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Hamrock, Jacobson and Schmid 1998 McGraw-Hill
RESORTES
Entia non multiplicantor sunt prater
necessitatum.
(No complicar el asumto ms de lo
necesario.)
Galileo Galilee
Imagen: Coleccin de resortes de
compresin helicoidales
Hamrock, Jacobson and Schmid 1998 McGraw-Hill
Un ciclo Esfuerzo-Deformacin
Curva Esfuerzo Deformacin para
un ciclo completo
Text Reference: Figure 16.1, page 737
Hamrock, Jacobson and Schmid 1998 McGraw-Hill
Materiales de resortes
Common name Specification Modulusof
Elasticity,E, psi
Shearmodulus ofelasticity,
G, psi
Density,, lbf/in.3
M aximumservice
temper atureF
Principal char acteristics
High car bon steelsMusic wire ASTM A228 30 x 10
611.5 x 10
60.283 250 High strength; excellent
fatigue lifeHard drawn ASTM A227
30 x 106 11.5 x 106 0.283 250General purpose use; poor
fatigue lifeStainless steelsMartensitic AISI 410, 420 29 x 106 11 x 106 0.280 500 Unsatisfactory for subzero
applicationsAustenitic AIAI 301, 302 28 x 106 10 x 106 0.282 600 Good strength at moderate
temperatures; low stressrelaxation
Copper-based alloysSpring brass ASTM B134 16 x 10
66 x 10
60.308 200 Low cost; high conductivity;
poor mechanical propertiesPhosphor bronze ASTM B159 15 x 106 6.3 x 106 0.320 200 Ability to withstand repeated
flexures; popular alloyBeryllium copper ASTM B197 19 x 106 6.5 x 106 0.297 400 High elastic and fatigue
strength; hardenable.Nickel-based alloys
Inconel 600 - 31 x 106
11 x 106
0.307 600 Good strength; high cor rosionresistance
Inconel X-750 - 31 x 106
11 x 106
0.298 1100 Precipitation hardening; forhigh temperatures
Ni-Span C - 27 x 106 9.6 x 106 0.294 200 Constant modulus over a widetemperature range
Tabla 16.1 Propiedades tpicas de materiales comunes para resortes
Text Reference: Table 16.1, page 738
Hamrock, Jacobson and Schmid 1998 McGraw-Hill
Coeficientes de esfuerzos
Material Size range Constant, Apin. mm m ksi Mpa
Music wirea
Oil-tempered wireb
Hard-drawn wirec
Chromium vanadiumd
Chromium siliconee
0.004-0.250
0.020-0.500
0.028-0.500
0.032-0.437
0.063-0.375
0.10-6.5
0.50-12
0.70-12
0.80-12
1.6-10
0.146
0.186
0.192
0.167
0.112
196
149
136
169
202
2170
1880
1750
2000
2000aSurface is smooth and free from defects and has a bright, lustrous finish.
bSurface has a slight heat-treating scale that must be removed before plating.
cSurface is smooth and bright with no visible marks.
dAircraft-quality tempered wire; can also be obtained annealed.
eTempered to Rockwel C49 but may also be obtained untempered.
Tabla Coeficientes usados en Ec. (16.2) para cinco materiales de resortes [Desde
Design Handbook (1987)]
Text Reference: Table 16.2, page 739
Hamrock, Jacobson and Schmid 1998 McGraw-Hill
Resorte Helicoidal
Figure Bobina helicoidal (a)
Alambre recto antes de hacer la
espira; (b) Alambre embobinado
mostrando el corte transversal (o
corte directo); (c) Bobina de
alambre mostrando el corte
torsional.
Text Reference: Figure 16.2, page 741
Hamrock, Jacobson and Schmid 1998 McGraw-Hill
Esfuerzos cortante en alambre y bobina
Figura Esfuerzos cortantes actuando en el alambre y bobina. (a) Carga de torsin
pura; (b) Carga transversal; (c) Carga torsional y transversal sin efectos de la
curvatura; (d) t Carga torsional y transversal con los efectos de la curvatura.
