UNIVERSIDAD DE ORIENTE NÚCLEO ANZOÁTEGUI ANZOÁTEGUI ESCUELA DE INGENIERÍA Y CIENCIAS APLICADAS DEPARTAMENTO DE INGENERÍA MECÁNICA SECCIÓN: 21
LABORATORIO DE INGENIERÍA MECÁNICA I Infor! " # MEDICIÓN DE VELOCIDAD
Revisado por:
Prof$ Prof$ L%no L%no C&&r' C&&r'oo
Bachilleres:
D&n%!( D&n %!( V%((&r %((&rro!( ro!( C$I$ C$I$ 2#)# 2#)#*2+, *2+, C!-&r V!(&-.o C$I$ 2)#1#1+,
B&r.!(on&/ 22 0! O.3r! 0! 241,
RESUMEN
L& 5r6.%. 5r6.%.&& & .on%n .on%n&.% &.%7n 7n %!n! %!n! .oo .oo f%n&(% f%n&(%0&0 0&0 5ro5or.% 5ro5or.%on&r on&r &( !-0% !-0%&n &n!! 0! In'!n In'!n%! %!r8 r8&& M!.6 M!.6n% n%.& .& (o(o- .on .ono. o.% %%! %!n noo- 36-% 36-%.o .o-- r!f!r r!f!r!n !n! !-- & (o(o- %n- %n-r r!n !noo%(%9&0o- 5&r& !0%.%on!- 0! !(o.%0&0$ En !-! .&-o/ -! !-0%&ron !( &.7!ro ; !( !-ro3o-.o5%o/ (o- .&(!- -on ; %(%9&0o- !n !( .&5o 0! (& %n'!n%!r8&/ ;& <! -! !n.&r'&n 0! !0%r (&- r!o(.%on!- 5or %no- =r5> 0! 6<%n&- .oo r3%n&-/ !( roor 0! n oor/ !?!- ; 0%-&n.%&- r!.orr%0&- 5or 3&n0&- o r!0&-/ &;0&n0o &-8/ !0%&n! (& r!'(&.%7n 0! !(o.%0&0!-/ !(o.%0&0!-/ & 0!!.&r f&((&- !n (&- 6<%n&- ; !?or&r - fn.%on&%!no/ (o <! 5!r%! <! &!n!n (&- '&n&n.%&- 5or r!n0%%!no !n (&!5r! !5r!-&-&-$$ S! %( %(%9 %977 .oo .oo &< &<%n %n&r% &r%&& !n !- !-0% 0%oo n .%.( .%.(7 7! !ro ro & 0%f! 0%f!r!n r!n! !-!(o.%0&0!-/ (&- .&(!- f!ron !0%0&- !n -!%- o.&-%on!-/ &no 5or !( &.7!ro 0! .on&.o .oo 5or !( !-ro3o-.o5%o/ 0! &.!r0o & - fn.%on&%!no .orr!-5on0%!n!$ S! r!&( r!&(%9 %9&r &ron on .r& .r&-- 0! .&(%3 .&(%3r&. r&.%7 %7nn ; .o5&r .o5&r&.% &.%7n 7n !nr !nr!! (o(o- 0o 0o-- %n- %n-r r!n !no o-%(%9&0o- ; -! 0!o-r7 <! &3o- -on 5r!.%-o- .oo @o0o 0! !0%.%7n 0! !(o.%0&0!- &n'(&r!-$
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1. INTRODUCCION
! G&(%(!o G&(%(!% <%!n/ !-0%&n0o !( o%%!no 0! (o- .!r5o- !n n 5(&no %n.(%n&0o/ ((!'7 & n .on.!5o 0! !(o.%0&0$ Lo <! F%9o f! 0%%0%r (& 0%-&n.%& r!.orr%0& !n n%0&0!- 0! %!5o/ !-o !-/ f%?7 n 5&r7n 0! n& n%0&0 0! %!5o/ .oo 5or !?!5(o 1 -!'n0o/ ; & 5&r%r 0! !-o r!(&.%on7 (& 0%-&n.%& r!.orr%0& 5or n .!r5o !n .&0& -!'n0o/ 0! !-& &n!r&/ G&(%(!o 0!-&rro((7 !( .on.!5o 0! (& !(o.%0&0 .oo n& &r%&.%7n 0! (& 0%-&n.%& r!.orr%0& 5or n%0&0 0! %!5o 0on0! 5o0!o- 0!f%n%r (& !(o.%0&0 .oo n& &'n%0 !.or%&( (& .&( %0! !( .&3%o 0! 5o-%.%7n !n n %n-&n! 0! %!5o$ S!'n !( (&5-o 0! %!5o r!.orr%0o/ (& !(o.%0&0 5!0! -!r 0! 0%!r-o- %5o-: !0%&/ %n-&n6n!& ; r!(&%&$ L& !(o.%0&0 !0%& r!5or& (& !(o.%0&0 !n n %n!r&(o 0&0o ; -! ((!'