- 1 -
St~ereolithographic Curl Reduction
Background of thcs Invention
1. Cross Reference to Related Applications
This applic<~tion is a divisional of Canadian Patent
Application Seri<~l No. 596,827 filed April 18, 1988 and is
related to Canadian Patent Application Serial Nos. 596,825;
596,850; 596,837; and 596,838.
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2. Field of the Invention
This invention relates generally to improvements in
methods and apparatus for forming three-dimensional objects
from a fluid medium and, more particularly, to a new and
improved stereol~~thography system involving the application of
enhanced data manipulation and lithographic techniques to
production of three-dimensional objects, whereby such objects
can be formed more rapidly, reliably, accurately and
economically, and with reduced stress and curl.
It is common pracl~ice in the production of plastic parts
and the like to first design such a part and then
painstakingly produce a prototype of the part, all involving
considerable time, effort and expense. The design is then
reviewed and, oftentimes, the laborious process is again and
again repeated until the design has been optimized. After
design optimization, the next step is production. Most
production plastic parts are injection molded. Since the
design time and t:oolinc~ costs are very high, plastic parts are
usually only practical in high volume production. While other
processes are availablE_ for the production of plastic parts,
including direct machine work, vacuum-forming and direct
forming, such methods are typically only cost effective for
short run production, <~nd the parts produced are usually
inferior in quality to molded parts.
Very sophisticated techniques have been developed in the
past for generating three-dimensional objects within a fluid
medium which is ~~elect:Lvely cured by beams of radiation
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brought to selective focus at prescribed intersection points
within the three-dimensional volume of the fluid medium.
Typical of such three-dimensional systems are those described
in U.S. Pat. Nos. 4,041,476; 4,078,229; 4,238,840 and
4,288,861. All of these systems rely upon the buildup of
synergistic energization at selected points deep within the
fluid volume, to the exclusion of all other points in the
fluid volume. Unfortunately, however, such three-dimensional
forming systems race a number of problems with regard to
resolution and exposure control. The loss of radiation
intensity and image forming resolution of the focused spots as
the intersection, move deeper into the fluid medium create
rather obvious complex control situations. Absorption,
diffusion, dispersion .and diffraction all contribute to the
difficulties of working deep within the fluid medium on an
economical and rE~liabl~e basis.
In recent years, "stereolithography" systems, such as
those described in U.S. Pat. No. 4,575,330 entitled "Apparatus
For Production Oi= Three-Dimensional Objects By
Stereolithographv" have come into use. Basically,
stereolithographv is a method for automatically building
complex plastic parts :by successively printing cross-sections
of photopolymer (such as liquid plastic) on top of each other
until all of the thin layers are joined together to form a
whole part. With this technology, the parts are literally
grown in a vat oo liquid plastic. This method of fabrication
is extremely
X340890
powerful for quickly reducing design ideas to physical
form and for making prototypes.
PhotocurablE: polymers change from liquid to solid in
the presence of light and their photospeed with ultra
s violet light (UV) is fast enough to make them practical
model building materials. The material that is not
polymerized when a part is made is still usable and
remains in the 'rat a~~ successive parts are made. An
ultraviolet laser generates a small intense spot of UV.
This spot is moved across the liquid surface with a
galvanometer mirror X-Y scanner. The scanner is driven by
computer generated vectors or the like. Precise complex
patterns can be rapidly produced with this technique.
The laser scanner, the photopolymer vat and the
elevator along with a controlling computer combine
together to form a stereolithography apparatus, referred
to as "SLA". An SLA is programmed to automatically make
a plastic part by drawing a cross section at a time, and
building the part. up layer by layer.
Stereolithog~raphy represents an unprecedented way to
quickly make complex or simp)A parts without tooling.
Since this technology depends on using a computer to
generate its cross sectional patterns, there is a natural
data link to CAD/CAM. However, such systems have
encountered diff:iculti~es relating to shrinkage, stress,
curl and other distortions, as well as resolution,
accuracy and difficulties in producing certain object
shapes.
Objects made: using stereolithography tend to distort
when the materials used change density between the liquid
state and the solid state. Density change causes material
shrinkage or expansion, and this generates stress as a
part is formed in a way to "curl" lower layers or adjacent
structure, giving an overall distortion. Materials with
less density change exhibit less curl, but many materials
that are otherwise uses=ul for stereolithography have high
shrinkage. The "curl" effect limits the accuracy of the
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object formation by stereolithography. This invention
provides ways to <~liminate or reduce the "curl" effect.
Material shrinkage is a common problem with polymer
materials, and with fabrication methods (such as plastic
5 molding) that use these materials. However, stereolitho
graphy is a new t:echnolLogy, and the problems associated
with distortion clue to shrinkage have not been widely
addressed. The other main approaches to reducing object
distortion taken by the inventors have been to use
photopolymer materials that have less shrinkage and
produce less stress, or materials that are less rigid and
are less capable of propagating strain.
These other methods are somewhat effective, but have
disadvantages. The earliest way to achieve low shrinkage
in a photopolymer was to use oligomeric materials with
high initial equivalent weights. These materials shrink
less because there is less new bond formation per unit
volume in the photo-initiated polymer reaction. However,
these high equivalent weight materials generally have
higher molecular weights and much higher viscosity at a
given temperature than the lower molecular weight
materials. The high viscosity leads to slow leveling of
the liquid surface. The high viscosity can be overcome by
using increased pror_ess temperature, but higher
temperatures limit= the :Liquid lifetime.
The shrinka<~e in photopolymers is due to the
shrinkage in the formation of the acrylic bonds.
Photopolymers can be made by reacting other functional
groups than acrylics, but they have substantially less
reactivity than the acrylic bonded materials, resulting in
generally inadequate speeds of solid material formation.
Materials that are somewhat flexible when formed
usually produce objects with less distortion, since they
cannot transmit si~rain Long distances through the object.
