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Belleville disc springs are usually spec'd with a free height, loaded height, and loaded force. From this information you can calculate the average spring rate of a belleville spring. However, what I would like to know if if the force is actually linear (or nearly linear).

I assume it is not, but don't know what curve the force might follow. Is there an equation that can predict the force-curve (plot of force versus height) of a belleville spring given ID, OD, free height, and thickness?

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  • $\begingroup$ From anecdotal experience, the rate gradually rises as you compress it $\endgroup$
    – Jonathan R Swift
    Dec 4, 2019 at 15:46

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The curve is not linear.

$s = $ actual deflection (mm)
$h_o = $ total possible deflection (mm)
$F = $ actual load (N)
$F_c = $ designed limit load (N)

enter image description here
Here you can see the original archive with the ploted graph from one industry (I usualy use this material for reference about these type of spring).

I don't know the exact formula. But the reasoning should be (this is my guess):

  • From 0% Force to ~70% force should be affected mostly by the compression between the inner diameter and outer diameter.
  • From ~70% Force to 100% should be affected mostly by bending.
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