' 6$' 'l a(/#/1 7&' "a('0a-! a"#$a0( " $0 a2'0#' $0 '-5'-a0#': Ga&8a Ba&0a Ca&l-! +<= L- "5$'-#- 2'0'&al'0#' $#/l/8a(- " '.&a(&'- ('l 0(/"' (' 1/-"-/(a( -0 Pl'& (' B$#/l'0: Pl'& (' M'#a"&/la#: Pl'& (' '-#/&'0 Al"al/8a(: ;:+:?: D'0-/(a(: La ('0-/(a( -' ('7/0' " la &'la"/30 '0#&' la a-a (' $0a -$-#a0"/a 9 'l 1l$'0 6$' "$5a: Pa&a l- l$%&/"a0#'- -' "5a&a 'l 5'- (' $0 ('#'&/0a( 1l$'0 "0 'l 5'- (' /2$al 1l$'0 (' a2$a ('-#/la(a! 2'0'&al'0#' -' /(' a +,C: U0/1'&-/(a( N'%&/.a E-#a ('0-/(a( -' 5$'(' "al"$la& '(/a0#' la -/2$/'0#' '5&'-/30 ρ= ρ15−( θ−15 ) .0 .0007 Kg / m
3
;:+:;: P$0# (' "02'la"/30: E- la #'5'&a#$&a a la "$al 'l l$%&/"a0#' -' "02'la! "$a0( '-# -$"'(' 'l l$%&/"a0#' 5/'&(' ##al'0#' -$ 1/-"-/(a( 9 "0 'lla -$ 7$0"/30: P& 'll 'l 5$0# (' "02'la"/30 ('%' -'& 'l 0/ 5-/%l': ;:+:,: P$0# (' '0#$&%/a/'0#: E- la #'5'&a#$&a a la "$al la- -$-#a0"/a- 5&'-'0#'- '0 'l l$%&/"a0#' '5/'8a0 a "&/-#al/8a&-'! &'($"/'0( la '7/"/'0"/a ('l l$%&/"a0#': El 5$0# (' '0#$&%/a/'0# ('%' -'& 'l 4- al# 5-/%l': ;:+:<: U0#$-/(a(: ++
S' ('7/0' " la 5&5/'(a( (' l- l$%&/"a0#'- (' a('&/&-' a la5a&'('- '0 "0#a"# a0#'0/'0( a- $0a 5'l"$la (' l$%&/"a0#' "0-#a0#'! /5/(/'0( 'l "0#a"# '0#&' la- 5/'8a-: ;:+:=: Cl& E- $0a 5&5/'(a( (' #(a- la- -$-#a0"/a- 5'& '0 'l "a- (' ll$%&/"a0#'- 'l "l& (' $0 l$%&/"a0#' 0- 5&5&"/0a la /07&a"/30 (' 5$&'8a: ;:+:>: Vla#/l/(a(: E- la 7a"/l/(a( '0 la "$al $0a -$-#a0"/a -' '1a5&a! '0 l- l$%&/"a0'- '%a.a 5'& 0 ('-5&'"/a%l': ;:):P&5/'(a('- $/"a-: ;:):+: P$0# (' /07laa"/30: E- la #'5'&a#$&a 0/a '0 la "$al -' ('-5&'0(' 2a-'- /07laa%l'- ('l l$%&/"a0#' 6$' 5(&a0 '0"'0('&-' "0 $0a "/-5a $0 5$0# /0"a0('-"'0#': El 5$0# (' /07laa"/30 (' $0 l$%&/"a0#' ('%' -'& l 4al# 5-/%l'! 9a 6$' 2'0'&al'0#' -' #&a%a.a "0 46$/0a- a 'l'1a(a#'5'&a#$&a- " 'l #& (' $0 a$#31/l: ;:):): P&5/'(a( a0#//(a0#': P&5/'(a( 6$' /0(/"a 6$' #a0 &'a"#/1 '- 'l l$%&/"a0#': L- l$%&/"a0#'- al 2'0'&al'0#' -' $#/l/8a0 '0 "0#a"# "0 '#al'-! a/&' 9 a 'l'1a(a- #'5'&a#$&a-! "0(/"/0'- '0 la "$al -' 5&($"' $0a &'a""/30 '0 "a('0a ('-"50/'0( al l$%&/"a0#': C 'l ING: Ca&l- Ba&0a Ga&8a! 5&'-'0#3 '0 -$ -'/0a&/ (' I02: M'"40/"a -%&' l$%&/"a"/30 /0($-#&/al La o!idación de un aceite lubricante es resultado de una reacción en cadena siendo los primeros productos "ormados peró!idos or#$nicos los cuales atacan al aceite % son nuevamente re#enerados por el o!eno del aire para continuar la reacción, la 'ue es llamada o!idación auto catal&tica (*ar+a arona -arlos, 1./, p$# ) E-#' 5&%l'a '- $9 2&a1' 5& 'll '- 0'"'-a&/ #a& '(/(a- 5a&a "0#&a&&'-#a& '-#a 5&5/'(a(! 2'0'&al'0#' -' l2&a aa(/'0( a(/#/16$' al#'&a0 -$ 5&5/'(a( a0#//(a0#': ;:):?: P&5/'(a( a0#/'-5$a0#': La "a5a"/(a( 6$' #/'0'0 l- l$%&/"a0#'- '0 7&a& '-5$a-: C$a0( l- l$%&/"a0#'- -0 a2/#a(- 2'0'&a '-5$a-! 6$' -0 %$&%$.a(' a/&' 9 6$' &'($"'0 la 1/-"-/(a( 5& 7al#a (' a"'/#' 2'0'&a0( +)
&8a/'0# '0#&' la- 5/'8a- '0 l- l$2a&'- (0(' -' '0"$'0#&a 0 la%$&%$.a- :A '-# 'l I02: Ga&8a &'"/'0(a 3vitar la a#itación e!cesiva del aceite, lo cual se lo#ra teniendo las l&neas de succión % retorno al tan'ue en e!tremos opuestos (*ar+a arona -arlos, 1./, p$# ) ;:):;: P&5/'(a( (' '#&'a 5&'-/30: E- la 7a"/l/(a( 6$' #/'0'0 l- l$%&/"a0#'- 5a&a #&a%a.a& a (/7'&'0#'5&'-/0'-: 5. Clasificación de los lubricantes.