& & !((& 0%%0%!n0o !( 0!-5(&9&%!no 5or !( %!5o r&n-.rr%0o/ 5or - (&0o (& %n-&n6n!& no- 5!r%! .ono.!r (& !(o.%0&0 0! n o3?!o <! -! !! 5or 0!!r%n&0o r&;!.o .on (& !-5!.%&( .&r&.!r8-%.& <! !( (&5-o 0! %!5o !%nf%n%&!n! 5!<!Ho/ -%!n0o &3%@n !( !-5&.%o <! r!.orr! ; 5!<!Ho/ r!5r!-!n6n0ono- &n -o(o n 5no 0! (& !n.%on&0& r&;!.or%& ; (& !(o.%0&0 r!(&%& !nr! 0o- o3-!r&0or!- -r'%r6 0!( &(or 0! (& !(o.%0&0 0! n o3-!r&0or !0%0& 5or !( oro$ L& !(o.%0&0 !- n .on.!5o &5(%&!n! %(%9&0o !n !( n0o 0!( 0!5or! &3%@n/ 0!3%0o & <! n& 3!n& 5&r! 0! (o- 0!5or!- <! -! 5r&.%.&n/ .oo -!r f3o(/ 36-<!/ Fo.!;/ !n%-/ !nr! oro-/ r!<%!r!n 0! n& %5or&n! 5r!5&r&.%7n r!-5!.o 0! !-&/ ;& <! 0! (& r!-%-!n.%& <! -! .on-%'& & n%!( 0! !(o.%0&0/ 0!5!n0!r6 !n .Fo !( @%o <! .on-%'& !( 0!5or%-& !n - .&rr!r&$
2. OBJETIVOS
2.1 O!e"ivo #e$eral
&%(%&r%9&r &( !-0%&n! .on (o- 0%f!r!n!- !0%0or!- 0! !(o.%0&0 &n'(&r <! -! -&n nor&(!n! !n (& %n'!n%!r8&$ 2$2 O!e"ivos Espec%&icos A5r!n0!r !( 5r%n.%5%o 0! fn.%on&%!no 0! (o- %n-r!no- 0! !0%.%7n 0! !(o.%0&0 &n'(&r -&0o- !n !( (&3or&or%o$ R!&(%9&r (&- .r&- 0! .&(%3r&.%7n 0! (o- %n-r!no- 0! !0%.%7n 0! !(o.%0&0 &n'(&r -!(!..%on&0o-
'. ()*NTE*MIENTO DE) (ROB)EM*
E- 0! .ono.%%!no 36-%.o !n (& %n'!n%!r8& <! o0& &<%n&r%& n!.!-%& n .orr!.o &n!n%%!no 0r&n! - !&5& 0! o5!r&.%7n$ A( 5&-&r !( %!5o/ 0!nro 0!( 63%o 0! r&3&?o !n (&- %n0-r%&- !- 0! .F& %5or&n.%& &n!n!r !n 75%o fn.%on&%!no o0&- (&- &<%n&-J 5&r& !((o !- fn0&!n&( ((!&r n .on-&n! !-0%o 0! - r!n0%%!no ; (&- .on0%.%on!- & (&- .&(!- o5!r&n$ En (o- .&-o- 0! r3%n&- ; oor!- 0! &<%n&r%&- 5or !?!5(o/ !- 5r%or0%&( !0%r .on%n&!n! (&- !(o.%0&0!- & (&- .&(!- fn.%on&n$ E-o &;0& & 0!!.&r f&((&- !n (&- &<%n&-/ !?or&r fn.%on&%!no ; 5!r%! <! &!n!n (&- '&n&n.%&- 5or r!n0%%!no !n (&- !5r!-&-$ P&r& ((!&r & .&3o !-& (&3or/ !n (& &.&(%0&0 !%-!n @o0o- ; o3?!o- .&5&.!- 0! .5(%r !-! o3?!%o 0! for& f6.%( ; 5r!.%-&$ Ar!f&.o- .oo (o- &.7!ro- ; !-ro3o-.o5%o- -! %(%9&r&n 5&r& ((!&r n r!'%-ro 0! (&- !(o.%0&0!- 0!( !(!!no !n !-0%o/ <! 5!r%& -&3!r -% !-6 r&3&?&n0o 0! (& &n!r& &0!.&0&$
+. M*RCO TEORICO
)a Velocidad:
L& !(o.%0&0 !- n& &'n%0 f8-%.& 0! .&r6.!r !.or%&( <! !5r!-& (& 0%-&n.%& r!.orr%0& 5or n o3?!o 5or n%0&0 0! %!5o$ S! r!5r!-!n& 5or
o V$
