# Belleville washer

Belleville washer

A Belleville washer, also known as a coned-disc spring,[1] conical spring washer,[2] disc spring, Belleville spring or cupped spring washer, is a type of spring shaped like a washer. It has a frusto-conical shape which gives the washer a spring characteristic. The Belleville name comes from the inventor Julian F. Belleville.[1]

## Design and use

Cross-sectional view of an M4 anti-tank mine (circa 1945) showing the steel belleville spring in the fuze mechanism
Cut-away view of an M14 antipersonnel landmine, showing the firing pin mounted in the centre of a plastic belleville spring

Belleville washers are typically used as springs, or to apply a pre-load of flexible quality to a bolted joint or bearing.

Some properties of Belleville washers include: high fatigue life, better use of space, low creep tendency, high load capacity with a small spring deflection.[3] and possibility for high hysteresis (damping) by stacking several belleville washers on top of each other in the same direction.

Belleville springs are also used in a number of landmines e.g. the American M19, M15, M14, M1 and the Swedish Tret-Mi.59. The target (a person or vehicle) exerts pressure on the belleville spring, causing it to exceed a trigger threshold and flip the adjacent firing pin downwards into a stab detonator, firing both it and the surrounding booster charge and main explosive filling.

Some makers of bolt-action target rifles use Belleville washer stacks in the bolt instead of a more traditional spring to release the firing pin, as they reduce the time between trigger actuation and firing pin impact on the cartridge.

They may also be used as locking devices, but only in applications with low dynamic loads, such as down-tube shifters for bicycles. Belleville washers are seen on Formula One cars, as they provide extremely detailed tuning ability. The World War II-vintage German Junkers Ju 88 aircraft's single strut main gear made primary use of belleville washers as its main shock absorption mechanism. At least one modern aircraft design, the Cirrus SR2x series, uses a Belleville washer setup to damp out nose gear oscillations (or "shimmy").

Belleville washers have been used as return springs in artillery pieces, one example being the French Canet range of marine/coastal cannon from the late 1800s (75 mm, 120mm, 152 mm).

Another example where they aid locking is a joint that experiences a large amount of thermal expansion and contraction. They will supply the required pre-load, but the bolt may have an additional locking mechanism (like Loctite) that would fail without the Belleville.

## Stacking

Multiple Belleville washers may be stacked to modify the spring constant or amount of deflection. Stacking in the same direction will add the spring constant in parallel, creating a stiffer joint (with the same deflection). Stacking in an alternating direction is the same as adding springs in series, resulting in a lower spring constant and greater deflection. Mixing and matching directions allow a specific spring constant and deflection capacity to be designed.

Example: 1 Spring is considered to be 1 in Parallel, 1 in Series. (This notation is needed for load calculations)

If n = # of springs in a stack, then: Parallel Stack (n in parallel, 1 in series) - Deflection is equal to that of one spring, Load is equal to that of n x 1 spring. i.e. Stack of 4 in parallel, 1 in series will have the same deflection as that of one spring and the load will be 4 times higher than that of one spring.

Series Stack (1 in parallel, n in series) - Deflection is equal to n x 1 spring, load is equal to that of one spring. i.e. Stack of 1 in parallel, 4 in series will have the same load of one spring and the deflection will be 4 times greater.

### Performance considerations

In a parallel stack, hysteresis (load losses) will occur due to friction between the springs. The hysteresis losses can be advantageous in some systems because of the added damping and dissipation of vibration energy. This loss due to friction can be calculated using hysteresis methods. Ideally, no more than 4 springs should be placed in parallel. If a greater load is required, then factor of safety must be increased in order to compensate for loss of load due to friction. Friction loss is not as much of an issue in series stacks

In a series stack, the deflection is not exactly proportional to the number of springs. This is because of a bottoming out effect when the springs are compressed to flat. The contact surface area increases once the spring is deflected beyond 95%. This decreases the moment arm and the spring will offer a greater spring resistance. Hysteresis can be used to calculate predicted deflections in a series stack. The number of springs used in a series stack is not as much of an issue as in parallel stacks.

Belleville washers are useful for adjustments because different thicknesses can be swapped in and out and they can be configured to achieve essentially infinite tunability of spring rate while only filling up a small part of the technician's tool box. They are ideal in situations where a heavy spring force is required with minimal free length and compression before reaching solid height. The downside, though, is weight, and they are severely travel limited compared to a conventional coil spring when free length is not an issue.

A wave washer also acts as a spring, but wave washers of comparable size do not produce as much force as Belleville washers.

### Calculation

2-3-1-2 stack of washers

If friction and bottoming-out effects are ignored, the spring rate of a stack of identical Belleville washers can be quickly approximated. Counting from one end of the stack, group by the number of adjacent washers in parallel. For example, in the stack of washers to the right, the grouping is 2-3-1-2, because there is a group of 2 washers in parallel, then a group of 3, then a single washer, then another group of 2.

The total spring coefficient is:

$K = \frac{k}{\sum_{i=1}^g \frac{1}{n_i}}$
$K = \frac{k}{\frac{1}{2}+\frac{1}{3}+\frac{1}{1}+\frac{1}{2}}$
$K = \frac{3}{7} k$

Where

• $n_i$ = the number of washers in the ith group
• g = the number of groups
• k = the spring constant of one washer

So, a 2-3-1-2 stack (or, since addition is commutative, a 3-2-2-1 stack) gives a spring constant of 3/7 that of a single washer. These same 8 washers can be arranged in a 3-3-2 configuration (K = 6/7*k), a 4-4 configuration (K = 2*k), a 2-2-2-2 configuration (K = 1/2*k), and various other configurations. The number of unique ways to stack n washers is defined by the integer partition function p(n) and increases rapidly with large n, allowing fine-tuning of the spring constant. However, each configuration will have a different length, requiring the use of shims in most cases.

## Standards

• DIN 2092 — Disc springs — Calculation
• DIN 2093 — Disc springs - Quality specifications - Dimensions[4]
• DIN 6796 — Conical spring washers for bolted connections[2]

## References

1. ^ a b Shigley, Joseph Edward; Mischke, Charles R.; Brown, Thomas H. (2004), Standard handbook of machine design (3rd ed.), McGraw-Hill Professional, p. 640, ISBN 978-0-07-144164-3.
2. ^ a b Smith, Carroll (1990), Carroll Smith's Nuts, Bolts, Fasteners, and Plumbing Handbook, MotorBooks/MBI Publishing Company, p. 116, ISBN 0-87938-406-9.
3. ^ Mubea Belleville Washer Properties
4. ^ Mubea Classification According to DIN 2093, Mubea Disc Springs, retrieved 2011-01-26.