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What are the Physics of Springs?

The humble spring is a work horse, found in everything from children’s toys to the locking latches on the Mars Rover. Here at Arrow Manufacturing, we’ve been producing custom-manufactured springs for a wide range of industries since 1951. What every spring has in common, whether it’s a micro-torsion spring for a medical device or a stamped metal piece for a household electronic, is that the way it works is governed by the laws of physics.

Today, our engineers use 3-D modelling software to help our customers perfect their custom spring designs and make sure it fits their specifications. However, even though our engineers may not be scribbling equations on notepads like you did in high school physics, the same math is still going on behind the scenes. And this means that the same variables are still very important to consider when you’re working on the design for a custom manufactured spring.

Basic physics of compression and extension springs

When thinking about the way a spring works, there are a few different variables at play. The two basics are the force exerted on the spring (the stress, sometimes written as σ) and how much the spring is compressed or extended (the strain, sometimes written as ϵ, which is defined as the change in length (ΔL) divided by the original length (Lo). The amount a spring will compress or extend under a given stress is determined by a some of the choices made during the custom spring design – the strength and gauge of the material used, the diameter of the spring, and any treatments the spring may have undergone in manufacturing, such as shot peening.

Hooke’s law

In the 1600s, a physicist named Robert Hooke was studying springs, and noticed that there seemed to be a fairly consistent relationship between the force needed to pull a spring a certain distance. Basically, extension is proportional to force – your spring will require linear increases in the amount of force needed to extend or compress it by linear increases in length. This is written as the equation F=-kx, where F is the force, x is the length of the extension or compression, and k is the spring constant (expressed in Newtons/ meter).

In practical terms, if you want a spring that requires more force to compress it – like the compression springs in a car’s suspension system, for instance – you would want a spring with a high spring constant. That is, a spring that only stretches or compresses when under more force.

Young’s modulus

Another 17th century physicist named Thomas Young built on Hooke’s work to define how resistant a spring is to being compressed or extended. Young’s modulus (known as E) is defined as stress (force exerted, σ) over the strain (the length it is compressed or extended ϵ). If you know Young’s modulus for a spring, you can also work out it’s constant. k=E(A/L), where A is the area over which the force is being applied (the diameter of your spring) and L is its length at rest (also called nominal length).

Email our design team today

If your head is spinning with equations, don’t worry! Our design team will work with you to ask the right questions and define all the variables necessary to make sure your customised spring meets your specified requirements. Of course, what we described above is only the most basic of situations, and the direction a spring sits, the direction of the force, the way it is positioned relative to gravity, and the arrangement of multiple springs will all have different consequences!