S- 0%!n-%on!- -on KLKT$ S n%0&0 !n !( S%-!& In!rn&.%on&( !- !( K-$ L& !(o.%0&0 !0%& o !(o.%0&0 5ro!0%o !- (& !(o.%0&0 !n n %n!r&(o 0! %!5o 0&0o$ S! .&(.(& 0%%0%!n0o !( 0!-5(&9&%!no =r> !nr! !( %!5o =>$ L& !(o.%0&0 %n-&n6n!& 5!r%! .ono.!r (& !(o.%0&0 0! n 7%( <! -! 0!-5(&9& -o3r! n& r&;!.or%& .&n0o !( %n!r&(o 0! %!5o !- %nf%n%&!n! 5!<!Ho/ -%!n0o !non.!- !( !-5&.%o r!.orr%0o &3%@n ; 5!<!Ho/ r!5r!-!n&n0o n 5no 0! (& r&;!.or%&$ L& !(o.%0&0 %n-&n6n!& !- -%!5r! &n'!n! & (& r&;!.or%&$ L& r&5%0!9 !- (& &'n%0 o !( &(or 0! (& !(o.%0&0/ ;& -!& !(o.%0&0 !.or%&( !0%&/ !(o.%0&0 !0%& -o3r! (& r&;!.or%&/ o !(o.%0&0 %n-&n6n!& =!(o.%0&0 !n n 5no>$ E( 70(o 0!( !.or 0! !(o.%0&0 %n-&n6n!& ; !( &(or n@r%.o 0! (& !(o.%0&0 %n-&n6n!& -o3r! (& r&;!.or%& -on %'&(!-/ %!nr&- <! (& r&5%0!9 5ro!0%o no n!.!-&r%&!n! !- %'&( & (& &'n%0 0! (& !(o.%0&0 5ro!0%o$ L& r&5%0!9 5ro!0%o =o !(o.%0&0 !0%& -o3r! (& r&;!.or%&> ; (& !(o.%0&0 !0%& %!n!n (& %-& &'n%0 .&n0o o0o !( o%%!no -! 0& !n n& 0%r!..%7n$ En oro.&-o-/ 5!0!n 0%f!r%r$ I$s"r,-e$"os para -edir Velocidad: Veloc%-e"ro:
E- n %n-r!no <! %0! !( &(or 0! (& r&5%0!9 !0%& 0! n !F8.(o$ D!3%0o & <! !( %n!r&(o !n !( <! %0! !-& r&5%0!9 !- '!n!r&(!n! ; 5!<!H& -! &5ro%& .Fo & (& &'n%0 0! (& V!(o.%0&0 %n-&n6n!&/ !- 0!.%r (& r&5%0!9 %n-&n6n!&$
Lo- !(o.8!ro- r&0%.%on&(!- !-6n .onro(&0o- 5or n .&3(! r!.3%!ro <! !- !n-%on&0o 5or n .on?no 0! 5!<!H&- r!0&- 0!n&0&- !n !( -%-!& 0! r&n-%-%7n$ S%n !3&r'o/ (o- 5r%!ro- Vo(-&'!n E-.&r&3&?o ; (&- oo.%.(!&!5(!&n n .&3(! or-%on&0o 5or n& r!0& 0!( fron&($ L& for& 6- .on 0! n !(o.8!ro 0!5!n0! 0! (& %n!r&..%7n 0! n 5!<!Ho %6n f%?&0o &( .&3(! .on n& 5!<!H& 5%!9& 0! &(%n%o .on for& 0! 0!0&( f%?&0& &( !?! 0!( %n0%.&0or$ A !0%& <! !( %6n ro& .!r.& 0!( 0!0&(/ (o- .&3%o- !n !( .&5o &'n@%.o %n0.!n .orr%!n! !n !( 0!0&(/ <! 5ro0.! & - !9 n n!o .&5o &'n@%.o$ E( !f!.o !- <! !( %6n &rr&-r& &( 0!0&(/ &-8 .oo &( %n0%.&0or/ !n (& 0%r!..%7n 0! - ro&.%7n -%n .on!%7n !.6n%.& !nr! !((o-$ E( !?! 0!( 5n!ro !- %5(-&0o F&.%& !( .!ro 5or n 5!<!Ho !((!$ E( 5&r 0! or-%7n !n !( 0!0&( -! %n.r!!n& .on (& !(o.%0&0 0! (& ro&.%7n 0!( %6n =<! !-6 .onro(&0& 5or (& r&n-%-%7n 0!( !F8.(o>$ A-8 <! n %n.r!!no 0! (& !(o.%0&0 0!( .o.F! F&.! <! !( 0!0&( ro! ; <! !( %n0%.&0or '%r! !n !( -!n%0o .onr&r%o &( !((!$ C&n0o !( 5&r 0! or-%7n 5ro0.%0o 5or (&- .orr%!n!- %n0.%0&- %'&(& &( 0!( !((! 0!( %n0%.&0or @-! -! 0!%!n! &5n&n0o !n (& 0%r!..%7n &0!.&0&/ <! .orr!-5on0! & n& .%fr& !n (& r!0& %n0%.&0or&$ E( !((! -! .&(%3r& 0! for& <! n& 0!!r%n&0& !(o.%0&0 0! r!o(.%7n 0!( .&3(! .orr!-5on0! & n& !(o.%0&0 !-5!.8f%.& !n !( !(o.8!ro$ E-! .&(%3r&0o 0!3! 0! r!&(%9&r-! !n%!n0o !n .!n& .Fo- f&.or!-/ %n.(;!n0o (&- 5ro5or.%on!0! (&- r!0&- 0!n&0&- <! .onro(&n &( .&3(! f(!%3(!/ (& &-& 0!( 0%f!r!n.%&( ; !( 0%6!ro 0! (o- n!6%.o-$ E( !.&n%-o 0!( !(o.8!ro & !n0o %!n! &.o5&H&0o 0! n o07!ro ; 0! n 5!<!Ho %n!rr5or <! !n8& 5(-o- & (& .o5&0or& 0!( !F8.(o$ Es"rooscopio:
