Designing Group 3 - Reduced Thickness Disc Springs

The Standard Disc Spring Calulations

The best known paper on disc springs is unquestionably Elastic Coned Discs authored by Almen and László (1939) and its results are still used as the prescribed method in the DIN-EN 16983 and SAE standards. The application of disc springs is far greater than perhaps initially envisaged, when the inital design calculations were formualted..

• Compared with helical springs, using the same dimensions, disc springs can support a larger load and spring characteristics can be designed to be linear, regressive or, with a suitable arrangement, also progressive.
• Furthermore, in comparison with helical springs, if the spring is properly dimensioned, it is possible to obtain a higher service life under dynamic loads

Consequently disc springs have a very wide set of applications and have become larger and are used in stacks, often weighing easily more than 200kgs. These larger disc springs require an updated design calculations.

Consider this seemingly trivial error based on an assumption that did work nicely for smaller values and was accepted in the calculation of a disc spring cone height, referenced most commonly as h₀. The accompanying diagram, shows how dated literature encourages an approximate calculation that is plain wrong. Here the value h is "equal" to (O.H. - t).

In fact, h = (O.H - Y), where Y = Cos(Beta)*t. For smaller thicknesses, this is not significant but with the larger disc springs being developed this becomes a major factor for accurate load and stress calculations, and manufacturing!

Another problem is that design calculations embedded in the standards and used by the larger established commercial players are insufficient for these larger disc springs, and these legacy issues have not been sufficiently addressed and attended to.

Moreover, the applicatrion of Contact Flats, as Group 3 Disc Springs require, introduces two more errors. Firstly the machining of the two contact flats, is not accounted for in the calculation of the cone height - h₀, and secondly the actual required width of the contact flat/annulus is very clearly not properly calculated. Fortunately, for those whose contact flats are not properly calculated, this also reduces the assoicated error in calculating - h₀

Contact Flats

We call the contact flat, an annulus, the DIN-EN 16983 standard refers to it as a ground surface end, and the SAE HS1582 Spring Design Manual as a Contact Bearing Flat. These have a purpose

1. to improve the definition of the point where the load is applied
2. and in stack configurations, to reduce the friction on the guide rod.

Using a contact flat shortens the the moment arm, think of a lever as it gets shortened, more force is needed, to move an equivalent load. Thus all things being equal, if you introduce a contact flat, the disc spring requires a greater load for the same deflection. For very practical reasons of interchangeability, which means maintaining the free height of a spring, and matching loads as closely as possible, the thickness of the disc spring must be reduced.

The standard has the following DIN-EN 16984 design requirement, "Single Disc Springs with ground ends shall have the same design load F, (where S is equal to 0.75 h₀), as ones without, where the principal dimensions are the same." (ie those that allow for interchangeability.

Requirements for a Valid Group 3 Disc Spring

To meet the requirments of a valid disc spring, a reduced height disc spring it is essential that:

1. The individual disc spring height, l₀, and, the overall height of any stack,L₀ using such a spring must remain unaltered.
2. The inside and outside diameters, D_i and D_e, must remain unaltered.
3. The spring load for a reduced height spring must be the same as for an unreduced spring when s = 0.75·h, where h is the free height of the unreduced spring.
4. t (original thickness) : t'(reduced thickness) ratios must meet those defined in the standard. (Series A and B are 0.94, Series C is 0.96)

The standard's design formaula introduces an additional term K4 (set to unity where no contact flats are used, to help deal with contact flat calculations but the width of the annulus is absent from any standard, (so mistakenly, it is still estimated at 1/150 of the external diameter of the disc spring which has its original in an old version of the SAE standard from decades ago.

BUT in fact the width of the annulus is inferred in the requirement we introduced above, and which is worth repeating; "Single Disc Springs with ground ends shall have the same design load F, (where S is equal to 0.75 h₀), as ones without, where the principal dimensions are the same.".

What's the Point?

There is an obvious contradiction embedded in the way that many manufacturers interpret the standard. It is clear that it is not possible to deal with disc springs with contact flats and reduced thickness without taking into consideration the incorrect width of the contact flats and consequently the base angle. Failing to do so produces disc springs that do not operate as they should, the least of these issues is premature relaxation and setting.

The example below illustrates using the popular standard 127x250x16 with t'=14.9mm. How significant these errors can be (and are very often!!).

Traditionally, h'₀ is calculated as 21.8 - 14.9 = 6.9mm - accounting for the erroneous assumption that cos(base angle) approximates to 1 because the base angle is small, and accounting as well for the removal of height because of the correct contact flats, we can see that the actual cone ehight is 7.29mm!

And what of the reduced thickness of 14.9mm? More like 16 x 0.94 = 15.04mm. Not getting the contact flats correct and any implementation using this disc spring will have unscheduled down time.!

Supporting Voices in the Wilderness

So if your better judgement prompts sceptisism (despite the calculations provided), then read the following papers.

1. Start off with The Ferrari Method. which artculates part of the problem nicely.
2. More complete is this paper on Trapezoidal Cross Sections and Rounded Edges., which we endorse.
3. But let's not forget Almen & Laslo, whose paper on Uniform Sections started it all.

Feel free to whatsapp or if its easier send a mail to our lead engineer, if you want to work through any detail.

Be assured that every reduced thickness disc sping using contact flats, produced by Reliable pressings, is a valid disc spring and that you can take some comfort that your disc spring will perform in its operational environment as required and expected, in line with theoretical calculations. For serious applications can you afford to not take Reliable as seriously?