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