A disc spring is the highest force per millimetre of axial space you can buy. The catch is that a single disc gives you almost no travel - typically a fraction of a millimetre. Stacking is how you trade that surplus force for the travel you actually need, and the arithmetic is simple enough to do on the back of an envelope.
What One Disc Gives You
A single disc has two numbers that matter:
- F₁ - the force at your chosen working deflection.
- h₀ - the travel available before the disc goes flat, which is the free height minus the material thickness.
Take the 20 mm disc from our stocked range: outside diameter 40 mm, inside diameter 20.4 mm, thickness 2.25 mm, free height 3.15 mm. Travel to flat is 3.15 − 2.25 = 0.9 mm. That is all the movement one disc has, and you should not use all of it - working to about 75% of travel is normal practice, because a disc run repeatedly to flat has a short fatigue life.
Design to roughly 75% of travel, not 100%. The last quarter of a disc spring’s travel costs a great deal of fatigue life and buys very little extra force, because the force curve is flattening off by then.
The Two Rules
Everything follows from two arrangements:
- Series - discs alternate direction, <><>. Deflections add; force stays that of one disc. Two in series gives twice the travel at the same force.
- Parallel - discs nest the same way, >>>. Forces add; deflection stays that of one disc. Two in parallel gives twice the force over the same travel.
Combine them and you can hit almost any force-travel target: build a set of i discs nested in parallel, then stack n of those sets in series. The stack then gives i × F₁ of force over n × h₀ of travel, from n × i discs.
Stack Configurations
Worked for the 20 mm disc above, so the travel figures are real:
| Arrangement (series × parallel) | Discs | Force | Travel to flat | Free stack height | Friction allowance |
|---|---|---|---|---|---|
| 1 × 1 | 1 | 1 × F₁ | 0.90 mm | 3.15 mm | — |
| 1 × 2 | 2 | 2 × F₁ | 0.90 mm | 6.30 mm | +3% |
| 1 × 3 | 3 | 3 × F₁ | 0.90 mm | 9.45 mm | +6% |
| 2 × 1 | 2 | 1 × F₁ | 1.80 mm | 6.30 mm | — |
| 4 × 1 | 4 | 1 × F₁ | 3.60 mm | 12.60 mm | — |
| 2 × 2 | 4 | 2 × F₁ | 1.80 mm | 12.60 mm | +3% |
| 4 × 2 | 8 | 2 × F₁ | 3.60 mm | 25.20 mm | +3% |
| 4 × 3 | 12 | 3 × F₁ | 3.60 mm | 37.80 mm | +6% |
Worked for the 20 mm disc from our stocked DIN 2093 range (O/D 40 mm, I/D 20.4 mm, thickness 2.25 mm, free height 3.15 mm), giving 0.9 mm of travel per disc. F₁ is the force of a single disc at the deflection you design to. Friction allowance is roughly 3% per nested interface and increases the force needed to compress the stack.
Designing a Stack
Work backwards from the joint, not forwards from the catalogue:
- Write down what you need: the force F the joint must hold, the travel s it must accommodate, and the axial space and bolt/bore diameter you have to work in.
- Pick a disc whose bore suits the bolt and whose outside diameter fits the pocket.
- Find the parallel count: i = F ÷ F₁, rounded up. This sets the force.
- Find the series count: n = s ÷ (0.75 × h₀), rounded up - the 0.75 keeps you off the flat. This sets the travel.
- Check the length: free stack height is n × i × t (thickness) plus n × h₀ of cone height. Compare against your pocket.
- Add the friction allowance - about 3% per nested interface - to the force needed to compress a parallel set.
- Sanity-check the aspect ratio before committing (see below).
If the stack comes out too long, go to a larger disc with more force per unit and fewer discs. If it comes out too short and too stiff, go smaller and use more of them.
Friction and Hysteresis
The clean arithmetic above ignores friction, and parallel stacks have plenty of it. Nested discs rub against each other over their full contact area as they deflect, so:
- Loading force is higher than calculated - roughly 3% per interface. A four-disc parallel set has three interfaces and needs about 9% more force than 4 × F₁.
