UNIVERSIDAD NACIONAL AUTONOMA DE MEXICO
FACULT ACULTAD DE ESTUDIOS SUPERIORES CUAUTITLAN CUAUTITL AN INGENIERIA MECÁNICA ELECTRICA
“MECANISMO DE MANIVELA CORREDERA ACOPLADA COMO HERRAMIENTA DE CORTE”
DINÁMICA DE MAQUINARIA MAQUINARIA Ing. PEDRO LEYVA JIMENEZ. PROYECTO FINAL
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INDICE
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Introducción 1
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Plan Plante tea aie ient nto o del del !ro" !ro"le lea a #
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Dia(nó&tico )
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DINAMICA DE MAQUINARIA MECANISMO MANIVELA CORREDERA CORREDERA
INDICE
-
Introducción 1
-
Plan Plante tea aie ient nto o del del !ro" !ro"le lea a #
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O"$eti%o&
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Dia(nó&tico )
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De&c De&cri ri!c !ció ión n de la et etod odol olo( o(*a *a +
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Pro!u ro!ue& e&ta ta de &olu olución ción 1,
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Anl Anli& i&i& i& Cine Cine ti tico co . Din Dinic ico o 1+
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Art*c rt*cul ulo o& de de con con& &ulta ulta #/
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- Siulacione& 0) - Eleento& con&tituti%o& del ecani&o ''
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2a"ricación del ecani&o
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V = abc
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I z=
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An!#"%"% 6un0 %u6$1"1 CINEMATICA
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DINAMICA DE MAQUINARIA MECANISMO MANIVELA CORREDERA
m 20 m ¿ ¿
IGG 2= Wr
( )( )
τ W 2 r =40 gr∗20 − g 2 π
mm∗28.2 s ∗40 gr 2∗ π ∗¿ 9810 mm 2 s
m 60 m ¿ ¿
IGG 3 =Wr
( )( )
τ W 2 r =85 gr∗60 − g 2 π
mm∗38.85 s ∗85 gr 2∗ π ∗¿ 9810 mm 2 s
m 110 m ¿
¿
IGG 4= Wr
( )( ) τ 2 π
−
W 2 r =110 gr∗110 g
mm∗64 s ∗110 gr 2∗π ∗¿ 9810 mm 2 s
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2
∗25 r =
−6.8 rad
s
2
2
2
a α 2 cos θ 2−a ω 2 senθ 2 + b ω 3 senθ 3 4∗ 40cos 35.26− 4∗25 sen 35.26 + 12∗−6.8 ∗sen 186.35 α 3 = = = bcosθ 3 12cos 186.35
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aG 2 N =r 2∗ω 2 ( cosθ 2 + senθ 2 ) 2
(
aG 2 N =2 cm∗
25 rad
s
)( 2
(
cos 35.26
)+ sen ( 35.26 ) )=1250 ∠ 35.26
aG 2 ! =r 2∗α 2 (−senθ 2 + cos θ 2 )
( P ! g " n &
DINAMICA DE MAQUINARIA MECANISMO MANIVELA CORREDERA aG 2 ! =2∗40∗(−sen (35.26 )+ cos ( 35.26 ) )=160 ∠ 125.26
2
aG 2=1250 ∠ 35.26 + 160 ∠ 125.26=1260.19 ∠ 42.55 cm / s
aG 3 N =r 3∗ω 3 ( cosθ 3 + sen θ 3 ) 2
(
)
2
−6.8 rad aG 3 N =6 cm∗ ( cos (186.35 )+ sen (186.35 )) =81.6 ∠ 6.35 s
aG 2 ! =r 3∗α 3 (−senθ 3 + cosθ 3 )
aG 3 ! = 6∗115.20∗( −sen ( 186.35 ) + cos ( 186.35 ) )=1380 ∠ −83.65
aG 3=81.6 ∠ 6.35 + 1380 ∠ −83.65 =1382.41 ∠ −80.26 cm / s
2
2
2
aG 4 N =−a α 2 senθ 2 −aω 2 cosθ 2 +bα 3 senθ 3 + bω 3 cosθ 3 aG 4 N =−4∗ 40∗sen ( 35.26 )− 4∗25
2
(
)
(
)
2
aG 4 N =−1734.87 ∠ 0
