Disc Springs

§1What a disc spring is

A washer pressed into a shallow cone: outside diameter D_e, bore d, material thickness t, and free cone height h. Load it axially and the cone flattens, the material working mostly in bending around its own ring.

The single most important number is the ratio h/t — cone height to thickness. It sets not the size of the spring’s force but the shape of its force–deflection curve, which is what §2 computes. Everything about a disc spring is compact: travel is a fraction of a millimetre to a few millimetres per disc, force runs from hundreds of newtons to hundreds of kilonewtons, and the package is a washer.

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§2The force–deflection character

Flattening a cone is not like stretching a coil. The classical (Almen–Laszlo) analysis gives a cubic-flavoured law — normalised below so the geometry’s effect stands alone.

Shape of the law (s = deflection, x = s/t, H = h/t) F ∝ x [ (H − x)(H − x/2) + 1 ] — plotted to the flat position s = h

Fig. 1. Computed force–deflection curves for three h/t ratios, each normalised to its flattening load. Low cones are almost linear; near h/t ≈ 1.4 the curve develops a working plateau — nearly constant force over real travel; higher still, force falls past the hump and the disc will snap through.

The plateau regime is the celebrated one: a stack held at mid-deflection delivers almost constant clamping force while the joint underneath it creeps, settles or wears — the live-load washer behaviour that keeps bolted joints and tool clamps tight. The snap-through regime, deliberately used, makes bistable elements and tactile switches; accidentally reached, it makes a preload vanish.

Real dimensions come from the catalogue

Standardised disc-spring series publish D_e, d, t, h and load tables; this page deliberately carries the mechanics, not those proprietary tables. Design against the manufacturer’s data for the series in hand — the character curves above tell you which corner of the catalogue to open.

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§3Stacking — series and parallel

One disc rarely suffices, and stacking arithmetic is mercifully simple: nested discs add force, opposed discs add travel.

m in parallel (nested): F × m, δ unchanged n in series (opposed): δ × n, F unchanged rate scales m/n

Example 1 — a series–parallel stack

A single disc gives 1200 N at 1.0 mm deflection. Three series groups, each of two discs in parallel: force 2 × 1200 = 2400 N, travel 3 × 1.0 = 3.0 mm, and the stack’s rate is 2/3 of the single disc’s. Same four washers nested the other way (six in parallel): 7200 N at 1.0 mm — the same steel rearranged into a completely different spring.

Parallel nesting adds inter-disc friction (see §4), which fattens the load–unload loop — sometimes a feature (damping), sometimes a tolerance problem. Keep parallel counts modest (2 – 3 is typical practice) and buy travel with series groups.

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§4Friction and guidance

A stack is a column of loose cones: it must be guided, and it will rub.

Stacks run over a guide pin or inside a sleeve; the guide surface should be hardened and lightly greased, with working clearance to the bore or OD kept small so discs stay square. Friction at the guide and between nested discs makes the unloading curve sit below the loading curve — a hysteresis loop whose area is damping. Long series stacks bow like the Columns page’s struts and share load unevenly through friction: common practice limits an unguided run to roughly two to three stack diameters and, for long travels, splits the column with washers or steps in the guide. Re-torque after first seating: a new stack beds in.

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§5Where disc springs win

Choose the cone over the coil when the specification says: huge force, tiny travel, no room.

The natural homes: bolted-joint live loading (holding preload through thermal cycling and gasket creep), tool and die clamping, overload protection in presses, spindle drawbars, pipework hangers and bearing preload — all places where a helical spring of equal force would be absurdly large. The disc also offers what no coil can: a tunable curve shape, including the constant-force plateau and controlled snap-through of §2. Its trade-offs are the coil’s virtues in reverse — short life at high working stroke fractions, friction scatter, and travel bought only by stacking.

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§6Quick reference

The working core of the page on one card rack.

