basic mechanical ppt

Hamrock • Fundamentals of Machine Elements

Chapter 17: Springs

Entia non multiplicantor sunt prater necessitatum.

(Do not complicate matters more than necessary.)

Galileo Gallilei


Figure 17.1 Stress-strain curve for one loading cycle.

Stress Cycle


Spring Materials

Table 17.1 Typical properties of common spring materials.


Strength of Spring Materials

Table 17.2 Coefficients used in Equation (17.2) for five spring materials.


Helical Coil

Figure 17.2 Helical coil. (a) Straight wire before coiling; (b) coiled wire showing transverse (or direct) shear; (c) coiled wire showing torsional shear.


Figure 17.3 Shear stresses acting on wire and coil. (a) Pure torsional loading; (b) transverse loading; (c) torsional and transverse loading with no curvature effects; (d) torsional and transverse loading with curvature effects.

Shear Stresses on Wire and Coil


Figure 17.4 Four end types commonly used in compression springs. (a) Plain; (b) plain and ground; (c) squared; (d) squared and ground.

Compression Spring End Types


Table 17.3 Useful formulas for compression springs with four end conditions.

Compression Spring Formulas


Figure 17.5 Various lengths and forces applicable to helical compression springs. (a) Unloaded; (b) under initial load; (c) under solid load.

Lengths and Forces in Helical Springs


Figure 17.6 Graphical representation of deflection, force and length for four spring positions.

Force vs. Deflection


Figure 17.7 Critical buckling conditions for parallel and nonparallel ends of compression springs.

Buckling Conditions


Figure 17.8 Ends for extension springs. (a) Conventional design; (b) Side view of Fig. 17.8(a); (c) improved design; (d) side view of Fig. 17.8(c).

Extension Spring Ends


Helical Extension Springs

Figure 17.9 Dimensions of helical extension spring.

Figure 17.10 Preferred range of preload stress for various spring indexes.


Figure 17.11 Helical torsion spring.

Helical Torsion Spring


Figure 17.12 Leaf spring. (a) Triangular plate, cantilever spring; (b) equivalent multiple-leaf spring.

Leaf Spring


Figure 17.13 Typical Belleville Spring.

Figure 17.14 Force-deflection response of Belleville spring.

Belleville Springs


Stacking of Belleville Springs

Figure 17.15 Stacking of Belleville springs. (a) in parallel; (b) in series.


Dickerman Feed Case Study

Figure 17.16 Dickerman feed unit.

Figure 17.17 Performance of the spring in the case study.

basic mechanical ppt

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