L& >u$1z& F6 $n $%0$ 8&% 8 $% un $8&n"% /"$#& &n"<$#& %$1! 8&1&80$1"z&4& 61 un& >u$1z& 4$ >1"88"2n $n $# $%#&/2n ' :u$ $% $# 810&419 %$ 8&1&80$1"z& 61 %$1 #& >u$1z& 4$ >1"88"2n :u$ &6&1$8$ &# 810&1 un &0$1"&#. "a= #d∗m∗g + ma 2
"a=.47∗.113 kg∗(9.81 m / s
(
cos 35.26 + 12∗115.20∗ sen 186.35 + 12∗−6.8 ∗cos 186.35
)+ 0=.52 N (, P ! g " n &
)
DINAMICA DE MAQUINARIA MECANISMO MANIVELA CORREDERA
DINAMICA Cu#&n4 #&% 86n$n0$% 4$ #&% 1$&88"n$% $n #% $%#&/n$% $n 8. $ 12=2 cm ∠ 35.26 $ 12 x =2 cos 35.26=−1.63 $ 12 y =2 sen 35.26 =−1.15 $ 32=2 cm ∠ 35.26 $ 32 x = 2cos 35.26 =1.63 $ 32 y =2 sen 35.26=1.15 $ 23=6 cm ∠ 186.35 $ 23 x =6 cos186.35=−5.96 $ 23 y = 6 sen 186.35 =−.66 $ 43 =6 cm ∠ 186.35 $ 43 x = 6 cos186.35 =5.96 $ 43 y =6 sen 186.35 =.66
Cu#&n4 86n$n0$% $n #&% &8$#$1&8"n$% g1&<"0&8"n&#$% $n #% $%#&/n$% $n 8%5 7 4$ #& >u$1z&. aG 2=1260.19 ∠ 42.55 aG 2 x = 928.36 aG 2 y = 852.18 aG 3=1382.41 ∠− 80.26 aG 2 x = 233.87 aG 2 y =−1362.48
(+ P ! g " n &
DINAMICA DE MAQUINARIA MECANISMO MANIVELA CORREDERA aG 4 =−1734.87 ∠ 0 aG 2 x =−1734.87 aG 2 y =0 "%= .053 ∠ 0 "%x=.053 "%y =0
Su%0"0u7$n4 &=1& nu$%01% 4&0% $n #& &01"z 6&1& 64$1 /0$n$1 #&% >u$1z&% 7 $# 01:u$
S$ /0u<"$1n " 12 x =−1121.8 kg " 12 y =−1967.2 kg " 32 x =1122.2 kg
" 32 y =1967.5 kg
(- P ! g " n &
DINAMICA DE MAQUINARIA MECANISMO MANIVELA CORREDERA " 43 x =1122.4 kg " 43 y =1966.4 kg
" 14 y = 1966.4 kg ! 12=−24.076 kg&m
An!#"%"% 6un0 "n>$1"1 CINEMATICA
Cu# 4$ #% $n0% 4$ &%& IGG 04 $6$1"$n0&# m 20 m ¿ ¿
IGG 2= Wr
( )( )
τ W 2 r =40 gr∗20 − g 2 π
mm∗28.2 s ∗40 gr 2∗ π ∗¿ 9810 mm 2 s
5* P ! g " n &
DINAMICA DE MAQUINARIA MECANISMO MANIVELA CORREDERA m 60 m ¿ ¿
IGG 3 =Wr
( )( )
τ W 2 r =85 gr∗60 − g 2 π
mm∗38.85 s ∗85 gr 2∗ π ∗¿ 9810 mm 2 s
m 110 m ¿
¿
IGG 4= Wr
( )−( ) τ 2 π
W 2 r =110 gr∗110 g
E%#&/2n
M&%&%
5 ) '
'* g1 +K g1 ((* g1
mm∗64 s ∗110 gr 2∗π ∗¿ 9810 mm 2 s
A8$#$1&8"2n &ngu#&1 '* 1&4%5
V$#8"4&4 &ngu#&1 5K 1&4%
#ng"0u4$% ' 8 (5 8 ((.K 8
Cn W55K 1&4% 7 X5'* 1&4%5 %$ /0u<"$1n #% %"gu"$n0$% 4&0%
( ) ∗25 r 12 cm∗cos ( 155.51 ) 4 cm∗cos 43.22
ω 3=
acosθ 2 ω 2= bcosθ 3
s
2
=
−−6.67 rad
s
2
2
2
a α 2 cos θ 2−a ω 2 senθ 2 + b ω 3 senθ 3 4∗ 40cos 43.22− 4∗25 sen 43.22+ 12∗−6.67 ∗sen 155.51 α 3 = = bcosθ 3 12 cos155.51
aG 2 N =r 2∗ω 2 ( cosθ 2 + senθ 2 ) 2
(
aG 2 N =2 cm∗
25 rad
s
)( 2
(
cos 43.22
)+ sen ( 43.22 ) )=1250 ∠ 43.22
5( P ! g " n &
DINAMICA DE MAQUINARIA MECANISMO MANIVELA CORREDERA aG 2 ! =r 2∗α 2 (−senθ 2 + cos θ 2 )
aG 2 ! =2∗40∗(−sen ( 43.22 ) + cos ( 43.22 ) ) =80 ∠ 133.22
2
aG 2=1250 ∠ 43.22 + 80 ∠ 133.22 =1252.55 ∠ 46.88 cm / s
aG 3 N =r 3∗ω 3 ( cosθ 3 + senθ 3 ) 2
(
aG 3 N =6 cm∗
−6.67 rad s
)( 2
(
cos 155.51
)+ sen ( 155.51 ) ) =40.02 ∠−24.49
aG 2 ! =r 3∗α 3 (−senθ 3 + cos θ 3 )
aG 3 ! = 6∗166.35∗(−sen ( 155.51 ) + cos ( 155.51 ) ) =998.1 ∠ −114.49
2
aG 3= 40.02 ∠ −24.49 + 998.1 ∠ −114.49= 998.90 ∠ −112.19 cm / s
2
2
aG 4 N =−a α 2 senθ 2 −aω 2 cosθ 2 +bα 3 senθ 3 + bω 3 cosθ 3 aG 4 N =−4∗ 40∗sen ( 43.22 )− 4∗25
2
(
)
(
)
2
aG 4 N =−618.06 ∠ 0
"a= #d∗m∗g + ma 2
"a=.47∗.113 kg∗(9.81 m / s
(
cos 43.22 + 12∗166.35∗ sen 155.51 + 12∗−6.67 ∗ cos 155.51
)+ 0=.52 N
55 P ! g " n &
)
DINAMICA DE MAQUINARIA MECANISMO MANIVELA CORREDERA DINAMICA $ 12=2 cm ∠ 43.22 $ 12 x =−1.45 $ 12 y =−1.36