However, this property _'Ls a disadvantage if the goal is to
make stiff objects. Some materials are soft when formed,
and then harden when post cured with higher levels of
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radiation or other means. These are useful materials for
stereolithography. ThE: whole subject of materials that
produce less distortion, because of the way they make the
transition from liquid to solid, is currently being
studied. However, materials do not currently exist which
produce distortion free parts.
There continues to be a long existing need in the
design and production arts for the capability of rapidly
and reliably moving from the design stage to the prototype
stage and to uli:.imate production, particularly moving
directly from the computer designs for such plastic parts
to virtually immediate prototypes and the facility for
large scale production on an economical and automatic
basis.
Accordingly, those concerned with the development and
production of three-dimensional plastic objects and the
like have long recognized the desirability for further
improvement in more rapid, reliable, economical and
automatic means which would facilitate quickly moving from
a design stage to the prototype stage and to production,
while avoiding the complicated focusing, alignment and
exposure problems of the prior art three-dimensional
production systems. The present invention clearly
fulfills all of these needs.
Summary of the Invention
The present invenition provides a new and improved
stereolithography system for generating a three-
dimensional object by forming successive, adjacent,
cross-sectional laminae. of that object at the face of a
fluid medium capable of altering its physical state in
response to appropriate synergistic stimulation, informa-
tion defining the objcact being specially processed to
reduce curl, stress and distortion, and increase resolu-
tion, strength and accuracy of reproduction, the
successive laminae being automatically integrated as they
are formed to define the desired three-dimensional object.
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Basically, a:nd in general terms, this invention
relates to a system fo:r reducing or eliminating the effect of
"curl" distortion in stereolithography. The term "curl" is
used to describe an ef:Eect similar to that found when applying
coatings to such things as paper. When a sheet is coated with
a substance that shrinlts, it curls up toward the coating.
This is because t:he coating both shrinks and sticks to the
sheet, and exerts a pu:Lling force on the top but not on the
bottom of the sheet. i~ sheet of paper has insufficient
restraining force' to resist the pulling, and most coatings
will curl paper. The same thing happens when a photopolymer
is cured on top of a thin sheet of already cured photo-
polymer.
According to one broad aspect, the invention
provides a stereolithographic apparatus for forming a
three-dimensiona7_ object substantially layer-by-layer out of a
material capable of se:Lective physical transformation upon
exposure to synergistic stimulation comprising: at least one
computer programmed to modify at least a portion of object
defining data, said data being descriptive of a desired
object, and said desired object having first and second
adjacent portion:, to obtain tailored object defining data,
specifying forming said first and second portions spaced from
each other, and f=orming rivets to attach said first and second
portions, to reduce pu:Lling effects otherwise transmitted
along said first portion; a container of said material; a
source of said synergistic stimulation; means for successively
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forming layers of said material; and means for receiving said
tailored object defining data and for selectively exposing
said layers of s<~id material to said synergistic stimulation
from said source in accordance with said tailored object
defining data to form said three-dimensional object
substantially layer-by-layer.
In a presently preferred embodiment, by way of
example and not necessarily by way of limitation, the present
invention harnes:~es the principles of computer generated
graphics in comb:Lnatio:n with stereolithography, i.e., the
application of lithographic techniques to the production of
three-dimensiona:L obje~~ts, to simultaneously execute computer
aided design (CAIN) and computer aided manufacturing (CAM) in
producing three-dimensional objects directly from computer
instructions. The invention can be applied for the purposes
of sculpturing models <~nd prototypes in a design phase of
product development, o:r as a manufacturing system, or even as
a pure art form.
The data base of a CAD system can take several
forms. One form consists of representing the surface of an
object as a mesh of triangles. These triangles completely
form the inner and outE=r surfaces of the object. This CAD
representation commonly also includes a unit length normal
vector for each t:riang:Le . The normal points away from the
solid which the t:riang:Le is bounding.
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"Stereolitho~3raphy" is a method and apparatus for
making solid objE~cts b:y successively "printing" thin layers of
a curable material, e.g., a W curable material, one on top of
the other. A programmed movable spot beam of UV light shining
on a surface or 7_ayer of W curable
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liquid is used to form a solid cross-section of the object
at the surface of the liquid. The object is then moved,
in a programmed manner, away from the liquid surface by
the thickness of one layer, and the next cross-section is
then formed and adhered to the immediately preceding layer
defining the objects. This process is continued until the
entire object is formed"
Essentially all types of object forms can be created
with the technique of the present invention. Complex
forms are more ea~:ily cheated by using the functions of a
computer to help generate the programmed commands and to
then send the program signals to the stereolithographic
object forming subsystem.
Of course, it.will be appreciated that other forms of
appropriate synergistic stimulation for a curable fluid
medium, such as particle bombardment (electron beams and
the like), chemical reactions by spraying materials
through a mask or by ink jets, or impinging radiation
other than ultraviolet 7Light, may be used in the practice
of the invention without departing from the spirit and
scope of the invention.
Stereolithography is a three-dimensional printing
process which users a moving laser beam to build parts by
solidifying successive layers of liquid plastic. This
method enables a designer to create a design on a CAD
system and build a.n accurate plastic model in a few hours .
In a presently preferred embodiment, by way of example and
not necessarily by way of limitation, the stereolitho-
graphic process is composed of the following steps.
First, the solid model is designed in the normal way
on the CAD system, without specific reference to the
stereolithographi~~ process. A copy of the model is made
for stereolithographic processing. In accordance with the
invention, as subsequEantly described in more detail,
objects can be designed with structural configurations
that reduce stress and curl in the ultimately formed
object.
