Helical Springs

Topics: Elasticity, Coil spring, Force Pages: 6 (1189 words) Published: August 10, 2013
Machine Design II

Prof. K.Gopinath & Prof. M.M.Mayuram

Design of Helical Springs
The design of a new spring involves the following considerations: • Space into which the spring must fit and operate. • Values of working forces and deflections. • Accuracy and reliability needed. • Tolerances and permissible variations in specifications. • Environmental conditions such as temperature, presence of a corrosive atmosphere. • Cost and qualities needed. The designers use these factors to select a material and specify suitable values for the wire size, the number of turns, the coil diameter and the free length, type of ends and the spring rate needed to satisfy working force deflection requirements. The primary design constraints are that the wire size should be commercially available and that the stress at the solid length be no longer greater than the torsional yield strength. Further functioning of the spring should be stable.

Stability of the spring (Buckling)
Buckling of column is a familiar phenomenon. Buckling of column is a familiar phenomenon. We have noted earlier that a slender member or column subjected to compressive loading will buckle when the load exceeds a critical value. Similarly compression coil springs will buckle when the free length of the spring is larger and the end conditions are not proper to evenly distribute the load all along the circumference of the coil. The coil compression springs will have a tendency to buckle when the

deflection (for a given free length) becomes too large. Buckling can be prevented by limiting the deflection of the spring or the free length of the spring.

Indian Institute of Technology Madras

Machine Design II

Prof. K.Gopinath & Prof. M.M.Mayuram

The behavior can be characterized by using two dimensionless parameters, critical length and critical deflection. Critical deflection can be defined as the ratio of deflection (y) to the free length (Lf) of the spring . The critical length is the ratio of free length (Lf) to mean coil diameter (D)

free to tip

fixed end (a) Non parallel ends constrained parallel

The critical deflection is a function of critical length and has to be below a certain limit. As could be noticed from the figure absolute stability can be ensured if the critical length can be limited below a limit. fixed end (b) parallel ends

Figure 4.16

Indian Institute of Technology Madras

Machine Design II

Prof. K.Gopinath & Prof. M.M.Mayuram

0.70 0.60 0.50 0.40 0.30 0.20 nonparallel ends 0.10 2 3 4 5 6 7 8 9 (b) (a) 10 ratio of free length/mean diameter Lf/D Figure 4.17 Similarly compression coil springs will buckle when the deflection (for a given free length) becomes too large. The condition for absolute stability can be given as:

stable

unstable

stable

unstable parallel ends

1 πD ⎡ 2(E − G) ⎤ 2 Lo < α ⎢ 2G + E ⎥ ⎣ ⎦
For steels this can be simplified as:
D α

Lo < 2.63

Where α is a constant related to the nature of support of the ends simply referred as end constant

Indian Institute of Technology Madras

Machine Design II

Prof. K.Gopinath & Prof. M.M.Mayuram

Spring Surge and Critical Frequency
If one end of a compression spring is held against a flat surface and the other end is disturbed, a compression wave is created that travels back and forth from one end to the other exactly like the swimming pool wave. Under certain conditions, a resonance may occur resulting in a very violent motion, with the spring actually jumping out of contact with the end plates, often resulting in damaging stresses. This is quite true if the internal damping of the spring material is quite low. This phenomenon is called spring surge or merely surging. When helical springs are used in applications requiring a rapid reciprocating motion, the designer must be certain that the physical dimensions of the spring are not such as to create a natural vibratory frequency close to the frequency of the applied force. The...
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