Geometry

cone h, thickness t

h/t sets the curve shape

Character

h/t ≲ 0.5 → near linear

≈1.4 plateau · beyond → snap-through

Stacking

parallel: F×m · series: δ×n

rate × m/n

Practice

guide the stack, grease the pin

parallel ≤ 2–3 discs

Use when

big force, short travel

live-loading bolted joints

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Handbook application: from concept to controlled practice

Purpose. This expanded section turns the original page into a practical handbook. It preserves the supplied material and adds a repeatable way to apply, check and review Disc Springs. It does not replace a contract, legislation, a controlled standard, competent engineering judgement or specialist advice.

The operating aim is to carry the subject from function and assumptions through design evidence, verification and controlled release. Read the original explanation first, then use the workflow and checks below to convert knowledge into evidence.

Apply Disc Springs by beginning with the duty, not the component or software command. Convert the key ideas—disc, springs, character, series, parallel—into measurable requirements and interfaces. Record operating and non-operating environments, duty cycle, expected life, loads, energy sources, human interaction and reasonably foreseeable abnormal conditions. When a value is not a project requirement or verified supplier datum, identify it as an assumption or illustrative value.

Create a calculation and evidence trail that another competent person can audit. Every input should carry a source, unit, revision and uncertainty or tolerance where relevant. Every model should state its boundary conditions and limitations. Keep nominal capacity separate from design capacity, and keep verification margin separate from an arbitrary safety factor. If a code or standard governs the work, confirm the applicable edition and contractual status rather than copying a number from a secondary summary.

Design for manufacture, assembly, inspection, operation and maintenance at the same time. A technically valid geometry can still fail because it cannot be fixtured, measured, cleaned, guarded, reached or replaced. Review process capability, datum or reference strategy, tolerance accumulation, access, error-proofing and changeover. Where people interact with plant, apply the hierarchy of controls and consult those who will operate, clean, maintain and recover the equipment.

Plan verification before release. Define the characteristic, method, equipment, sample or test condition, acceptance criterion, record and responsible person. Validation then asks a different question: whether the resulting system is effective and suitable in the intended use context. A passed drawing check or analysis does not by itself validate usability, maintainability or production performance.

Step-by-step operating method

Define the duty. Capture the required function, interfaces, operating environment, life, loads and unacceptable outcomes.
Establish the model. Identify governing principles, units, material or process data, assumptions and uncertainty.
Develop alternatives. Compare feasible concepts against performance, manufacturability, safety, maintainability and cost.
Verify the design. Use analysis, test, inspection or demonstration with acceptance criteria defined before execution.
Release and learn. Baseline the design, control changes, retain evidence and feed operating results into the next revision.

Illustrative design review record

Illustrative values only. Build a one-page record with the required function, input sources, assumptions, governing load or process condition, failure consequences, selected concept, verification method and acceptance criterion. Mark every numerical input as project requirement, verified supplier data, measured value, calculation output or assumption. Review the weakest evidence first. If an assumption can change safety, compliance, interchangeability or capacity, it must be resolved before release rather than buried in a calculation note.

Evidence class	Question	Release expectation
Requirement	What must the design do and under which conditions?	Approved and traceable
Input	Where did the load, property, tolerance or process limit come from?	Source, unit and revision recorded
Analysis	Which model and assumptions connect input to result?	Checkable calculation or simulation
Verification	How will conformity be demonstrated?	Method and acceptance criterion agreed
Validation	Will the solution work for intended users and conditions?	Representative use evidence

Common failure modes and recovery actions

1. Watch for

Starting detailed design before interfaces and operating limits are agreed.

Recovery: Return to the governing definition or requirement and restate the decision in one sentence.

2. Watch for

Using catalogue or typical values as though they were certified project inputs.

Recovery: Separate evidence from assumption, assign an owner and set a date for validation.

3. Watch for

Checking nominal performance while ignoring tolerances, degradation and foreseeable misuse.

Recovery: Run a small counterexample, boundary test, pilot or independent check before proceeding.

4. Watch for

Confusing verification of requirements with validation of user need.

Recovery: Record the consequence, decision and rationale, then update the controlled baseline.

5. Watch for

Releasing drawings or procedures without configuration, inspection and change controls.

Recovery: Escalate when the issue affects safety, compliance, acceptance, material value or an agreed tolerance.