Posted by John Swensen on June 05, 2001 at 18:59:05:
In Reply to: Re: Re: Hirsbrunner steel springs? posted by I'm not sure I understand.... on June 01, 2001 at 23:10:56:
Tapered springs do not lose their spring any easier than parallel (non-tapered) springs, but they can offer some potential advantages (and disadvantages).
When normal, parallel springs are compressed by pushing on them, they push back with a force that is pretty close to proportional to the distance they are compressed (this is the famous Hooke's law that you may remember from an elementary physics course); for example, compress a hypothetical spring an inch, it pushes back with a pound of force; compress it another inch and it pushes back with two pounds of force.
If a coil spring is tapered, the larger diameter end is less stiff than the smaller diameter end (as a result of the geometry), so, initially, the coil tends to compress more at the large end than the small end. As large-diameter coils bottom out, the stiffer, smaller diameter coils begin to compress more, with a net result that the spring pushes back harder at a rate that is greater than linear. If our tapered spring pushed back with one pound for one inch of compression, it might push back with three pounds of force for two inches of compression.
Tapered springs can be nice for vehicle suspensions (soft ride for small bumps, but get stiff to prevent totally bottoming out for really rough roads or fast driving). For piston valves, a tapered spring will be pushing up relatively harder in the down position than will a parallel spring, so that would tend to get a valve moving back up faster than with a parallel spring. On the down side, the tapered spring's lower force with the valve up would be less likely to move a slightly-sluggish valve back up the top of its travel after a very slight deflection.
Tapered springs also have different (and more complex) oscillations than constant-cross-section springs, and some people believe they damp out internal oscillations faster. With the exception of buzzing springs (caused by a two or more coils of a lopsided spring vibrating against each other), spring oscillation is not much of a problem with piston valves.
Dramatically tapered springs can nest as they compress, so the compressed spring height is much less than for a constant-cross-section spring. This might allow for shorter casings in a new design, or might allow larger-diameter spring wire to be used without running out of spring travel. This gives the valve designer more options, but casing height is not a terribly important parameter for tuba design.
Tapered springs are a little more expensive to manufacture than parallel springs, but only slightly more for single-tapered springs (hourglass-shaped springs are another matter, and require much more elaborate tooling). For that matter, clockwork springs are much more involved to wind than coil springs, and require very special tooling.
Finally, a well-designed spring that is properly stress relieved after manufacturing should not ``lose its spring'' in use, particularly for compression springs that just (safely) bottoms out when overloaded.