E( !-ro3o-.o5%o !- n 0%-5o-%%o <! !%! 0!-!((o- (%no-o- & n& fr!.!n.%& 5r!0!!r%n&0&$ D! !-& for& -! 5!0! !r n o3?!o <! '%r& & 'r&n !(o.%0&0 .oo -% !-%!r& %n7%( o '%r&n0o ; (!n&!n!$ P!r%! !n.!n0!r ; &5&'&r (.!-/ !n n (&5-o 0&0o/ (& .&n%0&0 0! !.!- <! no 0!-!!$ E-! 0%-5o-%%o !- ; %(%9&0o !n .(3!- no.rno-/ !n (o- &%on!- ; !n (& 5ro0..%7n 0! 5!(8.(&- 5&r& 0&r (& -!n-&.%7n 0! o%%!no- r65%0o-$ En !-!n.%& n !-ro3o-.o5%o !-6 0o&0o 0! n& (65&r&/ nor&(!n! 0!( %5o 0! 0!-.&r'& '&-!o-& 0! !n7n/ -%%(&r & (&- !5(!&0&- !n (o- f(&-F!- 0! foo'r&f8&/ .on (& 0%f!r!n.%& 0! <! !n ('&r 0! n 0!-!((o/ !%! n& -!r%! 0! !((o.on-!.%o- ; .on n& fr!.!n.%& r!'(&3(!$ S% !n!o- n o3?!o <! !-6 '%r&n0o & N r!o(.%on!- 5or %no ; r!'(&o- (& fr!.!n.%& 0!( !-ro3o-.o5%o & N 0!-!((o- 5or %no ! %(%n&o- .on @( !( o3?!o '%r&or%o/ @-!/ &( -!r %(%n&0o -%!5r! !n (& %-& 5o-%.%7n/ &5&r!.!r6 & (& %-& .oo %n7%($ S% (& fr!.!n.%& 0! (o- 0!-!((o- no .o%n.%0! !&.&!n! .on (& 0! '%ro/ 5!ro -! &5ro%& .Fo & !((&/ !r!o- !( o3?!o o!r-! (!n&!n!/ &0!(&n! o &r6-!'n <! (& fr!.!n.%& 0! 0!-!((o 0!( !-ro3o-.o5%o -!&/ r!-5!.%&!n!/ %nf!r%or o -5!r%or & (& 0! '%ro$ Tac-e"ro:
E- n 0%-5o-%%o <! %0! (& !(o.%0&0 0! '%ro 0! n !?!/ nor&(!n! (& !(o.%0&0 0! '%ro 0! n oor$ S! %0! !n r!o(.%on!- 5or %no =RPM>$ A.&(!n! -! %(%9&n .on &;or fr!.!n.%& (o- &.7!ro- 0%'%&(!-/ 5or - &;or 5r!.%-%7n$ E( 7r'&no 5r%n.%5&( 0! n &.7!ro !- n %6n 5!r&n!n!$ To0o %6n !-6 ro0!&0o 0! n .&5o &'n@%.o .;&- (8n!&- 0! f!r9& -! 5!0!n F&.!r %-%3(!.3r%!n0o !( %6n .on n& 5(&.& ; !-5&r.%!n0o (!'o (%&0r&- 0! F%!rro -o3r! !((&J
(&- (%&0r&- -! or0!n&n !non.!- !n !( !-5&.%o ; 5&-&n & 0%3?&r (&- (8n!&- 0! .&5o 0!( %6n$ S% F&.!o- '%r&r !( %6n !( .&5o 0! f!r9& '%r& &3%@n ?no .on @($ En !( .&-o 0!( &.7!ro/ !( %6n &(o?&0o !n - %n!r%or -! 5on! & '%r&r !n .&no &rr&n.& !( &o7%($ E( &..%on&%!no %!n! ('&r & r&@- 0! n& 5!<!H& r&-%-%7n ; 0!( ((&&0o 6r3o( 0!( &.7!ro <!/ & - !9/ !-6 &.o5(&0o &( 6r3o( oor o & n& 0! (&- r!0&- 0!(&n!r&-J .&no &;or -!& (& !(o.%0&0 0!( !F8.(o &no &;or !- &3%@n !( n!ro 0! r!o(.%on!- 0!( %6n$ En !( &.7!ro/ !( %6n 5!r&n!n! '%r& 0!nro 0! n &n%((o 0! &(%n%o .onQ .@nr%.o & @(/ ; - .