11-02-2016

UNIVERSIDAD TÉCNICA DE AMBATO FACULTAD DE INGENIERÍA CIVIL Y MECÁNICA

CARRERA DE INGENIERÍA MECÁNICA DISEÑO DE ELEMENTO DE MAQUIONAS II DOCENTE: Ing. Cesa A!"a In#egan#es: A$e% A$&a'(e A$)a! O#*+ Es#e"an Me,-a A$e V*$$a)a Ca$!s V*ea SEMESTRE: SETIMO /A0 PERIODO ACADÉMICO OCTUBRE – MARZO 2016

1. E$ e,e g*a a 234 5& 6 e'*"e 7.3 8 a #a)9s e ;n a'!5$a&*en#! <$e%*"$e. La 5!#en'*a se en#ega a ;n e,e a6a'en#e a #a)9s e ;n s!$! engane (e$*'!*a$ B. =;e #*ene ;n >ng;$! n!&a$ e 5es*?n e @4 6 ;n >ng;$! e (9$*'e e 13. E$ *>&e#! e 5as! e$ engane es e .11 5;$gaas. Se$e''*!ne e$ !a&*en#! A 6 C s*: a Se ;#*$*+a !a&*en#!s e '!n#a'#! ang;$a 5aa &!n#a,e en  &a'a FAG. " Se ;#*$*+a !a&*en#!s e '!n#a'#! ang;$a 5aa &!n#a,e en O &a'a FAG. ' Se ;#*$*+a !a&*en#!s -g*!s e "!$as e s;'! 5!<;n! &a'a FAG.  aa $!s $*#ea$es a"' 5!5!nga $a ge!&e#-a 5$an! =;e )a a #ene e$ e,e $a se''*?n e $a "an'aa =;e s!5!#a e$ !a&*en#!.

Da#!s e$ e,e'*'*!: N = 650 Rpm H = 7.5 Hp Dp = 4.141 plg

Engane 8e$*'!*a$ = 20

ᵒ

!= 15

ᵒ

R"#$m%&'(" A = ) R"#$m%&'(" B = )

Ca$';$! 5aa  Ca$';$! #:

1. E$ e,e g*a a 234 5& 6 e'*"e 7.3 8 a #a)9s e ;n a'!5$a&*en#! <$e%*"$e. La 5!#en'*a se en#ega a ;n e,e a6a'en#e a #a)9s e ;n s!$! engane (e$*'!*a$ B. =;e #*ene ;n >ng;$! n!&a$ e 5es*?n e @4 6 ;n >ng;$! e (9$*'e e 13. E$ *>&e#! e 5as! e$ engane es e .11 5;$gaas. Se$e''*!ne e$ !a&*en#! A 6 C s*: a Se ;#*$*+a !a&*en#!s e '!n#a'#! ang;$a 5aa &!n#a,e en  &a'a FAG. " Se ;#*$*+a !a&*en#!s e '!n#a'#! ang;$a 5aa &!n#a,e en O &a'a FAG. ' Se ;#*$*+a !a&*en#!s -g*!s e "!$as e s;'! 5!<;n! &a'a FAG.  aa $!s $*#ea$es a"' 5!5!nga $a ge!&e#-a 5$an! =;e )a a #ene e$ e,e $a se''*?n e $a "an'aa =;e s!5!#a e$ !a&*en#!.

Da#!s e$ e,e'*'*!: N = 650 Rpm H = 7.5 Hp Dp = 4.141 plg

Engane 8e$*'!*a$ = 20

ᵒ

!= 15

ᵒ

R"#$m%&'(" A = ) R"#$m%&'(" B = )

Ca$';$! 5aa  Ca$';$! #:

