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Sujetadores y Tornillos de Potencia
Engineers need to be continually reminded that nearly all engineering failures result from faulty judgments rather than faulty calculations.Eugene S. Ferguson, Engineering and the Mind’s Eye.
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Perfile roscado
Parámetros empleados para definir un perfil roscadoDiámetro mayor, d. Paso por pulgada p=1/n, nº roscas por pulgada
Diámetro de cresta, dc
Diámetro de paso, dp
Diámetro de raiz, dr
Text Reference: Figure 15.1, page 667
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Roscado
(a) Simple, (b) doble, y (c) triple.
Text Reference: Figure 15.2, page 667
AVANCEl = tipo roscado x p
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Perfiles de rosca
M;
C-basto
F-Fino
Ej.MF8X2-G6
dc/roscas/pulg/ajuste
UN; 8 series de rosca de paso
constante
C-basto
F-Fino
EF-Extra Fino
UN -- M
ACME
Uso: potencia, máquina - herramienta
Ej.UNF1/2X16-1B
dc/roscas/pulg/ajuste
Buttress
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Perfil M y UN
Detalle dimensiones de perfiles M y UN.
ht= 0.5p / tan 30º
Text Reference: Figure 15.4, page 668
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Ajuste
Serie pulgadas Serie métrica Tornillo Tuerca Tornillo Tuerca
1A 2A 3A
1B (suelto) 2B (normal)
3B (justo)
8g 6g 8h
7H 6H 5H
Equivalencias entre roscas
Text Reference: Table 15.1, page 669
Calidad 3(apretado)-9(Suelto)
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Tornillos de potencia: Perfil ACME
Detalle del perfil - Dimensiones. (valores en pulgadas)
Text Reference: Figure 15.5, page 670
Buscamos: mayor ventaja mecánica - posicionamiento.
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diametro Cresta, dc, in.
Numero rosca por pulgada, n
Area a tensión, At, in2
Shear stress area, As, in
2 1/4
5/16 3/8
7/16 1/2 5/8 3/4 7/8 1
1 1/8 1 1/4 1 3/8 1 1/2 1 3/4
2 2 1/4 2 1/2 2 3/4
3 3 1/2
4 4 1/2
5
16 14 12 12 10 8 6 6 5 5 5 4 4 4 4 3 3 3 2 2 2 2 2
0.02663 0.04438 0.06589 0.09720 0.1225 0.1955 0.2732 0.4003 0.5175 0.6881 0.8831 1.030 1.266 1.811 2.454 2.982 3.802 4.711 5.181 7.338 9.985
12.972 16.351
0.3355 0.4344 0.5276 0.6396 0.7278 0.9180 1.084 1.313 1.493 1.722 1.952 2.110 2.341 2.803 3.262 3.610 4.075 4.538 4.757 5.700 6.640 7.577 8.511
Text Reference: Table 15.2, page 671
Perfil ACME
Datos cortante para una longitud de roscado de 1 pulg
dp=dc-0.5p-0.01
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Tornillo de potencia con collarín
Text Reference: Figure 15.6, page 672
, Ángulo de avance=ArcTan [l/πdp]
Collarín de empuje
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Tornillo de potencia con collarín y husillos de bolas
Text Reference: Figure 15.6, page 672
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Fuerzas sobre el tornillo de potencia
Fuerzas actuando sobre. (a) paralelepípedo ; (b) sección axial; (c) plano tangencial.
Text Reference: Figure 15.7, page 673
∑Fv=0∑Fh x r =0
DC=OE θn
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Tipos de sujetadores roscados
(a) Tornillo y tuerca. (c) Tornillo de cabeza. (c) Birlo.
Nota:Arandela o roldana
Text Reference: Figure 15.8, page 679
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Par torsor el tornillo de potencia∑Fv=0∑Fh x r =0
DESCENSOASCENSO
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Ejercicios
1. Determine los pares de torsión, de elevación y de descenso, así coma la eficiencia del tornillo de potencia manufacturado con rosca ACME. ¿es autobloqueante? ¿cual es la contribución de la fricción del collarín, en comparación con la fricción del tornillo, si el collarín tiene, a) deslizamiento, m=0,15 b) rodamiento, m=0,02 ambos en aceite. W=1000lb. Rosca Acme 1,25-5 y Omedio collarín =1,75 in.
2. Mismo ejercicio con W=1000lb. Rosca Acme 1-5 roscado doble y Omc=1,5 in. m=0,16 rosca y 0,12 collarín.
3. Igual que el ejercicio dos, pero con roscado simple.
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Equivalencia de la conexión: Sistema de resortes
Bolt-and-nut assembly simulated as bolt-and-joint spring.