&5o &'n@%.o '%r&or%o '!n!r& !n 0%.Fo &n%((o .orr%!n!- 5&r6Q -%&- <!/ & - !9/ or%'%n&n oro .&5o$ L& &..%7n r!.85ro.& 0! &3o- .&5o- .r!& &-8 -o3r! !( &n%((o n o!no <! %!n0! & F&.!r(o '%r&r !n !( %-o -!n%0o <! !( %6n/ ; <! !- &no &;or .&no &;or -!& !( n!ro 0! r!o(.%on!- 0! !-! (%o$ S%n !3&r'o/ !( &.7!ro 5o-!! n !((! !-5%r&( <! %5%0! <! !( &n%((o '%r! (%3r!!n!/ ; -7(o (! 5!r%! '%r&r (!!!n! 0! &.!r0o .on !( o!no &5(%.&0o -o3r! @( =!n.%!n0o &( 5&r &n&'on%-& .r!&0o 5or !( !((!>$ Un& &'?& f%?&0& &( &n%((o -!H&(& (& !(o.%0&0 -o3r! n& !-.&(& 'r&0&0&$
/. M*TERI*)ES 0 EUI(OS /.1 E,ipos: Cicl-e"ro
M&r.&: A%r Con0%%on L&3or∨ Un% S!r%&(: )+)* P$A %(on LTD En'%n!!r%n'- So3orn!$ &n- En'(&n0$ •
)3-para es"rooscpica
M&r.&: Mon&r.F A5r!.%&.%7n: ± *4r5 Tac-e"ro
M&r.&: T!.(o. A5r!.%&.%7n: ± 2r5
4. (ROCEDIMIENTO E5(ERIMENT*)
1$ S! 5ro.!0%7 & 3-.&r (o- %n-r!no- 5&r& F&.!r (&- !0%.%on!- 0! !(o.%0&0 =E-ro3o-.o5%o ; T&.7!ro>$
2$ S! !n.!n0%7 !( !<%5o ro&%o ; -! f%?7 n& !(o.%0&0 &(!&or%&!n! !0%&n! n& &n%((&$ #$ S! o7 n& !0%.%7n 0! (& !(o.%0&0 f%?&0& &n!r%or!n! .on !( &.7!ro ; .on !( !-ro3o-.o5%o/ 5o-!r%or!n! -! &r%7 (& !(o.%0&0 ; -! r!5%%7 !( 5ro.!0%%!no ) !.!- 6-$ ,$ S! r!'%-r&ron ; -! 5ro!0%&ron (&- !(o.%0&0!- o3!n%0&- 0! .&0& %n-r!no$
6. RESU)T*DOS
Tala 71 Valores o"e$idos e$ la pr3c"ica
N8 de -edidas
Tacómetro(rpm)
Estroboscopio (rpm)
1
230
234
2
260
257
'
316
315
+
348
343
/
472
465
4
1100
1102
1200 1000 800 Es"rooscopio9rp-
600 400 200 0 0
200
400
600
800
Tac-e"ro 9rp-
;i<,ra 7 1 C,rva de caliraci$ del Es"rooscopio.
1000
1200
6 5 4 Es"rooscopio9rp-
3 2 1 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.11 Tac-e"ro 9rp-
;i <,ra 72 C,rva de velocidad li$eal e$ &,$ci$ del radio
=. *N*)ISIS DE RESU)T*DOS Br. Da$iel Villarroel C.I. 2'/'426+
A( &n&(%9&r (& 'r6f%.& !( .o5or&%!no <! 0!-.r%3! !- !( 0! n& (8n!& r!.& .;& 5!n0%!n! !- .!r.&n& &( &(or 0! 1 =4$* 1> o3!n%0& -&n0o 8n%o- .&0r&0o-/ (o <! %5(%.& <! !( !-ro3o-.o5%o !( .&( f! !( o3?!o & .&(%3r&r &rro?o r!-(&0o- -!!?&n!- & (o- 0!( &.7!ro .on n (!! &r'!n 0! !rror/ 0!o-r&n0o &-8 <! 5o-!! n& &.!5&3(! .&(%3r&.%7n$ S! 5!0! &-%r <! !( (!! &r'!n 0! !rror <! -! .o!%7 f! 0!3%0o & &('n !rror F&no &( o!no 0! %(%9&r (o- %n-r!no- 5&r& o&r (&!0%0&- .oo !( F&.!r .F& 5r!-%7n .on !( &.7!ro -o3r! !( !?! o no &n!n!r (& 5!r5!n0%.(&r%0&0 .on !( %-o$ L&- 0%-%n&- &5r!.%&.%on!- <! 5o-!!n (o- %n-r!no- =2r5 5&r& !( &.7!ro/ 1r5 5&r& !( !-ro3o-.o5%o> &3%@n %nf(;!n !n (o- 0%-%no&(or!- &rro?&0o- ; &( !f!.o 0! r!!n!r (& %&'!n !n (& r!%n& &( o!no 0! %(%9&r (& (65&r& !-ro3o-.75%.&$ Br. Cesar Velasco C.I. 2/'1'16+