H v

Wt =33000

v=

v=

п.dp.n 12

пx 4.141 x 650 12

V H 74.27 5*es&*n 7.5

Wt =33000

704.67

# H J31.@@$" Ca$';$!  = arctg

Ɵt

tg 20 cos15

Ɵt =20.64 ᵒ

*+ = ,( - (g20.64 *+ = 51.22(g20.64

 H 1J@.@K$" Ca$';$! a *$ = *( - (g 15 *$ = 251.22 (g 15

a H K.14K $" CALCULO DE REACCIONES EN A Y EN B LANO  Y

 &a H 4 51.22./  R3./5 = 0

R'+H  @14.7J $"  F6 H 4 R$3  *( R3 = 0 R$3 = 51.22  210.7

Ra6 H  14.K $" REACCIONES TOTALES R$( = / 0  1.  140.4 89 2 2 91.89 + 140.49 R$( = √ 91.89

Ra# H 127.7 L" Ra# H 473 N R( = / 0  40.4  210.7 89 2 2 40.4 + 210.73 R( = √ 40.4

R'# H @1.32 L" R'# H 4.K3 N SELECCIPN  RODAMIENTO EN 

0.95

:$ ; 0.5 /

057

+

0.75 057



a  1.K 4.1 N  1.K N FrB <$ = $  0.5 / YB  0.75

<$ = 0.41  0.5 /

057



FaH 1.47 N CALCULO DEL RODAMIENTO A: Fa = 1.14 Fr 1.07 0.95

=1.14

1.1J  1.1 P = 0.5.<+  0.57.<$ P=0.5 /0.5  0.57 /1.1

H 4.K722 N C$($l"g" p?g%'$ 21@
F$ H @
L( H 444 ( As;&*! K3 a1 H 4.2@ a@ H 1 a'e! aJ H 4.3  J. H 1.3 C = 0.766./ /4000 - 650 - 60  /0.62 -1.5 - 106   &l&$#" 1

CH 3.JK N CATALOGO FAG DE LA SERIE 7@41B: D H J@ &&  H 1@ && "HK C H 2.K3 N C! H J. N Ca$';$! D&: D& H /2  12  2 D& H @@ && Ca$';$! V*s'!s*a: < = 22 - 650

F) H 1J44 A = / 1000  650 &l&$#" 1

a H 1.13  1 a H1.13 4500

1 = 1.15. √ 650 x 22

V1 H J.@7 &&@ s FT = 40  G& $Gm& ᵒ

De $a g;-a 5aa se$e''*!na e$ a'e*#e: V4 H 4 74 ISO VG 2 T#a"a,! H 4 17 T#a"a,! H 37 V 37 C H @3&&@s ᵒ

 H )  )1  H @3  J.@7 H 4.37 Fa =0.8 Fr 1.07 0.95

=0.8

1.1@  4. P" = 0.6+ 0.5.$

! H 4.2.4.K3 4.3.1.47 ! H 1.143
FsH J.4 : = 1  2 1 = 0

:2 = 5. : = 5.

aJH 4.2 a1H 4.2@ a@H 1 8 = 0.62 - 1 - 0.46 / 5  0.766  - / 106  650-60

L( H K1.JK7 (!as <1 = / 1.7  500 &l&$#"1

F1 H 1.@3 CALCULO DEL RODAMIENTO B: N! e%*s#e e$ )a$! e Wa 5aa A: Fa = 1.14 Fr 0 < 1.14

P = <+

 H 4.73 N C$($l"g" p?g%'$ 21
F$ H @
L( H 444 (!as As;&* K3: a1 H 4.2@ a@ H 1 a'e! aJ H  4.3  J.  H 1.3 C = 0.75 / /4000 - 650 - 60   /0.62 - 1.5 - 106 &l&$#"1

C H .1J WN

CATALOGO FAG DE LA SERIE 7@44B: D H J4&&  H 14&& "HK C H 3 WN C! H @.3WN Ca$';$! e D&: D& H / 010   2 D& H @4&& Ca$';$! )*s'!s*a: < = 20 - 650

F) H 1J444 A = /1000 650 &l&$#" 1

A H 1.13  1 A H 1.13 4500

1 = 1.15 . √ 650 x 20

V1 H 3.J &&@ s FT = 40  $Gm%+ ᵒ

G;-a 5aa se$e''*!na e$ a'e*#e: V4 H 4  74 ISO VG 2 T#a"a,! H 4  17 T#a"a,! H 37 V37 C H @3&&@s ᵒ