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In accordance with the invention, when a stereo-
lithography line which i.s part of a vertical or horizontal
formation is drawn with breaks in the line instead of a
solid line, a/k/a the "dashed line" technique, the pulling
force normally tra.nsmitt:ed along the vector is eliminated,
and the curl effects is reduced. When a stereolithography
line which is part of a vertical or horizontal formation
is drawn with bends in the line instead of a straight
line, a/k/a the "bent-line" technique, the pulling force
normally transmiti_ed along the vector is reduced, and the
curl effect is reduced. When a stereolithography line
which is part of a vertical or horizontal formation is
drawn so that it does not adhere directly to the line
below or beside it, but. is attached, after it is formed
with a secondary structure, a/k/a the "secondary
structure" technique, the pulling force down the vector is
eliminated, the bending moment on adjacent lines is
reduced, and the curl effect is greatly reduced. When a
stereolithography line which is part of a vertical or
horizontal formation is drawn so that it does not adhere
directly to the line below or beside it until the material
is substantially reacted, a/k/a the "multi-pass"
technique, the pulling force down the vector is reduced,
the structure is more rigid so it can resist deformation,
and the curl effect is greatly reduced.
By way of example, and not necessarily by way of
limitation, the invention contemplates ways to draw rails
with reduced curl; 1) a dashed line, to provide isolation
of the pulling effect, 2) a line with short segments at
angles to each other t.o isolate the pulling effect, 3)'
lines that do not adhere to the layer below, to eliminate
the pulling effeci~, but which are held together with other
structure, and 4) lines that are as fully reacted as
possible before t:he exposure that extends the gel point
(and adhesion) to the lower layer is applied.
Model preparation for stereolithography involves
selecting the opi~imum orientation, adding supports, and
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selecting the operating parameters of the stereolitho-
graphy system. The optimum orientation will (1) enable
the object to drain, (2) have the least number of
unsupported surfaces, (3) optimize important surfaces, and
(4) enable the object to fit in the resin vat. Supports
must be added to secures unattached sections and for other
purposes; a CAD library of supports can be prepared for
this purpose. The stereolithography operating parameters
include selection of t:he model scale and layer (slice)
thickness.
The surface of thca solid model is then divided into
triangles, typic<illy "PHIGS". A triangle is the least
complex polygon for vector calculations. The more
triangles formed,, the better the surface resolution and
hence the more accurate: th_ formed object with respect to
the CAD design
Data points representing the triangle coordinates are
then transmitted to the stereolithographic system via
appropriate network communications. The software of the
stereolithographic sy;~tem then slices the triangular
sections horizons=ally (X-Y plane) at the selected layer
thickness.
The stereolithographic unit (SLA) next calculates the
section boundary, hatch, and horizontal surface (skin)
vectors. Hatch vector~> consist of cross-hatching between
the boundary vectors. Several styles are available. Skin
vectors, which a;ce traced at high speed and with a large
overlap, form the outside horizontal surfaces of the
object. Interior horizontal areas, those within top and
bottom skins, are not :Filled in other than by cross-hatch
vectors.
The SLA there form_=; the object one horizontal layer at
a time by moving the ultraviolet beam of a helium-cadmium
laser across the surface of a photocurable resin and
solidifying the liquid where it strikes. Absorption in
the resin prevents the laser light from penetrating deeply
and allows a thin layer to be formed. Each layer is
~~~ ~~9(~
comprised of vectors which are drawn in the following
order: 'border, h;~tch, .and surface.
TY.e first layer that is drawn by the SLA adheres to
a horizontal platform located just below the liquid
surface. This platform is attached to an elevator which
then lowers its vE~rtica:Lly under computer control. After
drawing a layer, the platform dips several millimeters
into the liquid t.o coat. the previously cured layer with
fresh liquid, them rises up a smaller distance leaving a
thin film of liquid from which the second layer will be
formed. After a pause: to allow the liquid surface to
flatten out, the next layer is drawn. Since the resin has
adhesive properties, t:he second layer becomes firmly
attached to the first. This process is repeated until all
the layers have been drawn and the entire three-
dimensional objeci~ is formed. Normally, the bottom 0.25
inch or so of the object is a support structure on which
the desired part is built. Resin that has not been
exposed to light remains in the vat to be used for the
next part. There is very little waste of material.
Post process p.ng involves heating the formed object to
remove excess resin, ultraviolet or heat curing to com-
plete polymerization, and removing supports. Additional
processing, including ~~anding and assembly into working
models, may also he performed.
The stereol:ithogr.aphic apparatus of the present
invention has many advantages over currently used
apparatus for producing plastic objects. The apparatus of
the present invent=ion avoids the need of producing design
layouts and drawings, <~nd of producing tooling drawings
and tooling. The designer can work directly with the
computer and a stereo-lithographic device, and when he is
satisfied with the deaign as displayed on the output
screen of the computer, he can fabricate a part for direct
examination. If the design has to be modified, it can be
easily done through th<~ computer, and then another part
can be made to verify that the change was correct. If the
.~,: ,,
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12
design calls for several parts with interacting design
parameters, the method of the invention becomes even more
useful because of all of the part designs can be quickly
changed and made again so that the total assembly can be
made and examined, repeatedly if necessary.
After the design is complete, part production can
begin immediately, so i;.hat the weeks and months between
design and producaion are avoided. Ultimate production
rates and parts cost; should be similar to current
injection moldings Costa for short run production, with
even lower labor co=;ts than those associated with
injection molding. Injection molding is economical only
when large numbers oi: identical parts are required.
Stereolithography is useful for short run production
because the need for tooling is eliminated and production
set-up time is minimal.. Likewise, design changes and
custom parts are easi_Ly provided using the technique.
Because of the ease of making parts, stereolithography can
allow plastic parts to be used in many places where metal
or other material parts are now used. Moreover, it allows
plastic models of objects to be quickly and economically
provided, prior i.o the decision to make more expensive
metal or other material parts.
Hence, the stereolithographic apparatus of the
present invention satisfies a long existing need for a CAD
and CAM system c~~pable of rapidly, reliably, accurately
and economicall;r designing and fabricating three
dimensional plastic parts and the like.
The above and other objects and advantages of this
invention will be apparent from the following more
detailed description when taken in conjunction with the
accompanying drawings of illustrative embodiments.
