Single Turn Wave Springs

This page will introduce our Single Turn Wave Spring Products, with an emphasis more on the terms and nomenclature that are necessary to apply the design and engineering equations we will introduce and demonstrate through worked examples.

We will cover Multi Turn Wave Springs separately, because all of what we will cover here on the Single Turn Wave Springs is relevant to Multi Turn Wave Springs, with just some slight modifications to the calculations. So what is a "Turn"?

Single Turn vs. Multi Turn Wave Springs


Fig 1.0.a - A Multi Turn Wave Spring Stack. Fig 1.0.b - A Single Turn Wave Spring.

These two different wave springs above, illustrate what is meant by a "Turn". A Single Turn Wave Spring, is merely a single washer made from Spring Steel, with a whole number (3, 4, 5, etc) of waves formed in it. A multi-turn Wave Spring is equivalent to a stack of single turn springs and is formed from a single continuous ribbon of Spring Steel so that the Peak of the Wave in any turns aligns with the Trough of the wave in the next turn. The number of waves per turn need not be an integer in the case of a Multi Turn Wave Spring (N could be 4.5 for example). You'll notice as well that Single Turn is usually dropped completely, and reference is only really made to the Turns when they are Multiple.

General Application

Single Turn Wave Spring Washers, also referred to as Wave Springs, or Wavy Washer Springs are metal washers designed to provide a predictable compensating spring force and ability to absorb shock when under load, by virtue of formed symmetrical waves that have crests and troughs, each of which acts as a contact point between the wavy washer itself and the opposing surfaces. These flexible washers act like springs to compensate for tolerance variations and uneven surfaces. Thus they are most often used to dampen vibrations or deal with heat expansion differentials, especially with deep groove ball bearing assemblies. They prevent loosening of fasteners, they facilitate the dampening of vibrations, the elimination of play and provide a more uniform distribution of load.

When referring to Wave Spring Washers we use a term called Spring Rate, which is a measure of the capacity or range of the spring. It describes the relationship between applied load and the resulting elastic and resisting deflection/compression/travel of the base material. Spring rate is influenced by most of the dimensions, as one would expect, but disproportionately so by the number of waves present, in fact to the fourth power! It is an important dimension to get right, but it the one that provides the most confusion. Let's get this out of the way.

Who´s who in the Zoo?

Have a look at the wave spring washer below. This shows the same wave spring from the 4 points of the compass, or rotated by 90° degrees each time. So, how many waves does it have? Not so easy to tell necessarily, and one can understand how confusion might arise.

Fig 1.1 - A Wave Washer Spring - seen from each 90° degree delta as the viewer rotates about it.

In general we describe a wave by its height (amplitude), frequency and wavelength.

The fact of the matter is that the Single Turn Wave Spring Washer depicted above in Fig 1.1 is incorrectly referred to as a Single Wave Washer, apparently because of the single wave that is seen when viewed from the side profile (as in frame I and III). and because of the term "Single Turn", having the "Turn" dropped. To be clear and to avoid confusion, the correct name is a Single Turn - Triple Wave Spring Washer!! More casually it is called a Triple Wavy Washer Spring, with the Single Turn term being dropped. Regardless, if viewed from the top, it is clear that the washer is made up of 3 distinct waves. Moreover, the term N (the number of waves) in the Load, Stress and Deflection calculations, will only produce a correct answer if the definition we use is applied.

Upper and Lower Contact Points

In an effort to remove confusion, we distinguish between wave washers by the number of contact points the wave spring washer has between itself and both the upper and lower surfaces of the fastening or mating component. Thus, the wavy washer spring in Fig 1.1 , has 3 Upper Contact Points and 3 Lower Contact Points. Our shorthand for this is LCP/UCP 3/3 as you will see in the catalogue listings. Once we have this information we know it has 3 Waves.

Fig 1.2 - A Wavy Washer, with 3 Upper and Lower Contact Points.

In this instance one can much more easily count that there are 3 points of contact on the top and similarly three on the lower surface of the Wave Spring Washer.