 H )  )1  H @3  3.J  H 4.33

P" = +

! H 4.73
FsH J.JJ : = 1  2 1= 0

@H 2 H 2 aJH 4.J a1H 1 a@H 1 8 = 0.62 - 1 - 0. /5 0.75  - / 106  650-60 

L( H 11J.143 (!as
F$ H 1.1 CALCULO DEL RODAMIENTO C: Ratotal=0.747 kN = F rA Rcotal =0.956 kN = F rB Fa = 1.14 Fr 0 < 1.14

P= Fr P=0.956 KN

Lh= 4000 h

AGm%+ "'%$9%l%#$# #&l 5K

$1 = 0.62 $2 = 1 $ = 0.5 – . $ = 1.5 $Gm%+

√

Lh∗n∗60 6 a 1∗a 2∗a 3∗10

C = P∗ 3

√

C =0.956 ∗3

4000∗650∗60 0.62 ∗1∗1.5∗10

C =5.27 KN

CATALOGO FAG 7@41B: D H J@&&  H 1@&& B H 14&& C H 2.K3 WN C4 H J. WN Dm=

32 + 12 2

Dm=22 mm Fv = Dm x n

Fv =22 x 650 Fv = 14300

As;&*: ∆  = 40 ! C am"#$nt$=17 ! C

6

tra"a%o= 40 +17 =57 !C

mm & 57! C ( 40−70 )

2

'

( )

1

( )

1

k =a =

k =a =

1000

3

n

1000

3

650

k =a k =1.15 > 1

& 1=k .

4500

√ n∗dm

& 1=1.15 .

4500

√ 650∗22

mm & 1=43.27 '

2

SELECCIONAMOS ISO VG 2: mm & 57! C =22.5 ' K =

& & 1

K =

22.5 43.27

K = 0.52

2

RODAMIENTO DE BOLAS: k 1= 0

LUBRICANTE CON ADITIVOS: k 2= 0 K = k 1 + k 2 K = 0 + 0 =0

a23=1.4

(

1∗1∗1.4∗

Lh=

6.95 0.956

)∗ 3

6

10

650∗60

Lh=13792.5 h

(l =

√ 3

13792.5 500

(l =3 . 02 > 2 S* C;&5$e

LITERAL D:

E$ e;'#! e !"$e e;''*?n 6 engane (e$*'!*a$ e $a <* g;a #as&*#e 3.4 8. E$ .e,e 1 es $a en#aa g*a a 144 5& 6 e'e5#a $a 5!#en'*a en n en $a #a"$a 1@. Caa engane #*ene ;n >ng;$! e 5es*?n n!&a$ e 1.3 6 ;n >ng;$! e (9$*'e e 3. Las '!&"*na'*!nes e (9$*'es *+=;*ea 6 ee'(a s!n #a$es =;e $as <;e+as a%*a$es se !5!nen en#e s* s!"e e$ e,e @ '!&! se *n*'a.

!5!nga e$ #*5! e !a&*en#! &!n#a,e 6 se$e''*!ne $!s !a&*en#!s AD EFG8 &a'a SF 6 ea$*'e ;n 5$an! e $a ge!&e#-a e$ e,e 6 $a "an'aa #!&e en ';en#a se';en'*a e &!n#a,e 6 es&!n#a,e.

Datos α= 14,5ᵒ Ψ= 45ᵒ H= 5 HP

EJE 1

d 3=

d 3=

N p P∗cos ) 12 8∗cos45

d 3=2,12

*t =

*t =

60000 ∗ H

+dn 60000∗5

( + ) ( 2,12 ) ( 1800 )

*t =2,5 KN

, cos )

