## Compression Spring Design – Part One – Basic Formula and Considerations

written by: johnsinit • edited by: Lamar Stonecypher • updated: 10/30/2009

Compression spring is one the most commonly used parts in machine mechanisms. A wide variety of coil compression springs are available as “on shelf" products – and sometimes a special coil spring is required. Understanding the basics of coil spring design is therefore very important. Read and learn

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### Introduction

Compression string is one of the most popular spring types, with a variety of uses in different industries. Statistically, over half of working mechanisms feature a spring – in most cases, as already said – a compression spring. Thus a mechanical engineer has to make himself familiar with the spring design process. In fact, even if you are not a mechanical designer – for instance, a system engineer or a project leader – it is probably a valuable piece of knowledge, that will help you to achieve better understanding of processes.

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### On –Shelf Products

While design of a compression string isnot very difficult (see below), the production of one is pretty complex. More precisely, it is simply a unique process, achieved with specially designated machining. Thus, in most cases, you will not be producing a compression spring, but rather ordering one from a specialized spring manufacturer. This makes the understanding of spring parameters even more important.

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### The Basic Spring Formula

The most important specification of a compression spring (true also for almost any other spring as well) is the spring constant, labeled k in engineering literature. This is the constant that bonds the force applied with deflection:

F = kΔH = k(Hfree-Hdef)

Where Hfree is uncompressed spring length and Hdef is spring length a a result of force applied.

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### The Compression Coil Spring Main Formula

The above formula is true for any compression spring. Being one of most basic spring, the coil compression spring has undergone various tests and studies, which allowed to come up with a formula (based on experiments only and can be viewed as a rule of thumb - but has been regarded as highly accurate) that connect the major coil spring parameters between themselves:

k = (Gd4) / 8D3Na

In this formula:

k- is the spring constant

G – is the Sheer Modulus of the spring material

d – is the wire diameter

D – is the spring mean diameter (the average between OD (outer diameter) and ID (inner diameter)

Na – is the number of active coils. This number will change based on type of coil spring, varying between Nc (total number of coils) and Nc-2.

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### The Next Step - The Design

Each one of the parameters presented above, should be given an attention while designing or choosing a compression coil spring. As you can easily see, the parameters are highly bonded one with another – so an optimal spring design can be achieved by finding an optimal combination of those parameter. Moreover, one needs to keep in mind the tolerance of each parameter, as it will have a considerable effect on the resulting spring constant. All those topics will be covered in the next article.