Calculate the mean stress, stress amplitude and fatigue utilization of a Belleville spring at the five characteristic stress locations (OM, I, II, III, IV) between two deflections s1 and s2. The stresses come unchanged from the validated EN 16983/EN 16984 stress core; you supply the permissible stress amplitude.
This is a generic Goodman model, not an EN 16983 fatigue diagram: the standard's diagram data is proprietary and neither embedded here nor invented.
Set the inputs and calculate.
Calculate a Belleville spring's mean stress, stress amplitude and fatigue utilization at its five characteristic stress locations between two deflections, building on the validated EN 16983/EN 16984 stress core.
The same geometry data as the existing EN 16983 Belleville-spring calculator (outside/inside diameter, nominal thickness, free height, parallel discs, series packs), plus two deflections s1/s2 and a permissible stress amplitude from your own source.
Nominal stresses at locations OM, I, II, III, IV are taken unchanged from the existing EN 16983/EN 16984 stress core, once at s1 and once at s2. For each location, the mean stress, stress amplitude and fatigue utilization (amplitude/permissible amplitude) follow; the location with the largest utilization governs.
For the EN 16983 reference series A40 (De=40, Di=20.4, t=2.25, l0=3.15 mm), at s2=0.675 mm location II gives a nominal stress of about 1328 MPa, independently corroborated by the SPIROL DSC design guide.
Sources and limits: Classical Goodman/Haigh diagram principle of fatigue strength assessment; EN 16983's own fatigue diagram is proprietary and is not reproduced here -- the permissible stress amplitude must come from your own documented source.
Calculate a Belleville spring's mean stress, stress amplitude and fatigue utilization at its five characteristic stress locations between two deflections, building on the validated EN 16983/EN 16984 stress core.
Fatigue utilization under the Goodman principle compares the actual stress amplitude at each of the five characteristic locations against an amplitude permissible for the given mean stress. It is therefore a general, material-independent fatigue assessment method -- the specific permissible-amplitude numbers are usually supplied by a Goodman diagram such as the one in EN 16983.
Utilization_X = sigma_X,amplitude / sigma_perm, for X in {OM, I, II, III, IV}
sigma_X,mean = (sigma_X,2+sigma_X,1)/2sigma_X,amplitude = |sigma_X,2-sigma_X,1|/2| Symbol / input | Meaning |
|---|---|
| sigma_OM, sigma_I..IV | Nominal stresses at the five characteristic locations, taken unchanged from the EN 16983/EN 16984 stress core. |
| sigma_perm | Permissible stress amplitude, from your own source (e.g. the EN 16983 Goodman diagram or the FKM guideline). |
The same geometry data as the existing EN 16983 Belleville-spring calculator (outside/inside diameter, nominal thickness, free height, parallel discs, series packs), plus two deflections s1/s2 and a permissible stress amplitude from your own source.
Enter the same geometry data as the existing Belleville-spring calculator (outside diameter De, inside diameter Di, nominal thickness t, free height l0, parallel discs, series packs). Add the two deflections s1/s2 and the permissible stress amplitude from your own documented source.
For the EN 16983 reference series A40 (De=40, Di=20.4, t=2.25, l0=3.15 mm), at s2=0.675 mm location II gives a nominal stress of about 1328 MPa, independently corroborated by the SPIROL DSC design guide.
The location with the largest utilization governs the spring's fatigue strength. A utilization below 100% at all five locations means each working point sits below the (externally determined) Goodman limit line.
Lengths in mm, permissible stress amplitude in MPa; results in MPa and percent or dimensionless.
Estimating whether a Belleville spring or uniform stack already sized to EN 16983 stays within a known permissible stress amplitude at all five characteristic locations under dynamic loading between two deflections (s1, s2).
Classical Goodman/Haigh diagram principle of fatigue strength assessment; EN 16983's own fatigue diagram is proprietary and is not reproduced here -- the permissible stress amplitude must come from your own documented source.
Common mistake: Don't confuse the five stress locations OM, I, II, III, IV -- they sit at different points of the disc (top/bottom surface, inner/outer edge) and can carry different utilizations depending on geometry and working point. The governing location can shift for a different geometry or different deflections.
Because the Goodman diagrams needed for that in EN 16983 are geometry- and material-dependent, copyrighted table data not available in this project without a verified source. Instead, the calculator evaluates the general Goodman relationship using a permissible stress amplitude you supply yourself.
EN 16983/EN 16984 distinguish five characteristic points (OM at the middle of the top surface, I through IV at the inner and outer edges of top and bottom), since bending stress is not distributed uniformly across the disc cross-section.
The existing calculator reports the five nominal stresses at a single deflection, but does not assess them against a permissible amplitude under cyclic loading. This calculator adds exactly that missing assessment at two working points.
The stress amplitude at the governing location exceeds the entered permissible stress amplitude -- a calculated fatigue risk suggesting either a spring redesign or a re-check of the permissible stress value.
Strictly speaking, no: a Goodman permissible amplitude always belongs to a particular mean stress, and the five locations have very different mean stresses -- in the reference case they span roughly -1,535 MPa (compression) to +931 MPa (tension). The calculator applies your entered value at every location and explicitly reports the mean stress at the governing one. Enter the value belonging to that mean stress, or evaluate the locations separately.