−1 tan

∅

t = tan

∅

t = tan

∅

t = 20,08

−1 tan14,5

cos 45

* r= *t ∗tan ∅ t * r=2,5∗ tan20,08 * r=0,913 KN

* a=*t ∗tan ) * a=2,5∗tan 45 * a=2,5 KN

Plano X-Y

- $ =2,5

2,12 2

- $ =2,65 KN

∑ - =0 F

0,913 ( 1 ) + R / (3,25 )−2,65 = 0

R /= 0,53 KN

∑ F Y =0 R /− 0,913 + R F/ = 0 R F/ = 0,38 KN

Plano X - Z

∑ - =0 F

0,913 ( 1 ) + R 0 ( 1,25 ) −0,913 ( 2,25 ) =0

R 0=1,14 KN

∑ F 0 =0 R F0 −0,913 −1,14 + 0,913 =0 R F0 =1,14 KN

R F =( 0,38 %+ 1,14 k ) KN R F =1,20 KN

R =( 2,5 # + 0,53 % −1,14 k ) KN R =2,79 KN

F r =1,20 + 2,79 =4 KN F a =2,5 KN

EJE 2

d 3=

d 3=


d 3= 4,24

*t =

*t =

60000 ∗ H

+dn 60000 ∗5

( + ) ( 4,24 ) ( 900 )

*t =2,50 KN

, cos )

−1 tan

∅

t = tan

∅

t = tan

∅

t = 20,08

−1 tan14,5

cos 45

* r= *t ∗tan ∅ t * r=2,5∗ tan20,08 * r=0,913 KN

* a=*t ∗tan ) * a=2,5∗tan 45 * a=2,5 KN

Plano X-Y

- a=2,5

4,24 2

- a=5,3 KN

∑ - =0 A

0,913 ( 5 ) + R A/ ( 10 ) −5,3 =0

R A/= 0,07 KN

∑ F Y =0 R D/ −0,913 + R A/= 0 R A/= 0,843 KN

Plano X - Z

∑ - =0 A

0,913 ( 5 ) + R D0 ( 5 ) −0,913 ( 10 )=0

R D0=0,913 KN

∑ F 1 = 0 R A0−0,913 −913 + 0,913 =0 R A0=0,913 KN

R D=( 0,843 % + 0,913 k ) KN R D=1,44 KN

R A =( 2,5 # + 0,07 % −0,913 k ) KN R A =2,86 KN

F r =1,44 + 2,86= 4,3 KN F a =2,5 KN

EJE 3

d 3=

d 3=


d 3=7,54

*t =

*t =

60000 ∗ H

+dn 60000∗5

( + ) ( 7,54 ) ( 300 )

*t =42,21 KN

, cos )

−1 tan

∅

t = tan

∅

t = tan

∅

t = 20,08

−1 tan14,5

cos 45

* r= *t ∗tan ∅ t * r= 42,21∗tan20,08 * r=15,42 KN

* a=*t ∗tan ) * a= 42,21∗tan 45 * a= 42,21 KN

Plano X-Y

- $ =42,21

7,54 2

- $ =159,13 KN

∑ - 2 =0 42,21 ( 1,5 ) + R H/ ( 3,5 ) −159,13 =0

R H/ =27,37 KN

∑ F =0 Y

R2/ −42,21 + R H/ =0 R2/ =14,84 KN

Plano X - Z

∑ - 2 =0 42,21 ( 1,5 ) + R H0 ( 2 )− 42,21 ( 3,5 )=0

R H0=42,21 KN

∑ F =0 0

R20 42,21− 42,21 + 42,21= 0 R20= 42,21 KN

R H =( 27,37 % + 42,21 k ) KN R H =50,30 KN

R2 =( 42,21 #+ 14,84 % − 42,21 k ) KN R2 =14,84 KN

F r =50,30 + 14,84 =65,14 KN F a =42,21 KN

Eje 1

F a =¿

2.5 KN

F r = 4 KN 5!

a1= 0.62 a2= 1 a3 =1

X= ".5#

Y = 1

F r

P= X $

% Y $

F a

P= ".5# $4 % 1$ 2.5 P = 4.&4

( L =3.5 3

Lh=( 3.5 ) ( 500 )

Lh=¿

2143&.5 '

√ 3

C= P

C= 4.74

√ 3

Lh∗n∗60 6 a 1∗a2∗a3∗10

21437.5 ∗1800∗60

C= 7.54 :N

nc =

nc =

P3 P 1.9 4.74

6

0.62∗1∗1∗10

nc = 0.4 dm=

120 + 55 2

=8

7.5

Fv =n∗dm

Fv =1800∗87.5 =157500

()* + 12 4500

4 1 = 2

√ dm∗n

4 1 = 2

4500

√ 87.5∗1800

4 1 = 11.34

 RAB

= &"

+= #.

