Transcript Chapter 15: Fasteners and Power Screws

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.
Perfile roscado
Parámetros empleados para definir un perfil roscado
Diámetro 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,
AVANCE
l = tipo roscado x p
Text Reference: Figure 15.2, page 667
y (c) triple.
Perfiles de rosca
ACME
UN -- M
Uso: potencia, máquina - herramienta
UN;
8 series de rosca de paso
constante
Roscas de paso
M;
Ej.UNF1/2X16-1B
dc/roscas/pulg/ajuste
Roscas de paso
C-basto
C-basto
F-Fino
F-Fino
Ej.MF8X2-G6
EF-Extra Fino
` dc/roscas/pulg/ajuste
Text Reference: Figure 15.3, page 668
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
Tornillo
Tuerca
1A
1B (suelto)
2A
2B (normal)
3A
3B (justo)
Serie métrica
Tornillo
Tuerca
8g
7H
6g
6H
8h
5H
Calidad 3(apretado)-9(Suelto)
Equivalencias entre roscas
Text Reference: Table 15.1, page 669
Tornillos de potencia: Perfil ACME
Detalle del perfil - Dimensiones. (valores en pulgadas)
Buscamos: mayor ventaja mecánica - posicionamiento.
Text Reference: Figure 15.5, page 670
Perfil ACME
diametro Cresta,
dc, in.
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
Numero rosca por
pulgada, n
16
14
12
12
10
8
6
6
5
5
5
4
4
4
4
3
3
3
2
2
2
2
2
Area a tensión, At,
in2
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
dp=dc-0.5p-0.01
Text Reference: Table 15.2, page 671
Shear stress area,
As, in2
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
Datos cortante para una
longitud de roscado de 1 pulg
Tornillo de potencia con collarín
, Ángulo de avance=ArcTan [l/πdp]
Collarín de empuje
Text Reference: Figure 15.6, page 672
Tornillo de potencia con collarín y husillos de bolas
Text Reference: Figure 15.6, page 672
Fuerzas sobre el tornillo de potencia
DC=OE
∑Fv=0
∑Fh x r =0
θn
Fuerzas actuando sobre. (a) paralelepípedo ; (b) sección axial; (c) plano tangencial.
Text Reference: Figure 15.7, page 673
Par torsor el tornillo de potencia
ASCENSO
DESCENSO
∑Fv=0
∑Fh x r =0
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.
Igual que el ejercicio dos, pero con roscado simple.
3.
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
P  Pi  k j ek  ( Pi  kbek )  0
Text Reference: Figure 15.11, page 681
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.
k ji 
Ei d c tan f
 ( Li tan f  d i  d c )(d i  d c ) 
2 ln 

 ( Li tan f  d i  d c )(d i  d c ) 
Text Reference: Figure 15.13, page 683
Gasketed Joint
Figure 15.17 Threaded fastener with unconfined
gasket and two other members.
3
3
Db
Nd
6
Text Reference: Figure 15.17, page 694
Db
Nd
6
Constants for Joint Stiffness Formula
Material
Steel
Aluminum
Copper
Gray cast iron
Poiss on’s
ratio, 
0. 291
0. 334
0. 326
0. 211
Modulus of
Elasticity, E,
GPa
206. 8
71.0
118. 6
100. 0
N umerical Constants
Ai
Bi
0. 78715
0.62873
0. 79670
0.63816
0. 79568
0.63553
0. 77871
0.61616
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
1
2
4
5
7
8
Range of
cres t
diameters,
in.
1/4 - 1 1/2
1/4 - 3/4
3/4-1 1/2
1/4 - 1 1/2
1/4 - 1
1 - 1 1/2
1/4 - 1 1/2
1/4 - 1 1/2
Ultimate
tensile
s trength, S ut,
ksi
60
74
60
115
120
105
133
150
Yield
strength, S y,
ksi
36
57
36
100
92
81
115
130
Proof
s trength, S p ,
ks i
33
55
33
65
85
74
105
120
Table 15.4
Strength of steel bolts for various sizes in inches.
Text Reference: Table 15.4, page 687
Strength of Bolts (Millimeters)
Ultimate
Crest
tensile
Yield
diameter, dc ,
strength, Sut,
strength, S y,
Metric grade
mm
MPa
MPa
4.6
M 5-M 36
400
240
4.8
M 1.6-M 16
420
340a
5.8
M 5-M 24
520
415a
8.8
M 17-M 36
830
660
9.8
M 1.6-M 16
900
720a
10.9
M 6-M 36
1040
940
12.9
M 1.6-M 36
1220
1100
aYield strength approximate and not included in standard.
Table 15.5
Strength of steel bolts for various sizes in millimeters.
Text Reference: Table 15.5, page 687
Proof
strength, Sp ,
MPa
225
310
380
600
650
830
970
Coarse and Fine Thread Dimensions
Cres t
diameter,
d c, in.
