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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.
Hamrock, Jacobson and Schmid©1998 McGraw-Hill
ANALISIS DE ELEMENTOS DE SUJECION.
Universidad de Talca.
Facultad de Ingeniería.• Ingeniería Mecánica/Mecátronica
Profesor : José Villalobos Rojas.-
Ingeniero Civil Mecánico.
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
Roscado
(a) Simple, (b) doble, y (c) triple.
Text Reference: Figure 15.2, page 667
AVANCEl = tipo roscado x p
Perfiles de rosca
M;
Roscas de paso
C-basto
F-Fino
Ej.MF8X2-G6` dc/roscas/pulg/ajuste
Text Reference: Figure 15.3, page 668
UN; 8 series de rosca de paso
constante
Roscas de paso
C-basto
F-Fino
EF-Extra Fino
UN -- MACME
Uso: potencia, máquina - herramienta
Ej.UNF1/2X16-1B
dc/roscas/pulg/ajuste
Perfil M y UN
Detalle dimensiones de perfiles M y UN.
ht= 0.5p / tan 30º
Text Reference: Figure 15.4, page 668
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)
Tornillos de potencia: Perfil ACME
Detalle del perfil - Dimensiones. (valores en pulgadas)
Text Reference: Figure 15.5, page 670
Buscamos: mayor ventaja mecánica - posicionamiento.
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
Tornillo de potencia con collarín
Text Reference: Figure 15.6, page 672
, Ángulo de avance=ArcTan [l/πdp]
Collarín de empuje
Tornillo de potencia con collarín y husillos de bolas
Text Reference: Figure 15.6, page 672
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
Par torsor el tornillo de potencia∑Fv=0∑Fh x r =0
DESCENSOASCENSO
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 auto bloqueante? ¿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.
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
Equivalencia de la conexión: Sistema de resortes
Bolt-and-nut assembly simulated as bolt-and-joint spring.
Text Reference: Figure 15.9, page 680
Force vs. Deflection of Bolt and Member
Force versus deflection of bolt and member. (s) Seperated bolt and joint; (b) assembled bolt and joint.
Text Reference: Figure 15.10, page 680
Fueza vs. Deflexión
Text Reference: Figure 15.11, page 681
0)( kbikji ekPekPP
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
Bolt and Nut Assembly
Figure 15.13 Bolt-and-nut assembly with conical fustrum stress representation of joint.
Text Reference: Figure 15.13, page 683
))(tan(
))(tan(ln2
tan
cicifi
cicifi
fciji
ddddL
ddddL
dEk
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
Constants for Joint Stiffness Formula
Poiss on’sModulus of
Elasticity, E, Numerical ConstantsMaterial ratio, GPa Ai B i
SteelAluminumCopperGray 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
Example 15.6
Figure 15.14 Hexagonal bolt-and-nut assembly used in Example 15.6. (a) Assembly and dimensions; (b) dimensions of frustum cone. (All dimensions are in millimeters.)
Text Reference: Figure 15.14, page 685
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
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.
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
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, mm2Pitch, 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
--
Ejercicio – Cilindro hidráulico
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
Métrica
Área esfuerzo,
mm2
Material disponible:calidades
10 61.2 5.8,8.8, 9.8 y 10.9
12 92.1 e juntas=0,25
mm
16 167 0.5-1-2-3-4
20 272 E2/E1=1400
Separación de juntas
Figure 15.15 Separación de juntas.
Text Reference: Figure 15.15, page 690
Ciclos de carga
Figure 15.16 Forces versus deflection of bolt and joint as function of time.
Text Reference: Figure 15.16, page 691
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,axial=1
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)
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
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.)
Ejemplo : 15.9
Text Reference: Figure 15.19, page 697
Text Reference: Figure 15.19, page 697
Cortante debido a la torsión
03000225,075,00 BA PPM
Ejemplo : 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 están 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
Filete de soldadura
Figure 15.21 Fillet welds. (a) Cross section of weld showing throat and legs; (b) shear planes.
Text Reference: Figure 15.21, page 701
Geometria y and Parámetros de Soldaduras
Text Reference: Table 15.9, page 703-704
Table 15.9 Geometry of welds and parameters used when considering various types of loading. [From Mott (1992)]
Geometria y Parámetros de Soldaduras (cont.)
Table 15.9 Geometry of welds and parameters used when considering various types of loading. [From Mott (1992)]
Text Reference: Table 15.9, page 703-704
Geometria y Parámetros de Soldadura (cont.)
Table 15.9 Geometry of welds and parameters used when considering various types of loading. [From Mott (1992)]
Text Reference: Table 15.9, page 703-704
Propiedades de los Electrodos.
Electrode Number Ultimate tensilestrength, Su, ksi
Yield strength, Sy,ksi
Elongation, ek,percent
E60XXE70XXE80XXE90XX
E100XXE120XX
62708090
100120
5057677787
107
17-252219
14-1713-16
14
Table 15.10 Resistencia minima de propiedades de tipos de electrodos .
Text Reference: Table 15.10, page 705
Ejemplo : 15.11
Figure 15.22 Welded bracket used in Example 15.11. (a) Dimensions, load and coordinates; (b) torsional shear stress components at points A and B. (All dimensions are in millimeters.)
Text Reference: Figure 15.22, page 706
Fatigue Strength Reduction Factors
Type of weldFatigue stress
concentration factor, Kf
Reinforced butt weldToe of transverse fillet weldEnd of parallel fillet weldT-butt joint with sharp corners
1.21.52.72.0
Table 15.11 Fatigue strength reduction factors for welds. [From Shigley and Mischke (1989)]
Text Reference: Table 15.11, page 709
Adhesive Bonded Joints
Figure 15.23 Four methods of applying adhesive bonding. (a) Lap; (b) butt; (c) scarf; (d) double lap.
Text Reference: Figure 15.23, page 710
Scarf Joint
Figure 15.24 Scarf joint. (a) Axial loading; (b) bending; (c) torsion.
Text Reference: Figure 15.24, page 711
Integrated (Snap) Fasteners
Figure 15.25 Common examples of integrated fasteners. (a) Module with four cantilever lugs; (b) cover with two cantilever and two rigif lugs; (c) seperable snap joints for chassis cover.
Text Reference: Figure 15.25, page 714
Cantilever Snap Joint
Figure 15.26 Cantilever snap joint.
Text Reference: Figure 15.26, page 714
Figure 15.27 Permissible deflection of different snap fastener cantilever shapes.
Text Reference: Figure 15.27, page 715
Snap Fastener Design
Friction Coefficients for PolymersCoefficient of f rictio n
MaterialOn steel On s elf -mated
po ly merPolytetrafluoroethylene PTFE (Teflon)Polyethylene (rigid)Polyethylene (flexible)PolypropylenePolymethylmethacrylate (PMMA)Acrylonitrile-butadiene-styrene (ABS)Polyvinylchloride (PVC)PolystyrenePolycarbonate
0.12-0.220.20-0.250.55-0.600.25-0.300.50-0.600.50-0.650.55-0.600.40-0.500.45-0.55
-0.40-0.500.66-0.720.38-0.450.60-0.720.60-0.780.55-0.600.48-0.600.54-0.66
Table 15.12 Coefficients of friction for common snap fastener polymers [From Bayer Corporation (1996)]
Text Reference: Table 15.12, page 716
Cylinder End Cap Section
Figure 15.28 End cap of hydraulic cylinder for baler application.
Text Reference: Figure 15.28, page 717