## Selasa, 19 Juli 2011

### Belleville Washer/ Spring

A Belleville washer, also known as a coned-disc spring, conical spring washer, 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.

Belleville springs are a type of disc-shaped washer with an extremely high tensile strength. Originally developed in the mid-19th century by Julian Belleville, belleville springs are used in a variety of environments in which a heavy load bearing ability is required. Many high performance cars use a type of belleville spring in their shock absorbing systems, and belleville springs are also used in manufacturing equipment, as well as electronics.
Belleville springs can be made in a wide range of sizes, from very small washers to very large discs. In shape, they resemble a shallow soup bowl with the bottom cut out, and they are generally made from tempered steel and other similar metals that can stand up to immense pressures. Most manufacturers pre-stress belleville springs before delivering them to consumers, to make sure that they won't fail in practical applications.
Because of their construction, belleville springs can be subject to very heavy loads, and they will distribute the weight evenly around their circumference. As a result, they can be used to hold substantial loads and to distance parts of machinery from each other. They are highly useful in areas subject to thermal expansion or contraction, vibration, high bolt loads, and bolt creep, in which bolts may move around or wedge themselves out.
In the simplest of applications, belleville springs may be placed convex side out between a bolt and the surface they are attaching to. Sometimes, a small washer is used to help further balance the load, although the belleville spring is usually strong enough on its own. If a washer is used, it is placed under the outside diameter of the spring. When the bolt is subjected to stress, the belleville spring will help to distribute it evenly so that the bolt won't move or inadvertently release.
There are a number of other configurations for belleville springs in practical use, however. Sometimes they are installed in a parallel stack, increasing the amount of load they can accept. In other cases, the springs may be stacked in a series, either in front-to-front or back-to-back springs, to increase deflection. In a parallel series, the two systems are combined to increase load bearing ability and deflection. In all instances, belleville springs are said to have reached their maximum load capacity when they have flattened out.
Belleville springs are in use in a wide variety of commercial and consumer environments. In many instances in which the ability to withstand a heavy load in a small space is required, belleville springs are a good choice to balance that load safely and evenly.

## Design and use

Belleville washers are typically used as springs, or to apply a pre-load or flexible quality to a bolted joint or bearing.
Some properties of Belleville washers include: high fatigue life, better space utilization, low creep tendency, and high load capacity with a small spring deflection.
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.
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 1800's (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 differently 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 similar device is a wave washer.

### 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
• ni = 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]
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