Text Reference: Figure 15.9, page 680
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Force vs. Deflection of Bolt and Member
Force versus deflection of bolt and member.
(a) Seperated bolt and joint.
(b) assembled bolt and joint.
Text Reference: Figure 15.10, page 680
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Fueza vs. Deflexión
Text Reference: Figure 15.11, page 681
0)( kbikji ekPekPP
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Bolt and Nut
Figure 15.12 Bolt and nut. (a) Assembled; (b) stepped-shaft representation of shank and threaded section.
Text Reference: Figure 15.12, page 682
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Bolt and Nut Assembly
))(tan(
))(tan(ln2
tan
cicifi
cicifi
fciji
ddddL
ddddL
dEk
Figure 15.13 Bolt-and-nut assembly with conical fustrum stress representation of joint.
di=dw= diámetro menor del cono de presión
)5,2577,0()5,0577,0(
5ln2
577,0
ci
ci
ciji
dLdL
dEk
))(tan(
))(tan(ln2
tan
cicifi
cicifi
fciji
ddddL
ddddL
dEk
Simplificación tal que el diámetro de la cara de arandela es aproximadamente 50% mayor que el diámetro de la espiga del sujetador en el caso de tornillos de maquinaria y pernos con cabeza hexagonal de tipo estandar
(dw=1,5dc y α=30º)
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Constants for Joint Stiffness Formula
Poiss on’sModulus of
Elasticity, E, Numerical ConstantsMaterial ratio, GPa Ai B iSteelAluminumCopperGray cast iron
0.2910.3340.3260.211
206.871.0
118.6100.0
0.787150.796700.795680.77871
0.628730.638160.635530.61616
Table 15.3 Constants used in joint stiffness formula [Eq. (15.26)] [From Wileman et al (1991)]
Text Reference: Table 15.3, page 684
)(, i
ciL
dB
iii
im eAdEk
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Gasketed Joint
63 Nd
Db
Figure 15.17 Threaded fastener with unconfined gasket and two other members.
Text Reference: Figure 15.17, page 694
63 Nd
Db
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))(tan(
))(tan(ln2
tan
cicifi
cicifi
fciji
ddddL
ddddL
dEk
)(
, i
ciL
dB
iii
im eAdEk
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Strength of Bolts (Inches)
SAE grade
Range ofcres t
diameters,in.
Ultimatetensile
s trength, Sut,ksi
Yieldstrength, S y,
ksi
Proofs trength, S p,
ks i12
45
78
1/4 - 1 1/21/4 - 3/43/4-1 1/2
1/4 - 1 1/21/4 - 1
1 - 1 1/21/4 - 1 1/21/4 - 1 1/2
607460115120105133150
3657361009281115130
335533658574
105120
Table 15.4
Strength of steel bolts for various sizes in inches.
Text Reference: Table 15.4, page 687
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Strength of Bolts (Millimeters)
Table 15.5
Strength of steel bolts for various sizes in millimeters.
Text Reference: Table 15.5, page 687
Metric grade
Crestdiameter, dc,
mm
Ultimatetensile
strength, Sut,MPa
Yieldstrength, Sy,
MPa
Proofstrength, Sp,
MPa4.64.85.88.89.8
10.912.9
M5-M36M1.6-M16M5-M24M17-M36M1.6-M16M6-M36
M1.6-M36
400420520830900
10401220
240340a
415a
660720a
9401100
225310380600650830970
aYield strength approximate and not included in standard.
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Coarse and Fine Thread DimensionsCoarse Threads (UNC) Fine Threads (UNF)
Crestdiameter,d c, in.
Number ofthreads per
inch, n
Tensiles tress area,A t, in. 2
Number ofthreads per
inch, n
Tensiles tress area,A t, in. 2
0.06000.07300.08600.09900.11200.12500.13800.16400.19000.21600.35000.31250.37500.47350.50000.56250.62500.75000.87501.0001.1251.2501.3751.5001.7502.000
-64564840403232242420181614131211109877665
4 1/2
-0.002630.003700.004870.006040.007960.009090.01400.01750.02420.03180.05240.07750.10630.14190.1820.2260.3340.4620.6060.7630.9691.1551.4051.902.50
807264564844403632282824242020181816141212121212--
0.001800.002780.003940.005230.006610.008300.010150.014740.02000.02580.03640.05800.08780.11870.15990.2030.2560.3730.5090.6630.8561.0731.3151.581
--
Table 15.6 Dimensions and tensile stress areas for UN coarse and fine threads.