C -' '0"/03 a0#'&/&'0#' la 1/-"-/(a( '- la 5&5/'(a( '0 la 6$' -' 0- %a-a- 5a&a "la-/7/"a& a l- l$%&/"a0#'-: A&a -' 5&'-'0#a&a l5&/0"/5al'- #/5- (' "la-/7/"a"/30 -'20 -$ 1/-"-/(a(: ,:+:V/-"-/(a( Sa9%l#: S$ $0/(a( '- 'l -'2$0( Sa9%l# $0/1'&-al SSU: C0-/-#' '0 '(/& 'l #/'5 '0 6$' <*"" (' l$%&/"a0#' ('&a '0 7l$/& a #&a1@- (' $0 &/7/"/ '0 $0a #'5'&a#$&a (' '0#&' +**F 9 )+*7: A a9& #/'5! a9& 1/-"-/(a(: E0 la 7/2$&a ) -' $'-#&a 'l /0-#&$'0# $#/l/8a( 5a&a '(/& la 1/-"-/(a( Sa9%l#:
+?
*+,R- 2edición de la iscosidad abolt
Fuente: 4N646U67 63-N7L7*4-7 U839479 U-93,iscosidad a%bolt,21 de ma%o del 2012, recuperado el 12 de setiembre de 2015, de electromecanicosucreblo#spotpe;p;propiedades
,:):V/-"-/(a( C/0'4#/"a: M/(' la V/-"-/(a( a%-l$#a (' $0 l$%&/"a0#'! -$ $0/(a( '- 'l "'0#/-#' CST! 6$' /0(/"a 'l #/'5 (' 7l$/('8 (' $0 l$%&/"a0#' '0 $0 #$% "a5/la&: La $0/(a( (' la 1/-"-/(a( a%-l$#a '- 'l P/-': A:S La &'la"/30 '0#&' la 1/-"-/(a( "/0'4#/"a 9 a%-l$#a '- la -/2$/'0#' Viscosidad Absoluta=Viscosidad Cinemetica ×Gra vedad Especifica
,:?:V/-"-/(a( SAE: E- $0a '-"ala (/-'a(a 5& la S"/'#9 7 A$##/1' E02/0''&- 5a&a a"'/#'- (' #& 9 5a&a "a%/- (' 1'l"/(a(: S$ "la&/(a( '- $9 -/5l' 9 5& 'll 'l 4- $#/l/8a( a la &a (' "la-/7/"a& a"'/#'-: C0-/-#' '0 /0(/"a& la #'5'&a#$&a '0 la "$al 'l l$%&/"a0#' '- 4- a5&5/a(! 5& '.'5l 'l SAE ;* '- 4- a5&5/a( 5a&a "l/a- "al$&--! 'l SAE )* 5a&a "l/a- 4- 7&- 9 'l SAE ?* 5a&a "l/a- #'5la(-: CAL 6. ricción.
