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Another atypical 3-D printing process I’d like to try out: injecting
binder into a powder bed through an array of needles as they are
withdrawn from the powder bed.  Unlike normal powder-bed processes,
this doesn’t require depositing the powder layer by layer or smoothing
each layer.

Basic single-needle process
---------------------------

You have a build chamber filled with loose powder.  In the simplest
form, there is a long hollow hypodermic needle sunk all the way
through the build chamber.  The needle is filled with a fluid binder,
like those used in inkjet powder-bed 3-D printing processes.  It is
withdrawn gradually, during which time the flow of binder through them
is alternately forced by pressure and stopped by a valve.  This
results in selectively depositing binder along the path of the needle,
selectively solidifying the powder bed at the locations where binder
is being extruded.  When the needle is fully withdrawn, it is moved
laterally and inserted in the new location, and then the process is
repeated.

You need to inject enough binder to affect a radius in the powder bed
equal to at least half the hole spacing.  Assuming the powder-bed
material is isotropic, this limits your resolution in the along-needle
axis as well; for example, if the holes are 10 mm apart, you need to
inject enough binder to spread 5 mm in all directions from the
insertion point, which probably means you can’t get much better than
10-mm resolution in the needle-withdrawal direction.  You can probably
control a small valve at 1 kHz or so (reed relays go up to 30 kHz, and
inkjet print head pumps are controlled at some 5–20 kHz), so the limit
on printing speed is then the needle withdrawal speed, unless you’re
withdrawing the needle at 10 m/s or more.  This speed is probably
limited by needle breakage.

Multi-needle variants
---------------------

This can be done with many needles in parallel.  Inserting sixteen
parallel needles, moved as a single unit in a carriage, offers the
possibility of printing sixteen times as fast as the single-needle
process; additionally, if sixteen pixels in one dimension is adequate,
the movement mechanics can support only two orthogonal axes rather
than the three needed by the single-needle process.

More generally, if you have enough needles to cover an entire
dimension of the build chamber, you can use only two orthogonal axes
of movement.  For example, with 2-mm needle spacing and 100
100-mm-long needles, you could print a 200 mm by 100 mm by 1000 mm
print space with a single fast movement axis of a bit over 100 mm
(probably moving the needles) and a single much slower 1000-mm
movement axis (probably moving the powder bed).

If you have a larger number of needles, you can print with only a
single axis of movement; for example, with 20-mm needle spacing and
144 needles of 120 mm each, you could print a 240 mm by 240 mm by
120 mm print volume in a single movement.

I suspect machines with large numbers of needles will tend to be
unreliable, as the larger numbers of needles may experience clogging,
breakage, and plastic flexion more often.

Layered hybrid
--------------

Ultimately the needle length will limit positioning precision, due to
flexions from vibration and random powder-bed anisotropies or
nonuniformities during insertion; reliability, due to needle breakage;
and extrusion rate, if that isn’t limited by valve speed, due to
larger fluid friction in longer needles.

A more complex machine that combines some of the advantages of
traditional powder-bed 3-D printers with the advantages of this design
would deposit a thick layers rather than the usual thin layers, insert
the needles only to the bottom of the new layer, and selectively bind
that layer in 3-D.  This permits the use of shorter needles at nearly
the same printing speed.  Some designs of machine may be able to use
the needle carriage positioning to compact and level the powder bed.

Speed comparison
----------------

RepRap-descended FDM printers have a precision of about 100 μm and a
deposition rate of about 20 mm/sec (times 500 μm times 300 μm,
typically, although this depends on your print settings).  If we
approximate crudely, this amounts to a “voxel rate” of about 3000
voxels per second, but you only pay for the part of the build volume
you’re actually building things in.

This needle-binder-injection printing process can produce about 1000
voxels per second per needle, so with 16 needles, it should be about
16000 voxels per second.  However, this includes the unused parts of
the build volume.  So that variant should be similar to RepRap-style
printers in its productive capacity; the variants with more needles
should be faster.

Inkjet-based powder-bed processes like those pioneered by Open3DP
produce much higher voxel rates, on the order of 100k voxels per
second.

Needle diameter and packing
---------------------------

Narrower needles are more flexible and, barring some kind of active
control, will produce larger positioning errors.  They are also more
prone to breakage and produce more fluid friction.  However, it’s
desirable for the powder-bed particles to be larger than the needle
opening to limit clogging during insertion.

