Designing Group 3 Reduced-Thickness Disc Springs When the standard approximations stop working
In certain instances, the standard formulae use approximations that were once valid but no longer are. Be warned!
The Standard Disc Spring Calculations
The best-known paper on disc springs is unquestionably The Uniform-Section Disk Spring by Almen and László (1936), and its results are still the prescribed method in DIN EN 16984 and the SAE standards. Disc springs are used far more widely than was perhaps envisaged when those design calculations were first formulated:
- Compared with helical springs of the same dimensions, disc springs can support a larger load, and their characteristic can be designed to be linear, regressive or, with a suitable arrangement, progressive.
- Also compared with helical springs, a properly dimensioned disc spring can achieve a longer service life under dynamic loads.
Consequently, disc springs have a very wide range of applications. They have become larger and are used in stacks that easily weigh more than 200 kg. These larger disc springs need updated design calculations.
Consider this seemingly trivial error, based on an assumption that worked nicely for smaller sizes and was accepted in the calculation of the cone height, h0. The diagram shows how dated literature encourages an approximate calculation that is plain wrong: here h is taken as “equal” to (O.H. − t), the overall height minus the thickness.
In fact, h = (O.H. − Y), where Y = t · cos β and β is the cone (base) angle. For smaller thicknesses this is not significant, but for the larger disc springs being developed it becomes a major factor for accurate load and stress calculations, and for manufacturing!
Another problem is that the design calculations in the standards, as used by the large established commercial players, are insufficient for these larger disc springs, and these legacy issues have not been properly addressed.
Moreover, the contact flats that Group 3 disc springs need introduce two more errors. Firstly, machining the two contact flats is not accounted for in the calculation of the cone height, h0. Secondly, the required width of the contact flat (annulus) is very clearly not calculated properly. Fortunately, for those whose contact flats are not calculated properly, this also reduces the associated error in h0.
Contact Flats
We call the contact flat an annulus. DIN EN 16983 refers to it as a ground surface end, and the SAE HS-1582 Spring Design Manual as a contact bearing flat. Contact flats have a purpose:
- to improve the definition of the point where the load is applied;
- in stack configurations, to reduce the friction on the guide rod.
Using a contact flat shortens the moment arm. Think of a lever: as it gets shorter, more force is needed to move the same load. So, all else being equal, if you add contact flats, the disc spring needs a greater load for the same deflection. For very practical reasons of interchangeability, which means keeping the free height of the spring and matching the loads as closely as possible, the thickness of the disc spring must be reduced.
DIN EN 16984: a single disc spring with ground ends shall have the same design load F at s = 0.75 h0 as one without, where the principal dimensions are the same.
This is the rule that allows interchangeability.
Requirements for a Valid Group 3 Disc Spring
For a reduced-thickness disc spring to be valid, it is essential that:
- the free height of the single disc spring, l0, and the overall height of any stack using it, L0, remain unaltered;
- the inside and outside diameters, Di and De, remain unaltered;
- the spring load of the reduced-thickness spring is the same as that of the unreduced spring at s = 0.75 h0, where h0 is the cone height of the unreduced spring;
- the ratio of reduced thickness t′ to original thickness t meets the standard: about 0.94 for Series A and B, and about 0.96 for Series C.
The standard’s design formula introduces an additional factor, K4 (equal to 1 when there are no contact flats), to deal with contact flats. But no standard gives the width of the annulus, so it is still, mistakenly, estimated as 1/150 of the outside diameter of the disc spring. That estimate has its origin in an old version of the SAE standard from decades ago.
In fact, the width of the annulus follows from the requirement above, which is worth repeating: a single disc spring with ground ends shall have the same design load F at s = 0.75 h0 as one without, where the principal dimensions are the same.
What’s the Point?
There is an obvious contradiction in the way many manufacturers interpret the standard. You cannot deal with reduced-thickness disc springs with contact flats without taking into account the width of the contact flats, and with it the base angle. Getting these wrong produces disc springs that do not work as they should. The least of the problems is premature relaxation and setting.
The example below uses the popular 127 × 250 × 16 with t′ = 14.9 mm, and shows how significant these errors can be (and very often are!).
Traditionally, h′0 is calculated as 21.8 − 14.9 = 6.9 mm. Correcting the erroneous assumption that cos(base angle) is close enough to 1 because the angle is small, and accounting for the height removed by correctly sized contact flats, the actual cone height is 7.29 mm!
And what of the reduced thickness of 14.9 mm? It should be closer to 16 × 0.94 = 15.04 mm. Get the contact flats wrong and any installation using this disc spring will have unscheduled downtime!
Supporting Voices in the Wilderness
If your better judgement prompts scepticism (despite the calculations provided), read the following papers.
1. The Ferrari method
Start here: a new calculation method for disc springs with contact flats and reduced thickness, which articulates part of the problem nicely.
Download PDF →2. Trapezoidal cross-sections
More complete: disc spring calculations for trapezoidal cross-sections and rounded edges, which we endorse.
Download PDF →3. Almen & László
Let’s not forget the original paper on uniform-section disc springs that started it all.
Download PDF →Feel free to WhatsApp or, if it’s easier, send an email to our lead engineer if you want to work through any detail.
Be assured that every reduced-thickness disc spring with contact flats produced by Reliable Pressings is a valid disc spring, and that it will perform in its operating environment as required and expected, in line with the theoretical calculations. For serious applications, can you afford not to take Reliable seriously?
Designing a large Group 3 stack?
Send us your dimensions and loads. We’ll check the cone height, contact flats and stresses before anything is made.