pc
cd
rbg
rbp pd
φ
N g = 40 N p = 16 pd = 2 pulg −1 φ = 20
= π/p 571 pulg pc = π /pd = π/ π /2 pulg = pulg = 1, 571 pulg
cd =
dg =
N g 40 = = 20 20 pulg pulg pd 2
d p =
N p 16 = = 8 pulg 8 pulg pd 2
(d p + dg ) (8 + 20) = = 10 10 pulg pulg 2 2
rbp =
8 d p cosφ = cosφ = cos20 cos20 2 2
rbg =
dg 20 cosφ = cosφ = cos20 cos20 2 2
pulg
pulg
cd = 14 14,, 25 25 pulg pulg
cd =
(d p + dg ) = 2
2(14, 25) = 28, 28, 5 pulg ⇒ d p + dg = 2(14,
m =
∴
dg d p = N g N p 16 40 = d p dg
d p = 28, 5
16 28,5−dg
− dg
=
40
dg
16dg = 40(28, 5)
− 40dg
56dg = 1114 dg = 20, 36 pulg
d p = 28, 5
− 20, 36 = 8, 143 pulg
pd =
N p 16 = = 1, 965 pulg d p 8, 143
pd =
N g 40 = = 1.965 pulg dg 20, 36
pc =
π π = = 1, 599 pulg pd 1, 965
= 22, 60
= 22, 60
rbp φ = arc cos = arc cos r p
rbg φ = arc cos = arc cos r p
3, 759 8,143 2
9, 367 20,36 2
σtp
N g = 70 N p = 20 pd = 8 pulg bw = 1, 5 pulg Qv = 6 N ap = 1750 rpm h p = 25 hp
σtg
d p =
vt =
N p 20 = = 2, 5 pulg pd 8
πd p N ap π(2, 5)(1750) = = 1145 pies/min 12 12
W t =
126050h p 126050(25) = = 720, 3 lbf d p N ap (2, 5)(1175)
Y jp = 0, 34 Y jg = 0, 42
σtp =
W t pd K a K s K m (720, 3)(8)(1, 0)(1, 18) = = 29410 psi (1, 5)(0, 34)(0, 68) bw Y jp K v
K a = 1, 5
K s = 1, 0 K m = 1, 18
bw /d = 0, 6
K v = 0, 68
vt = 1145 pies/min
σtg = σ tp Y jp /Y jg = 29410(0, 34)/0, 42 = 23810 psi
σ perm n = σ perm /σ
Qv = 6
bw
n = 5 σc
N g = 72 N p = 18 m = 4 mm S y = 720 M pa N ap = 1500 rpm H = 3, 2 kW φ = 20 n = 5
σtp =
W t pd K a K s K m S y 720 = = = 144 M P a bw K v Y j n 5 dg = N g m = (72)(4) = 288 mm
(18)(4) = 72 mm
W t =
60 103 H = 566 N πd p N ap
×
pd = 1/m = 1/0, 004 m = 250 m−1 bw 144 M P a = 144 MP a =
W t pd K a K s K m bw K v Y j
(566)(250) (1)(1)K m = bw (0, 625)(0, 325)
⇒ bw = 4, 84 mmK m
d p = N p m =
Y jp = 0, 325 N p = 18
N g = 72
K a = 1, 0 K s = 1, 0
m = 4 < 5
K v = 0, 625 1113 pies/min
vt = πN ap d p = π(1500 rpm) Qv
≤ 5 K m
bw
K m = 1, 1
1 = Rx
1 1 + d p dg
2 = senφ
1 1 + 72 288
bw
1, 0 K m 1, 8 = 5, 324 mm 6 mm
≤
≤
2 sen20
Rx = 9, 85 mm E = 207 GP a E =
2 2
1−ν a
E a
2
+
1−ν
=
b
E b
ν = 0, 3
E 207 = = 227 GP a 1 ν 2 1 0, 32
−
−
E Rx
W t
566 cosφ W cos20 W = = = = 4, 49 bw E Rx bw E Rx (0, 006)(227 109 )(0, 00985)
×
σc = E
σc = (227
9
× 10 )
4, 49
W K a K s K m 2π K v
× 10
2π
−5
1/2
(1)(1)(1, 1) (0, 625)
1/2
−5
× 10
= 767 M P a
72 mm 12×25,4
=
pc = π/pd = π/14 = 0, 224 pulg = 5, 700 mm
cd =
d p + dg N p + N g = = 5, 25 pulg = 133, 4 mm 2 2 pd
r p =
N p 21 = = 0, 75 pulg 2 pd 2(14)
rg =
126 N g = = 4, 5 pulg 2 pg 2(14)
rbp = r p cosφ = 0, 75 cos20 rbg = r g cosφ = 4, 5 cos20
rop = r p + a = r p +
1 pd
rog = r g + a = r g +
1 C r = (0, 2244) cos20
+
pulg = 17, 90 mm
pulg = 107, 4 mm
1 pulg = 0, 8214 pulg = 20, 86 mm 14
1 1 = 4, 5 + pd 14
2
(0, 8214)
2
− (0, 7048)
+
pulg = 116, 1 mm
2
(4, 571)
2
− (4, 229)
−
5, 250 tan20 0, 2244
C rt = C r + C ra = 1, 712 +
C ra = ∴
(1, 8) tan30 = 6, 343 0, 2244
bw tanψ = 3, 00 pc
− 1, 712 = 1, 288
tanψ = (1, 288) (0, 2244) /1, 8 ψ = 9, 122
d =
N Pt
d =
18 6
d = 3 pulg
pt =
π P t
pt =
π 6
pt = 0, 5236 pulg
P t cosψ
