KEVOS® MAKEOS · Springs
Disc Spring Stack Design
How many disc springs in series and in parallel give this force over this stroke?
Design of a disc (Belleville) spring stack from a single disc’s dimensions: the number of discs in series so that each deflects no more than a chosen share of its cone height over the stroke, the number in parallel to reach the force (Almen–László characteristic, as the disc spring tool), the stack force, free and solid heights, and the top inner-edge stress against an allowable.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Outside diameter | mm | Outside diameter of one disc. |
| Inside diameter | mm | Inside diameter. |
| Thickness | mm | Disc thickness. |
| Cone height h₀ (unloaded, inside) | mm | Unloaded cone height of one disc (overall height minus thickness). |
| Elastic modulus | GPa | Elastic modulus. |
| Poisson’s ratio | Poisson’s ratio. | |
| Force required at the working stroke | N | Force the stack must give at the working stroke. |
| Working stroke of the stack | mm | Total compression of the stack at the working point. |
| Largest deflection per disc (share of h₀) | % | Largest share of cone height each disc may deflect (75% keeps clear of flat). |
| Allowable stress at the top inner edge | MPa | Allowable static stress at the top inner edge (from the spring maker). |
Method and formulas
- Series count n_s = ⌈stroke ÷ (share × h₀)⌉; deflection per disc s = stroke ÷ n_s.
- Force per disc F(s) by Almen–László: F = 4E ÷ (1 − ν²) × t⁴ ÷ (K₁ D_e²) × (s ÷ t) [(h₀ ÷ t − s ÷ t)(h₀ ÷ t − s ÷ 2t) + 1].
- Parallel count n_p = ⌈F ÷ F(s)⌉; stack force = n_p F(s).
- Unloaded stack height = n_s (h₀ + n_p t); solid height = n_s n_p t.
- Example: 12000 N over 3 mm needs 3 groups in series of 3 discs in parallel.
Limitations
- Friction between nested discs raises force when compressing and lowers it when releasing (not included).
- Long series stacks need guiding to stay aligned.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Design a disc spring pack for a clamp, brake or bolted joint
- Find how many discs a stroke and force need
- Check stack height for the space available
Who it is for
- Design engineers
- Spring buyers
- Machine designers
What you get
- Discs in series and parallel
- Stack force and deflection per disc
- Unloaded height, solid height and stress
Interpreting the result
- Parallel discs multiply force; series discs multiply stroke.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 350–353. Topic reference; no source tables or recommended settings are reproduced.
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