The space occupied by the needles after insertion probably needs to be
occupied by void spaces between particles in the powder bed before
insertion.  This limits the needle diameter to a fraction of the hole
spacing.  This can be partly circumvented, in the designs that need
more than a single insertion to complete a print, by spacing the
needles on the carriage much further apart than the holes.  For
example, printing a 512×512 matrix of 1-mm-apart holes with 16
needles, the needles can be in a line in a 495-mm-long carriage spaced
33 mm apart rather than 1 mm apart, and can be moved laterally by 1 mm
in between insertions rather than 16 mm, so that after printing a
whole 513-mm-long slab of holes, each needle has made 32 adjacent
holes rather than 32 holes spaced 16 mm apart interspersed with the
holes from the other needles.

(Variants: a hexagonal matrix is better than a square matrix, and
staggering the needle insertion order somewhat, so that subsequent
holes are not spatially adjacent, is probably better than making holes
one next to the other.)

Needle design
-------------

To ameliorate the clogging tradeoff, perhaps the needle opening could
be smaller than the bore through the center of the needle, unlike the
usual practice with hypodermic needles.  This would allow the needle
to have the clog-avoidance capability of a very thin needle, but the
stiffness and much of the fluid friction of a much thicker one.

A potential problem is that, once the needle is partly withdrawn, the
empty bore behind it may channel binder being injected into what we
hoped was higher up, allowing the binder to affect a much larger area
than desired.  It might be possible to ameliorate this somewhat by
locating the binder injection ports on the side of the needle, some
distance away from its tip, like the inflation needle for a
basketball, rather than its end.  Binder could still diffuse back into
the channel from the powder bed, but the problem would be less
serious.

Materials
---------

Most of the material systems published by Open3DP should work,
although the viscosity of the liquid binder may be a smaller
consideration than it was for them.  Not only might this reduce the
need for alcohol, it opens up the potential of injecting more viscous
binders such as sodium silicate.

Many of the candidate material systems described in file
`flux-deposition` and file `powder-bed-3d-printing` are also
applicable to this form of 3-D printing.  Some of them will not work
as described because there is no practical solvent to dissolve the
binder in, but perhaps some of them can be made to work by depositing
a soluble precursor (such as calcium sulfate instead of calcium
hydroxide); by including all the reagents and a low-temperature
organic binder such as carboxymethylcellulose in the powder bed, then
injecting simply a solvent such as water, then removing unbound powder
before firing; or by including all the reagents, and injecting a
suitable solvent and/or catalyst to allow them to react.

However, as I’ve envisioned it here, this device can probably finish a
print faster (in minutes), so faster-hardening binder systems may be
worthwhile.  And the needles have the possibility of injecting gases
as well as liquids; two very interesting gases in this context are CO₂
and steam.  CO₂ and heat applied with steam might be able to
accelerate the hardening of slaked lime, which normally takes hours.
And CO₂ injection is well-known as a way to harden sand that is stuck
together with unhardened sodium silicate, acting within a few seconds.
(Afterwards, you can wash off the unhardened sand and sodium silicate
with water.)  As I suggested in file `powder-bed-3d-printing`,
possible alternative sources of CO₂ include CaCO₃ and NaHCO₃.

Steam can deliver a great deal of heat very quickly to a fairly
precisely located position, but of course it heats up the needle to
100°, or more at greater-than-atmospheric presure.  This means that
the needle needs to be withdrawn quickly enough so that conduction
from the needle surface is very small compared to the heat delivered
by the condensing steam.

Particular cements that might be amenable to fast steam hardening
include plaster of Paris, hygroscopic salts (such as NaCl, CaCl₂,
sodium acetate, sodium silicate, or magnesium oxide), and organic gums
and other organic binders (such as carboxymethylcellulose, gelatin,
agar, guar gum, and gum arabic).  Under pressure, steam condensation
can reach high enough temperatures to melt many organic
thermoplastics, but most of them are vulnerable to hydrolysis and must
usually be dried before softening with heat.

Needle injection of nonpolar organic solvents like acetone, methyl
ethyl ketone, ethyl acetate, or alcohol, either in liquid or vapor
form, might be a reasonable way to cement a powder bed containing
soluble organic plastics in powder form as a binder.  It might also be
an effective way to selectively deposit heat within the powder volume
without subjecting fragile plastic molecules to
aggressively-hydrolyzing water.

Either reactive gases like H₂S, Cl₂, or SO₂ or solvents might also be
usable to provoke either hardening chemical reactions, or, in a
reversal, the destruction of a previously solid binder and the
selective conversion of remaining inert fillers into powder.  This
does, however, require that the solid material be sufficiently
yielding and/or porous to get the needles into it in the first place.
Selectively dissolving styrofoam with acetone, ethyl acetate, or
gasoline is one example, though lacking in filler; EVA foam is another
candidate material.