+;
S' ('7/0' " la &'-/-#'0"/a al 1//'0# &'la#/1 '0#&' (- "$'&5- '0 "0#a"#: Pa&a ('-l/8a& l- "$'&5- $0- -%&' #&- -' 0'"'-/#a 1'0"'& a $0a 7$'&8a! '-#a 7$'&8a 6$' -' 50' al ('-l/8a/'0# -' "0"' " 7&/""/30: E0 la 7/2$&a ? -' $'-#&a 2&47/"a'0#' la- 7$'&8a- 6$' 5a/"/5a0 '0 'l /0/"/ ('l ('-5la8a/'0# (' $0 %.'#: D0(' -' '1/('0"/a .$-#a'0#' 6$' la 7$'&8a (' &8a/'0# F 7 -' 50' al ('-5la8a/'0#: *+,R- 3 ricción
Fuente:Fisica,Fricción,(15 de mar+o de 2015)recuperado el 1> de setiembre,2015,de: =ttps:;;dani>0a#ua%o?ordpresscom;2015;0>;15;"isica
<:+:Ca$-a-: La 7&/""/30 -' 5&($"' ('%/( al "0#a"# '0#&' (- -$5'&7/"/'- &$2-a-! la &$2-/(a( (' '-a- -$5'&7/"/'- ('5'0(' ('l a#'&/al 9 'l #&a#a/'0# 6$' -' l' (a! 5'& 5& 4- l/- 6$' -'a $0a -$5'&7/"/' -/'5&' -' '0"0#&a&a0 (//0$#a- 5&#$%'&a0"/a- 6$' -' #&a#a&a0 (' '0la8a&-' 9 a2a&&a&-': E-#a- 5&#$%'&a0"/a- -0 la "a$-a (' 6$' '/-#a la 7& /""/30: <:):E7'"#-: Pa&a 1'0"'& la 7&/""/30 -' &'6$/'&' $0a 7$'&8a! 6$' '0 $0a a6$/0a -/20/7/"a&a 6$' 5a' (' la '0'&2a ('-#/0a(a a -$ 7$0"/0a/'0# -' ('-1/a&a! "a-/0a0( $0a %a.a (' 5#'0"/a 9 "0 'll '7/"/'0"/a! a('4- ('l "al& 2'0'&a( 5& 'l &8a/'0# 9 'l ('-2a-#' '0#&' la-$5'&7/"/'-: P'& #a%/@0 #/'0' -$ $#/l/(a(! " 5& '.'5l "$a0( "a/0a- la 7&/""/30 '0#&' la -$'la ('l 8a5a# '1/#a 6$' 0$'-#& 5/' -' ('-l/"' a"/a a#&4-! " -$"'(' al "a/0a& '0 /'lQ #a%/@0 '- a5&1'"a( '0 l-
+,
7&'0- (' la- 46$/0a-! 5&/'& '0 'l (/-" 9 ('-5$@- '0#&' la lla0#a 9 'l 5a1/'0#: Pa&a a5&1'"a& 5&'1'0/& la 7&/""/30 -' /0#&($. $0 7a"#& "0"/( " "'7/"/'0#' (' 7&/""/30 6$' 0- 5'&/#' "al"$la& la 7$'&8a 0'"'-a&/a <:?:C'7/"/'0#' (' 7&/""/30: E- $0 0'& 6$' /0(/"a la &$2-/(a( (' $0a -$5'&7/"/'! a- #a%/@0 &'la"/0a la 7$'&8a 0'"'-a&/a 5a&a 1'0"'& la 7$'&8a (' &8a/'0#! /'0#&a- a9& -'a 'l "'7/"/'0#' (' 7&/""/30 4- &$2-a '- la -$5'&7/"/' 9 4- 7$'&8a -' &'6$'&/&4 5a&a /0/"/a& -$ 1//'0#: Coeficiente de friccion ( μ )=
Fuerza de friccion Carga perpendicular a la superficie
La l$%&/"a"/30 -' '0"a&2a (' &'($"/& 'l "'7/"/'0#' (' 7&/""/30 a0#'0/'0( $0a 5'l"$la (' l$%&/"a0#' '0#&' a%a- -$5'&7/"/'-! 5a&a -/-#'a- "&&'"#a'0#' (/-'a(- 9 l$%&/"a(- 'l "'7/"/'0#' (' 7&/""/30 5$'(' ll'2a& a #a& $0 1al& (' *!**,! 9 '0 "0(/"/0'- $9 '-5'"/al'-' a l2&a( "0-'2$/& "'7/"/'0#'- (' a-#a *:*****,! 'l %.'#/1 'a"'&"a&-' l 4- 6$' -' 5$'(' a $0a -$5'&7/"/' "5l'#a'0#' l/-a μ=0 ¿
: Ga&8a Ba&0a Ca&l-! +<=
!. "es#aste.
