Belleville Washers: Stacking Curves for Controlled Preload
Short answer: a Belleville washer is a conical disc spring that delivers high force in very little axial space, and its load-deflection curve is tunable by geometry — flatten the disc only partway and the curve stays steep, or design the cone height to about 1.4× the thickness and the spring holds a nearly constant force across a wide deflection band. Stack discs in parallel and force multiplies by the number of discs; stack them in series and deflection multiplies instead. That makes Bellevilles the standard answer for bolt preload, thermal-expansion compensation, and high-load short-travel duties.
A Belleville washer — the same part engineers call a disc spring or coned-disc washer — looks like a plain washer with a cone pressed into it. That simple cone is a precision spring: its outer edge bears on one seat, its inner edge on the other, and flattening the cone generates the load. Because the whole disc works in compression across its circumference, a single small washer can carry forces that would need a large coil spring, and stacks of discs multiply the behavior in either direction. This guide explains the load curve, the stacking math, materials, and the design rules that keep a Belleville stack from failing in service.
The Load-Deflection Curve and the h/t Ratio
The defining feature of a Belleville is its non-linear load-deflection curve, and the shape of that curve is set by one ratio: the cone height h divided by the material thickness t. Below about h/t = 0.4 the disc behaves almost linearly, like a stiff washer spring. As h/t rises toward roughly 1.4, the curve develops a wide flat region where load stays nearly constant while deflection keeps increasing — the famous constant-force behavior. Push h/t much higher, above about 2.8, and the curve develops a descending branch: beyond a peak, load actually falls with further deflection, and the disc can snap through from one stable shape to another. That snap-through is a feature in some toggle mechanisms and a danger in others, so the h/t ratio must be chosen deliberately, never by accident.
| h/t ratio | Curve shape | Typical use |
|---|---|---|
| Under ~0.4 | Nearly linear | Stiff washers, play removal, light preload |
| ~0.4 to ~1.3 | Progressive, steepening | General disc springs, defined-rate stacks |
| ~1.4 | Flat plateau, near-constant force | Constant-load clamps, compensators |
| Above ~2.8 | Descending branch, possible snap-through | Snap/toggle action; avoid for normal preload |
For most bolted-joint and short-travel duty, designers stay in the linear-to-moderately-progressive range or deliberately pick the flat region when the load must not drift as parts wear or expand. A small change in cone height moves the curve noticeably, which is why disc springs are made to tight free-height tolerances and why the spring tolerance standards discussion matters more for Bellevilles than for many other spring forms.
Stacking: Parallel, Series, and Hybrid
One disc gives one curve. Stacking changes the answer in a simple, additive way. Stack discs facing the same direction — crest to crest — and they share the load in parallel: total force multiplies by the number of discs while deflection per disc stays the same. Stack them alternating direction — crest to trough — and they act in series: deflection multiplies by the number of discs while the load stays the same. Hybrid stacks combine groups in parallel and those groups in series to hit a force and travel that no single disc size offers.
| Configuration | Total load | Total deflection | Use when |
|---|---|---|---|
| Single disc | F | s | Space is minimal, one disc suffices |
| n discs, parallel | n × F | s | Need more force in same travel |
| n discs, series | F | n × s | Need more travel at same force |
| m parallel groups × n in series | m × F | n × s | Force and travel both exceed one disc |
Two practical cautions. First, discs in a parallel stack share load only if their heights match, so they are always supplied and assembled as matched sets, and even then the first disc to go flat carries a disproportionate share unless a flat shim plate is used. Second, sliding between discs creates friction and hysteresis — load on the way down reads lower than load on the way up — which is why stack force is usually specified with lubrication and why dynamic applications need a correct stack count rather than an optimistic one. If fatigue is a concern, review the deflection limit per disc against the guidance in our spring fatigue life design guide before finalizing the stack.
Materials, Sizes, and Surface Treatment
Disc springs are stamped or machined from spring strip and plate, then hardened and tempered. The standard European series is DIN 2093, which defines metric disc springs with outer diameters from roughly 6 mm to 250 mm and thicknesses from about 0.2 mm to 14 mm; the common material is chrome-vanadium steel (51CrV4) for its strength and fatigue behavior, with stainless and high-temperature alloys for special environments.
| Material | Continuous service temp | Notes |
|---|---|---|
| Chrome-vanadium 51CrV4 / 6150 | ~200-250°C | DIN 2093 default, good fatigue |
| Carbon steel (Ck67 etc.) | ~120-150°C | Economy, indoor use |
| 302/301 stainless | ~250-300°C | Corrosion resistance |
| 17-7PH / Inconel | 350°C and up | High temp, aggressive media |
Surface treatment matters as much as base material. Phosphate or zinc plating for corrosion in normal duty, and shot peening on the tensile faces for dynamic applications, because disc springs fail from fatigue cracks starting at the inner and outer edges where bending stress concentrates. Set (compressing the disc flat once or several times before assembly) improves dimensional stability and is standard practice for precision stacks — the same presetting logic used across the spring industry to lock in the working curve.
