~The cymatic transitions between regular patterns and
chaotic forms have inspired many visual artists, such as
Alexander Lauterwasser who published a book of
photographs of light reflecting from the surface of water
set in motion by sine waves and music [2]. The light
levels from photographs of sound vibrations in water
were height mapped to generate a sculptural object, titled
48Hz and shown in Figure 3, that can be purchased from
the Shapeways.com digital fabrication community site
[3].
Figure 3. 48Hz - digital fabrication of a cymatic form
A search for "sound" on the Shapeways site returns
CAD models of flutes, pan-pipes and whistles that can
be fabricated in plastic or metal. There is also a windchime that can be fabricated in glass or ceramic to
produce tinkling sounds. These examples demonstrate
the potential to use CAD tools and digital fabrication
services to custom design acoustic forms and musical
objects.
In the lead up to the new Millennium in 2000, Neale
McLachlan proposed a project to construct 200
harmonically tuned bells for a public sculpture called the
Federation Bells, shown in Figure 4. Traditionally bells
are tuned by craftsmen who lathe the thickness profile of
a cast bell. However the high cost offhand crafting led
McLachlan to choose a mechanical process of pressing
sheet metal, which is also very precise and consistent.
Finite mesh simulations of bell shapes were used to
identify the geometric factors that influence the acoustics
and harmonics that included thickness profile, curvature,
conical angle, circumference of the opening rim,
thickness of the rim, and the overall width and height of
the bell [4]. The curvature of the fixed thickness metal
sheets was varied to produce the desired harmonic
structure during fabrication.
Figure 4. CAD designed Federation Bells.
Digitally designed bells have also been fabricated by 3D
printing in stainless steel as part of an experiments in the
Acoustic Sonification of digital datasets [5]. The bells
were constructed from a dataset that measures the acuity
of human spatial hearing in 3D, and fabricated by laser
sintering to produce an irregular bell where the timbre
and pitch of the ringing tone changes with the dataset
that has been mapped onto the shape. These Sonification
bells ring for 1-2 seconds, demonstrating that it is
feasible to digitally fabricate sounding objects.
3. DIGITAL FABRICATION OF A BELL
Digital fabrication places constraints on size, thickness
and level of detail, depending on the material. The
Shapeways.com [6] service constrains stainless steel to a
maximum bounding box of 1000x450x250mm, wall
thickness of 3mm, and detail of 0.6mm. A simple bell
shaped 3D mesh was constructed from graphic
primitives using the Processing open source environment
for programming 3D meshes [7]. An outer hemispherical
shell with diameter 42mm and height 34mm was
algorithmically constructed. This outer shell was then
duplicated, scaled and translated to make an inner shell.
The rims of the outer and inner shells were "stitched"
together with polygons to make a watertight shape. A
handle was added so the bell could be held without being
damped. The digitally constructed bell, shown in Figure
5, was saved as a CAD file in STL format.
Figure 5. Graphic rendering of CAD mesh
File uploads to the Shapeways site are limited to 64MB
and 1 million polygons. This may seem like a lot of
polygons for a simple structure but the process has been
set up to allow more complex structures. The high
19 2013 ICMC
