KEVOS® MAKEOS · Springs
Disc (Belleville) Spring Load and Stress
What force and stress does this disc spring, or stack, give at a deflection?
Load, flat load and top inner-edge stress of a disc (Belleville) spring by the Almen–László method, and the force and travel of series and parallel stacks.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Outside diameter | mm | Outside diameter from the catalogue. |
| Inside diameter | mm | Inside diameter from the catalogue. |
| Thickness | mm | Disc thickness. |
| Cone height h₀ (free height − thickness) | mm | Unloaded height l₀ minus thickness t, from the catalogue. |
| Elastic modulus | GPa | Elastic modulus of the spring steel. |
| Poisson’s ratio | Poisson’s ratio (about 0.3). | |
| Deflection of one disc | mm | Deflection of a single disc at the working position (no more than h₀). |
| Discs in series (alternating) | discs | Number of single discs (or parallel sets) stacked in alternating directions. |
| Discs in parallel (nested) | discs | Number of discs nested in the same direction in each set. |
Method and formulas
- δ = De ÷ Di; K₁ = (1/π)((δ − 1)/δ)² ÷ ((δ + 1)/(δ − 1) − 2/ln δ).
- F = 4E ÷ (1 − ν²) × t⁴ ÷ (K₁De²) × (s/t) × [(h₀/t − s/t)(h₀/t − s/2t) + 1].
- σI = −4E ÷ (1 − ν²) × t² ÷ (K₁De²) × (s/t) × [K₂(h₀/t − s/2t) + K₃], with K₂ = (6/π)((δ − 1)/ln δ − 1)/ln δ and K₃ = (3/π)(δ − 1)/ln δ.
- Stack force = F × parallel count (friction neglected); stack travel = s × series count.
- Example: the default disc gives 4,762.1 N at 1.05 mm deflection and 5,897.9 N at flat.
Limitations
- Discs without contact flats; friction in parallel stacks raises loading force and lowers unloading force.
- Fatigue needs the tensile stresses at the lower edges (σII, σIII) and the maker’s fatigue diagrams.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Size disc stacks for bolted joints, clutches and valves
- Check load at a set deflection
- Compare series and parallel stacking
Who it is for
- Design engineers
- Spring buyers
- Maintenance engineers
What you get
- Force of one disc and of the stack
- Force at flat
- Top inner-edge stress (σOM and σI)
- Stack travel
Interpreting the result
- Keep the working deflection at or below about 75% of h₀ for a predictable, near-linear characteristic.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 350–359. Topic reference; no source tables or recommended settings are reproduced.
- EN 16983:2016 Disc springs — Quality specifications — Dimensions; EN 16984:2016 Disc springs — Calculation
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