Design Rules for Bolted Joints and Short-Travel Duty
For bolted preload, a Belleville stack sits under the bolt head or nut and maintains clamping force as the joint settles, gaskets creep, or temperature cycles change part lengths. The design sequence is short: determine the preload force the joint needs, decide how much relaxation travel the stack must absorb, then pick a disc and stack arrangement whose load at working deflection stays above the minimum clamp force across the whole travel band. Because Belleville load can be tuned to stay nearly flat, a well-chosen stack holds joint force far more stable than an elastomer or a soft coil over a temperature cycle. Guide the discs on a shaft or inside a bore with modest clearance, keep the seating surfaces flat and parallel, and lubricate interfaces in dynamic stacks to control friction loss. Never load a disc past flat for sustained duty unless the design intentionally uses the flat position, since the edge stresses rise sharply in that region and relaxation and fatigue follow.
When Belleville Washers Are the Wrong Choice
Bellevilles earn their place with high force, short travel, and compact axial space, but they are not a general-purpose spring. They deliver small deflection per unit of cost compared with a coil spring, so anything needing large travel is better as a helix or a compression spring assembly. They also transmit load through small edge contacts, so very soft or very high-cycle duties need careful edge treatment. And while the h/t curve is a design asset, it is also a trap: a disc selected without checking its h/t ratio can behave progressively, flat, or snap-through when the designer assumed linear. Specify the disc size, the h/t class, and the stack arrangement explicitly on the drawing, and let the factory verify the curve on a spring tester rather than assuming catalog behavior holds at your operating point.
Verifying a Belleville Stack Before Production
A Belleville stack should be verified the same way it will be used: load the assembled stack on a calibrated spring tester and compare the measured force at your working deflection against the specified curve. Typical load tolerance for disc springs is about ±10-15% depending on the class specified, and the tolerance applies to the stack as assembled, not just to a single disc — which is why matched sets matter in parallel configurations. Two extra checks catch the failures that geometry alone cannot. First, measure the load on the way up and on the way down: a large gap between the two readings is friction and hysteresis between discs, and it tells you whether lubrication and surface treatment are adequate for a dynamic duty. Second, confirm the stack never reaches its flat position in service unless the design intends it, since the stress rise near flat is where relaxation and edge cracking begin.
For dynamic applications, review the per-disc deflection against the recommended fatigue limits before approving the design, and shot peening plus edge treatment should be confirmed on the drawing rather than assumed. Dimensional checks belong in the same first-article inspection: free height of the stack, parallelism of the end discs, and the clearance between disc bore and its guiding shaft or sleeve, because edge contact against the guide is a common cause of premature failure. A supplier that ships each batch with measured load-at-deflection data, and that flags any material or heat-treatment change that would move the curve, is the kind of partner a preload-critical design needs.
Frequently Asked Questions
Q: What is the difference between a Belleville washer and a regular washer?
A: A regular washer is a flat spacer that distributes load statically. A Belleville washer is coned and acts as a spring: it deflects under load, stores energy, and returns, so it can maintain preload, absorb thermal movement, or provide a controlled force where a plain washer merely sits.
Q: How do I stack Belleville washers for more force or more travel?
A: Stack discs in the same direction for parallel action, which multiplies force by the number of discs while deflection stays the same; alternate the direction for series action, which multiplies deflection at the same force. Combine parallel groups in series when you need both more force and more travel.
Q: What does the h/t ratio mean for a Belleville washer?
A: It is the cone height divided by the material thickness, and it sets the shape of the load-deflection curve: low ratios behave almost linearly, a ratio near 1.4 gives a flat constant-force region, and ratios above roughly 2.8 can produce a descending load and snap-through behavior. Specify it deliberately for your application.
Q: Can Belleville washers be used for high-cycle dynamic loads?
A: Yes, with correct design: keep the deflection per disc inside the recommended dynamic range, shot peen the tensile faces, and guide the stack to prevent edge loading. Friction between discs in parallel stacks also causes hysteresis, so lubrication and matched disc sets are part of a reliable dynamic design.
Q: What standard Belleville washer sizes are available?
A: The DIN 2093 metric series covers disc springs from roughly 6 mm to 250 mm outer diameter and about 0.2 mm to 14 mm thickness, most commonly in chrome-vanadium steel. Non-standard sizes are produced with stamping or machining plus hardening and tempering when the envelope demands it.
Related Resources
- Which Spring Type Should You Use? — compare disc springs with coil, wave, and leaf forms before committing.
- Custom spring products — compression, disc, and specialty springs from a Dongguan source factory.
- About BQUQ — an ISO9001-certified factory running spring, stamping, CNC, and heat sink lines in Dongguan.
- Contact us — send your load, travel, and envelope and get a spring stack quote within 12 working hours.
Authored by the BQUQ Engineering Team. BQUQ is an ISO9001-certified source factory in Dongguan, China, running CNC machining, metal stamping, custom springs, heat sink and collet lines under one roof. Send drawings to sc@bquq.com or WhatsApp +86 13713157787 for a quote within 12 working hours. www.bquq.com
