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Disc spring calculation: force, stresses and stacks

Force and stresses of a disc spring at a given deflection, and characteristic of a stack with springs in parallel and in series.

Disc springsEN 16983DIN 2093Spring stacksBelleville
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CalculatorThe result updates as you type
Spring
mm
mm
mm
mm
Load and stack
mm
In service up to 0.75 · h0
MPa

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Indicative results, provided for preliminary estimation. They do not replace the design and verification of the real case by a qualified professional.

How to use it

Enter the dimensions of the spring and the deflection at which it works. You get the force, the stresses at the characteristic points of the cross-section and the force at the flat position. With springs in parallel (stacked the same way up) the force is multiplied; with groups in series (alternated) the deflection is multiplied.

Formulas used

Diameter ratio δ = De / Di cone height h0 = l0 − t K1 = (1/π) · [(δ−1)/δ]² / [(δ+1)/(δ−1) − 2/ln δ] Force F = 4E/(1−μ²) · t⁴/(K1·De²) · (s/t) · [(h0/t − s/t)(h0/t − s/2t) + 1] Stack F total = n · F s total = i · s L0 = i · [l0 + (n−1)·t]

The stresses σ I, σ II, σ III and σ OM are obtained with the coefficients K2 and K3 of the same standard. They apply to springs without contact flats, that is, groups 1 and 2.

What remains to be checked

The values are theoretical, without friction. For varying loads a fatigue check is needed on the tensile stresses σ II and σ III, with the minimum preload that prevents cracks at the inner edge. For stacks, guidance, clearance and maximum length matter. The dedicated service is disc spring calculation.

FAQ

What is the difference between springs in parallel and in series?

In parallel the springs are stacked the same way up: the force adds up and the deflection stays that of one spring. In series they alternate: the deflection adds up and the force stays that of one spring.

How far can the deflection go?

In service one stays within 75% of the cone height h0. Beyond that, the spring bears on its edges, the real characteristic stiffens and the formula no longer applies.

EN 16983 o DIN 2093?

EN 16983 and EN 16984 replaced DIN 2093 and DIN 2092. The dimensions of the series and the calculation formulas have remained the same.

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