K =

K =

4 4 1

6.8 11.34

=0.599

( o∗ F a C 5

=

13∗2.5 45

L= 0.56 = 1.55

Pcorr$g#do

=X$

Pcorr$g#do

= ".5# $4 % 1.55$ 2.5

Pcorr$g#do

= #.115

nc =

nc =

P3 P 1.9 6.115

nc = 0.31

F r

% Y $

F a

=0.72 1.0

a 6KF =3 c p

¿ ¿ Lh=a 1∗a2∗a3 ¿

73.54 6.115

¿ ¿

Lh=0.62∗1∗1 ¿ Lh=¿

5.0 

( L =

( L =

√ 3

√ 3

Lh 500

9985.03

( L =¿

500

2.71

E,e @ F a =¿

2.5 KN

F r = 4.3 KN 5!

a1= 0.62 a2= 1 a3 =1

X= ".5# Y = 1 P= X $

F r

% Y $

F a

P= ".5# $4.3 % 1$ 2.5 P = 4."

( L =4 3

Lh=( 4 ) ( 500 )

Lh=¿

32""" '

C= P

√

C= 4.74

√

3

3

Lh∗n∗60 6 a 1∗a2∗a3∗10

32000∗900∗60

C= 66.71 :N

nc =

nc =

P3 P 2.04 4.9

nc = 0.41

6

0.62∗1∗1∗10

dm=

130 + 75 2

=¿ 102.5

Fv =n∗dm

Fv =900∗102.5=92250

()* + 22 4500

4 1 = 2

√ dm∗n

4 1 = 2

4500

√ 102.5 ∗900

4 1 = 14.2

 RAB

= &"

+= 

K =

4 4 1

K =

( o∗ F a C 5

9 14.82

=

=0.61

15∗2.5 49

L= 0.56 = 1.55 Pcorr$g#do

=X$

Pcorr$g#do

= ".5# $4 % 1.55$ 2.5

Pcorr$g#do

= #.115

nc =

nc =

P3 P 2.04 6.115

F r

% Y $

F a

=0.76

nc = 0.33

a 6KF =3

c p

¿ ¿ Lh=a 1∗a2∗a3 ¿ 66.71 6.115

¿ ¿

Lh=0.62∗1∗1 ¿ Lh=¿

1406.6 

( L =

( L =

√ 3

√ 3

Lh 500

14906.69

( L =¿

500

.1

EXE J

F a =¿

42.21 KN

F r =65.14 KN 5!

a1= 0.62 a2= 1 a3 =1

X= ".5# Y = 1

F r

P= X $

% Y $

F a

P= ".5# $#5.14 % 1$ 42.21 P = &.#

( L =4 Lh=() ( 500 ) 3

Lh=32000

'

√ 3

C= P

C= 7.6

Lh∗n∗60 6 a 1∗a2∗a3∗10

√ 3

32000 ∗300∗60

C= 767.72 :N

nc =

P3 P

6

0.62∗1∗1∗10

nc =

27 78.68

nc = 0.34 dm=

920 + 630 2

=¿ 775

Fv =n∗dm Fv =300∗775 =232500

()* + 12 4500

4 1 = 2

√ dm∗n

4 1 = 2

4500

√ 775∗300

4 1 = .33

 RAB

= &"

+= #.

K =

4 4 1

K = ( o∗ F a C 5

6.8 9.33

=

0.72

16∗42.21

=

1760

L= 0.56 = 1.71 Pcorr$g#do

=X$

Pcorr$g#do

= ".5# $#5.14 % 1.&1$ 42.21

Pcorr$g#do

= 1".#5

nc =

nc =

P3 P 27 108.65

nc = 0.24

F r

% Y $

F a

= 0.38

a 6KF =0.45

11-02-2016

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