Brief Description of the Drawings
FIG. 1 illustrates rail formation with
stereolithography;
FIG. 2 illustrates reactive region detail:
13
FIG. 3 is a perspective view of a dashed line rail;
FIG. 4 is a perspective view of a short segment or
bent line rail;
FIG. 5a is an end elevational view of a rail with no
adhesion except for the attaching secondary structure;
FIG. 5b is a perspective view of a rail with no
adhesion except for the attaching secondary structure;
FIG. 6 is a rail held together with rivets;
FIG. 7 is a quarter cylinder;
FIG. 8 is a flow chart illustrating the software
architecture of a suitable stereolithography system in
which the present invention may be produced;
FIG. 9 is <in overall block diagram of a stereo
lithography system for the practice of the present
invention;
FIGS. 10 and 11 are flow charts illustrating the
basic concepts employed in practicing the method of
stereolithography of the present invention;
FIG. 12 is ~~ combined block diagram, schematic and
elevational sectional view of a system suitable for
practicing the invention;
FIG. 13 is an elevational sectional view of a second
embodiment of a stereolithography system for the practice
of the invention;
FIG. 14a ill.ustrat:es the pulling effect of one line
on another line below i.t;
FIG. 14b illustrates the lines of FIG. 14a, which are
curled upwards because of the pulling effect;
FIG. 15a ill_ustrat=es two already-cured lines with a
gap of uncured resin between them;
FIG. 15b illustrates the countervailing forces
exerted when the uncured resin in the gap of FIG. 15a is
cured;
FIG. 16a illustrates the cure depth achieved when a
particular expeo=_>ure is delivered in a single pass;
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14
FIG. 16b i17_ustrat~es the cure depth achieved through
the lensing effect, when the exposure of FIG. 16a is
delivered through multiple passes;
FIG. 17a ill_ustrat=es the problem of downward bending
in the multipass technique;
FIG. 17b illustrates a possible solution to the
problem of FIG. 17a, lby increasing the exposure on the
early passes of t:he multipass technique;
FIG. 18 is a sample report showing REDRAW commands in
the .L file;
FIG. 19 is a sample report showing REDRAW commands in
the .R file;
FIG. 20 is a sample report showing REDRAW default
parameters in the .PRM file;
FIG. 21a illustrates vectors spanning a cross section
of an object;
FIG. 21b Illustrates the impact of finite jumping
time on the drawing of the vectors of FIG. 21a;
FIG. 21c illustrates the use of the zig-zag technique
to alleviate the problem of FIG. 21b;
FIG. 22a shows sid view of stacked lines from
different layers;
FIG. 22b il_Lustra'tes the use of a riveted secondary
structure to attach adjacent lines of a particular layer;
FIG. 22c illustrates a side view of the riveted
secondary structu re of FIG. 22b;
FIG. 22d ill.ustrat:es the use of rivets to attach the
secondary structures from adjacent stacked layers;
FIG. 22e illustrates a top view of the riveted
secondary structure of FIG. 22b;
FIG. 23a illustrates rivets, where the diameter of
the rivets is much smaller than the width of the lines;
FIG. 23b illustrates rivets, where the diameter of
the rivets is larger than the rivets of FIG. 23a;
FIG. 23c illustrates rivets, where the diameter of
the rivets is larger than the width of the lines;
. . ,~,;. ,r . : , ; :~
i,. ~;;
1~~~89~
FIG. 24a is ~~ side view of stacked lines connected by
rivets;
FIG. 24b is a top view of oversized rivets;
FIG. 24c is a top view of offset rivets;
5 FIG. 24d is a top view of rivets used to connect
stacked support lines;
FIG. 25a illustrates a side view of secondary
structure used to connect adjacent lines;
FIG. 25b is a top view of the structure of FIG. 25a
10 showing rivets used to connect stacked secondary
structure;
FIG. 25c is a side view of the secondary structure
and rivets of FIG. 25b;
FIG. 26a shows a part made according to the dashed
15 line technique;
FIG. 26b shows a part made according to the bent line
technique;
FIG. 26c shows a part made according to the secondary
structure technique;
FIG. 27a shows the use of bricks and mortar with the
dashed line technique;
FIG. 27b show the cure sequence for the bricks and
mortar variant of the dlashed line technique;
FIG. 27c shows the. cure sequence for another variant
of the dashed line technque;
FIG. 27d shows the: cure sequence for a third variant
of the dashed line technique;
FIG. 27e show the cure for a fourth variant of the
dashed line technique;
FIG. 28a shows the: relieving of stress from the bent
line technique;
FIG. 28b shows the bent line technique with a gap
size of 40-300 mi.l;
FIG. 28c shows the bent line technique with a smaller
gap size than in FIG. :?8b;
FIG. 28d shows a 'variant of the bent line technique
having a triangular shape;
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FIG. 28e shows another variant of the bent line
technique;
FIG. 28i= show; the angles associated with the
variant of FIG. 28e;
FIG. 28c~ shows a third variant of the bent line
technique;
FIG. 28h shows a bricks and mortar variant of the
bent line technique;
FIG. 28i show; the cure sequence for the variant of
FIG. 28h;
FIG. 28j shows the cure sequence for another bricks
and mortar variant: of the bent line technique;
FIG. 29~~ illustrates an undistorted cantilevered
section;
FIG. 29b illu:~trates a distorted cantilevered
section;
FIG. 29c: illu:~trates a top view of vectors that
contribute to adhesion :in a cantilevered section built to
reduce curl;
FIG. 30 is a sample report showing the specification
of critical areas in a critical .BOX file;
FIG. 31 is a sample report showing the specification
of RIVET commands in thE~ .L file;
FIG. 32 is a :ample report showing the specification
of default RIVET parameters in the .PRM file;
FIG. 33 is a sample report showing a .V file;
FIG. 34a is a side view of a quarter cylinder before
the effects of upward curl have been introduced;
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~340$gp
FIG. 34b is a side view of a distorted quarter
cylinder;
FIG. 34c is a top view of a layer of the quarter
cylinder;
FIG. 34d is a top view of the layer of FIG. 34c
showing the effects of horizontal curl;
FIG. 35a is a side view of a quarter cylinder
showing its upper, support, post, and base layers;
FIG. 35b is a top view of a quarter cylinder showing
the inner and outer concentric circularly curved rails;
FIG. 35c: is a top view of a quarter cylinder showing
the angle subtended by i~he curved rails;
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17
FIG. 35d is top view of a quarter cylinder showing
a
the inner and oui~er rails connected by cross-hatch;
FIG. 35e is top view of a quarter cylinder showing
a
the use of to connect the stacked cross hatch
rivets of
FIG. 35d;
FIG. 35f is perspective view of a quarter cylinder;
a
FIG. 35g is a side view of a distorted quarter
cylinder illustrat ing 'the definition of curl factor;
FIG. 36a i~> a side view of a part having slotted
sections;
FIG. 36b is frontal view of the part of FIG. 36a;
a
FIG. 36c is top view of the part of FIG. 36a; and
a
FIG. 36d is a side view of the part of FIG. 36a
showing t he s of sneer.