El ('-2a-#' '- 'l ('#'&/&a /'0# (' $0 %.'#! "$&&' 5& la /0#'&a""/30 (' la- &$2-/(a('- '0#&' (- 5/'8a- 9 -' 5$'(' &'($"/& a0#'0/'0( la- 5/'8a'0 1//'0# 7$'&a (' "0#a"# '(/a0#' $0a "a5a (' l$%&/"a0#': =:+:T/5- (' ('-2a-#': =:+:+: D'-2a-#' a('-/1: S' 5&($"' "$a0( la- /&&'2$la&/(a('- /0#'&a"#a0 (/&'"#a'0#'! '-# 5&($"' 6$' (/"a- /&&'2$la&/(a('- -' '02a0"'0 9 6$/'%&'0! ('.a0( &'-/($-: E-#- &'-/($- -0 5'&.$(/"/al'- 5a&a "$al6$/'& #/5 (' a6$/0a&/a 9a 6$' la 1/-"-/(a( 9 "a5a"/(a( (' l$%&/"a"/30 -' 1'&4 2&a1''0#' a7'"#a(a 5'&.$(/"a0( 'l 5&"'- 9 la 5/'8a (' la a6$/0a&/a: E-#' 5&"'- -' 1' /l$-#&a( '0 la 7/2$&a ;! -#&a0( "a(a '#a5a ('l 5&"'- (' ('-2a-#': +<
*+,R- 4 "es#aste
Fuente: @es#aste,recuperado el 1> de setiembre de 2015, de : =ttp:;;#enerar< srlcomar;docs;lubricacionAo"icialpd"
=:+:): D'-2a-#' "&&-/1: S' 5&($"' "$a0( la- -$-#a0"/a- '0 -0 "&&(a-! 5& a#'&/al'" 4"/(- " 9a -a%'- 5& 'l "0#a"# '0#&' 'l l$%&/"a0#' 9 'l a/&': $. Co%inetes.
E- $0 (/-5-/#/1 6$' 5'&/#' $0 1//'0# 0/ '0#&' la- (5/'8a- '0 "0#a"#! /0//8a0( la 5'&(/(a (' '0'&2a! la 7&/""/30 9 'l ('-2a-#' (' la- 5/'8a-! 5& l "$al '- "0 '0"0#&a&l '0 la /0#'&a""/30 (' '-#a-: Ha9 #&'- #/5- (' "./0'#'- >:+:C./0'#'- C/l0(&/"-: E-#' #/5 (' "./0'#'- 0- 5'&/#' 6$' ('-l/"' -/0 l$%&/"a0#' 5& 'l '.'! 5a&a l "$al la- 5/'8a- '0 "0#a"# #/'0'0 6$' '-#a& 'la%&a(- "0 $0a -$5'&7/"/' 5&-a! 9 "0 la a9$(a( (' &(a/'0#-: La 5'l"$la ('l l$%&/"a0#' ('%' '-#a& 5&'-$&/8a( l "$al '- "0-'2$/( 5& '7'"#- /(&(/04/"-! 5'& -$- "0(/"/0'- -0 ('7/0/(a- 5& la "a&2a &a(/al 9 la 1'l"/(a( (' 2/& ('l '.' >:):C./0'#' (' F&/""/30:
+=
E- $#/l/8a( 5a&a 5/'8a- 6$' -' '0"$'0#&a0 a %a.a- 1'l"/(a('- (' 2/&! -0 (@%/l'- 5& l "$al -5a0 /2$al "a&2a 6$' l- &(a/'0#-: &. Tipos de Lubricación.
Pa&a ('7/0/& l- #/5- (' l$%&/"a"/30 (' /0#&($"/&4 $0 "'7/"/'0#'
γ
('7/0/( 5& γ =
espesor minimo de pel icula rugosidad dela superficie
:+:L$%&/"a"/30 5'&7'"#a γ > 3.5 ¿ C -' $'-#&a '0 la 7/2$&a , la- (- -$5'&7/"/'- '-#40 5'&a0'0#''0#' -'5a&a(a- 5& $0a "a5a (' l$%&/"a0#'! &'la#/1a'0#' a5l/a -/0 #"a&-' '0 0/020 5$0#: *+,R- 5 Lubricación perfecta
Fuente: lide8la%er,6ecnolo#ia de uper"icies,(setiembre de 20 1B),recuperado el 25 de setiembre de 2015,de: ##5-l/('5la9'&:'--l/('+<)<)>>
:):L$%&/"a"/30 /#a 1 < γ < 3.5 ¿ P&($"/(a 5& 'l a$'0# (' 5&'-/30! 1/-"-/(a( 9 la 1'l"/(a( &'1l$"/0'- (' l- '.'-! '-# a"' 6$' l- 31/l'- '-#@0 (/-#a0"/a(a5& $0a 5'l"$la (' l$%&/"a0#' $0/7&'! 5'& ('l2a(a! l "$al "a-/0a $0 "0#a"# '#al'#al! ('%/( a la- &$2-/(a('-! #al " -' $'-#&a '0 la 7/2$&a <: *+,R- 6 Lubricación )ita
+>
Fuente: lide8la%er,6ecnolo#ia de uper"icies,(setiembre de 20 1B),recuperado el 25 de setiembre de 2015,de: ##5-l/('5la9'&:'--l/('+<)<)>>
:?:L$%&/"a"/30 l//#' : γ < 1 ¿ E- "a-/0a( 5& $0a 1a&/a"/30 '0 la $0#$-/(a( '0 la "5-/"/30 6$/"a (' la- 5/'8a- '0 "0#a"#! -$ 7$0"/30 4- /5a0#' '- la (' &'($"/& 'l "0#a"#! 5'& -/0 a7'"#a& 'l %$'0 7$0"/0a/'0#! '(/a0#' "'- '0#&' la- (- 5/'8a-! la- "$al'- 5(&a0 -'& &'al/8a(a- 5& la al#a a('&'0"/a (' la- 5/'8a- "0"'0#&a&l- '0 $0 5$0# (' 1a5&/8a"/30 al#: *+,R- ! Lubricación li)ite.
