New Scientist - Last Word
contributions by Dr Hugh Hunt

12 September 2007

Q: Highly Sprung: Photographed are six springs taken from various ballpoint pens. Why are they so different from each other? In particular, why do some pens have a "squashed-up" bit in the middle? And is it unusual for someone to dismantle pens compulsively during meetings?


It would seem the different sized springs are because of different-sized pens. There's more than one way to build a moustrap.

A simply truncated helical spring has a open end that gives several design disadvantages: snags easily, misaligns the end (so the spring snakes when compressed), lowers fatigue strength, reduces concentricity of guidance. So to solve these problems designers add extra closed coils. In particularly demanding applications, e.g. valve springs for internal combustion engines, the spring ends can even be ground flat.
In these pen examples the closed coils at the ends are probably mainly stabilising the spring and giving smooth function. The fatigue life is probably a secondary consideration, if at all, in this case as the number of operating cycles is low. The number of end coils is a trade-off between cost of material and function, and different manufacturers will make that differently.
I would guess that the closed coils in the centre are also stabilisers: preventing an snaking (lateral buckling) of the spring. They would achieve this by adding a rotational constraint to the centre of the spring. A similar principle applies to buckling of columns, where lateral constraint, or shorter column, or wider column, increases the load before buckling occurs.
Any lateral buckling of a spring is (a) unsightly, and (b) reduces the consistency of the generated force.
The best designed spring in this batch is the second from right: you will notice that it is not cylindrical but of variable diameter along its length. This is yet another feature to reduce buckling. Springs like these are produced on computer numerical control (CNC) wire formers. Finally, the springs are all symmetrical, as you may have noticed, because orienting a part at assembly adds to assembly time, hence cost. So, even though you can???t see them, the plastic shoulders in the pen/refil will be designed to be the same size on both ends, thus the spring can be assembled in either orientation.
The things we design engineers do to ???delight the customer???, and then you show your appreciation by ripping our products apart in destructive acts of bureaucratic-induced boredom!

Since when does a spring under compression "pull" at one end? All springs push both ways...

A few years ago, I got this bright idea to make my own springs using wire, a propane torch, and a tub of water. Well, I still think it is a good idea, but I concluded that the soft cheap [(steel) (19 ga.)] wire at the local retail outlet is low in carbon, too low to make good steel, such as spring steel or hardened steel. So what kind of wire did each of these springs start as?

It's maybe possible that the closed-coil section in the centre of the spring is an anti-tangling feature. When springs (or similar components) are delivered in large quantities they're prone to tangling together, and it could be that this feature reduces that likelihood.

OK, I have to confess to being an engineer myself. I have worked professionally as a mechanical design engineer and now I teach all aspects of mechanics and structures at tertiary level. The spring question came up a number of years back and I have on numerous occasions posed it to my colleagues, both in the university and in industry. People have come up with all sorts of theories - like those listed above - and some of these people are seriously clever and others are seriously practical. But ultimately everyone is guessing! I'd really like to hear from a manufacturer/designer of springs for pens who can give a definitive answer.
I'd have thought it has to come down to cost - after all, why spend more money making something than is necessary? All the springs shown in the picture work fine, and they are size-for-size interchangeable. I really don't think buckling (snaking) is an issue - the ink cartridge acts as a guide. And fatigue - well, I've never had a pen fail due to spring fatigue, even with the simplest design of spring.
I like the anti-tangling idea that mc said. Now, here are some ideas that my colleagues and I have come up with - perhaps they are silly:
1. that springs are made in a long continuous length with regular close-coiled bits, and they can be cut to whatever length, in multiples of a minumum, so that the spring ends are always close-coiled;
2. that a spring is first made open-coiled and "tuned" to a given stiffness by squashing up a certain number of coils;
3. that a factory somewhere makes these partially-closed-coil springs in huge quantities for other purposes and that they happen to be OK for pens, and the pen manufacturer picks them because they're the cheapest;
4. the close-coils are used to identify a certain "model" of spring - like a bar code - because it's hard to write anything on a spring;
5. that there are patents protecting the simple/best spring designs, so different manufacturers are forced to use different shapes.
Does anyone really know the true answer? I'm desperate to know!
By Hugh Hunt on October 13, 2007 9:33 AM

Hugh Hunt, Dynamics and Vibration Research Group, Department of Engineering, University of Cambridge, UK

(there were several other contributions - see the full New Scientist article at 8 Sept 2007)

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