- Unloading force is lower by a similar margin. The gap between the loading and unloading curves is hysteresis, and it means a parallel stack does not return exactly the force it took.
- Series stacks barely suffer - discs touch only at their edges, so there is very little rubbing between them.
The practical consequence: if you need a predictable force, keep parallel sets small - two or three discs - and get the rest from series. If you need damping, a deep parallel stack provides it, and that is sometimes exactly why one is chosen.
Guidance and Stack Length
Every stack needs a guide. Disc springs are laterally unstable and a stack under load will buckle sideways without one. Guide either internally on a bolt or rod, or externally in a sleeve or bore - internal is usually preferred, as it is easier to make and easier to keep clean.
- Leave clearance. The discs must slide freely as they flatten, because their bore grows slightly under deflection. A guide that is too tight will jam the stack partway and destroy the force characteristic.
- Harden the guide. The disc bores bear and rub on it; a soft guide rod wears grooves and the stack starts to hang up. Guides for dynamic applications should be hardened.
- Watch the aspect ratio. As a rule of thumb, keep the free stack height under about three times the outside diameter. Beyond that, buckling and friction dominate and the stack behaves nothing like the calculation - split it into two shorter stacks with a guided spacer between them.
- Support the ends flat. The end discs need square, flat seats. A cocked seat loads one side of the stack and skews the whole characteristic.
Errors That Flatten a Stack
- Getting the orientation wrong. Assembling a stack you intended to be series as parallel gives a stack many times stiffer with a fraction of the travel. Count the discs and check the pattern before closing the joint.
- Running to flat. Fatigue life falls away sharply in the last part of the travel. Design to about 75%.
- No guide, or a sloppy one. An unguided stack buckles; an over-tight guide binds.
- Mixing disc sizes or series. Every disc in a stack must be identical. A single odd disc becomes the weak link and takes a disproportionate share of the deflection.
- Ignoring settling. New stacks lose a little preload on first compression. Where preload matters, cycle the stack a few times during assembly, then set the final load.
- Forgetting the coefficient of friction in the joint. A stack under a bolt head also has to overcome friction at the seat faces; this shows up as scatter in the achieved preload.
Tell us the force and travel you need and the space you have, and we will propose a stack from our stocked DIN 2093 range rather than leaving you to iterate the arithmetic.
Need Disc Springs for a Stack?
DIN 2093 disc springs for bolt sizes 4 to 55 mm, ex-stock Mumbai - tell us your force and travel and we will work the stack with you.
View Disc SpringsFrequently Asked Questions
What is the difference between series and parallel disc spring stacking?
In series the discs alternate direction and their deflections add while the force stays that of a single disc - so you get more travel. In parallel the discs nest the same way and their forces add while deflection stays that of a single disc - so you get more force. Combining the two, with parallel sets stacked in series, lets you hit almost any force-travel target.
How do I calculate the force of a disc spring stack?
Force is set only by the parallel count: a set of i discs nested together gives i × F₁, where F₁ is the force of one disc at your working deflection. Series stacking does not change the force. Add roughly 3% per nested interface for friction when calculating the force needed to compress a parallel set.
How much can a disc spring be compressed?
The geometric limit is the travel to flat, which is the free height minus the thickness. In practice design to about 75% of that. The last quarter of the travel costs a lot of fatigue life and adds little force, because the force curve is already flattening off.
Do disc spring stacks need a guide rod?
Yes. Disc springs are laterally unstable and a loaded stack will buckle sideways without guidance, either internally on a bolt or rod or externally in a sleeve. Leave clearance so the discs slide freely as their bores grow under deflection, and harden the guide for dynamic applications, since a soft rod wears grooves and the stack starts to hang up.
How long can a disc spring stack be?
As a working rule keep the free stack height under about three times the outside diameter. Beyond that, buckling and friction dominate and the stack no longer behaves like the calculation. If you need more travel than that allows, split it into two shorter stacks with a guided spacer between them.
Why does my parallel stack need more force than calculated?
Friction. Nested discs rub against each other over their full contact area as they deflect, adding roughly 3% to the loading force per interface - so a four-disc parallel set needs about 9% more than four times the single-disc force. The same friction reduces the force on unloading, which is the hysteresis you see between the two curves.