Size a disc spring (Belleville washer) per DIN 2092 using the Almen-Laszlo formula. Calculates single-disc force, stack force (parallel nesting) and stack travel (series stacking), with the K1 geometry factor derived analytically from the diameter ratio. Formula: F = (4E/(1−ν²))·(t⁴/(K1·De²))·(s/t)·[(h0/t−s/t)(h0/t−s/2t)+1].
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The 1936 Almen-Laszlo equation codified in DIN 2092 gives axial force vs deflection for a single conical disc.
K1 = (1/π)·((δ−1)/δ)²/[((δ+1)/(δ−1))−2/lnδ], derived analytically from δ = De/Di — no chart lookup.
The cone-to-thickness ratio h0/t decides whether the disc stiffens (<0.4), is near-linear (~0.4), or snaps through (>1.4).
Parallel nesting (>>>) multiplies force; series stacking (><><) multiplies travel — trade force for stroke without changing the disc.
Deflection capped at 0.75·h0 per DIN 2093 to avoid overstressing at flat position.
E ≈ 206000 MPa, ν ≈ 0.3 for 51CrV4 spring steel; adjustable for other alloys.
Input outer De, inner Di, thickness t and free height l0.
Enter Young's modulus E (steel 206000 MPa) and Poisson's ratio ν (0.3).
Specify deflection s and parallel/series counts np, ns.
Read single-disc force, stack force, stack travel and pass/fail.
Enter disc dimensions and material to get single-disc force, stack force and travel.
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