Belleville washer

Type of spring shaped like a washer

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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 conical shell which can be loaded along its axis either statically or dynamically. A Belleville washer is a type of spring shaped like a washer. It is the shape, a cone frustum, that gives the washer its characteristic spring.

The "Belleville" name comes from the inventor Julien Belleville who in Dunkerque, France, in patented a spring design which already contained the principle of the disc spring.[1][3] The real inventor of Belleville washers is unknown.

Through the years, many profiles for disc springs have been developed. Today the most used are the profiles with or without contact flats, while some other profiles, like disc springs with trapezoidal cross-section, have lost importance.

Features and use

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Cross-sectional view of an M4 anti-tank mine (circa ) 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

In the different fields, if they are used as springs or to apply a flexible pre-load to a bolted joint or bearing, Belleville washers can be used as a single spring or as a stack. In a spring-stack, disc springs can be stacked in the same or in an alternating orientation and of course it is possible to stack packets of multiple springs stacked in the same direction.

Disc springs have a number of advantageous properties compared to other types of springs:[4]

• Very large loads can be supported with a small installation space,
• Due to the nearly unlimited number of possible combinations of individual disc springs, the characteristic curve and the column length can be further varied within additional limits,
• High service life under dynamic load if the spring is properly dimensioned,
• Provided the permissible stress is not exceeded, no impermissible relaxation occurs,
• With suitable arrangement, a large damping (high hysteresis) effect may be achieved,
• Because the springs are of an annular shape, force transmission is absolutely concentric.

Thanks to these advantageous properties, Belleville washers are today used in a large number of fields, some examples are listed in the following.

In the arms industry, Belleville springs are used, for instance, 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.

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 s (75 mm, 120 mm, 152 mm).

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.[5]

Belleville washers, without serrations which can harm the clamping surface, have no significant locking capability in bolted applications.[6]

On aircraft (typically experimental aircraft) with wooden propellers, Belleville washers used on the mounting bolts can be useful as an indicator of swelling or shrinkage of the wood. By torquing their associated bolts to provide a specific gap between sets of washers placed with "high ends" facing each other, a change in relative moisture content in the propeller wood will result in a change of the gaps which is often great enough to be detected visually. As propeller balance depends on the weight of blades being equal, a radical difference in the washer gaps may indicate a difference in moisture content &#; and thus weight &#; in the adjacent blades.

In the aircraft and automotive industries (including Formula One cars[7][better source needed]) disc springs are used as vibration-damping elements because of their extremely detailed tuning ability. The Cirrus SR2x series of airplanes, uses a Belleville washer setup to damp out nose gear oscillations (or "shimmy").[8]

In the building industry, in Japan stacks of disc springs have been used under buildings as vibration dampers for earthquakes.[9]

Belleville washers are used in some high pressure air regulators, such as those found on paintball markers and air tanks.

Stacking

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Belleville spring stack in series Belleville spring stack in parallel

Multiple Belleville washers may be stacked to modify the spring constant (or spring rate) or the 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 common 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.

Generally, if n disc springs are stacked in parallel (facing the same direction), standing the load, the deflection of the whole stack is equal to that of one disc spring divided by n, then, to obtain the same deflection of a single disc spring the load to apply has to be n times that of a single disc spring. On the other hand, if n washers are stacked in series (facing in alternating directions), standing the load, the deflection is equal to n times that of one washer while the load to apply at the whole stack to obtain the same deflection of one disc spring has to be that of a single disc spring divided by n.

Performance considerations

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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 as 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 even if, generally, the stack height should not be greater than three times the outside diameter of the disc spring. If it is not possible to avoid a longer stack, then it should be divided into 2 or possibly 3 partial stacks with suitable washers. These washers should be guided as exactly as possible.

As previously said, 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, nor can they be stacked in series.

For disc springs with a thickness of more than 6.0 mm, DIN specifies small contact surfaces at points I and III (that is the point where the load is applied and the point where the load touches the ground) in addition to the rounded corners. These contact flats improve definition of the point of load application and, particularly for spring stacks, reduce friction at the guide rod. The result is a considerable reduction in the lever arm length and a corresponding increase in the spring load. This is in turn compensated for by a reduction in the spring thickness.

The reduced thickness is specified in accordance with the following conditions:[4]

• The overall height remains unaltered,
• The width of the contact flats (that is the annulus width) is to be approximately 1/150 of the outside diameter,
• The load applied to the reduced-thickness spring to obtain a deflection equal to the 75% of the free height (of an unreduced spring) must be the same as for an unreduced spring.

As the overall height is not reduced, springs with reduced thickness inevitably have an increased flank angle and a greater cone height than springs of the same nominal dimension without reduced thickness.[4] Therefore, the characteristic curve is altered and becomes completely different.

Calculation

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Parameterization of a Belleville disk spring

Starting from , when J. O. Almen and A.Làszlò published a simplified method of calculation,[10] always more accurate and complex methods appeared also in order to include in calculations disc springs with contact flats and reduced thickness. So, although today there are more accurate methods of calculation,[11] the most used are the simple and convenient formulas of DIN as, for standard dimensions, they produce values which correspond well to the measured results.

