Springs are used throughout mechanical engineering to store energy, apply forces or torques, absorb movement and shock, maintain contact between components, and return mechanisms to a required position.
Choosing a spring is not simply a matter of finding one that fits the available space. The engineer must consider the required force or torque, movement, spring rate, available envelope, operating life, material, temperature, fatigue, stability and, in rapidly operating machinery, dynamic behaviour.
This guide introduces the main spring types and the engineering decisions involved in selecting and designing them. Links throughout the page lead to the detailed RoyMech reference pages containing the equations and design data.
Before choosing a spring type, define what the spring must achieve in the mechanism.
Typical spring functions include:
A compression spring becomes shorter when loaded and produces a force opposing that compression.
The familiar cylindrical helical compression spring is one of the most widely used spring forms. It is suitable where an approximately axial force is required over a linear movement.
Typical applications include valves, machine mechanisms, vehicle components, tooling, switches and return mechanisms.
Consider a compression spring when: you need an axial force that increases as two components move towards one another.
Detailed calculations: Helical Springs
An extension or tension spring becomes longer when loaded. Hooks, loops or other end features transmit the tensile load into the spring body.
Unlike an ordinary compression spring, an extension spring may be manufactured with initial tension. This means that a finite force may be required before the coils begin to separate.
Consider an extension spring when: two components must be pulled towards one another or returned together after being separated.
Detailed calculations: Helical Springs
A helical torsion spring applies a torque when its legs are rotated relative to one another.
Although it has a helical appearance, the wire in a torsion spring is principally subjected to bending rather than the torsional loading that dominates an axial helical compression spring.
Typical applications include hinges, clips, catches, levers and return mechanisms.
Consider a torsion spring when: the required output is a torque or angular restoring action.
Detailed calculations: Torsion Springs
Disc springs are conical annular discs that flatten elastically under axial load. They are also commonly called Belleville springs.
A disc spring can produce a relatively large axial force within a small axial space. Individual discs can also be arranged in series, parallel or combined stacks to alter the required force and deflection characteristics.
Consider disc springs when: high axial force is required in a restricted space, or when the load and deflection characteristics can usefully be adjusted by stacking discs.
Detailed calculations: Disc Springs
A leaf spring stores energy by bending a strip or assembly of strips. Unlike a helical spring, the spring element itself can also form a structural member of the mechanism.
Leaf springs are strongly associated with vehicle suspension but the same bending-spring principle is used in many mechanisms, electrical contacts, clips and flexible components.
Consider a leaf spring when: a bending member suits the geometry of the mechanism or the spring must also provide structural guidance or support.
Detailed calculations: Leaf Springs
A spiral spring consists of a flat strip wound into a spiral. Rotation changes the curvature of the strip and stores elastic energy.
These springs are useful where energy must be stored or a restoring torque produced through angular movement.
Consider a spiral spring when: rotational movement and energy storage are required in a relatively flat package.
Detailed calculations: Spiral / Clock Springs
| Requirement | Spring Type to Consider | Detailed RoyMech Page |
|---|---|---|
| Axial force when compressed | Helical compression spring | Helical Springs |
| Pulling or return force in tension | Extension spring | Helical Springs |
| Torque through angular movement | Helical torsion spring | Torsion Springs |
| High axial load with small axial movement | Disc spring | Disc Springs |
| Spring action through bending | Leaf spring | Leaf Springs |
| Rotational energy storage | Spiral / clock spring | Spiral Springs |
One of the most important quantities in spring design is the spring rate, sometimes called spring stiffness.
For a linear spring:
where:
For example, a spring having a rate of 20 N/mm requires an additional 20 N of force for each additional millimetre of deflection, provided it is operating within its linear elastic range.
For a spring producing torque through angular movement, the equivalent relationship is:
where T is torque and θ is angular deflection in radians.
A useful way to think about any spring is through its load-deflection characteristic.
For an ideal linear spring:
The load-deflection graph is therefore a straight line. Real spring systems may instead have progressive, degressive or otherwise non-linear characteristics.
The area beneath the load-deflection curve represents the elastic energy stored by the spring.
For a linear spring loaded from zero force:
For more information see General Spring Notes.
A spring does not necessarily operate between zero load and its maximum load. Many springs are installed with an initial deflection so that they already exert a force before the mechanism begins its working movement. This is called preload.
Suppose a mechanism requires a spring force of 100 N at one position and 180 N after moving 20 mm. The required working spring rate is:
The spring therefore requires a rate of 4 N/mm, but it must already be deflected sufficiently at the first working position to produce the required 100 N preload.
Springs work by allowing controlled elastic deformation of their material. That deformation creates stress.