Text Reference: Table 15.6, page 687
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Coarse and Fine Thread Dimensions - Metric
Table 15.7 Dimensions and tensile stress areas for metric coarse and fine threads.
Text Reference: Table 15.7, page 69
Coarse Threads (MC) Fine Threads (MF)Crest
diameter,d c, mm
Pitch, p ,mm
Tensiles tress area,A t, mm2
Pitch, p ,mm
Tensiles tress area,A t, mm2
11.62
2.534568
101216202430364248
0.250.350.40.450.50.70.81
1.251.51.75
22.53
3.54
4.55
0.4601.272.073.395.038.7814.220.136.658.084.315724535356181711211473
-0.20.25.35.35.5.5.751
1.251.251.51.5223--
-1.572.453.705.619.7916.122
39.261.292.1167272384621865
--
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Ejercicio – Cilindro hidraúlico
Un cilindro hidráulico de do=150mm y e=2mm sometido a Pi= 250 Kg/cm2 se ha de diseñar con n=1(mínimo). Se embridan las piezas de acero, con una junta elástica. Determinar: tornillo a colocar, calidad, pretensado considerando un 5% de relajación y espesor de juntas. Atornillos=7% At,junta
Roscas finas MF
MétricaÁrea
esfuerzo, mm2
Material disponible:calidades
10 61.2 5.8,8.8, 9.8 y 10.9
12 92.1 L= 4 mm
16 167 0.5-1-2-3-4
20 272 Junta de Cobre
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Separation of Joint
Figure 15.15 Separation of joint.
Text Reference: Figure 15.15, page 690
Pretensado
Unión permanente: 0,9FpUnión desmontable: 0,75Fp
Fp, carga límite
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Cyclic Load
Figure 15.16 Forces versus deflection of bolt and joint as function of time.
Text Reference: Figure 15.16, page 691
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Cyclic Load
ma
y
e
u
iua
e
aumima
eaa
a
Snfluenciaa
SS
SS
S
SSSGoodmanSS
PSADS
n
/__1
)1(:
0// min,
Gráfica – Líneas/puntos
•L de carga: (si,0) (sm sa)•L de rendimiento: (Sy,0) (0, Sy)•L de Goodman: (Se,0) (0, Su)
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Factor Concentración Fatiga
SAE gradeMetricgrade
Rolledthreads
Cutthreads
Fillet
0-24-8
3.6-5.86.6-10.9
2.23.0
2.83.8
2.12.3
Factor de concentración de esfuerzos, incluye el factor acabado superficial
Text Reference: Table 15.8, page 692
Kb y Kc,axial=1
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Ejercicio Fatiga
Diseñar la junta atornillada que se situaría al extremo de un recipiente tal que su presión varia de 75 a 150 kg/cm2.
a) Pi y n, tal que a 160kg/cm2 actúe como válvula (suponiendo que no hay fatiga).
b) causa de rotura con el Pi y tornillo anterior.c) Diámetro de tornillo para evitar fatiga y n fatiga.
Datos: k1=0,153.Tornillo: Calidad 8.8 y 9.8. relajación 5%.,Nt(15:25)
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Failure Modes of Riveted Fasteners
Figure 15.18 Failure modes due to shear loading of riveted fasteners. (a) Bending of member; (b) shear of rivet; (c) tensile failure of member; (e) bearing of rivet on member or bearing of member on rivet.
Text Reference: Figure 15.18, page 695
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Text Reference: Figure 15.19, page 697
Group of riveted fasteners used in Example 15.9. (a) centroid of rivet group Assembly; (b) radii from centroid to center of rivets; (c) resulting triangles; (d) direct and torsional shear acting on each rivet; (e) security beding factor (side view of member). (All dimensions are in inches.)
Example 15.9
ØA=5/8 ØB=7/8
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Text Reference: Figure 15.19, page 697
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Text Reference: Figure 15.19, page 697
Cortante debido a la torsión
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03000225,075,00 BA PPM
DATOS Un paso para peatones se remacha a un puente de acero como se indica en la figura. La carga máxima sobre el paso es equivalente a una carga de 3 000 N, localizada a 2 m del costado del puente de acero por cada par de remaches. Se supone un factor de seguridad de 5.
HALLAR: El diámetro del remache que se necesita si los remaches estan hechos de acero AISI 1040.
Text Reference: Figure 15.20, page 699
25,075,0BA PP
Nota: las fuerzas de tensión que actúan sobre los dos remaches son proporcionales a la distancia desde el extremo inferior de la ménsula
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Cylinder End Cap Section
Figure 15.28 End cap of hydraulic cylinder for baler application.
Text Reference: Figure 15.28, page 717