Considering a Belleville washer with outside diameter D e {\displaystyle {D_{e}}} , inside diameter D i {\displaystyle {D_{i}}} , height l {\displaystyle {l}} and thickness t {\displaystyle {t}} , where h 0 {\displaystyle {h_{0}}} is the free height, that is the difference between the height and the thickness, the following coefficients are obtained:

δ = D e D i {\displaystyle \delta ={\frac {D_{e}}{D_{i}}}}

Load-deflection curves for Belleville springs, normalized by height, as described by Almen and Làszlò

C 1 = ( t &#; t ) 2 ( 1 4 &#; l t &#; t &#; t + 3 4 ) &#; ( 5 8 &#; l t &#; t &#; t + 3 8 ) {\displaystyle {C_{1}}={\frac {\left({\frac {t'}{t}}\right)^{2}}{\left({\frac {1}{4}}\cdot {\frac {l}{t}}-{\frac {t'}{t}}+{\frac {3}{4}}\right)\cdot {\left({\frac {5}{8}}\cdot {\frac {l}{t}}-{\frac {t'}{t}}+{\frac {3}{8}}\right)}}}}

C 2 = C 1 ( t &#; t ) 3 &#; [ 5 32 &#; ( l t &#; 1 ) 2 + 1 ] {\displaystyle {C_{2}}={\frac {C_{1}}{\left({\frac {t'}{t}}\right)^{3}}}\cdot \left[{\frac {5}{32}}\cdot \left({\frac {l}{t}}-1\right)^{2}+1\right]}

K 4 = &#; C 1 2 + ( C 1 2 ) 2 + C 2 {\displaystyle {K_{4}}={\sqrt {-{\frac {C_{1}}{2}}+{\sqrt {\left({\frac {C_{1}}{2}}\right)^{2}+C_{2}}}}}}

The equation to calculate the load to apply to a single disc spring in order to obtain a deflection s {\displaystyle {s}} is:[12]

F = 4 E 1 &#; μ 2 &#; t 4 K 1 &#; D e 2 &#; K 4 2 &#; s t &#; [ K 4 2 &#; ( h 0 t &#; s t ) &#; ( h 0 t &#; s 2 t ) + 1 ] {\displaystyle F={\frac {4E}{1-\mu ^{2}}}\cdot {\frac {t^{4}}{K_{1}-{D_{e}}^{2}}}\cdot {K_{4}}^{2}\cdot {\frac {s}{t}}\cdot \left[{K_{4}}^{2}\cdot \left({\frac {h_{0}}{t}}-{\frac {s}{t}}\right)\cdot \left({\frac {h_{0}}{t}}-{\frac {s}{2t}}\right)+1\right]}

Note that for disc springs with constant thickness, t &#; {\displaystyle {t'}} is equal to t {\displaystyle {t}} and consequently K 4 {\displaystyle {K_{4}}} is 1.

For what concerns disc springs with contact flats and reduced thickness it has to be said that a paper published in July , demonstrated that the K 4 {\displaystyle {K_{4}}} equation as defined inside the standard norms is not correct as it would result in every reduced thickness being considered right and this is, of course, impossible. As written in that paper K 4 {\displaystyle {K_{4}}} should be replaced with a new coefficient, R d {\displaystyle {R_{d}}} , which depends not only from the t &#; t {\displaystyle {\frac {t'}{t}}} ratio but also from the flank angles of the spring.[13]

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The spring constant (or spring rate) is defined as:

k = d F d s {\displaystyle {k}={\frac {dF}{ds}}}

Belleville washer stack illustration

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 = k &#; i = 1 g 1 n i {\displaystyle K={\frac {k}{\sum _{i=1}^{g}{\frac {1}{n_{i}}}}}}

K = k 1 2 + 1 3 + 1 1 + 1 2 {\displaystyle K={\frac {k}{{\frac {1}{2}}+{\frac {1}{3}}+{\frac {1}{1}}+{\frac {1}{2}}}}}

K = 3 7 &#; k {\displaystyle K={\frac {3}{7}}\cdot {k}}

Where

• n i {\displaystyle n_{i}}

• g {\displaystyle {g}}

• k {\displaystyle {k}}

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 {\displaystyle K={\frac {6}{7}}\cdot k} ), a 4-4 configuration ( K = 2 &#; k {\displaystyle K=2\cdot k} ), a 2-2-2-2 configuration ( K = 1 2 &#; k {\displaystyle K={\frac {1}{2}}\cdot k} ), and various other configurations. The number of unique ways to stack n {\displaystyle {n}} washers is defined by the integer partition function p(n) and increases rapidly with large n {\displaystyle {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

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• DIN EN formerly DIN &#; Disc springs &#; Calculation
• DIN EN formerly DIN &#; Disc springs - Manufacturing & Quality specifications

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• DIN &#; Conical spring washers for bolted connections

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References

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To keep bolted connections tight, we can choose from several methods. The most common is the insertion of a locking device between the rotating part (nut) and the parts being fastened (i.e., bus bars). That locking device often is a split-ring lockwasher. Such a device does not meet all locking device requirements, however. Enter, the Belleville washer.