Fuente: lide8la%er,6ecnolo#ia de uper"icies,(setiembre de 20 1B),recuperado el 25 de setiembre de 2015,de: =ttp:;;slidepla%eres;slide;1/2/2;
1'.Re#()enes de lubricación.
+*:+: L$%&/"a"/30 /(&-#4#/"a: E- "$a0( 'l $- (' l$%&/"a0#' -' 2a&a0#/8a 2&a"/a- a $0a 5&'-/30 "0-#a0#' '0 la 80a (' a5l/"a"/30! a5&5/a(a 5a&a l"a"/0'- (' 1//'0# l'0#! 9a 6$' 'l 0/1'l (' &8a/'0# #/'0(' a -'& %a.: U-$al'0#' a9 la 5&'-'0"/a (' $0 'l''0# &'2$la(& llaa( "a5/la&! 5a&a a- 5('& 7&a& la "a5a (' a"'/#'! a59a( 5& la 0/a 1'l"/(a( (' l- '.'-! 9 a- a9a $0 "&&'"# a&&a06$' (' la- a6$/0a-: E-#' #/5 (' l$%&/"a"/30 5&'-'0#a $"- /0"01'0/'0#'- '0 'l #aa +
"-# (' l- "./0'#'-! 9a 6$' ('5'0(' ('l 7$0"/0a/'0# (' la%%a- 6$' -' '0"$'0#&a0 al '#'&/&! 9 -$ a%a-#'"//'0# (' a"'/#': E0 'l "./0'#' /(&-#4#/"! la- -$5'&7/"/'- (' la- 5/'8a- -' '0"$'0#&a0 -'5a&a(a- 5'&a0'0#''0#' 5& $0a 5'l"$la (' a"'/#'! 9a 6$' -0 la6$' -5a0 la "a&2a! 5& la ('#'&/0a0#' la%&! -0 "0-#/#$/(- 5& l#/5l'- "'l(a-! la- "$al'- -0 l$%&/"a(a- /0('5'0(/'0#''0#'! l "$al 2a&a0#/8a 6$' "a(a $0a #'02a $0a 5&'-/30 (/-#/0#a: E0 la 7/2$&a > -' $'-#&a la- "a&a"#'&-#/"a- '-'0"/al'- (' $ #/5 (' "./0'#' /(&-#4#/": *+,R- $ Co%inete idrost7tico.
Fuente: Universidad -arlos 444 de Cadrid (2005) Lubricación Cadrid, Drea 4n#enier&a Cec$nica, e!tra&do el 25 octubre de 2015, de: =ttp:;;oc?uc>mes;in#enieria< mecanica;tecnolo#ia
E/-#'0 ) #/5- (' "./0'#'- /(&-#4#/"- +*:+:+: A "a$(al "0-#a0#': S$ "a&2a '- '"@0#&/"a 9a 6$' la 5&'-/30 0 '- "0-#a0#'! la&'-/-#'0"/a- -' %#/'0'0 '(/a0#' la &'$#/l/8a"/30 (' #$%- "a5/la&'a0#'&/&'0#' "al/%&a(-! '- 'l 4- %a&a# 9a 6$' -l $-a $0a %%a! "0 la a9$(a (' &'-/-#&'-! l "$al a"' 6$' #a%/@0 -'a 'l 4- $#/l/8a( '0 la- a6$/0a-:
+*:+:):
A 5&'-/30 "0-#a0#': )*