The important stress depends on the spring type:
This is why the stress equation from one type of spring must not simply be applied to another.
Spring materials must withstand significant elastic strain without permanent deformation and may also need to survive a very large number of load cycles.
Material selection can depend on:
Carbon and alloy spring steels are widely used, while stainless steels, copper alloys and other materials may be selected where environmental or special operating requirements justify them.
Detailed material information: Spring Materials
Many springs operate under repeated fluctuating loads. A spring may therefore fail by fatigue even though its maximum stress is below the stress that would cause immediate yielding.
Two quantities are particularly important when examining a fluctuating spring load:
Both affect fatigue performance.
Surface condition is particularly important because fatigue cracks commonly initiate at the surface. Manufacturing defects, corrosion, damage and rubbing against guides can therefore reduce spring life.
Processes such as shot peening may be used to improve fatigue performance in appropriate spring applications.
Detailed calculations and fatigue criteria: Fatigue in Springs
A long compression spring may become laterally unstable as it is compressed. Instead of simply becoming shorter, it begins to bow sideways. This is known as buckling.
Buckling becomes increasingly important as the free length becomes large relative to the spring diameter.
The spring end conditions also matter. A spring restrained between suitable parallel seats behaves differently from one having poorly restrained ends.
Where sufficient inherent stability cannot be achieved, the spring may require:
Guidance itself must be designed carefully because rubbing can introduce friction, wear and surface damage.
Detailed buckling calculations: Compression Spring Stability and Buckling
Static spring calculations are not always sufficient for rapidly operating mechanisms.
A spring has mass as well as stiffness and therefore possesses natural frequencies. Rapid cyclic loading can cause vibration waves to travel through a helical spring. Under suitable conditions these can form standing waves, a phenomenon known as spring surge.
If an excitation frequency is sufficiently close to a significant natural frequency, resonance can increase spring movement and dynamic stress.
Surge should be considered particularly in rapidly reciprocating mechanisms, high-speed machinery and other applications involving significant periodic excitation.
Detailed theory and equations: Spring Surge and Natural Frequency
Determine the available outside diameter, inside diameter and axial or radial space before completing the spring design. Remember that the spring geometry can change as it deflects.
Check the spring throughout its complete travel, not only at its normal operating position.
Real springs cannot be manufactured to exact theoretical dimensions or forces. The mechanism should accommodate the relevant spring and assembly tolerances.
Material properties change with temperature. Springs operating at unusually high or low temperatures require suitable material selection and design allowances.
Corrosion can reduce section size and create surface defects that are particularly damaging to fatigue performance. Material, coating and environmental protection should therefore be considered together.
The way load enters the spring matters. Compression-spring seats, extension spring hooks and torsion-spring legs can all influence stress, alignment and service life.
Check that the spring does not unintentionally contact shafts, bores, adjacent components or itself during its complete working movement.
Is the movement linear or angular? How far must the mechanism move?
Determine the required force or torque at the beginning and end of the working movement.
Use the change in force divided by the corresponding change in deflection, or the change in torque divided by angular movement.
Choose a compression, extension, torsion, disc, leaf or spiral spring based on the required motion, load and available geometry.
Determine the maximum and minimum permitted spring dimensions throughout the complete mechanism movement.
Choose a material and initial spring dimensions suitable for the required load, environment, temperature and manufacturing process.
Use the detailed equation appropriate to the selected spring type and check the most severe operating condition.
For cyclic applications, determine the mean and alternating stresses and apply an appropriate fatigue assessment.
For compression springs, check buckling where appropriate. For rapidly operated springs, consider natural frequency and surge.
Review clearances, guides, seats, hooks, tolerances, corrosion protection, temperature and interaction with surrounding components.
| Reference | Use It For |
|---|---|
| General Spring Notes | Spring rate, load-deflection behaviour, energy storage and general spring terminology. |
| Spring Materials | Spring material properties, strength and material selection. |
| Helical Springs | Compression and extension spring geometry, rate, stress and deflection. |
| Torsion Springs | Helical torsion spring torque, angular deflection and bending stress. |
| Disc Springs | Disc spring force, deflection, stress and series/parallel stacking. |
| Leaf Springs | Leaf-spring bending stress, deflection and spring-rate calculations. |
| Spiral / Clock Springs | Spiral spring torque, angular deflection, strip length and bending stress. |
| Fatigue in Springs | Mean and alternating stress, endurance, finite-life assessment and fatigue criteria. |
| Spring Stability and Buckling | Compression-spring slenderness, critical deflection, end conditions and buckling. |
| Spring Surge and Natural Frequency | Spring-mass natural frequency, spring surge, vibration modes and dynamic spring behaviour. |