Engineering

Belleville Disc Spring Calculator

Estimate Belleville disc spring force at a selected deflection, including simple series and parallel stack effects for nested disc springs.

belleville-disc-spring-calculator
This is an engineering estimate for plain disc springs without contact flats. Fatigue, stress limits, friction, manufacturing tolerances, guide clearance, set, and DIN/EN compliance need manufacturer data.
Disc spring result
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Single disc force—
Stack travel—
Approx. spring rate—
Geometry warning—
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How Belleville disc spring stacking changes force and travel

Nested discs in parallel increase force because each disc deflects by the same amount and their loads add. Opposed sets in series increase travel because the total deflection is shared across the series sets. Manufacturers also note that friction and stack efficiency can change real stack force.

For practical design rules, review manufacturer guidance such as Schnorr’s Handbook for Disc Springs and verify final choices against actual catalog data.

Worked example

De = 50 mm, Di = 25 mm, t = 2 mm, h0 = 1.2 mm Total deflection = 0.6 mm 1 parallel × 1 series The calculator evaluates the nonlinear force at s = 0.6 mm and also estimates flat load at s = h0.

The force is nonlinear, so doubling deflection does not necessarily double force. Always check the intended working range rather than only the flat load.

Disc spring limitations

This calculator does not perform fatigue-life calculations, stress-point checks, contact-flat corrections, presetting, dynamic loading, temperature derating, corrosion checks, or tolerance stack-up. For critical bolted joints, valves, clutches, brakes, and safety assemblies, use certified manufacturer data.

Common questions

  • h0 is the free cone height available for deflection, often taken as the free overall height minus the material thickness for a plain disc. Some catalogues define dimensions differently, so match the calculator inputs to the manufacturer drawing.
  • Parallel, or nested, discs increase load at roughly the same deflection. Series, or opposed, arrangements increase deflection travel while the force is roughly that of one set, before friction and tolerances are considered.
  • Use it for preliminary checks only. DIN or EN disc springs should be selected from manufacturer tables because geometry, contact flats, tolerances, stress limits, and fatigue diagrams matter.
  • A plain disc spring should not be calculated beyond flat using this simple model. Over-flattening can permanently set or damage the spring and can create high stresses.
  • No. Friction can raise loading force and lower unloading force, especially in tall stacks. The final design should include manufacturer friction guidance and testing where preload is critical.