S$ "a&2a '- "&&/'0#'! (' 2&a0 "a5a"/(a( 9 0 5&'-'0#a -%&'-al#-! 9a 6$' $#/l/8a 1a&/a- %%a- 5a&a a-'2$&a& 'l "&&'"# 7l$.! 5'& '- 5" 1al&a(a 5& la 7$'' /01'&-/30 6$' &'6$/'&' 5a&a $#/l/8a&la-! a('4- ('l al# "-# (' a0#'0//'0# 6$' '/2': +*:): L$%&/"a"/30 H/(&(/04/"a El '-#$(/ (' '-#a l$%&/"a"/30 -' (/ a "0"'& '0 la #'&a (' B'a$"a5 T'& /02l'-! 5&($"# (' $0 '&&&! 9a 6$' '-#a%a '0"a&2a( (' '-#$(/a& la l$%&/"a"/30 '0 l- "./0'#'- (' l- 7'&&"a&&/l'9 (a& a "0"'& $0a 7&a 5a&a $0a l$%&/"a"/30 4- -'0"/lla 9 '7/"/'0#': P&($"/( -l '0#&' (- -$5'&7/"/'- '0 1//'0# "0-#a0#' "0 'l 2/& ('l '.'! 6$' 1/l/8a 'l l$%&/"a0#' "&'a0( 80a- (' ('5&'-/30! ll'2a a 7&a& $0a "$a (' 7l$/( a 5&'-/30 6$' -'5a&a l- (- "$'&5- 5& $0 #/'5 5&l02a(! a('4- (' -5a& la "a&2a a la 6$' '-#40 -'#/(a-! 5'& '-# ('5'0(' (' la 1'l"/(a( &'1l$"/0'- ('l '.'! 1/-"-/(a( ('l l$%&/"a0#' $ #&- 7a"#&'- '#'&0-: Pa&a 6$' -' 5$'(a 7&a& $0a 5'l"$la /(&(/04/"a 'l '-5a"/ '0#&' la- -$5'&7/"/'- (' la- 5/'8a- '0 "0#a"# ('%' -'& a9& a -$&$2-/(a('-! -$- -$5'&7/"/'- 0 ('%'0 -'& 5a&al'la-! 0/ #'0'& $0 1//'0# &'la#/1! l "$al 2'0'&' $0 7l$/( 1/-"- 9 $0#$- S/ la a6$/0a #&a%a.a&a a('"$a(a'0#' "0 la l$%&/"a"/30 /(&(/04/"a! 'l a"'/#' l$%&/"a0#' 2'0'&a( '0 $0 "./0'#' #'0(&a $0 '-5'-& a9& 6$' l- ('-0/1'l'- (' l- -3l/(- 5$'-#-: E-#a #'&a 5-#$l al2$0a- /53#'-/- 5a&a 5('& ('-a&&lla&-' La- -$5'&7/"/'- (' la- 5/'8a- (' "0#a"# -0 ($&a- 9 #/'0('0 a •
•
a('&/&-' '0#&' -/ N -' #a '0 "$'0#a la- 7$'&8a- (' /0'&"/a 9 -/ la l'9 (' N'#0
('l 1//'0# El 7l$. ('l l$%&/"a0#' '- la/0a& ' /0"5&'0-/%l' Al 7all'"'& T'&! O-%&0' R'90l(- %a-40(-' '0 la /01'-#/2a"/30 (' •
T'& 5la0#' $0a l'9 '0 la "$al 'l l$%&/"a0#' -' a(/'&' a la- -$5'&7/"/'(' la- (- 5/'8a- '0 "0#a"#! 5a&a l$'2 -'& /5$l-a( 5& 'l 1//'0# a $0a "$a! l "$al 2'0'&a%a $0a 5&'-/30 -$7/"/'0#' 5a&a -5a& la "a&2a '0 'l "./0'#': E-#a l'9 &'la"/0a la 5&'-/30 ('l 7l$/(! 'l "'7/"/'0#' (' 7&/""/30 9 la 1'l"/(a( &'la#/1a! 5& l "$al 0- (a a "0"'& $0a '"$a"/30 (/7'&'0"/al '0 la "$al -' ('-5&'"/a0 la- 7$2a- la#'&al'-
)+
( ) 3
d ! dp =−6 " d! d n d d "e)ostración U0/1'&-/(a( Ca&l- III (' Ma(&/(! )**,
C0-/('&'- 'l -/2$/'0#' "a- S'a $0 $30 6$' 2/&a '0 -'0#/( &a&/ -5a( 5& $0a "a5a (' l$%&/"a0#' (' '-5'-& 1a&/a%l' “” -%&' $0 "./0'#' 5a&"/al '-#a"/0a&/a: *+,R- & Co%inetes de Contacto.