effect
Description of the Preferred Embodiment
The present invention is an improved stereolitho-
graphic method and apparatus of the type for building up
successive layers of photopolymer, where each layer is
formed by drawing a series of vectors with a light pencil
on the liquid surface that defines each cross-section of
the object, wherein the improvement comprises reducing or
eliminating cur:L. A number of techniques have been
examined by building rails that are a series of layers of
straight lines, and examining the resulting distortion.
The force, or stress, in this case is generated at the
interface where the photopolymer cures (and shrinks) and
adheres to the layer below, as shown in the following
diagram.
Referring now to the drawings and particularly to
FIGS. 1 and 2 thereof, light pencil 3 moves across liquid
2 in the direction shown, converting it to solid 1. This
forms a solid top layer 4, that adheres to lower layer 5.
The term light pencil refers to synergistic stimulation
such as UV light which impinges on the surface of the
liquid photopolymer.
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In the expanded diagram (FIG. 2), the light from the
pencil is shown ps:netrat=ing into the photopolymer, forming
reactive region 6. :~olid/liquid interface 9, or gel
point, is indicated. However, the polymeric state of the
material in the active region is more complex. All of the
material in the region is reacting. The material at the
upper left of the region is most reacted, because the
light is most intense and the pencil has been in this area
the most time. The material at the lower right, just
above the lower layer, is the least reacted, because the
light is the lea st intense and the pencil has been in this
area the least time.
As the material reacts, it changes density. This
discussion assumes that the density change causes
shrinkage, but s~xpans:Lon is also possible. Reactive
region 6 acts as a complex shrinking cylinder, and
shrinkage 7 is toward t=he interior of this cylinder. In
the lower left area of the reactive region 6, the new
solid material of top layer 4 attaches to the lower layer
5 with adhesion 8.
When a layE~r forms without attaching to a layer
below, there is no "curl" distortion because as the
reactive region shrinks, it is only attached to (and
constrained by) p_ts own layer. In achieving this single
layer "adhesion", the layer is placed in compression, but
there is no bending moment generated. This is because all
of the horizontal. forces from the shrinking reaction have
no firm base to grip other than the just formed layer, and
the new solid reacting material is allowed to displace
slightly to the 7~_eft a;~ it is formed.
However, when a layer is formed and simultaneously
attached to a lower layer, the portion of the attached
material in the reactive region is still shrinking. This
shrinking is now coupled to the rest of the rail two ways:
a. The mat=erial directly over the adhesion point is
shrinking. Since this shrinking material now can use the
top of the lower layer. as a firm base, it puts compres-
19
sional stress into this; base. As the new layer is formed,
all of the top of the previous (lower) layer is com-
presse3, and this cauaas a bending moment in the lower
layer.
b. The reactive region shrinks, and is attached to
the now forming top layer. This region is pulled to the
left, as when an unattached layer is formed. However, the
reactive region is now also attached to the lower layer,
so that it resists the movement to the left, and so the
shrinking also gulls vthe top layer to the right. This
causes a bending moment in the rail.
It should be noted that there are two types of
shrinkage with photopolymer reactions. The first
mechanism is that the :polymer shrinks due to polymer band
formation. The :result is that the solid polymer state is
more dense than 'the liquid pre-polymer state, and hence a
given amount of polymer takes up less volume than the
pre-polymer that. it was formed from. This shrinkage
mechanism is essentially instantaneous compared to the
time taken to generate laser patterns (i.e., less than a
microsecond).
The second mechanism is a thermal effect. Photo-
polymers are exathermi.c, so they give off heat when they
react. This heat. raises the temperature of the polymer,
and it expands upon formation. The subsequent cooling and
shrinkage has the same effect as the shrinkage due to the
change of state, except it is slower, and is long compared
to the time taken to generate laser patterns (seconds).
For the current photopolymers worked with, the change of
state mechanism is the larger of the two types of
shrinkage.
A typica)_ example of a stereolithographic
photopolymer is DeSoi~o SLR800 stereolithography resin,
made by DeSoto, Inc. , 1700 South Mt. Prospect Road, Des
Plaines, Illinois 600:L8.
20
Methods to Control Curl
In accordance with the invention, when a stereolitho-
graphy line which is part of a vertical or horizontal
formation is drawn with breaks in the line instead of a
solid line, a/k/a the "clashed line" technique, the pulling
force normally transmitted along the vector is eliminated,
and the curl effe~~t is reduced. When a stereolithography
line which is part of a vertical or horizontal formation
is drawn with bends in the line instead of a straight
line, a/k/a the "bent line" technique, the pulling force
normally transmitted along the vector is reduced, and the
curl effect is reduced. When a stereolithography line
which is part of a vertical or horizontal formation is
drawn so that it does not adhere directly to the line
below or beside it, but. is attached, after it is formed,
with a secondary structure, a/k/a the "secondary
structure" technique, the pulling force down the vector is
eliminated, the bending moment on the adjacent lines is
reduced, and the curl Effect is greatly reduced. When a
stereolithography line which is part of a vertical or
horizontal formation is drawn s~ that it does not adhere
directly to the line beJLow or beside it until the material
is substantially reacted, a/k/a the "multi-pass"
technique, the pulling force down the vector is reduced,
and the structure is more rigid so it can resist curl.