Nomenclature

The following terms, and their symbolic representation are important to know and helpful when using the calculations provided.

Term Use Description Units
De dimension External Diameter in the free / unloaded position mm
D'e dimension External Diameter with Working Load, used to check clearances mm
t dimension Material Thickness mm
k The relationship between Load/Force applied and the resulting deflection/compression of the Spring N/mm
E - Young's Modulus of Elasticity is a Constant Value - a property A measure of the ability of a material to withstand changes in length when under tension or compression. For Spring Steel we use 207,000 MPa = = 30,000,000 psi MPa
σ Induced Stress is a Transient Property of Load Stress expresses the internal forces that neighbouring particles of a continuous material exert on each other, especially when a force is acting upon them MPa or N/mm2
L0 Free Height is a dimension The Overall Height of the Spring without a load mm
WH WH = L0 - t - s The Height of the Compressed Spring at which it reaches its intended Design / Working Load mm
D The Mean Diameter of the Washer section of the Spring mm
b Radial Wall Width of the Washer section of the Spring mm
N Attribute This is the number of waves in a single Turn (whole integer in single turn, and integer + 1/2 in multi-turn springs decimal
(k) Derived from Number of Waves per Turn Wave Factor is an empirically derived correction factor. 3.88 / 2.90 /2.30 / 2.13
WT L0 - WH - t Working travel (s is also used) or deflection - the difference between Free Height, Working Heights and material thickness mm
HL dimension Also called WH, The Nominal Height of the Wave Washer at Designed Working Load mm
Pobs and Pder Observed means empirically tested, Derived is according to theory We provide this data, because although our Wave Spring Washers are made with great care, and despite our confidence in our calculations, we do empirically test our products. There are instances where theory and reality do diverge by as much as 15%.

All these various dimensions and terms allow us to derive useful metrics, such as:

Adding Waves - So what?

The addition of waves to the profile of the washer spring, and hence the addition of more contact points between the washer spring and the relevant surfaces, has some interesting dynamics to it.

Fig 1.3 - Points of Stress on a Single Turn 3 Wave Spring Washer as it takes Load.

Fig 1.4 - Points of Stress on a Single Turn 4 Wave Spring Washer as it takes on Load.

Useful Equations

The equations used for the calculations of Load, Deflection and Stress are derived from those for a simple beam and have the application of some corrective factors based on empirical measurements and experience.
These equations for loads & stresses, are not precise solutions, but they do provide very useful engineering estimates. As a measure of usefulness, they are more accurate and useful than any of the forecasting models Economists use to explain Recessions, but not nearly as accurate as Cosmologists employ to calculate the Hubble Constant.
Some skepticism should be expected if Forces are provided in Newtons with decimal places.
We can now derive various useful metrics, such as:

  1. Required Material Thickness - t, to support a Load:


  2. Deflection - s, expected from a Load:


  3. Induced stress - σ, created by a Load:


  4. Deflection - s, expected at stress threshold:

Typically, the Load Characteristic Curve for a Wave Washer Spring is only linear between 20% and 60% of s/h0, after which the Load/Deflection relationship becomes digressive (i.e. The relationship between compression and load is no longer linear, in fact, the delta in Load/Force as the final 25% of the Free Travel is compressed yields none or very little delta in Load) - this can be very useful. The waves are formed during manufacture when the metal is in its annealed state in order to achieve the peaks and troughs that make the wave. As a good rule of thumb, the ratio of the Mean Diameter (D) to the Radial width of the spring (b) should be between 7 and 16. This dimensional relationship achieves a balance between load-carrying ability and flexibility.

What should you use and when?


Single Turn 3 and 4 Wave Spring Washers, are the most common of the Wave Springs and have the widest range of dimensions which match the Single Row Deep Groove Ball Bearings designations. The Single Turn 5, 6 and 7 Wave Springs with more contact points to distribute the load, provide a more balanced support than the lower wave washer springs and also can bear far higher loads, but are they always necessary?.

We will work through an example, and show how the calculation formulae we have provided are used,