A( r!&(%9&r (& .r& 0! .&(%3r&.%7n -! (o'r& &5r!.%&r <! (& r!(&.%7n !n (& o3!n.%7n 0! 0&o- !nr! no ; oro &r!f&.o no 0%f%!r! 0!&-%&0o/ &('o <! ;& -! 5o08& no&r .&n0o -! o&3&n (o- 0&o-$ AFor& 5or !0%o 0! (& 'r6f%.& <!0& 0!o-r&0o/ ; !-o !- 0!3%0o & <! (& 5!n0%!n! o n &(or 0! 4$*/ (o <! -'%!r! n& 5ro5or.%on&(%0&0 .&-% !&.& !nr! (o- 0&o&rro?&0o- 5or !( !-ro3o-.o5%o ; !( &.7!ro$ To0o !-o -'%!r! <! &3o- &r!f&.o- f!ron 5r!.%-o- .&(.(&n0o (o&(or!- 0! (& !(o.%0&0 0! '%ro !n .&0& .&-o 0!( .%.(7!ro$ L&- 5!<!H&0%f!r!n.%&- !n (&- !0%0&- o3!n%0&- -! 5!0!n &-o.%&r .on -- 0%f!r!n!&5r!.%&.%on!- =
±
2RPM 5&r& !( &.7!ro/
± 1RPM
5&r& !(
!-ro3o-.o5%o>/ -&0o & &('n !rror & (& For& 0! !5(!&r(o-/ ;& <! no -! !n8& .F& !5!r%!n.%& %(%96n0o(o-$
>. CONC)USIONES Br. Da$iel Villarroel C.I. 2'/'426+ •
E( !-ro3o-.o5%o -! !n.!nr& .&(%3r&0o 0&0o <! (o- &(or!- o3!n%0o- f!ron
•
-!!?&n!- & (o- 0!( &.7!ro$ L& &5r!.%&.%7n 0!( !-ro3o-.o5%o !- !nor & (& 0!( &.7!ro$ L& (65&r& !-ro3o-.75%.& !- 6- &5& 5&r& o&r !0%0&- 0! 'r&n0!-
•
!<%5o- & &(&- r!o(.%on!-$
•
E( &.7!ro !- %0!&( 5&r& !<%5o- 0! !nor &&Ho -%!5r! <! - !?! -!&
•
&5o 5&r& &0&5&r(o$ A( fn.%on&r 0! &n!r& !.6n%.& !( &.7!ro !- 5ro5!n-o & 0&H&r-! .on !( %!5o -% no -! -& &0!.&0&!n!$
Br. Cesar Velasco 2/'1'16+
E( &.7!ro ; !( !-ro3o-.o5%o/ &( &(!rn&r-! .oo !0%0or 5&r7n/ &no no .oo !( oro &rro?&3&n &(or!- ; -!!?&n!-/ (o <! -'%!r! n& .orr!.& .&(%3r&.%7n !n &3o-$ Coo !0%0or!- 0! !(o.%0&0 0! ro&.%7n/ &3o- %n-r!no- -on (o -f%.%!n!!n! 5r!.%-o-$ E( &.7!ro 0!3! 0! -%&r-! .orr!.&!n! !n for& 5!r5!n0%.(&r &( !?! 5&r& f&.%(%&r !( 5ro.!-o 0! !0%.%7n ; 5&r& <! (&- !-r&- o&0&- -!&n 5r!.%-&-$ E( !-ro3o-.o5%o !- 6- &0!.&0o 5&r& r!&(%9&r !-0%o- 0! &<%n&r%&- !n (&<! no !- %&3(! o -!'ro !( .on&.o 0%r!.o .on !-o-$
1?. BIB)IO#R*;I* ;,e$"es elec"r$icas: 1. @iAi-edia
;o,$da"io$
I$c.
92?1+.
Es"rooscopio.
En:
F5:!-$%%5!0%&$or'%%E-ro3o-.o5%o 2. @iAi-edia
;o,$da"io$
I$c.
92?1+.
Velocidad.
En:
92?1+.
Tac-e"ro.
En:
F5-:!-$%%5!0%&$or'%%V!(o.%0&0 '. @iAi-edia
;o,$da"io$
I$c.
F5:!-$%%5!0%&$or'%%T&.o!ro
+. *i$s"r,-e$"os 92?1?. Es"rooscopios I$d,s"riales (or"3"iles.
En:
F5:$&3
>4G (rod,c"os. En: F5:&5!$!-%n0!$5F5W(&n'X4&50X1%0&nX2,
*(ENDICES *(ENDICE *. E!e-plos de c3lc,lo: 1. E!e-plos de c3lc,lo c,rva caliraci$ del es"rooscopio e$ &,$ci$ del "ac-e"ro.
