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Belleville disc spring

Load and edge stress at the installed (preload) and working deflection of a single conical disc, by the Almen-László / DIN 2092 formulas, plus an indicative fatigue check between the two points. The cone-height-to-thickness ratio h₀/t tells you if it's a stiff linear spring, a constant-force element, or a bistable snap.

Conical disc — cross-section F = —

Outer dia D_e mm

Inner dia D_i mm

Thickness t mm

Cone height h₀ mm

Preload deflection s₁ mm

Working deflection s₂ mm

Material

Engineering notes

Two operating points (Almen-László / DIN 2092)

F = (4E/(1−ν²))·(t⁴/(K₁·D_e²))·(s/t)·[(h₀/t−s/t)(h₀/t−s/2t)+1] at preload (s₁) and working (s₂).
σ_OM = (4E/(1−ν²))·(t²/(K₁·D_e²))·(s/t)·[K₂(h₀/t−s/2t)+K₃] (upper inner edge, controls static).
K₁, K₂, K₃ are the standard geometry factors in δ = D_e/D_i.

Fatigue & stacking

Fatigue here is indicative: a Goodman estimate from the OM stress range. Real disc-spring life uses the DIN 2092 fatigue diagrams (lower-edge tensile stresses σ_II/σ_III, by group) — use them for anything safety-critical.
Behaviour by h₀/t: ≲0.4 near-linear, ≈1.4 constant-force near flat, >1.4 regressive / snap-through.
Stack in series to multiply deflection, in parallel to multiply load (parallel loses force to friction). Valid only up to flat (s = h₀).

Result

Live