Belleville Springs

I've used them a fair amount, though never with a two ton load. I suggest calling an applications engineer at Belleville and running it past him/her. What I've seen is a tendency to do two things: (1) stack too many springs; and (2) stack them backwards.

Their phone is

+44 (0)1527 500500

I currently use Belleville Washers (or springs). You should take care of a couple of limitations as:

- never load over 075..0.8 of maximal stroke ( I think about the dynamical load in transportation)

- if you stack in parallel then you should not neglect the friction between surfaces and it would be better to preview a grease lubrication

- the guides either internal or external have to be according to the recommendations with about 1% smaller for internal and 1% bigger for external (from corresponding diameters).

- it would be better if you center the springs with a bushing and the bushing internal diameter has the possibility to accommodate with the position deviations of the pins.

Hello PC,

How are you? With ref to the springs I list below the actual belleville sites and what may be detailed info there. Hope it is of use. I have know idea what a 'belleville' spring is, but can try to help.

http://www.google.com/search?client=safari&rls=en-us&q=belleville+springs%3F&ie=UTF-8&oe=UTF-8

bb

search in wikipedia.

I used in centrifuge. Even I dont know how it helps. It was under the vertical shaft assembly (under bearing Housing).

be in touch. Nice forum.

Hello pc,

Just a couple of things: A Belleville washer acts as a non linear spring. Only if relative deflection is small, it can be supposed linear.

To avoid friction problems when stacking parallel, think that two parallel Belleville washers are equivalent to one with double thickness (other dimensions equal).

I've used this spring type even for loads (not weight supporting) over 5 Tons.

Kind regards

The non linearity of the Belleville springs depends on the relative thickness, the thinner the less linear. The ratio s/t =0.4...0.5 leads to a quite linear spring (s= maximal possible stroke/ t= thickness).

With respect to the recommendation I can say, based on measurements I did that it is wrong!

The thickness is present at power 3 in the force-deformation equation which corresponds to measurements I have done. Your suggestion leads to a force about 8x higher!

Of course friction has an effect on the stiffness when stacked in parallel but not as important as you claim and friction can be reduced either by using greases (better on MoS2 basis) or other anti-friction surface treatments.

Hi nick name,

Surely we have a misunderstanding. When I talk about "parallel" stacking I tried to say that two washers with "t" thickness in parallel behave the same as one washer with "2t" thickness

AFAIK, since 3rd decade of past century, Belleville springs are intrinsically non linear, that is, the function which relates forces and displacements is not a straight line (according to Almen and Laszlo). The relationship is a function of thickness of course but also of height and angle and you know... if a trigonometric function is involved... well it doesn't behave linear.

The thickness is present at power 3 in the force-deformation equation which corresponds to measurements I have done. Your suggestion leads to a force about 8x higher!: Of course, if you use a double thickness, you get 2³ = 8 times.

Maybe you remember this old Timoshenko figure and its corresponding solution (in which the variation of angle is disregarded):

Kind regards

Dear Kwetz,

It is good to defend what you write. In one of the European countries is said " not only one mother has clever children" and as usual no one knows every thing and every body can make errors.

I unfortunately have a driver problem with my scanner so that I cannot answer today your comments by a counter figure so nice as yours but I shall do it as soon as I can.

Thank you for the explanation about trigonometric functions, in fact I finished my years in the college so long ago that I could have had the time to forget all of it if I would not have been continuously in touch with the different aspects of physics and mathematics applied in complex engineering.

Allow me to comment and discuss your assertions:

- as you surely know for small angles the sinus is approximated with the angle since the other terms of the series are very small. In general the angles in this "spring" are under or around 6° = 0,10471976 rad and sin(6°)=0,10452846 The ratio of the values is 1.00183. The non linearity error is the around 0.18%. A lot isn't it?

Recommended changes in the angle due to deformation are in the range of 4°. So that the process is between 2° and 6° For 2° =0.034906585 sin(2°)=0.034899497 which gives a ratio 1.000203. This time the error is 0.02%. Again very far from 1 or am I wrong?