The methods to control curl depend on building parts
in ways so that: the effects (a) and (b) above are
eliminated or reduced. There are several simple examples
of ways to draw rails with reduced curl; 1) a dashed line,
to provide isolation of the pulling effect, 2) a line with
short segments air angles to each other, to isolate the
pulling effect, 3) lines that do not adhere to the layer
below, to eliminate the pulling effect, but which are held
together with other structure, and 4) lines that~are as
fully reacted as possible before the exposure that extends
the gel point (and adhesion) to the lower layer is
applied. These techniques are referred to respectively as
21
the dashed line, bent) line, secondary structure, and
multi-pass techniques. These basic rails are further
described hereinafter.
A rail made with a dashed line is illustrated in
FIG. 3. FIG. 4 shows a rail made with short segments at
angles to each other. hIGS. 5a and 5b illustrates a rail
made with lines that do not adhere to the layer below but
which are held together with other structure.
To understand how t:o react lines as fully as possible
prior to their adhering to the line below, requires an
under-standing of the solid formation process. The amount
of reaction tame 'taken to form a layer in
stereolithography depends on the layer thickness, the
adsorption rate of the incident reactant energy, and the
reactant rate of 'the material.
The thickness response curve to form a solid film on
a liquid surface. with incident reactant energy is a
logarithmic function. The solid material at the
liquid/solid interface is just at the gel point, and the
solid material at the surface is the most reacted. After
a film is formed, subsequent exposures increase the
reaction at the surface:, but extend the thickness of the
film less and less.
An effective way to control curl is to choose a layer
thickness that is large enough so that the bulk of the new
top layer is highly cured (reacted). It is even more
effective to curs' this layer with multiple exposures so
that only the last few exposures achieve the adhesion.
In this case, most of the material in the reactive region
has already chang~sd density before adhesion occurs. Also,
the new top layer and the lower layers are more fully
cured and more able to resist deformation.
In a presently preferred embodiment of the invention,
a rail is built with two parallel walls close to each
other, with exposure small enough so the layers do not
adhere, and the walls are connected with short perpen-
dicular vectors that a:re exposed to a depth great enough
13~U89U
- 22 -
so that the layers adhere at these points and hold the
structure togethe=r .
In this method, t=he vectors for the two walls are both
grown for each layer, .and the adhesion is achieved by using
additional exposure for the connecting vectors.
This concepi~ has :been generalized as a part building
method. In this method, a part is designed with an inner wall
and an outer wal:L, and with connecting webs.
FIG. 7 of the drawings show this part. This building
style is referred to as "riveting", where the higher exposed
connecting vecto~_s are called rivets.
In using th:Ls building style, when the inner and outer
walls are exposed enough to cause adhesion, the amount of curl
of the part depends on the amount of exposure beyond that
required to make the polymer depth equal to the layer depth.
That is, the morf~ the 'walls are exposed beyond the point where
the layer touche:~ the layer below, the more the part curls.
This is, in fact, the basis of a standard "curl test" for
different resins described in more detail further on in this
application. According to this test, a series of these
quarter cylinder; are built at different exposures, and the
curl versus exposure is plotted. Using this test, it has been
discovered that different resin formulas curl differently, and
this allows the selection of the best resins.
Also note t:zat the methods described herein to reduce
curl are also ap;~licable to the technique of building parts by
fusing metal or ;plastic powder with a heat generating laser.
1340890
- 23 -
In fact, the powder fusing technique may be even more
susceptible to curl than by building with photopolymers, and
the curl reduction techniques are needed even more with this
method.
Note also treat with the general building algorithms as
set forth in the previously described related co-pending
Canadian application, 3.N. 596,825, a part can be designed by
CAD, sliced using X-ax_Ls hatch and 60 degree and 120 degree
hatch, and with ~~n appropriate MIA specified to produce near
radial cross-hatch. I:fthis part is then exposed with large
exposure for cross-hatch and lower exposure for the
boundaries, then the part building method described in the
paragraphs above has been implemented via CAD design. FIG. 8
of the drawings illustrates an overall stereolithography
system suitable for this purpose which is described in more
detail in the above-re:Eerenced co-pending application.
Variations of the basic invention are possible, such as
the broken lines or bent lines can be "filled" with lower
exposure dashed .Lines to even out the surface structure.
Dashed or broken lines can be used as the support lines that
do not adhere directly to the line below or next to them. The
unsupported liner are connected to the support lines with
small additional structure lines. The secondary structure to
attach unsupportf~d lines can be "rivets" of higher exposure on
top of these lin~ss to connect them to the lines below.
Thinner layers can be formed by adjusting the absorption
of the material ao that a given exposure produces a thinner
~3~0890
- 24 -
film, while the materi<~l near the top surface is still almost
fully reacted.
The various methods described to control curl are
additive. That i.s, if two or more of them are combined, the
curl is reduced even further. Also, there are many other
possible variations of the described techniques.
Referring now to the drawings, and particularly to FIG. 9
of the drawings, there is shown a block diagram of an overall
stereolithograph~~ systfsm suitable for practicing the present
invention. A CAI) generator 2 and appropriate interface 3
provide a data de:scripi:.ion of the object to be formed,
typically in PHIGS format, via network communication such as
ETHERNET or the .Like to an interface computer 4 where the
object data is manipulated to optimize the data and provide
output vectors which reduce stress, curl and distortion, and
increase resolution, strength, accuracy, speed and economy of
reproduction, even for rather difficult and complex object
shapes. The intESrface computer 4 generates layer vector data
by successively :dicing, varying layer thickness, rounding
polygon vertices, filling, generating flat skins, near-flat
skins, up-facing and down-facing skins, scaling,
cross-hatching, offsetting vectors and ordering of vectors.
