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Originally Posted by
HimyKabibble
This is making my head hurt! :-)
If you stack Bellevilles so they "nest" (i.e. -concave sides all pointing the same direction), you will increase the load at a given displacement by the number of springs you've stacked. This is typically referred to as "parallel" stacking. So, if one spring gives 10# when displaced by 0.050", then two springs pointing the same way will give 20# when displaced by 0.050". No matter how many you stack, the maximum displacement of the stack will remain the same as the maximum displacement of a single spring. You can visualize this as being exactly equivalent to putting coil springs between two metal plates. If you put two springs between the plates, placed next to each other, the force required to achieve a given displacement doubles. With three springs, it triples, etc.
If you now reverse one of them them, you increase the available displacement, with no increase in load for a given displacement. This is typically referred to as "series" stacking, in which each spring is facing opposite the direction of its neighbors. This is exactly equivalent to stacking coil springs one on top of another in series between two metal plates. Each spring you add, allows you to increase the maximum displacement by the maximum displacement of that spring. So, if the above spring has a maximum displacement of 0.100" (at which point it's completely flat), then two springs facing opposite directions will still give you 10# when displaced by 0.050", but you will be able to compress the pair by 0.200" before they become flat.
When you combine parallel and series stacking, things get a little more complicated. The coil spring analogy only works well here if you have a symmetrical stack. Suppose you have a stack of two springs pointing up, then two pointing down, then two more pointing up, then two more pointing down. Think of this as two stacks of four springs between the metal plates. You'll have twice the force at a given displacement, and four times the maximum displacement.
When springs are stacked in parallel, you can think of each parallel sub-stack as a single spring having a spring constant equal the n times the spring constant of a single spring, where n is the number of springs in the sub-stack. So, in the above example, you can think instead of a stack of four springs, each with a spring constant equal to twice the constant of a single real spring. Again, this will double the force for a given displacement, and quadruple the maximum displacement.
If you have a parallel/series stack with unequal numbers of springs facing the two directions it gets confusing, so I'm not going to go there.
Regards,
Ray L.