It is true that Belleville springs are not linear but it depends on their geometry and usage range. We consider an engineering problem and not the abstract notion of perfect linearity. Even in force or torque transducers of high quality a non-linearity of 0.25% is considered as good and here we discuss a suspension spring!

- now let us consider two Belleville springs with same geometry and different thicknesses. I shall take as an example D=100 d= 51 and

t= 2.7, 4 and 6It is common standard dimension with values computed and checked and the same in different sources.

According to the catalogue of Bauer (which I strongly recommend but you also can use the one from MUBEA also a very highly specialised manufacturer) the corresponding forces for a 1 mm deformation are:

5300/11200/31000 N (values taken from the graphs in the catalogue)

If you compute the ratios of thickness and forces you obtain a relationship with a power of around 2 ( 1.9 in one case,2.2 and 2.5 in the other two). I recognize I wrote 3 and this was too much since I neglected some other aspects which have a reduction effect. But let it be 2 this means that if thickness is increased by a factor of 2 the force for same deflection will be 4x higher and of course not only 2x the force of one spring. So that if you couple in parallel 2 springs you get a force increased by a factor of 2 + friction effect (if you want I can give you some indications how high it runs) and if you consider a spring with a thickness 2xt you get a force about 4x the force of one spring.

Is it what you wanted to say? If I misunderstood then please accept me to apologise.

I would like to explain my error, I assumed that the stiffness of the spring is proportional to "t^3" as it is in beams. I did not take the time to have a look at the different equations since anyway I considered your assumption -as I understood it- as wrong. Sorry I would have had a more professional approach from the start.

very kind regards and it is a pleasure to have such exchanges,

Nick name

Here is the site which gives formulae for belleville spring.

http://www.engineersedge.com/belleville_spring.htm

I referred some books which state that as far as deflection to thickness is around 0.4 springs are linear, check out second graph in the following site. They have mistakenly not given relation of the curve but it is 'deflection/thk' as I am having the same graph in my ref book.

http://www.bellevillesprings.com/disc-spring-characteristics.html

I have one query, there are some belleville spring which can exert a force of around 25000 kgf for deflection of 20 mm, are they really reliable in practical sense for long life & for handling dynamic loads.

It is OK you have same curves and equations as I have. If you have a look at the force equation you will notice that the thickness is present at power 3 so that my memory was not so wrong and also the ratio deflection/thickness has similar values.

With respect to your last question send me the geometry (D/d/t/ho) and I shall have a look. Any way the stroke you mention cannot be obtained with only one spring at the force level you want to work. You should consider a stack. As an example a spring 250x127x14 (lo= 19.6)accepts at 0.75 s=0.75*(19.6-14)=4.2mm a force of 248800N. It seems that you need at least 5 springs of this type in series for the 20 mm stroke. Now is the force the very peak? or can it be due to dynamical effects even higher? The best is to be sure that the maximal worst case force does not go over the limit.

Basically: as long as the von Mises stress there where it is at its maximum (in the tension regions) does not go over the fatigue limit (safety considered) the spring can work. As far as I can presume this application is related to the damper. So that I continue to make an assumption: in this case the number of cycles full stroke will not be very important. If you have a mass on the springs and a permanent oscillation is applied then the problem is less critical since the fatigue is related to the asymmetry factor R=min stress/max stress of the cycle. You should consider that the different coefficients for reduction of fatigue limit are quite important since the surfaces are not very smooth and due to the heat treatment there are a lot of internal strains even if it was tried to reduce them after quenching. A verification must be done even if the catalogue says ok, errors are always possible. If you get the MUBEA cat then you can have a programme giving the number of cycles depending on the force, if you make a back computation you can obtain the values of the considered fatigue stresses used for the cycling. And use them for other springs.

For the spring I gave as example the life expectancy from load 0 to max is 20cycles with a pre-load of 93250 N the number of cycles goes as high as 3300.

You see the influence of the R factor.

If you expect a higher number of cycles then you should work in series+parallel in order to reduce the stress. From 0 to 135000N/spring the cycles go up to 1.9 E6!

Touché

Kind regards

Try Solon Manufacturing Co. for your Belleville Spring inquiries

http://www.solonmfg.com/springs/index.cfm