The vector data and parameters from computer 4 are
directed to a controller subsystem 5 for operating the system
stereolithograph~y laser, mirrors, elevator and the like.
25
FIGS. 10 and 11 are flow charts illustrating the
basic system of the present invention for generating
three-dimensiona:L objects by means of stereolithography.
Many liquid state chemicals are known which can be
induced to change to solid state polymer plastic by
irradiation with ultraviolet light (UV) or other forms of
synergistic stimulation such as electron beams, visible or
invisible light, reactive chemicals applied by ink jet or
via a suitable mask. UV curable chemicals are currently
used as ink for high speed printing, in processes of
coating of paper and other materials, as adhesives, and in
other specialty <~reas.
Lithography is the art of reproducing graphic
objects, using various techniques. Modern examples
include photographic reproduction, xerography, and
microlithography, as is used in the production of
microelectronic circuit boards. Computer generated
graphics displayed on .a plotter or a cathode ray tube are
also forms of lithography, where the image is a picture of
a computer coded object.
Computer aided design (CAD) and computer aided
manufacturing (CAM) are techniques that apply the
capabilities of comput=ers to the processes of designing
and manufacturing. A typical example of CAD is in the
area of electronic printed circuit design, where a
computer and plotter draw the design of a printed circuit
board, given the design parameters as computer data input.
A typical exam~~le of CAM is a numerically controlled
milling machine, where a computer and a milling machine
produce metal parts, given the proper programming
instructions. Both CAD and CAM are important and are
rapidly growing technologies.
A prime object of the present invention is to harness
the principles of computer generated graphics, combined
with the use of UV curable plastic and the like, to
simultaneously e~xecutE~ CAD and CAM, and to produce three-
imensional obje~~ts directly from computer instructions.
13~o~9f~
- 26 -
This invention, referred to as stereolithography, can be used
to sculpture models and prototypes in a design phase of
product development, or as a manufacturing device, or even as
an art form. The: present invention enhances the developments
in stereolithography set forth in U.S. Patent No. 4,575,330,
issued March 11, 1986, to Charles W. Hull, one of the
inventors herein.
Referring now more specifically to FIG. 10 of the
drawings, the stereolithographic method is broadly outlined.
Step 8 calls for gener<~tion of CAD or other data, typically in
digital form, representing a three-dimensional object to be
formed by the sy:~tem. This CAD data usually defines surfaces
in polygon format., triangles and normals perpendicular to the
planes of those triangles, e.g., for slope indications, being
presently preferred, a:nd in a presently preferred embodiment
of the invention conforms to the Programmer's Hierarchial
Interactive Graphics System (PHIGS) now adapted as an ANSI
standard. This standard is described, by way of example, in
the publication "Understanding PHIGS", published by Template,
Megatek Corp., S<~n Diego, California.
In Step 9, l~he PHIGS data or its equivalent is converted,
in accordance wii~h the invention, by a unique conversion
system to a modi:Fied data base for driving the
stereolithography output system in forming three-dimensional
objects. In this regard, information defining the object is
specially processed to reduce stress, curl and distortion, and
increase resolution, strength and accuracy of reproduction.
- 26a -
Step 10 in FIG. 10 calls for the generation of individual
solid laminae representing cross-sections of a
three-dimensiona7_ object to be formed. Step 11 combines the
successively formed adjacent laminae to form the desired
three-dimensiona=~. object which has been programmed into the
system for selective caring.
~3~9890
27
Hence, the stereolithographic system of the present
invention generates three-dimensional objects by creating
a cros=-sectional. pattern of the object to be formed at a
selected surface of a fluid medium, e.g., a UV curable
liquid or the like, capable of altering its physical state
in response to ap~~ropriate synergistic stimulation such as
impinging radiation, electron beam or other particle
bombardment, or applied chemicals (as by ink jet or
spraying over ~~ mas;k adjacent the fluid surface),
successive adjacent laminae, representing corresponding
successive adjaccant cross-sections of the object, being
automatically formed and integrated together to provide a
step-wise laminar or i:hin layer buildup of the object,
whereby a three-dimen=;ional object is formed and drawn
from a substanti<~lly planar or sheet-like surface of the
fluid medium dur~_ng ths~ forming process.
The aforede:~cribed technique illustrated in FIG. 10
is more specifically outlined in the flow chart of FIG.
11, where again Step 8 calls for generation of CAD or
other.data, typically in digital form, representing a
three-dimensiona:L object to be formed by the system.
Again, in Step 9,. the 1?HIGS data is converted by a unique
conversion system to a modified data base for driving the
stereolithograph y output system in forming
three-dimensional objects. Step 12 calls for containing
a fluid medium capable of solidification in response to
prescribed reaci~ive :stimulation. Step 13 calls for
application of that stimulation as a graphic pattern, in
response to data output from the computer 4 in FIG. 9, at
a designated flu:~d suri_ace to form thin, solid, individual
layers at that surface, each layer representing an
adjacent cross-section of a three-dimensional object to be
produced. In th~~ practical application of the invention,
each lamina will be a thin lamina, but thick enough to be
adequately cohesive in forming the cross-section and
adhering to the adjacent laminae defining other
cross-sections of the object being formed.
28
Step 14 in FIG. 13 calls for superimposing successive
adjacent layers or laminae on each other as they are
formed, to integrate t:he various layers and define the
desired three-dimensional object. In the normal practice
of the invention, as the fluid medium cures and solid
material forms to define one lamina, that lamina is moved
away from the working surface of the fluid medium and the
next lamina is formed in the new liquid which replaces the
previously formed lamina, so that each successive lamina
is superimposed and -integral with (by virtue of the
natural adhesive properties of the cured fluid medium) all
of the other cross-sectional laminae. Of course, as
previously indic~~ted, the present invention also deals
with the problems. posedl in transitioning between vertical
and horizontal.