P n = P n =
6 cos
P n = 8, 485 dientes/pulg
φt = tan−1 φt = tan−1
tanφn cosψ
tan14, 5 cos45
φt = 20, 09
108
K o = 1 Y P = 0, 303 Y G = 0, 412 P t = P n cosψ = 10 cos30 = 8, 66 dientes/pulg dP = N P /P t = 17/8, 66 = 1, 963 pulg dG = (52/17)1, 963 = 6, 004 pulg mG = 52/17 = 3, 06
V =
π dP n P π (1, 963) 1800 = = 925 pies/min 12 12 W t =
33000 (4) = 142, 7 lbf 925
B = 0, 25(12
2
− 6) = 0, 8255 A = 50 + 56 (1 − 0, 8255) = 59, 77 √ ,
K V =
59, 77 + 925 59, 77
φt = tan −1
3
tanφn cos
0 8255
= 1, 404
= tan−1
tan20 cos30
rP = d P /2 = 1, 963/2 = 0, 9815 pulg rG = 3, 06(0, 9815) = 3, 004 pulg a = 1/P n = 1/10 = 0, 1 pulg
= 22, 796
(rb )P = r P cosφt = 0, 9815 cos22, 796 = 0, 9048 pulg (rb )G = r G cosφt = 3, 004 cos22, 796 = 2, 769 pulg
Z = Z =
(rP + a)
2
(0, 9815 + 0, 1)
2
2
− rbP + 2
− 0, 9048
+
(rG + a)2
(3, 004 + 0, 1)2
Z = 0, 5924 + 1, 4027
2
− 2, 769 − (0, 9815 + 3, 004) sen22, 796
− 1, 54427 = 0, 4509 pulg
π π cos20 = cos20 = 0, 2952 pulg P n 10
pN = p n cosφn =
mN =
2
− rbG − (rP + rG ) senφt
pN 0.2952 = = 0, 6891 0, 95 Z 0, 95(0, 4509)
I =
I =
cosφt senφt mG 2 mN (mG + 1)
sen22, 796 cos22, 796 3, 06 2 (0, 6891) (3, 06 + 1) I = 0, 195
J P = 0, 45
J G = 0, 54
J P = 0, 45(0, 94) = 0, 423 J G = 0, 54(0, 98) = 0, 529
√ √ √
1 K s = = 1, 192 kb (K s )P = 1, 192 (K s )G = 1, 192
C pf =
F 10d
F Y P
1, 5 0, 303 10
1, 5 0, 412 10
0.0535
0.0535
= 1, 043
0.0535
= 1, 052
− 0, 0375 + 0, 0125 F
C pf =
1, 5 10 1, 963
− 0, 0375 + 0, 01251, 5 = 0, 0577 C mc = 1 C pm = 1 C ma = 0, 15 C e = 1
K m = C mf = 1 + C mc (C pf C pm + C ma C e ) K m = 1 + (1) (0, 0577 (1) + 0, 15 (1)) = 1, 208
−8
(Y N )P = 1, 558(10 )−0,0178 = 0, 977 8
(Y N )G = 1, 558(10 /3, 06)−0,0178 = 0, 996
K r = 0, 0657
− 0, 0759 ln(1 − 0, 9) = 0, 833 K T = 1 C f = 1
107 (S t )P = 77, 3(240) + 12800 = 31352 psi (S t )G = 77, 3(200) + 12800 = 28260 psi
σ = W t K o K V K s σ = 142, 7(1)1, 404(1, 043) σ perm =
8, 66 1, 208(1) = 3446 psi 1, 5 0, 423
31352(0, 977) = 36773 psi (1)0, 833
(S F )P =
36773 = 10, 7 3446
σ = 142, 7(1)1, 404(1, 052) σ perm =
P d K m K B F J
8, 66 1, 208(1) = 2778 psi 1, 5 0, 529
28260(0, 977) = 33145 psi (1)0, 833
(S F )G =
33145 = 11, 9 2778
M = 4 Dρ = 7, 6 cm D = 23, 2 cm b = 3, 5 cm N sf = 1, 2
N = 58 N = 19 Dρ = 7, 6 cm M = 4 N sf = 1, 2 b = 3, 5 cm D = 23, 2 cm
F t =
4500 CV vm
CV vm F t CV CV =
vm = πDρ n = π(
√
F t vm 4500
7, 6 )(1160) = 276 mpm 100
√
27, 6 + vm 27, 6 + 276 V F = = = 1, 6 27, 6 27, 6
F d = (V F )N sf K m F t K m = 1.15 N sf = 1, 2 F t
F d = 1, 6
× 1, 2 × 1, 15F t = 2, 20F t
F t
F s =
sd bjM K l 10 K s K t K r
sb = 1335 b = 3, 5 j = 0, 2 M = 4 K l = 1 K s = 0, 629
M = 4 t < 70 o C
K t = 1 K r = 1, 1
F s =
1335
× 3, 5 × 0, 2 × 4 10
s2 F w = Dρ bI cd2 C e
1 = 540 kg 0, 629 1, 1
×
2
× C l K t C r
103
Dρ = 7, 6 cm b = 3, 5 cm I = 0, 082 s2cd = 90
6
× 10 C e = 551 × 10
6
C l = 1 K t = 1
t < 70 o C
C r = 1, 1
F w = 7, 6 F w < F s F w = F d
× 3, 5 × 0, 081 ×
2
6
90×10
551×106
×
× 1
1,1
103 = 291 kg
F t F d = 2, 20F t
∴
CV =
F t = 132 kg
F t vm 132 276 = = 8, 09 CV 4500 4500
×
J
Y N
Z N
I
j