&.%!n0o -o (o- 0&o- o3!n%0o- !n (& !5!r%!n.%& &no 0!( T&.7!ro .oo 0!( E-ro3o-.o5%o -! 5ro.!0! & r!&(%9&r (& .&(%3r&.%7n 0! @-! (%o &5(%.&n0o 8n%o- .&0r&0o-$
P&r& !((o o3-!r&o- <! (& 'r6f%.& <! -! o3o !- .&-% (%n!&( 5or (o &no -&o- 0%.F& -!!?&n9& .on (& !.&.%7n 0! n& (8n!& r!.&:
y =mx + b
D7n0!: H: R!o(.%on!- 5or %no !0%0&- 5or !( E-ro3o-.o5%o -: P!n0%!n! 0! (& .r&$ : R!o(.%on!- 5or %no !0%0&- 5or !( T&.7!ro$ : Pno 0! .or! .on !( !?! 0! (&- or0!n&0&- =E?! !-ro3o-.o5%o>
[!0&n0o !non.!- <! (& !.&.%7n <! r%'! !-& !5!r%!n.%& .on (& .&( -! .&(%3r& !( !-ro3o-.o5%o !- 0! (& for&: Rpm Estroboscopio=m∗ RpmTacometro+ b
E.&.%7n 5&r& !( .6(.(o 0! (& 5!n0%!n! .on 8n%o- .&0r&0o-: m=
n
∑ xy−∑ x ∑ y n ∑ x −( ∑ x ) 2
2
R(M N Tac-e"ro Es"rooscopi 95 o 90
1 2 # , )
2#4 2*4 #1* #, ,+2
2#, 2)+ #1) #,# ,*)
*
1144
1142
2
5K0
)#24 **24 ),4 11#*, 21,4
)244 *+*44 )* 12114, 222+, 121444 1212244 4
To"ales:
∑ X
2+2*
∑ X ∗Y
X
1++122,
∑ Y
∑ X
2
2+1*
1++,2,,
Caliraci$ del Es"rooscopio por -%$i-os c,adrados
m=
n
∑ xy−∑ x ∑ y n ∑ x −( ∑ x ) 2
2
S-%;!n0o (o- &(or!- o3!n%0o- !n (& for(& -! o3%!n! n &(or 5&r& (& 5!n0%!n!: m=
6∗1771224−7403816 6∗1774244−7431076
m = 1.003
S! .&(.(&
b
<!
.orr!-5on0! &( .or! 0! (& r!.& .on !( !?! 0! (&-
or0!n&0&-:
∑ x ∑ y −∑ x ∑ xy b= n ∑ x −(∑ x ) 2
2
b=
2
1774244∗2716 −2726∗1771224 6∗1774244−7431076
b =−2.959
L& !.&.%7n 0! (& r!.& 5&r& (& .&(%3r&.%7n 0!( E-ro3o-.o5%o !-:
2.
Rpm Estroboscopio=1.003∗ RpmTacómetro−2.954
E!e-plos de c3lc,lo c,rva de
velocidad li$eal e$ &,$ci$ del radio del ve$"ilador
C&(.(&n0o (&- !(o.%0&0!- &n'(&r!-:
( ) ( ) ( )
π rad rad 30 seg ω1 =230 rpm∗ =24,09 1 rpm seg
ω3 =316 rpm∗
π rad 30 seg 1 rpm
=33,09
rad seg
π rad 30 seg rad ω5 =472 rpm∗ = 49,43 seg 1 rpm
S&3%!n0o <! (& !(o.%0&0 (%n!&( -! 0!f%n! .oo !( 5ro0.o 0! (& !(o.%0&0 &n'(&r 5or !( r&0%o 0! (& .%r.nf!r!n.%& 0!.%o- <!: V li =w i∗r i
C&(.(&n0o (&- !(o.%0&0!- (%n!&(!- .on r!-5!.o & .&0& ω1 =24,09 V l 1=24,09∗0,02=0,4818 V l 1=24,09∗0,04 =0,9636 V l 1=24,09∗0,06=1,4454 V l 1=24,09∗0,08=1,9272 V l 1=24,09∗0,1=2,409
ω
!n!o- <!:
ω3 =33,09 V l 3=33,09∗0,02=0,6618 V l 3=33,09∗0,04 =1,3236 V l 3=33,09∗0,06= 1,9854 V l 3=33,09∗0,08=2,6472 V l 3=33,09∗0,1 =3,309 ω5 =49,43 V l 5= 49 , 43∗0,02 =0 , 9886 V l 5= 49,43∗0,04 =1 , 9772 V l 5= 49,43∗0,06 =2 , 9658 V l 5= 49,43∗0,08 =3,9544 V l 5= 49,43∗0, 1= 4 , 943
*(ENDICE B. *si<$aci$
a.
Epli,e el pri$cipio de &,$cio$a-ie$"o del co$"ador de revol,cio$es.
