Compression springs are very common and used in many industries today to store (or release mechanical energy). A compression spring pushes back when an axial force is applied, allowing engineers to achieve energy conservation in many applications like vibration damping, door locks, and ballpoint pens.

Although compression springs appear to have a very simple function, there are multiple factors that engineers must consider when specifying these springs for a particular application. For example, engineers must know the ideal spring dimensions and engineering materials for that particular application.

This article covers some of the key design considerations for compression spring design. It will also get to the basics of compression springs and explain key terminologies that every designer must know.

## Hooke's Law

Consider Figure 1, where an axial load (P) is applied to a spring and causes it to compress.

Figure 1. Diagram of spring loads. Source: Yapparina/CC [1.0][SA]

Hooke’s law simply states that the force needed to compress (or extend) an elastic material (such as spring) by some distance is proportional to that distance. So, when a spring is compressed so that its length changes by an amount DL from its equilibrium position, the spring exerts a force (F) towards its equilibrium position. This force is mathematically expressed as:

where:

Lo = Uncompressed spring length

L = Spring length as a result of force applied

k = Spring stiffness (or spring constant)

The negative sign is customarily added to signify that the direction of restoring force (F) due to the spring is opposite to force (P), which caused the displacement.

Spring stiffness (or spring constant), k, is a measure of the resistance offered by the spring to deformation. It is mathematically expressed as:

Where:

G = Shear modulus of spring material

D = Mean diameter of the spring

d = Wire size

N = Number of active coils

Active coils are coils that do all the work and handle all of the stresses in the spring. Table 1 shows formulas for estimating the number of active coils for different types of spring ends.

Table 1. Different spring ends with their corresponding number of active coils.

Where Nt = Total coils

## Factors to consider when specifying springs

### No. 1: Free length and solid length

Free length is the length of a spring when no force is applied to it. In contrast, solid length (or slut height) is the axial length of the spring when fully loaded (or when all adjacent coils touch one another). Look at it this way; solid length is the shortest possible length for a compression spring without crushing it beyond recognition.

Figure 2. Solid length of a compression spring Source: Yapparina/CC [1.0][SA]

As a rule, engineers should specify a spring with a solid length that matches their application requirements. This can be done by comparing the application force requirements with force required to compress the spring to its solid length. If the spring compresses to its solid length before all the force is applied, then be sure that the product will not work as it is supposed to.

### No. 2: Pitch and spring index

To help better understand pitch and spring index, take a look at Figure 3 (a section view of a compression spring).

Section view of a compression spring Source: Yapparina/CC [1.0][SA]

Pitch (p) is the axial distance from the center of one coil to the center of the adjacent coil. In contrast, spring index (C) is the ratio of the mean diameter of the spring to the diameter of the wire from which the spring is constructed. Mathematically, this is expressed as:

Spring index is among the parameters that give engineers insights into the manufacturability and the cost of manufacturing their spring design. As a general rule, design compression springs to have a spring index within 5 and 12.

Compression spring designs with a spring index of less than 5 or greater than 12 are generally more challenging and expensive to manufacture. Springs with a low spring index will typically increase tooling wear and require additional processing to ensure adequate life. In contrast, springs with a high spring index require additional tolerance on length and diameter.

### No. 3: Material

With the broad range of engineering materials available today, it can be overwhelming to specify a material for compression springs.

There is no perfect spring material; the ideal choice will depend on your application requirements and budget.

Stainless steel is an ideal spring material for applications where high heat and corrosion resistance are a must. Nickel alloy springs offer high strength and durability, making them ideal in harsh and demanding applications. Hard-drawn carbon steels also offer high durability but are only ideal for low-stress applications.

## Conclusion

Compression springs offer several advantages as long as engineers correctly size and specify them to satisfy their application requirements. While this article provides engineers with helpful information about compression springs, there are still many factors to consider when specifying springs. For example, designers still have to deal with spring stresses, energy absorption, and loading factor, among others.

Engineers are advised to reach out to spring manufacturers to discuss their application requirements