# Designing Group 3 - Reduced Thickness Disc Springs

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 2092 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 h_{0}. 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.

The problem is that design calculations embedded in the standards and used by the larger commercial players are insufficient for these larger disc springs.

## Contact Flats

We call the contact flat, an *annulus*, the DIN 2092 refers to it as a *ground surface end*, and the SAE HS1582 Spring Design Manual as a *Contact Bearing Flat*.
These have a purpose

- to improve the definition of the point where the load is applied
- 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.

This is the reason we have the following DIN2092 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.

## Valid Disc Spring Requirements

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

- The disc spring height, l, and, the overall height of any stack using such a spring must remain unaltered.
- The inside and outside diameters, d and D, must remain unaltered.
- The spring load for a reduced height spring must be the same as for an unreduced spring if s = 0.75·h, where h is the free height of the unreduced spring.
- The width of the contact flats should be approximately 1/150 of the outside diameter.
- 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 DIN2092 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 completed absent from any standard, and it is merely estimated at /150 of the external diamter of the disc.

## So what?

There is an obvious contradiction embedded in 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 width of the contact flats and consequently the base angle. Failing to do so produces dangerously wrong results.

At the heart of the matter is the estimation used when calculating the new base angle that is required because of the reduced thickness. The assumption that cos(base angle) approximates to 1 because the base angle is small is incorrect since the base angle value is derived from the length of the contact flat. As disc springs get bigger the error only gets worse.

On investigation, one will discover that the vast majority of commercailly available type 3 disc springs do not meet the standard requirments of a disc spring, and mor importantly the theoretical calculations deviate dangerously from reality. For a mathematical analysis, The Ferrari Method. is essential reading.

So, if you look at the range from Mubea, Schnor et al, their larger disc springs with contact flats do not conform to the technical requirements of a disc spring. This becomes evident in more demanding heavier load environments, is compounded by dynamic loads and is an obvious issue for stacks.

This in our opinion is a serious issue, and where large disc springs are used in mission critical applications, such as Breaking Mechanisms on mining head gear, this is a critical consideration, as lives depend on it. This is why we provide a detailed design document to our customers, that requires sign-off, as well as independent 3rd party Load Characteristic Testing Certs for stack applications - nobody else provides this level of manufacture excellence.

## Illustrating the problem

To illustrate how serious a problem not using updated design methods are, we have provided three sets of results for a valid single disc (note the same commercially available disc spring from the major international producers is NOT valid!!) and in a stack configuration. The disc spring is a relatively common, 127 x 250 x 14.5, used in a stack configuration, made up of 8 packets, where each packet had a total of 4 springs, with 2 in parallel.

- What you would normally get: The std method alone
- What you should get if you use the standard method: The std method accounting for friction
- What you would get from us: The updated Ferrari method, accounting for friction

## Solving the Problem.

Firstly, Almen & Laszlo’s standard method must always include considerations for friction, and then either the reduced thickness must be changed or the width of the annulus changed. Changing the reduced thickness has obvious implications, but changing the width of the annulus needs us only to challenge the 1/150th of the spring OD rule. If the whole purpose of using an annulus/contact flat in the first place is to stabilise the working surface of the spring through which any load/force is applied, especially where spring stacks are concerned so as to reduce the friction on the guiding rod, as well as to improve the working life of the spring by removing fatigue inducing stress dynamics, then increasing the annulus is actually a good thing to do! All that’s needed is a grasp of the updated models.

So how do manufacturers get around this problem? Not at all as far as we are concerned, most just pretend or don’t even realise, (which is worse?? and does it really matter anyway??) that the problem exists. This is why we as a business only keep stock for disc springs 6mm and thinner, and anything thicker and requiring contact surfaces/annuli is:

- designed from first principles, using enhancements to the Almen & Laszlo method.
- in stack applications, our designs account for friction
- and we test our stacks against theory and provide these results to you

Every disc sping using contact flats, produced by Reliable pressings, is a valid disc spring and you can take some comfort that your disc spring will perform in its operational environment as expected with theoretical calculations. For serious applications this is extermely important.