Design of Mechanical Springs

Concept

Mechanical springs are elastic machine components used to exert force, store energy, or absorb shock. The most common type is the helical compression spring, made of wire coiled into a cylindrical shape. The fundamental characteristic of a spring is its stiffness (or spring rate), which defines the linear relationship between the applied load and the resulting deflection in the elastic range. Designing a spring involves selecting the wire diameter, coil diameter, and number of coils to achieve the desired stiffness while ensuring the internal shear stress does not exceed the material's yield strength under the maximum static load.

Formula & Method

For a helical spring, the stiffness ($k$) and the maximum shear stress ($\tau$) under an axial load ($F$) are given by:

Where $K_s$ is the shear stress correction factor (to account for the direct shear stress added to the torsional shear stress):

Worked Example

A detailed worked example for designing a mechanical spring with an interactive system is available at Calculation Example: Mechanical Spring Design.

Engineering Meaning

The spring index $C$ is a critical design parameter. If $C$ is too small (e.g., less than 4), the spring is difficult to manufacture due to severe bending of the wire. If $C$ is too large (e.g., greater than 12), the spring tends to buckle and tangle. Ensuring that the maximum shear stress $\tau$ is safely below the torsional yield strength of the material guarantees that the spring can return to its original free length without permanent deformation.

Engineering Check

Always check that the calculated number of active coils will result in a practical solid length (length when fully compressed). A spring should be designed so that its maximum working deflection does not cause the coils to clash, which would result in the stiffness increasing to infinity and could cause structural damage.

Explicit Exclusions

This fundamental article does not cover fatigue life calculations for springs under dynamic cyclic loading. It also excludes the analysis of wave springs, Belleville washers, and stresses at extension spring hooks.