Re: Where to bend needle springs?
The following is a "cut and paste" from a private forum of which I am a member.....I thought it too good not to share. It's been posted all over the net (on at least three other groups of which I am a member) and is pretty much what you need to know about springs. This is not my original material.
“Elastic limit” is when the metal stops behaving like a rubber band, and obtains a permanent distortion, such that it does not return to its original shape.
Unless woodwind springs are operating close to their elastic limit, they have an increased 'sluggish' feel. This is because the % increase in force needed by the finger, is too great during the travel of the key. A good example of sluggishness is when springs are too short for their diameter. did it on some of the flute G# springs. Buffet have been doing it for years on the key-mounted F#/C# key. Buescher did it on their clarinet side key flat springs. Some makers do it by using a needle spring on the clarinet throat A key. It is common on sax G# levers, clarinet G#/D# key, clarinet alt B/F# key, etc.
This sluggish feel can be worked out mathematically… Spring force=displacement x “stiffness” (inherent in the shape and material). Say the stiffness is 20. If displacement (when the key is operated) is going from 2 to 3, then force goes from 40 to 60 (an increase of 20, i.e. 50% increase over what was the spring’s initial “pre-tension” load of 20.) If displacement goes from say 5 to 6, then force goes from 100 to 120, an increase still of 20, but this is only a 20% increase.
So it is desirable to have a high elastic limit, but without the risk of “brittle failure”.
Also, for many springs, we want as high a force as possible from them before the elastic limit is reached. Extreme examples are springs fighting other springs such as G# lever spring.
For most ferrous alloys, the elastic limit and point of brittle failure can be adjusted, within limits, by heat treatment.
For copper, gold, and silver alloy springs, the elastic limit can be raised by work hardening, but if overdone, it introduces brittle failure.
(Nickel titanium can nave some most intriguing properties, including extremely high elastic limit, and low possibility of brittle failure.)
The stiffness depends on the “stiffness constant” for the particular alloy, and also on the diameter and length of the spring. (Larger diameter and shorter length increase stiffness.
For getting very low sluggishness, ideally we would use a spring with:
1. Low stiffness, achieved by large length to diameter ratio
2. High elastic limit (and lack of brittleness) so extreme bending did not break the spring
3. A lot of initial relaxed-state curve in the spring, so that by the time the spring is placed in the cradle, it is near its elastic limit. (However it must not actually reach its elastic limit during operation.)
I encountered this combination in some old flutes, including Bonneville. The combination is typically achieved in coil springs. (As in the Grafton sax! And certain clarinet throat A and C#/G# springs.) But for technicians, such springs are a nuisance because they leap about.
Unfortunately, for our needle springs:
· 1 is difficult to obtain because it would increase spacing between the posts supporting a key, and increase the weigh of the instrument in the form of longer key barrels.
· 3 is a huge nuisance. Imagine all the springs bent to semicircles, and how that would interfere with putting the keys on. Not to mention pricking fingers.
Therefore compromises are made, usually in the form of thicker springs. This introduces sluggishness. Ideally, if they are thicker, then they should be longer, which is not always possible between pillars. To manage and minimise these design problems, we need the best possible alloys.
What a merry-go-round of design compromises. Some manufactures do it well, while others make unimpressive efforts with shabby results.
Of course there are further design issues related to the shape of the bottom of the cradle, the displacement of the cradle for the key's axis, and whether the spring is pointed. I think these have been discussed fairly recently.
The term you should be using to keep spring diameters as small as possible is "Yield Strength" which is the internal stress (ksi or psi) where permanent distortion will occur.
"Elastic Limit" is a statistically interesting idea, and is usually quoted as lower than yield strength. This shows the stress at which, under repeated loading/unloading cycles, a particular material will after a certain number of cycles tend to fail from fatigue. The Elastic Limit is a measure of how suitable a material is to have a spring made from it. Actual elastic limits are a function of precise metallurgical condition for each alloy, and are represented by a curve. The "elastic limit" given is a point at which some percentage of tested pieces (usually a bell curve distribution) tend to last a certain number of cycles.
For our purposes, a high yield strength and a high elastic limit are both needed. An example of a possible spring material with high yield strength but not high enough elastic limit is a small diameter gage pin or drill blank.
Many materials do not have a flat part of the stress/strain curve. Those materials rupture before elastic deformation ever happens. That would be what a brittle blued spring looks like. For these materials you cannot pre-load the spring by bending it while installing. It breaks before any possible use.
Soft materials (phosphor bronze) lack a high enough modulus of elasticity so you need a larger diameter to get enough force to open/close the key. A soft steel spring has a high enough modulus, but the yield strength is so low that before you can pre-load the spring enough, it deforms before the very first use and is too "soft".
So a proper spring has a high enough modulus, has high enough yield strength that you can get enough force from a smaller diameter, has some elastic limit behavior so you can bend it while installing, overstressing it intentionally to get the intial bend without snapping the springs, AND have a high enough endurance limit so it will not fail prematurely over time.
Believe me, all these things and the quality of manufacturing all come into play when specifying how ww springs are made.