Fuente: lide8l%er,-ojinetes de contacto,(enero,2015),recuperado el 1/ de octubre,2015,de: =ttp:;;slidepla%eres;slide;B1..21;
A"'5#a0( la /53#'-/- a0#'&/& (' "./0'#' 5la0! -' 7/.a $0 -/-#'a (' &'7'&'0"/a! "0 la- -/2$/'0#'- "0-/('&a"/0''l "./0'#' 9 'l $30 -' 5&l02a0 /0('7/0/(a'0#' '0 la (/&'""/30 “”: la 5&'-/30 '0 "0-#a0#' '0 la (/&'""/30 “Y”! 5& #a0# la 5&'-/30 -l ('5'0(' (' “”: La 1'l"/(a( (' $0a 5a"$la (' l$%&/"a0#' -l ('5'0(' (' la"&('0a(a- “Y” 9 “”: S$502a- $0a 5a"$la (' l$%&/"a0#' (' (/'0-/0'- (9! (! (8 '0 'l -'0 ('l 7l$/( '0 'l 6$' "al"$la- l- '-7$'&8- 6$' a"#a0 -%&' -$"a&a-: S%&' la "a&a ('&'"a ' /86$/'&(a ('l 'l''0# a"#a0 7$'&8a- 0&al'('%/(a- a la 5&'-/30 9 -%&' la- "a&a- -$5'&/& ' /07'&/& a"#a0 7$'&8a#a02'0"/al'- ('%/(a- a la 1/-"-/(a( 9 la 1'l"/(a( ('l 7l$/(: % $ d ) d# dz + $ddz − ( $ + d# d dz − p d# dz =0 ∑ F : ( p + dp d %# )
S/5l/7/"a0( ))
dp % $ = ( 1) d % v
P& -'& $0 7l$/( 0'#0/a0 7$'&8a #a02'0"/al 5&5&"/0al a la 2&a(/'0#' (' 1'l"/(a( '0 'l -'0 ('l 7l$/(: La "0-#a0#' (' 5&5&"/0al/(a( '- la 1/-"-/(a( (/04/"a! '(/(a '0 Pa:- %μ %#
$ =n
S$-#/#$9'0( '0 + 2
dp =n % μ2 d %#
Ma0#'0/'0( “” "0-#a0#' ' /0#'2&a0( la '5&'-/30 (- 1'"'- &'-5'"# a “9” -' %#/'0' % μ 1 dp = + C 1 % # n d μ=
dp 2 # + C 1 # + C 2 2 n d 1
P$(/'0( -'& la- "0-#a0#'- (' /0#'2&a"/30 7$0"/0'- (' “”: S$50/'0( 6$' 0 '/-#' ('-l/8a/'0# '0#&' 'l l$%&/"a0#' 9 la-$5'&7/"/'- ('l 2&&30 9 'l "./0'#': μ=−" μ=0 9* Q 9 T'0/'0( '0 "$'0#a 6$' '- 7$0"/30 (' “” 5('- %#'0'& la"0-#a0#'- (' /0#'2&a"/30: C 1 =
−" !
−
! dp C 2=0 2 n d
E- ('"/& la '"$a"/30 (' (/-#&/%$"/30 (' 1'l"/(a( ('l l$%&/"a0#' -'&/a u=
dp 2 ( # −!# ) − " # 2 n d ! 1
)?
S/ '- 'l 7l$. '0 la (/&'""/30 (' “” $0/(a( (' a0" '0 la (/&'""/30 (' “8”: !
∫
&= ' μ d # = 0
−"! 2
3
−
!
dp 12 n d
S$-#/#$9'0( 'l 1al& ('
μ
' /0#'2&a0(! (a( 6$' 'l 7l$/( -'
"0-/('&a /0"5&'0-/%l' 9 la "0#/0$/(a( (' la a#'&/a! 'l "a$(al 6$' 5a-a 5& "$al6$/'& -'""/30 #&a0-1'&-al 5'&a0'"' "0-#a0#' d& − " d! d = − 2 d d d
(
!
3
)
dp =0 12 n d
( ) 3
d ! dp =−6 " d! d n d d
E"$a"/30 "l4-/"a (' R'90l(- 5a&a 7l$. $0/(/'0-/0al! ('-5&'"/a0( 7$2a- la#'&al'-! '- ('"/& 7l$. '0 la (/&'""/30 “8”: A&a -/ 0 -' ('-5&'"/a0 '-#a- 7$2a-! "0 $0 ('-a&&ll -//la& -' %#/'0' $0a '"$a"/30 -/0 -l$"/30 2'0'&al: S/0 '%a&2 A: Ra/0(/ 9 J0 B9( $-a&0 #@"0/"a- (' /#'&a"/30 5a&a &'-l1'& la '"$a"/30 (' -'&7'l(! %#'0/'0( 2&a7/"a- 6$' $#/l/8a%a0 'l 0'& (' -'&7'l( 0'& "a&a"#'&-#/" ('l "./0'#': U0/1'&-/(a( Ca&l- III (' Ma(&/(! )**, 2
r n) ( =( ) c *
D0(' l- -%l- "&&'-50('0 a S N "a&a"#'&-#/" ('l "./0'#' & Ra(/ ('l $30 " Hl2$&a &a(/al 0 V/-"-/(a( a%-l$#a N V'l"/(a( &'la#/1a '0#&' $30 9 "./0'#' P Ca&2a 5& $0/(a( (' 4&'a 5&9'"#a(a E0 l- a0'- -' $'-#&a0 la- 2&47/"a- 6$' %#$1/'&0 Ra/0(/ 9 B9( ∙
∙
∙
∙
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∙
