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]

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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  Additional resources:
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  For more bell washerinformation, please contact us. We will provide professional answers.

References

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Belleville washers

Belleville washers

trudels

(Mechanical)

(OP)

9 Sep 11 15:38

Hi guys,

I need an info on Belleville washers. I want to know what is the max number of times a single belleville washer can be used/reused. I want to know this because the mechanics where I work were once told to only use the same washer twice. We have a LOT of washers here and I wonder if they could use them more than 2 times.

Thanks a lot for your time,

Simon
 

Replies continue below

Recommended for you

RE: Belleville washers

Tmoose

(Mechanical)

9 Sep 11 15:52

sounds like a question for the manufacturer about specific part numbers.  

then there may be a problem of keeping track of how many time they have been re-used

RE: Belleville washers

JohnRBaker

(Mechanical)

9 Sep 11 16:05

Based on this impression, it would appear that this is an issue which the manufactures are talking about without really being prompted to do and as such it suggests a couple of things. 1) it feels as if there has been problems in the past, which could very well explain why your mechanics warned you about this, but 2) it would also appear that the manufactures may have responded to this by producing better products and backing them up with test data.  I would say that

Tmoose

might have the right idea, check with the manufacture of the washers that you're using and see what they have to say about the fatigue life of their particular products.  

I just did a simple Google search and turned up many instances where the manufactures of Belleville Washers go out of their way to promote the idea that they have done extensive fatigue testing and they assure the buyer that their products are resistant to fatigue failure.Based on this impression, it would appear that this is an issue which the manufactures are talking about without really being prompted to do and as such it suggests a couple of things. 1) it feels as if there has been problems in the past, which could very well explain why your mechanics warned you about this, but 2) it would also appear that the manufactures may have responded to this by producing better products and backing them up with test data. I would say thatmight have the right idea, check with the manufacture of the washers that you're using and see what they have to say about the fatigue life of their particular products.

John R. Baker, P.E.
Product 'Evangelist'
Product Design Solutions
Siemens PLM Software Inc.
Industry Sector
Cypress, CA
http://www.siemens.com/plm
UG/NX Museum:   http://www.plmworld.org/p/cm/ld/fid=209

To an Engineer, the glass is twice as big as it needs to be.
 

RE: Belleville washers

rb

(Aerospace)

9 Sep 11 16:07

it'd depend on whether the washer has been deformed ... no?

RE: Belleville washers

desertfox

(Mechanical)

9 Sep 11 16:12

This site has an FAQ asking you're question.

http://www.bellevillesprings.com/disc-springs-faqs.html

Regards

desertfox

Hi trudelsThis site has an FAQ asking you're question.Regardsdesertfox

RE: Belleville washers

trudels

(Mechanical)

(OP)

9 Sep 11 16:17

Thanks a lot guys for your answers, I will contact my supplier to have more info!

Thank again

RE: Belleville washers

Cockroach

(Mechanical)

10 Sep 11 12:42

Do the research and ensure the Belleville Washer application suits the components needed.

There are a tremendous amount of computational engines for stress analysis on the web. Your issue is one of cyclic loading and lifetime. You can definitely re-use a Belleville Washer stack more than twice, depending on your application. In my experience, rare to use them only twice, probably a mis-spec of the application. They are way more reliable than that!Do the research and ensure the Belleville Washer application suits the components needed.

Kenneth J Hueston, PEng
Principal
Sturni-Hueston Engineering Inc
Edmonton, Alberta Canada

RE: Belleville washers

unclesyd

(Materials)

10 Sep 11 13:29

If you want to educate yourself on the application and design of disk spring components here is a link to the Schnoor handbook.

Key Bellevilles has a CD for the design and application of disk springs
 
http://schnorr.com/docs/Handbook.pdf

I would definately follow the advice posted above about contacting you spring manufacturer for information on the specific characteristics of your spring as there are numerous designs for different applications.If you want to educate yourself on the application and design of disk spring components here is a link to the Schnoor handbook.Key Bellevilles has a CD for the design and application of disk springs

RE: Belleville washers

drawoh

(Mechanical)

10 Sep 11 16:38

   Roark's Equations has a section explaining Belleville washers.  You can work out the stress for yourself, and analyse for fatigue.  They are springs.  They are under a lot of stress.

trudels,Roark's Equations has a section explaining Belleville washers. You can work out the stress for yourself, and analyse for fatigue. They are springs. They are under a lot of stress.

               JHG

RE: Belleville washers

Grindy

(Industrial)

10 Sep 11 17:54

I used to work with machine tools and they are often used to securely hold tools in place. These tools could be subjected to 'tool changes' many hundreds of times per shift. This would constantly be putting the washers under stress/fatigue. In seven years I didn't have to replace a single one.

That said I have seen failures with them in my current job, but they are subjected to far greater forces (400 Tonne presses) and in a harsh environment (concrete products).

RE: Belleville washers

fastline12

(Aerospace)

11 Sep 11 14:10

Agree with Grindy.  We own many CNC machines and have rebuilt many draw bar systems that retain a machine tool holder in the spindle.  It is very common to get approx 100,000 tool changes without issue.  They are usually compounded in series and parallel to achieve a target amount of travel and force.  They are usually compressed to max every time, then released BUT they are usually at about 20-40% of compression when released so they retain a draw force on the tool when running in the spindle.  

