Belleville Disc Spring Sizer v3.0

Units

Length / force display

Geometry

Outer diameter De disc OD Inner diameter Di disc ID Thickness t Free height lo disc free length

Stack configuration

Parallel n discs sharing load Series i discs stacked tip-to-tip

Material

Preset

E (MPa) nu sy (MPa) Fatigue derate

Operating point

Nominal preload s1 stack deflection at assembly

Force at preload

sigOM at preload

sigOM / sy

Force at yield

Force at flat

Defl. to flat

delta = - h0/t = - De/t = - k0 stack = -

Loading points

Label	Mode	Value	s_stack	L_inst	F	sigOM	sigII	k_tan	sigOM/sy	dF

Lookup table (single-disc deflection 10..100% of h0)

%h0	s_disc	s_stack	L_inst	F	sigOM	sigI	sigII	sigIII	k_tan	sigOM/sy

How to read this tool. Enter geometry on the left and a nominal preload (stack deflection at assembly) at the bottom of the input panel. Add loading points to the table below the chart - either as absolute stack deflections or as signed deltas from preload. The chart shows force-deflection (left), per-disc stresses with yield lines (middle), and the Schnorr / DIN 2093 fatigue diagram with the loading-point cycle envelope (right). The validity row above the chart confirms whether De/Di, h0/t, and De/t fall in the Schnorr / DIN 2093 recommended bands. Static yield reference is sigOM / sy: under 1.00 is conservative, 1.00-1.20 is allowed by Schnorr with mild setting, over 1.20 is not recommended. Save to file downloads a .json with all current settings (rename it to whatever you want); Load file opens it back. The tool also autosaves to your browser every change, so a refresh recovers the last state.

Theory and limitations

Force / stress equations follow the Almen-Laszlo formulation as published in the Schnorr Handbook for Disc Springs and DIN 2092 / 2093. Single-disc force F(s) = (4E/(1-nu^2)) * t^4/(K1*De^2) * (s/t) * [(h0/t - s/t)(h0/t - s/(2t)) + 1]. Stack force = n*F (parallel). Stack deflection = i*s (series); per-disc deflection = stack deflection / i. Stresses sigma_1...sigma_4 are evaluated at the four edges of the cross-section per Schnorr Section 3. K coefficients assume no contact flats (K4 = 1).

Static yield check follows Schnorr Section 2.1: reference stress is sigma_OM (membrane at OM) compared to material sigma_y. Catalog DIN 2093 springs can legitimately operate up to ~120% of sy with only slight setting in service. sigma_II and sigma_III are fatigue-driving tensile stresses, not static yield limits, and routinely exceed sy at high deflection without causing structural failure.

Fatigue diagram uses simplified Schnorr Group 1 lines (DIN 2093 thin discs) for 1e5, 5e5, and 1e7 cycles. Lines are derated by the material fatigue factor. The blue marker pair shows the loading-point envelope of sigma_II values across all loading points. Use only as a sizing aid - verify final design against catalog data and conduct fatigue analysis for cyclic applications.

Geometry validity bands (Schnorr / DIN 2093):

De/Di in 1.75 - 2.50 (delta sweet spot)
h0/t in 0.40 - 1.30 (avoids snap-through and excessive setting)
De/t in 16 - 40 (manufacturable range)