The Belleville is a disk spring that applies pressure to the connection once you clamp down on it with the proper amount of force. The advantage of this washer is that it applies clamping pressure along a continuous arc pattern, instead of concentrating it at one point the way a split-ring lockwasher does. While you should use a split-ring washer only at the nut end of the connection (normally), you can use Belleville washers in tandem. One at the nut end and one at the bolt head end. This is a common way to use these washers, especially when assembling bus bar.

Most often, you'll find Belleville washers in applications where you have to connect bare, soft aluminum to aluminum or copper, or where you have conditions of high current loading or cycling. These washers do wonders for accommodating thermal cycling, but they can't eliminate all the problems resulting from poor workmanship. You must prepare the joint properly (as with any connection), but the key is selecting the proper design and size of Belleville washer for the fasteners and conditions of your application.

Selecting the right Belleville washer You have to deal with three parameters here: torque, diameter, and finish. Vendors publish the specification data you need in various media, such as booklets, CD-ROMs, and websites. These are high-end fasteners for electrical applications, so your source would most likely be your electrical supply house you normally deal with. Let's look at these three parameters.

Torque. This is the force you need to place on the bolt to flatten the washer to its optimum shape for proper clamping. Remember, the way a bolt makes a tight connection is by your tightening it to the point where its threads just start to deform. Bolts of various hardness, diameter, and material configurations require varying amounts of torque to reach that tightness. This is the same with Belleville washers. So that the bolt and Belleville washers work together, make sure the torque for your Belleville washers matches that of your bolts.

If you exceed a locking washer's torque by more than a few percent during assembly, you destroy the locking washer. Again, Belleville washers are no exception. If you undertorque, you won't make use of the washer's abilities to provide a reliable connection.

Diameter. A Belleville washer generates a clamping force along the tip of its cup perimeter. If the cup overhangs the connection (e.g., it's too big), you'll have much less clamping force than you thought you had.

One misguided solution to an overhanging Belleville washer is to put an oversized flat washer underneath it. What happens? The flat washer deflects (bends) away from the Belleville washer, instead of transmitting clamping force to the connection. So, except for special cases, it's pointless to apply a Belleville washer whose diameter exceeds that of the connection pad you're going to use it on. If you can't find a Belleville washer that fits your application, a product applications engineer may design a custom setup that includes an oversized flat washer.

Finish. In most cases, you can select a standard finish. However, if you have any process fumes or solvents present in your environment, you should talk to a manufacturer's product applications engineer. The wrong finish can result in a connection that literally falls apart. For example, electroplated Belleville washers become brittle in the presence of hydrogen. If you subject a hydrogen-exposed electroplated washer to impact or severe vibration, that washer will break into pieces.

Tips for correct Belleville washer installations For some materials, you use a flat washer under the Belleville washer, and for some you can't. The softer the material, the more likely you'll require a flat washer. If you find the Belleville is too large, do not try to compensate by placing a flat washer underneath it.

Mount the washer so its cup points toward the connection (away from the bolt head or nut). Mounting it upside down (reversed), adds little clamping force to the connection. The number of reversed Belleville washers in existing installations is staggering, so it is an important consideration.

Though the illustrations (on page 53) show a pronounced dish, most Bellevilles actually have shallow dishes. Sometimes, it's hard to tell which end is up. If that happens to you, lay the washer on a flat surface and look at it from the side, as shown in Fig. 1.

Assemble the joint as shown in Figs. 2 and 3, using flat washers only as appropriate. If you have more than one bolt in the joint you are assembling, use a torquing pattern (as opposed to tightening each bolt from zero to maximum torque one at a time), and use multiple stages of tightening. Let's say you have a four-bolt assembly, and each Belleville washer requires 55 ft-lb of torque. You might tighten the upper left bolt to 30 ft-lb, then do the same to the lower right, lower left, and upper right, in that order. Then repeat at 45 ft-lbs and finally at 55 ft-lbs.

Don't assume the washer in your hand is the correct one. Check the first one or two with a torque wrench. When the washer goes flat, you'll notice an abrupt change in the feel of the wrench. Once you can see these deform properly (flatten) at the specified torque, you can do the rest without the torque wrench; you may want to go more than three levels of tightening in your torque sequence to prevent warping the clamped part. Make sure you repeat the torque-wrench procedure if you change bolt sizes or pick up a box of Belleville washers you weren't using before. Of course, if you're using powered wrenches, you'll need to insert a torque limiter and use it each time.

Belleville washers cannot substitute for good workmanship. No matter how secure your connection is, unclean contact surfaces will give you a resistance at the point of contact. That resistance will cause a voltage drop and heat, and the connection will eventually work itself loose. Always use the proper joint compound, not just what's handy.

Tighten the connection to the recommended torque and no more.

In a Belleville washer application, the manufacturer may say to flatten the washer and then back off slightly. Make sure you don't back off too far, because when you flatten the washer a second time, it will have less clamping force than it was designed to have.

Before energizing the system, check each connection to see if the Belleville washers are flat and not cracked.

After the system has had some load cycling, give the bolted connections another visual check. If you assembled them properly, they will be secure.

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