IMO, you can get a lot of cycles from them.  IMO, the nasty vibrations and harmonics from machining largely contributes to the failure of the washers, not just the fatigue limits.   

RE: Belleville washers

rmw

(Mechanical)

11 Sep 11 18:40

I know of a product where belleville washers are used as spring packs for actuators where the actuator can and often does drive into the spring pack when subjected to high operating torque.  The flexure of the spring pack allows the mechanism to flex so that a torque switch can be made (or broken) when the flexure exceeds a preset value.

These washers flex to some extent every time the actuator operates if it is operating at or near its rated torque and only flex to the maximum extent so as to trip the torque switch if the design torque value is exceeded.

These belleville washers certainly are "reused" time and time again without ever being disassembled.

rmw

RE: Belleville washers

dgallup

(Automotive)

12 Sep 11 18:10

My Honda VF750F uses a belleville washer to clamp the clutch pack. Still working fine after 28 years.

The Help for this program was created in Windows Help format, which depends on a feature that isn't included in this version of Windows.
 

RE: Belleville washers

looslib

(Mechanical)

13 Sep 11 10:28
 

A lot depends on your type of application and requirement for reliability. In race cars, teams typically use new parts everytime they rebuild the car between races. Might be excesssive and waste some good parts, but they can't afford any chances. Nuts, bolts and washers are the most common parts that are not reused.

"Wildfires are dangerous, hard to control, and economically catastrophic."

Ben Loosli

RE: Belleville washers

MiketheEngineer

(Structural)

13 Sep 11 12:10

Tend to agree with looslib...

The mfg will probably say change them every time - since they are in the business of "selling" them.

For non-critical apps - I am sure they can be re-used.  But if you are building space shuttles or holding jet engines on airplanes or building race cars - I think I would use new ones every time.

RE: Belleville washers

Tmoose

(Mechanical)

13 Sep 11 17:04

Sometimes NEW = Never Ever Worked (before), especially in this age of components from suppliers from far away.  Not that it was all good in the good old days, or sometimes they make 'em much better than they used to, but..............

Some moderately strict MIL spex allow reusing nylon locking nuts multiple times, or until the prevailing torque drops below some nominal value.

Some Bellevilles are designed so as to not exceed their yield strength when squashed completely flat, so would be hard to damage in that regard by tightening very hard.

RE: Belleville washers

israelkk

(Aerospace)

14 Sep 11 04:26

I am watching this post for sometime and without dis-respect I am disappointed with the shallow discussion regarding Belleville spring selection and design. No one even mentioned that the theory and closed form design and analysis formulations or Belleville springs (cone disc springs) are well known for decades. Every engineering graduate student should be able to use those formulas to design a new spring and to check how an existing of off the shelf spring will fit the design goals.

When a Belleville spring is compressed to flat or even beyond flat, three types of stresses are usually needed to be taken into account. One is a compressive strength at the top inside diameter of the spring and the other two are tensile strength (one at the bottom large outside diameter and one at the top inside diameter of the disc). Therefore, for cyclic operation only the tensile stresses should be taken into account. However, most if not all Belleville spring manufacturing processes include a preset (scraging or set remove as it is sometimes called) process as that last process that induces favorable residual compressive stresses at the points where tensile stress governs the design. Therefore, much higher loads are able from such a spring compared to a spring that didn't include a preset process in it's manufacturing process.

RE: Belleville washers

drawoh

(Mechanical)

14 Sep 11 11:48

   I set up a spreadsheet using the Belleville spring equations from Roark's, and some similar equations from the SAE spring handbook.  I wanted to design my own Belleville springs.  As a sanity check, I pulled out my

   Your preset would increase the maximum stress a bit, but the Schnorr washers can be compressed flat, according to my calculations.  Couldn't you just punch them out of (fairly) soft metal and then heat treat them?

   I wound up designing some delrin lens preloaders, and I left strict instructions to not compress them flat.  

israelkk,I set up a spreadsheet using the Belleville spring equations from Roark's, and some similar equations from the SAE spring handbook. I wanted to design my own Belleville springs. As a sanity check, I pulled out my Schnorr catalogue, and I punched in their values. My spreadsheet and Schnorr were in fairly close agreement. I was happy.Your preset would increase the maximum stress a bit, but the Schnorr washers can be compressed flat, according to my calculations. Couldn't you just punch them out of (fairly) soft metal and then heat treat them?I wound up designing some delrin lens preloaders, and I left strict instructions tocompress them flat.

               JHG

RE: Belleville washers

rmw

(Mechanical)

14 Sep 11 21:33

Nice tutorial for our shallow minds israelKK, He now knows the theory behind how they are made, but you didn't answer the OP's question - how many times can he reuse his belleville washer?

rmw

RE: Belleville washers

israelkk

(Aerospace)

15 Sep 11 01:08

rmw

Knowing the formulations, the loads and deflections on a spring, a competent designer can easily calculate/estimate the stresses and the fatigue life. To answer a question, preliminary specific data is needed including the spring dimensions, loads and deflections. The fact that none of this is given by trudels and your post proves my point.  

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