Text Reference: Figure 16.3, page 743
Hamrock, Jacobson and Schmid 1998 McGraw-Hill
Ends Used in Compression Springs
Figura Cuatro tipos de extremos generalmente usados en resortes de
compresin. (a) Simples; (b) Simples rebajados; (c) Cerrados sir
rectificar; (d) Cerrados y rectificados.
Text Reference: Figure 16.4, page 746
Hamrock, Jacobson and Schmid 1998 McGraw-Hill
Compression Spring Formulas
Type of spring endTerm Plain Plain and
groundSquared or
closedSquared and
ground
Number of end coils, Ne 0 1 2 2T otal number of coils, Nt Na Na+1 Na+2 Na+2Free length, lf pNa+d p(Na+1) pNa+3d pNa+2dSolid length, ls d(Nt+1) dNt d(Nt+1) dNtpitch, p (lf-d)/Na lf/(Na+1) (lf-3d)/Na (lf-2d)/Na
Table 16.3 Useful formulas for compression springs with four end conditions.
Text Reference: Table 16.3, page 746
Hamrock, Jacobson and Schmid 1998 McGraw-Hill
Lengths and Forces for Compression Springs
Figure 16.5 Various lengths and forces applicable to helical compression springs. (a)
Unloaded; (b) under initial load; (c) under operating load; (d) under solid load.
Text Reference: Figure 16.5, page 747
Hamrock, Jacobson and Schmid 1998 McGraw-Hill
Force vs.
Deflection
Figure 16.6 Graphical
representation of
deflection, force and
length for four spring
positions.
Text Reference: Figure 16.6, page 747
Hamrock, Jacobson and Schmid 1998 McGraw-Hill
Buckling Conditions for Compression Springs
Figure 16.7 Critical buckling conditions for parallel and nonparallel ends of
compression springs. [From Design Handbook (1987).]
Text Reference: Figure 16.7, page 748
Hamrock, Jacobson and Schmid 1998 McGraw-Hill
Ends for Extension Springs
Figure 16.8 Ends for extension springs.
(a) Conventional design; (b) side view of
Fig. 16.8 (a); (c) improved design over
Fig 16.8 (a); (d) side view of Fig. 16.8
(c).
Text Reference: Figure 16.8, page 756
Hamrock, Jacobson and Schmid 1998 McGraw-Hill
Preferred Range of Initial Shear Stress
Figure 16.10 Preferred range of initial shear stress for various spring indexes [From
Almen and Laszlo (1936).]
Text Reference: Figure 16.10, page 757
Hamrock, Jacobson and Schmid 1998 McGraw-Hill
Torsion Spring
Figure 16.11 Helical torsion spring.
Text Reference: Figure 16.11, page 761
Hamrock, Jacobson and Schmid 1998 McGraw-Hill
Leaf Spring
Figure 16.12 Leaf spring. (a) Triangular-plate, cantilever spring; (b)
equivalent multiple-leaf spring.
Text Reference: Figure 16.12, page 765
Hamrock, Jacobson and Schmid 1998 McGraw-Hill
Belleville Spring
Figure 16.13 Typical Belleville spring.
Text Reference: Figure 16.13, page 768
Hamrock, Jacobson and Schmid 1998 McGraw-Hill
Belleville Spring Behavior
Figure 16.14 Force-deflection response of Belleville spring [From Norton
(1996)].
Text Reference: Figure 16.14, page 768
Hamrock, Jacobson and Schmid 1998 McGraw-Hill
Stacking of Belleville Springs
Figure 16.15 Stacking of Belleville spring. (a) In parallel; (b) in series.
Text Reference: Figure 16.17, page 769
Hamrock, Jacobson and Schmid 1998 McGraw-Hill
Dickerman Feed Unit
Figure 16.16 Dickerman feed unit. [From SME (1984).]
Text Reference: Figure 16.16, page 770
Hamrock, Jacobson and Schmid 1998 McGraw-Hill
Case Study - Dickerman Feed Unit Spring
Figure 16.17 Figure used in case study.
Text Reference: Figure 16.17, page 771