$ 32=2 cm ∠ 43.22 $ 32 x =1.45 $ 32 y =1.36 $ 23=6 ∠ 155.51 $ 23 x =−5.46 $ 23 y =2.48
$ 43 =6 ∠ 155.51 $ 43 x =5.46 $ 43 y =−2.48
aG 2=1252.55 ∠ 46.88 aG 2 x =856.15 aG 2 y = 914.26 aG 3= 998.90 ∠ −112.19 aG 3 x =−377.26 aG 3 y =−924.91 aG 4 =−618.06 ∠ 0 aG 4 x =−618.06 aG 4 y =0 "%= .053 ∠ 0 "%x=.053 "%y =0
Su%0"0u7$n4 &=1& nu$%01% 4&0% $n #& &01"z 6&1& 64$1 /0$n$1 #&% >u$1z&% 7 $# 01:u$
5) P ! g " n &
DINAMICA DE MAQUINARIA MECANISMO MANIVELA CORREDERA
S$ /0u<"$1n " 12 x =−13.52 kg
" 12 y =−22.89 kg " 32 x =13.86 kg
5' P ! g " n &
DINAMICA DE MAQUINARIA MECANISMO MANIVELA CORREDERA " 32 y =23.26 kg " 43 x =13.54 kg " 43 y =22.47 kg " 14 y = 22.47 kg ! 12=−23.24 kg&m
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>()9 % &5 C5 &) C) [ % * >()9 % &5 S5 &) S) $ * P4$% n0&19 :u$ $# 61$%$n0$ &n!#"%"% 8"n$!0"8 4$# $8&n"% 5, P ! g " n &
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ω 3=
a2 * θ 2 ω2−1 −a2 Cθ 2 ω 2 0 a3 C θ 3
=−ω
2
a 2 Cθ 2 a 3 Cθ 3
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#na vez realizado el an%lisis cinem%tico del mecanismo de manivela biela manivela, es necesario determinar las aceleraciones de los centros de masas de los eslabones del mecanismo. Considere la 'iura que muestra los vectores desde una revoluta 2asta el centro de masas de los eslabones.3
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5+ P ! g " n &
DINAMICA DE MAQUINARIA MECANISMO MANIVELA CORREDERA
4ectores Adicionales ara la 1ocalización de los Centros de asas de los *slabones de un ecanismo de anivela 5iela Corredera. 1as aceleraciones de los centros de masas de los eslabones est%n dadas por0
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“*n eneral, un sistema de múltiples eslabones, est% 2ec2o por numerosos componentes que lo conforman, que pueden ser divididos en enlaces con una eometr!a y ;untas que convenan, lo cual introduce restricciones en el movimiento relativo y movimiento de múltiples eslabones del mecanismo. #sualmente los eslabones son modelados como r!idos, o cuerpos que no sufren deformación. 1as metodolo!as y procedimientos usados en este cap!tulo son aplicados a un mecanismo de manivela corredera, que incluyen ambos, eslabones de revolución y translación en su dinamismo." <
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DINAMICA DE MAQUINARIA MECANISMO MANIVELA CORREDERA cuarto barras, que consiste en cuatro cuerpos r!idos, dos eslabones idealmente de revolución y uno idealmente translacional. (&?3 y @ respectivamente)
#n una ;unta de revolución, como un rodamiento, se encuentra en la cone+ión entre la corredera y el acoplador. 1a manivela, es el eslabón de rotación impulsor, ira a una velocidad anular constante (al menos de manera ideal) de <rpB (para el caso del e;emplo del te+to citado). 1a con-uración inicial del mecanismo se de-ne con la manivela y el acoplador colineares entre s!, con sus ;untas conc$ntricas. “ 1a respuesta din%mica es decir, la aceleración y velocidad del mecanismo de manivela?corredera es obtenida y representada en el siuiente r%-co"
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