Selecting a Compression Spring for Smooth and Precise Control

Wave springs can be designed for flexibility across a wide range of applications

Imagine you have been tasked to design a spring system for a pressure relief valve.  One of the requirements is that it has to maintain linear behavior through 80% of its compression range to allow smooth and precise control of both flow and pressure.

There are many spring types that could factor into your mechanical design.  They all share a common principle of storing and releasing energy by resisting or promoting movement between mechanical components.


Selecting a compression spring for a pressure relief valve
As you consider the spring rate and deflection that your pressure relief valve requires, you find numerous types that could fit.  You might even find a table(1) like the one below that lists spring types and their associated actions. 


Type of spring

Compressive Helical compression springs
Belleville springs
Wave Springs
Flat springs; e.g. cantilever or leaf springs
Tensile Helical extension springs
Flat springs; e.g. cantilever or leaf springs
Drawbar springs
Constant force springs
Radial Garter springs
Elastomeric bands
Spring clamps
Torque Torsion springs
Power springs

Table I

You could choose helical round wire (Figure 1) for your pressure relief valve.  It’s a common choice for compression applications in a wide range of equipment and products.

Figure 1

Or you could use another type of compression spring, a wave spring. The profile of this type of spring shown in Figure 2.

Figure 2

This is a Smalley Crest-to-Crest wave spring created using several layers, or turns, of wave material (Figure 3). Each turn reduces the spring rate allowing more movement between the 2 contacting surfaces.  A combination of increasing number of turns and increasing material thickness allow for great flexibility in the spring rate characteristics while still meeting space requirements.

Figure 3

The wave spring uses a nearly rectangular cross section that can help you achieve the needed spring rates in a more compact installation. Under load, the rectangular cross section flexes similar to a beam in bending.  Forces are generated from bending instead of torsion.

Figure 4-Shear Stress Plot

Figure 5

When higher spring rates are required for larger loads, the wave spring can be “nested” as shown in Figure 5. A higher spring rate and load capacity can be achieved within the same axial height.  Smalley Steel Ring Company manufactures this configuration in a wide range of diameters and heights. These nested springs give a spring rate proportional to the number of turns of the waves. This allows for customization for a near unlimited range of forces and deflections.

If you were to choose a wave spring for your pressure relief valve, as shown on Figure 6, a pressure applied to the plate surface will compress the wave spring and open the sealing surface.  The amount of pressure required to break the seal can be controlled by customizing the counteracting force on the plate. This can be achieved by stacking the springs and/or modifying the thickness of the material cross section.

Figure 6 – Pressure Relief Valve

The impact of varying the number of turns, increasing material thickness, and other customizable options can be determined from the following formula

b = Radial Wall, in. [(O.D. – I.D.) ÷ 2]
Dm = Mean Diameter, in. [(O.D. + I.D.) ÷ 2]
E = Modulus of Elasticity (psi)
f = Deflection (in.)
H = Free height (in.)
I.D. = Inside Diameter (in.)
K = Multiple Wave Factor
L = Length, overall Linear (in.)
N = Number of Waves (per turn)
O.D. = Outside Diameter (in.)
P = Load (lb.)
S = Operating Stress (psi)
t = Thickness of Material (in.)
W.H. = Work Height (in.) [H-f]
Z = Number of Turns

For example, increasing the number of turns, as reflected in the parameter Z, allows more deflection for a given amount of force or pressure (i.e. lower spring rate). Also, for a given space that the spring occupies, the material thickness can be varied to greatly affect the spring rate.  For example a 50% adjustment in thickness can vary the spring rate by nearly a factor of 3.

In addition to spring rate requirements, many applications require uniform loading at the spring interface surfaces. For these cases, the Smalley Crest-to-Crest® Wave Springs with Shim Ends (Figure 7) are a good fit. They incorporate a bearing surface at each end of the wave spring stack.  This allows for a more even distribution of forces at the bearing surfaces of the mated parts.  Point contact is eliminated, which can be helpful for soft materials that may experience local depressions in the material by the point contact with the wave spring crest.

Figure 7

Another example: Flow valves
If instead you were tasked to select a compression spring for a flow valve, you might go through a similar design process. 

As fluid pressure increases, the Wave Spring precisely controls the linear displacement of the piston, which positions the orifice for proper fluid flow.  Here also the application makes use of the mostly linear behavior of the wave spring which allows more precise and repeatable control.


Wave Springs for Heavier Loading
There are times when precision control is not as high a priority as higher load capacity. You might consider a Belleville washer (Figure 8) for these cases.  These types of springs have strong applications in higher load bearing service.

Figure 8

However, a variation of the wave spring, produced from round wire, can accommodate higher loads.  The Smalley Wavo® spring, shown in Figure 9, can be an alternative to the Belleville while still maintaining an accurate spring rate.

Figure 9

1 Childs, Peter R.N. (2014). Mechanical Design Engineering Handbook. Elsevier.

Note: Smalley Steel Ring has paid a fee for promotion of their wave springs to  They have had no editorial input to this post.  All opinions are mine. – Attilio Colangelo