Un .on&0or 0! r!o(.%on!- !- n &r!f&.o %(%9&0o 5&r& 0!!r%n&r .6no- .%.(ofn.%on&(!- r!&(%9& !( !?! 0! n& &<%n& !n n 0!!r%n&0o %n!r&(o 0! %!5o$ M!0%&n! 0%-%n&- for&- ((!& & .&3o - fn.%7n/ (& .&( !- o3!n!r (&- r!o(.%on!- o !(&- <! !.&5&9 0! .5(%r n !?! !n n %n-&n! !-5!.8f%.o$ E%-!n &r%o- %5o- 0! .on&0or!- 0! r!o(.%on!- ; &n 0!-0! .on&0or!!.6n%.o- F&-& 75%.o- ; 0%'%&(!-J (o- .&(!- .5(!n .on !( %-o f%n 5!ro 0! for& 0%-%n&$ Pr%n.%5&(!n! (o- !.6n%.o- 3&-&n - fn.%on&%!no !n !( .on&.o 0%r!.o .on !( !?! !-0%&0o/ n !?!5(o 0! !-! !- !( &.7!ro$ A( '%r&r & (& 5&r .on !( !?! -! (o'r& !0%r (& .&n%0&0 0! !(&- <! r!&(%9& !n n %n!r&(o$ Lo- 75%.o- ; 0%'%&(!- -on 6- o0!rno- ; !n .%!r& for& 6- f6.%(!- ; .onf%&3(!0! -&r$ Y& -!& !0%&n! 0!-!((o- 0! (9 o !%-%on!- 0! on0&-/ !-o- %5o- 0! .on&0or!!-r&n !0%&n! n& 5&n&((& (& .&n%0&0 0! r!o(.%on!- <! '!n!r& n !?!$ L& o3!n.%7n 0! 0&o- !0%&n! !( -o 0! .on&0or!- -! r!&(%9& !n .oro- (&5-o- -&n0o .&(<%!r& 0! !-o- &r!f&.o- 0! !0%.%7n/ ;& <! -! o3%!n!n 0&o- !n %n!r&(o- 0! 5o.o-!'n0o- ; !0%&n! n f&.or .on-&n! o3%!n!n (o- &(or!- 0! for& 0!-!&0&/
'!n!r&(!n! !n r5 =r!%n>$ Por !?!5(o/ n &.7!ro %0! 0r&n! * -!'n0o- (& .&n%0&0 0! r!o(.%on!- <! r!&(%9& n !?!/ (!'o !-! &(or (o (%5(%.& 5or 14 ; &-8 o3%!n! !( &(or 0! (&- r5 0! 0%.Fo !?!$ . Clasi&i,e H epli,e el pri$cipio de &,$cio$a-ie$"o de los di&ere$"es i$s"r,-e$"os de velocidad. Tac-e"ro
E( &.7!ro !- !( !0%0or 0! r!o(.%on!- <! -! !5(!& 5&r& %n0%.&r (& !(o.%0&0 0! &&n.! %n-&n6n!&$ E%-!n 0%!r-o- &.7!ro- -%!n0o (o- 6- -&0o- (o- 75%.o- ; 0! .on&.o$ Lo- &.7!ro- 75%.o- -on (o- 6- o0!rno-J !0%&n! n F&9 0! (9 %-%3(! <! -! r!f(!?& -o3r! !( &r!f&.o '%r&or%o -! o3%!n!n -- r5$ E( &(or 0! (&- r5 -! !r6 !n !( &.7!ro &o6%.&!n!$ Son !f!.%o-/ &( %'&( <! (o- !-ro3o-.o5%o-/ 5&r& r&3&?&r .on !?!- 0! r3%n&- ; &<%n&- %n0-r%&(!-$ E( &.7!ro 0! .on&.o -! &.o5(& !0%&n! &0&5&0or!- &( !?! ; ((!& n& !0%0& 0! (&- !(&- <! -! '!n!r&n !n n %!5o !-5!.8f%.o !0%&n! !( -o 0! n .ron7!ro %n!rno$ E-o- &(or!- -on -&(!n! ((!&0o- & r!o(.%on!- 5or %no %n!rn&!n! !n (o- &5&r&o- !0%&n! n& .on-&n! n@r%.&$ Es"rooscopio
Un !-ro3o-.o5%o !- n &5&r&o <! !%! 0!-!((o- .on n& fr!.!n.%& r!'(&3(!$ S fn.%on&%!no -! 3&-& !n F&.!r .o%n.%0%r (& fr!.!n.%& 0! !-o- 0!-!((o- .on (& 0!( '%ro 0!( !?! !n !-0%o/ !- 0!.%r 5or .o%n.%0!n.%& 0! fr!.!n.%&-$ S! 0!3! !n!r n& &r.& '8& !n !( !?! 5&r& -&r(& .oo r!f!r!n.%& !n !( o!no 0! %'&(&r (&- fr!.!n.%&-J 0%.F& &r.&/ .&n0o -! %'&(!n (&- fr!.!n.%&- 0! (o- 0o- &r!f&.o-/ -! 0!no&r& %n7%( & (& %-& ; !&F8 .&n0o -! 0!3! o&r !0%0& 0! (&- r5 o-r&0&- 5or (& (65&r& !-ro3o-.75%.&$ c. U$a r,eda realiLa 2/ revol,cio$es e$ 6 se<,$dos. E$c,e$"re s, velocidad a$<,lar e$ revs H rads. Rev 2/rev
6se<
5
1se<
X =
1 rev
2,5 rev∗1 seg rev =0,3571 7 seg seg
2P rad
0,3571
( )
rev 2 πrad seg 1 rev
=2,2437
rad seg
d. Q, velocidad de des"ellos se $ecesi"ar%a para -edir las rp- de ,$a r,eda co$ ,$a velocidad a$<,lar de /? rads e.
Vdestellos = ?
ω =50
(
rad 1 rev seg 2 πrad
)(
3600 seg 1 min
)=
28647,7 rpm
L& !(o.%0&0 0! 0!-!((o- !- (& %-& <! (& .&n%0&0 0! r!o(.%on!- 5or %no/ %n.(-%! 50%!-! o&r-! .oo r!f!r!n.%& !n r!o(.%on!- 5or -!'n0o &3%@n$
&. S,po$
A 5!-&r 0! <! (&- !(o.%0&0!- no -on %'&(!-/ (& r!0& 0& 0o- !(&- .&0& !9 <! (& (65&r& !%! n 0!-!((o/ 5or !-o 5&r!.%!r& <! (& r!0& -! 0!%!n!$