Alex den Ouden wrote:
> Some guesstimates and some thoughts.
> Firstly, on a *spot* sintering method
> We're talking about making small products of none-too-high
> accuracy. Say, a maximum "printing" volume of an A4 (30*20 cm
> roughly) by 8 cm high. I interpret "none-too-high accuracy" as,
> say, 0.5 mm characteristic length for the finest details (and thus
> also for minimum layer height). That would mean a sintering spot
> of roughly 0.5*0.5*0.5 mm3.
Alex, your estimates on selective solar sintering bring out some of the
tradeoffs very clearly.
The sun's distance from us is about 100 times its diameter. A 50mm focal
length lens pointed at the sun will produce a solar image spot of the
size you mention--- 0.5mm diameter. This is a focal length familiar to
photographers. The widest aperture 50mm camera lens on the market is an
f/1.0. In direct sunlight this lens will collect and focus about 2 watts
of sunlight. (Note that if we try to pre-concentrate the light coming
into the lens, we will only get a wider image spot).
Of course two watts will not sinter much material in a day. We can do
better than f/1.0 since our lens needs only a very narrow field. The
very best we can do is a "full-aperture" lens which collects four times
as much light as f/1.0. This is an absolute and commonsense performance
limit: when a bug at the focal point sees the sun's surface filling his
entire sky, making it any bigger will not make any difference to him!
Researchers at the University of Chicago have virtually reached the
full-aperture limit, but their method would require placing optics very
close to the powder surface. More conventional methods can achieve about
twice the performance of an f/1.0 lens. That leaves us with a 4 watt
Since that still will not sinter much material in a day, the likely
trade off is for much coarser resolution and a heftier power rating.
(The kind of products we will end up making is an open question---even
cinder blocks and sewer pipes are not out of bounds.)
Suppose we pick a 100 watt power rating, that scales us up to a spot of
2.5mm diameter. That sounds awful as a resolution if we are raster
scanning, but it is not so awful as a minimum wall thickness if we are
smoothly tracing the contours of a cross-section.
Layer thickness would be increased proportionately. For any
geometrically similar temperature distribution in the same material the
heat flux density scales inversely to length. So at this coarser
resolution we would expect to be able to sinter the same materials as a
0.5mm-spot/20w laser. Still not too impressive, but the option to scale
up to coarser resolution and larger products is almost open ended.
> Let's suppose a sintering speed of 1
> m/s (rather less than commercial speeds, but consider the hardware
> needed to control the path of the spot). This would mean we'd have
> to heat roughly 250 mm3 (1/4 cm3) of material to sintering
> temperature each second. Specific heat and "semi"-melting heat of
> course depend very much on the material we want to sinter. Once
> we've decided which material we'd like to use for the first
> experiments, we could calculate the number of J/s (i.e. W) needed.
> And from that, given a solar energy density of ... W/m2, the area
> of sunlight to be concentrated into our sintering spot of 1/4 cm2.
Because of the lower flux density a solar sinterer really needs to spend
as much time over each location as is consistent with the effect of
thermal diffusion on spatial resolution. Even at 0.5mm scale I expect
the speeds to be in the millimeters per second. They scale even slower
with a bigger spot size.
> To concentrate sufficient sunlight is not all that difficult, see
> the webpages Jim mentions on parabolic mirrors (composed of a
> multitude of flat mirrors) and on Fresnel lenses. However. We're
> talking about a spot of light focused to about 0.5*0.5 mm2 and a
> facetted parabolic mirror will not be able to produce that
> directly, i.e., without further lenses or an objective. The
> Fresnel lens has another problem. It does not focus the light into
> a focal point, but rather into a focal volume (due to the
> differences in optical path - the "removed" sections of the lens).
> I expect that the focal depth will be well over the required 0.5
> mm for most lenses easily available. So again, we would need a
> concentrating lens or objective. Remember, both the facetted
> mirror and the Fresnel lens are designed for sun "furnaces" in
> which a high energy density over an area of several cm2 is very
> useful while small spots would not do at all.
Your point about Fresnel optics is probably well taken. I don't know.
> The SSS-machine would comprise several sections:
> - energy provision (lens/mirror plus concentrator)
> - spot control (movement, possibly by small galvanometer mirrors)
> - table mechanism (with a stroke equalling the maximum working
> - powder handling unit
> - computer plus software and interface to operate the controlling
> - software to calculate the required sections
> Just a suggestion - would it be an idea to work in polar
> coordinates instead of rectangular? Just think of that discarded
> two-speed CD-player waiting for us to put it out into the sun ....
The spot motions will be so slow that there are a variety of home and
office mechanism that could be "hacked" for this kind of work. Your
polar coordinate approach would certainly simplify the mechanics.
> Secondly, on a *surface* sintering method.
> I've not yet considered this idea in more depth, it came up when
> writing the above. Say we could use a more or less standard
> printing or copying technology to produce a series of masks. And
> then use these masks to sinter the full area of a given layer in
> one go with concentrated sunlight? In fact, something in between
> mask exposure stereolithograpy and selective sintering.
The large research solar furnaces do have the power to sinter an entire
powder layer in one flash. Maybe they will give it a try.
Heliakon Solar Sintering Lab
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