0.0600
0.0730
0.0860
0.0990
0.1120
0.1250
0.1380
0.1640
0.1900
0.2160
0.3500
0.3125
0.3750
0.4735
0.5000
0.5625
0.6250
0.7500
0.8750
1.000
1.125
1.250
1.375
1.500
1.750
2.000
Coars e Threads (U NC)
N umber of
Tens ile
threads per
s tres s area,
inch, n
A t, in. 2
64
0.00263
56
0.00370
48
0.00487
40
0.00604
40
0.00796
32
0.00909
32
0.0140
24
0.0175
24
0.0242
20
0.0318
18
0.0524
16
0.0775
14
0.1063
13
0.1419
12
0.182
11
0.226
10
0.334
9
0.462
8
0.606
7
0.763
7
0.969
6
1.155
6
1.405
5
1.90
4 1/2
2.50
Fine Threads (U N F)
N umber of
Tens ile
threads per
s tres s area,
inch, n
A t, in. 2
80
0.00180
72
0.00278
64
0.00394
56
0.00523
48
0.00661
44
0.00830
40
0.01015
36
0.01474
32
0.0200
28
0.0258
28
0.0364
24
0.0580
24
0.0878
20
0.1187
20
0.1599
18
0.203
18
0.256
16
0.373
14
0.509
12
0.663
12
0.856
12
1.073
12
1.315
12
1.581
-
Text Reference: Table 15.6, page 687
Table 15.6 Dimensions
and tensile stress areas for
UN coarse and fine
threads.
Coarse and Fine Thread Dimensions - Metric
Cres t
diameter,
d c, mm
1
1.6
2
2.5
3
4
5
6
8
10
12
16
20
24
30
36
42
48
Coars e Threads (MC)
Tens ile
Pitch, p,
s tres s area,
mm
A t, mm2
0.25
0.460
0.35
1.27
0.4
2.07
0.45
3.39
0.5
5.03
0.7
8.78
0.8
14.2
1
20.1
1.25
36.6
1.5
58.0
1.75
84.3
2
157
2.5
245
3
353
3.5
561
4
817
4.5
1121
5
1473
Fine Threads (MF)
Tens ile
Pitch, p,
s tres s area,
mm
A t, mm2
0.20
1.57
.25
2.45
.35
3.70
.35
5.61
.5
9.79
.5
16.1
.75
22
1
39.2
1.25
61.2
1.25
92.1
1.5
167
1.5
272
2
384
2
621
3
865
-
Text Reference: Table 15.7, page 69
Table 15.7 Dimensions
and tensile stress areas for
metric coarse and fine
threads.
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
Métric
a
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
Separation of Joint
Figure 15.15 Separation of joint.
Text Reference: Figure 15.15, page 690
Cyclic Load
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 grade
0-2
4-8
Metric
g rade
3.6-5.8
6.6-10.9
Ro lled
threads
2.2
3.0
Cut
threads
2.8
3.8
Fillet
2.1
2.3
Factor de concentración de esfuerzos, incluye el factor
acabado superficial
Kb,axial=1
Text Reference: Table 15.8, page 692
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
Example 15.9
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.)
Text Reference: Figure 15.19, page 697
Text Reference: Figure 15.19, page 697
Cortante debido a la torsión
Text Reference: Figure 15.19, page 697
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.
Nota: las fuerzas de tensión
que actúan sobre los dos
remaches son proporcionales a
la distancia desde el extremo
inferior de la ménsula
 M  0  0,75P
A
 0,25PB  2  3000 0
PA
P
 B
0,75 0,25
Text Reference: Figure 15.20, page 699
Fillet Welds
Figure 15.21 Fillet
welds. (a) Cross
section of weld
showing throat and
legs; (b) shear planes.
Text Reference: Figure 15.21, page 701
Geometry and Parameters of Welds
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
Geometry and Parameters of Welds (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
Geometry and Parameters of Welds (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
Electrode Properties
Electrode Number
E60XX
E70XX
E80XX
E90XX
E100XX
E120XX
Ultimate tensile
strength, S u, ksi
62
70
80
90
100
120
Yield strength, Sy,
ksi
50
57
67
77
87
107
Table 15.10 Minimum strength properties of electrode classes.
Text Reference: Table 15.10, page 705
Elongation, ek,
pe rcent
17-25
22
19
14-17
13-16
14
Example 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 weld
Reinforced butt weld
Toe of transverse fillet weld
End of parallel fillet weld
T-butt joint with sharp corners
Fatigue stress
concentration factor, Kf
1.2
1.5
2.7
2.0
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
Snap Fastener Design
Figure 15.27 Permissible deflection of different snap fastener cantilever shapes.
Text Reference: Figure 15.27, page 715
Friction Coefficients for Polymers
Material
Polytetrafluoroethylene PTFE (Teflon)
Polyethylene (rigid)
Polyethylene (flexible)
Polypropylene
Polymethylmethacrylate (PMMA)
Acrylonitrile-butadiene-styrene (ABS)
Polyvinylchloride (PVC)
Polystyrene
Polycarbonate
Coefficient of f rictio n
On steel
On s elf -mated
po ly mer
0. 12-0. 22
0. 20-0. 25
0. 40-0. 50
0. 55-0. 60
0. 66-0. 72
0. 25-0. 30
0. 38-0. 45
0. 50-0. 60
0. 60-0. 72
0. 50-0. 65
0. 60-0. 78
0. 55-0. 60
0. 55-0. 60
0. 40-0. 50
0. 48-0. 60
0. 45-0. 55
0. 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