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