" -l$"/30: +*:?: L$%&/"a"/30 Ela-#H/(&(/04/"a: C 9a 1/- '0 la l$%&/"a"/30 /(&(/04/"a! -' %#/'0' la '"$a"/30 (' R'90l(- "0-/('&a0( $0a -'&/' /53#'-/- 6$' 5'&/#/'&0 );
-/5l/7/"a&l: S/ '%a&2 -/ la- "a&2a- a"#a0 '0 -$5'&7/"/'"0-/('&a%l''0#' 5'6$'a-! -$&2'0 (- /53#'-/- 6$' 0 7$'&0 "0-/('&a(a- 5& R'90l(-: la 1/-"-/(a( a$'0#a "0 la 5&'-/30: la- -$5'&7/"/'- -' ('7&a0 'l4-#/"a'0#': C '-# -' 2'0'&a '0 -/#/- "0 "a&2a- al#a- (0(' la- 5/'8a-/'5&' '-#40 '0 "0#a"#! 5& '.'5l '02&a0a.'-! " "0-'"$'0"/a (' la- 'l'1a(a- "a&2a- a$'0#a la 1/-"-/(a( 9 la- ('7&a"/0'- ('l l$%&/"a0#'! a$'0#a0 'l '-5'-& (' la 5'l"$la! la "$al '- (' $0 #aa /"&-"35/" $" '0& a la
(' la 5'l"$la /(&(/04/"a: El
l$%&/"a0#' '- a&&a-#&a( a la- 4&'a- (' "0#a"# (0(' -5a $0a 2&a0 5&'-/30! 6$' (/-#&/%$9' la "a&2a 5& "a-/ la ##al/(a( (' la -$5'&7/"/': E-#' '"a0/- (' "3 -' 2'0'&a la 5'l"$la (' l$%&/"a0#' '"0"/( " L$%&/"a"/30 Ela-#/(&(/04/"a: Pa&a "$a0#/7/"a& la #'&a (' l$%&/"a"/30 'la-#/(&(/04/"a! '0'"'-a&/ "0.$2a& '-#a- #&'- '"$a"/0'- +*:?:+: E"$a"/30 (' la 1/-"-/(a( '0 7$0"/30 (' la 5&'-/30 RUA! -:7:: n ( * +, )= F ( , ) e
$*
− − − D30(' $ #/'0' 1al&'- #5/"- '0#&' 2.10 9 6.10 *a +*:?:): E"$a"/30 (/7'&'0"/al (' R'90l(- J-' D/ Pal! +,: 8
8
1
p ( ) = p ( − - )+ 12 n"
∫ ( !−! C ) d 3
− -
+*:?:?:
E"$a"/0'- (' la ('7&a"/30 'l4-#/"a (' l- "$'&5-
Na1a&&: E0 'l '.' . =
1
E
[ / − v (/ +/ ) ]
#
z
E0 'l '.' Y 1
. # = [ / # −v ( / + / z ) ] E
E0 'l '.' ),
. z=
1
[ / −v ( / + / )]
E
z
#
D0(' .i 3($l (' Y$02 3($l (' 'la-#/"/(a( l/0'al: E &/2/('8 (' $0 a#'&/al: / i '-7$'&8 '0 'l '.' /: La l$%&/"a"/30 'la-#/(&(/04/"a "/'08a "0 la '"$a"/30 a0al#/"a (' G&$%/0 '0 +;: P-#'&/&'0#'! W'%'&! Saa7'l( 9 P&'#&$-'1/" 5&5&"/0a0 -l$"/0'- 5a&"/al'- ('l -/-#'a (' '"$a"/0'-: E- a 5a/& (' +,! "0 D-0 9 H/22/0-0 "$a0( -' a1a08a (' 1'&(a( '0 '-#' "a5! "0 la &'al/8a"/30 (' $l#/#$( (' '5'&/'0#- 6$' 5'&/#/'&0 la "$a0#/7/"a"/30 (' la (/-#&/%$"/30 (' 5&'-/0'-: '-5/08a! )**=
)<
CONCLUSIONES L- l$%&/"a0#'- -0 7l$/(- (' $0a 2&a0 /5a0"/a! 2&a"/a- a -$ "a5a"/(a( (' &'($"/& la 7&/""/30 9 'l ('-2a-#'! ('%/( a -$- 5&5/'(a('-! la- "$al'" 9a -' a 1/-# 5-''0 7$0(a'0#- #'3&/"- 6$' -0 1'&/7/"a(- "0 l- &'-$l#a(- '5'&/'0#al'-! a- #a%/@0 "0"'- l- 5'&-0a.'- 6$' a5a&0 -$- /('a- 6$' -/&1/'&0 " %a-' ('l 5-#'&/& ('-a&&ll (' $0a #'&a 6$' -' -$-#'0#3 "0 ('l- a#'4#/"-: E- /5a0#' &'"0"'& la- 5&/0"/5al'- a5l/"a"/0'- (' l- l$%&/"a0#'- '0 la- /0($-#&/a- " '0 '02&a0'- 9 %al'&-! -/-#'a- /(&4$l/"-! #&'- (' "%$-#/30 /0#'&0a 9 a"'/#'- 5a&a "' 9 &'7&/2'&a"/30Q 9 .$-#a'0#' 5& -$ a5l/"a"/30 '0 'l '&"a( '- 6$' ('-a&&ll la #'&a (' l$%&/"a"/30! " $0a '&&a/'0#a 6$' %$-"a 7$0(a'0#al'0#' a$'0#a& la '7/"/'0"/a (' la /0($-#&/a 9 "0 'lla -$ 5&($"#/1/(a(:
)=
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