Disc Spring Calculator Force, stress, spring rate and stack length for conical disc springs
Enter your disc spring dimensions, material and deflection. The loads, stresses and stack lengths update as you type, using the Almen–László method of DIN EN 16984.
HOW TO READ THE RESULTS
- Deflection, compression and travel all mean the same thing.
- Lower case is for a single disc spring, upper case for the stack: s is the travel of one disc, S that of the stack; l0 is one disc’s free height, L0 the stack length.
- A prime (′) marks a value based on the reduced thickness t′ of a Group III spring, so h′0 = l0 − t′.
- Stresses follow DIN: compressive stresses are negative.
Disc Spring Force & Stress Calculator
This is a basic tool. Please verify critical designs from first principles, or send them to us to check.
At your deflection
| Single disc travel, s | – | mm |
|---|---|---|
| Stack travel, S | – | mm |
| Stack load, F (no friction) | – | N |
| F on loading (with friction) | – | N |
| F on unloading (with friction) | – | N |
| Spring rate, single disc, R | – | N/mm |
| Spring rate, stack, R · n / i | – | N/mm |
| Unloaded stack length, L0 | – | mm |
| Loaded stack length, Ls = L0 − S | – | mm |
Stresses at this deflection
| σOM – upper inside edge (theoretical) | – | MPa |
|---|---|---|
| σI – upper inside edge | – | MPa |
| σII – lower inside edge | – | MPa |
| σIII – lower outside edge | – | MPa |
| σIV – upper outside edge | – | MPa |
Stack load at quarter deflections
| s / h0 | S (mm) | F (N) | Loading (N) | Unloading (N) |
|---|---|---|---|---|
| 0.25 | – | – | – | – |
| 0.50 | – | – | – | – |
| 0.75 | – | – | – | – |
| 1.00 (flat) | – | – | – | – |
Flat load Fc (s = h0): – N
Data used and ratios
| Young’s modulus, E | – | MPa |
|---|---|---|
| Poisson’s ratio, μ | – | |
| Cone height, h0 = l0 − t | – | mm |
| δ = De / Di | – | |
| h0 / t | – | |
| De / t | – |
Load–deflection curve (stack, no friction)
Drawn with the same DIN EN 16984 equations as the tables above, from S = 0 to flat (S = i · h0; h0′ for Group III). Hover or tap the graph to read off S and F. Disc springs should normally work below 0.75 h0.
Induced stresses and fatigue life
Would you like to calculate the stresses induced in your stack between preload and final load, and estimate its fatigue life to DIN EN 16984? It uses the disc spring and stack entered above.
- E and μ are taken from the material and temperature above (spring steel: E = 206,000 MPa, μ = 0.3 at 20 °C).
- Fatigue limits are the DIN EN 16984 diagram lines for disc springs to DIN EN 16983, at room temperature, with a sinusoidal load between F1 and F2. Groups 1 and 2 (t ≤ 6 mm) are not shot-peened; Group 3 (t > 6 to 14 mm) is shot-peened, as in the standard.
- The governing position is the one of II (lower inside edge) or III (lower outside edge) with the larger stress range.
- Friction and stack length effects on the stress are ignored. This is an estimate only; send critical designs to us to check.
Working points
| Preload (1) | Final load (2) | |
|---|---|---|
| Stack travel S (mm) | – | – |
| Single disc travel s (mm) | – | – |
| s / h0 | – | – |
| Stack load F (N) | – | – |
Bold values were entered; grey italic values (calc.) were calculated from the load–deflection curve.
Stresses (MPa, compressive negative)
| Position | At preload | At final load | Range σh |
|---|---|---|---|
| σOM upper inside edge (theoretical) | – | – | – |
| σI upper inside edge | – | – | – |
| σII lower inside edge | – | – | – |
| σIII lower outside edge | – | – | – |
| σIV upper outside edge | – | – | – |
Static check: σOM with the spring pressed flat (s = h0) = – MPa.
Fatigue check (–)
| Governing position | – | |
|---|---|---|
| Lower stress, σu | – | MPa |
| Upper stress, σo | – | MPa |
| Stress range, σh = σo − σu | – | MPa |
| Allowable σh, N ≥ 2 × 106 | – | MPa |
| Allowable σh, N = 5 × 105 | – | MPa |
| Allowable σh, N = 105 | – | MPa |
Need a disc spring made to your design?
Send us your drawing (or even a sample), material and quantity, and we’ll come back with a price.