The process of producing such cross-sectional laminae
is repeated over and over again until the entire three-
dimensional object has been formed. The object is then
removed and the system is ready to produce another object
which may be identical to the previous object or may be an
entirely new of>ject formed by changing the program
controlling the ~~tereo~Lithographic system.
FIGS. 12-1_~ of the drawings illustrate various
apparatus suitable for implementing the stereolithographic
methods illustrated and described by the systems and flow
charts of FIGS . :L - 3 .
As previously indicated, "Stereolithography" is a
method and apparatus for making solid objects by
successively "printing" thin layers of a curable material,
e.g., a UV curable material, one on top of the other. A
programmable movable spot beam of UV light shining on a
surface or layer of UV curable liquid is used to form a
solid cross-section of the object at the surface of the
liquid. The object is then moved, in a programmed manner,
away from the liquid surface by the thickness of one layer
and the next cross-section is then formed and adhered to
~34~890
29
the immediately preceding layer defining the object. This
process is continued until the entire abject is formed.
Essentially all types of object forms can be created
with the technique of the present invention. Complex
forms are more easily created by using the functions of a
computer to help generate the programmed commands and to
then send the program signals to the stereolithographic
object forming subsystem.
The data base of a CAD system can take several forms.
One form, as previously indicated, consists of represent
ing the surface of an object as a mesh of triangles
(PRIGS). These triangles completely form the inner and
outer surfaces of the object. This CAD representation
also includes a unit length normal vector for each
triangle. The normal points away from the solid which the
triangle is bounding. This invention provides a means of
processing such CAD data into the layer-by-layer vector
data that is necessary for forming objects through
stereolithography.
For stereol.ithography to successfully work, there
must be good adhesion from one layer to the next. Hence,
plastic from one layer must overlay plastic that was
formed when the previous layer was built. In building
models that are m;~de of vertical segments, plastic that is
formed on one lay~sr wil:L fall exactly on previously formed
plastic from the ~?receding layer, and thereby provide good
adhesion. As one starts to make a transition from
vertical to horizontal features, using finite jumps in
layer thickness, a point will eventually be reached where
the plastic formed on one layer does not make contact with
the plastic formed on t:he previous layer, and this causes
severe adhesion problems. Horizontal surfaces themselves
do not present adhesion problems because by being
horizontal, the whole erection is built on one layer with
side-to-side adhesion maintaining structural integrity.
This invention provides a general means of insuring
adhesion between layers when making transitions from
~~~~~~39~J
vertical to horizontal or horizontal to vertical sections,
as well as providing a way to completely bound a surface,
and ways to reduce or eliminate stress and strain in
formed parts.
5 A presentl~~ prei:erred embodiment of a new and
improved stereolithogra~phic system is shown in elevational
cross-section in FIG. 12. A container 21 is filled with
a UV curable liquid 22 or the like, to provide a
designated working surface 23. A programmable source of
10 ultraviolet light 26 or the like produces a spot of
ultraviolet light: 27 in the plane of surface 23. The spot
27 is movable across the surface 23 by the motion of
mirrors or other optical or mechanical elements (not shown
in FIG. 12) used with the light source 26. The position
15 of the spot 27 on surface 23 is controlled by a computer
control system 28. As previously indicated, the system
28 may be under control of CAD data produced by a
generator 20 in a CAD design system or the like and
directed in PHIGS format or its equivalent to a
20 computerized conversi~an system 25 where information
defining the object is specially processed to reduce
stress, curl and dist=ortion, and increase resolution,
strength and accu racy of reproduction.
A movable elevator platform 29 inside container 21
25 can be moved up and down selectively, the position of the
platform being control7Led by the system 28. As the device
operates, it produces a three-dimensional object 30 by
step-wise buildup of integrated laminae such as 30a, 30b,
30c.
30 The surface of the UV curable liquid 22 is maintained
at a constant level in. the container 21, and the spot of
UV light 27, or other suitable form of reactive
stimulation, of sufficient intensity to cure the liquid
and convert it t:o a solid material, is moved across the
working surface 23 in a programmed manner. As the liquid
22 cures and solid material forms, the elevator platform
29 that was initially just below surface 23 is moved down
r- ~ '
~~
I~4089U
31
from the surface in a programmed manner by any suitable
actuator. In this way, the solid material that was
initially formed is taken below surface 23 and new liquid
22 flows across the surface 23. A portion of~this new
liquid is, in turn, converted to solid material by the
programmed UV 7_ight spot 27, and the new material
adhesively connects to the material below it. This
process is continued until the entire three-dimensional
object 30 is fon~ned. The object 30 is then removed from
the container 21, and the apparatus is ready to produce
another object. Another object can then be produced, or
some new object can be made by changing the program in the
computer 28.
The curable liquid 22, e.g., UV curable liquid, must
have several important properties: (A) It must cure fast
enough with the: available UV light source to allow
practical objeci~ fo nnation times. (B) It must be
adhesive, so that successive layers will adhere to each
other. (C) Its viscosity must be low enough so that fresh
liquid material will quickly flow across the surface when
the elevator moves the: object. (D) It should absorb UV
light so that the film formed will be reasonably thin.
(E) It must be reasonably insoluble in that same solvent
in the solid stare, so that the object can be washed free
of the UV cure liquid a.nd partially cured liquid after the
object has been formed. (F) It should be as non-toxic and
non-irritating a;s possible.
The cured material must also have desirable
properties once it is in the solid state. These
properties depend on the application involved, as in the
conventional use of other plastic materials. Such
parameters as color, texture, strength, electrical
properties, flammability, and flexibility are among the
properties to be considered. In addition, the cost of the
material will be important in many cases.
The UV curable material used in the presently
preferred embodiment of a working stereolithography system
~.3~08~0
32
(e. g., FIG. 12) i.s DeSoto SLR 800 stereolithography resin,
made by DeSoto, Inc. of Des Plains, Illinois.
The light s~~urce 26 produces the spot 27 of UV light
small enough to allow the desired object detail to be
formed, and intense enough to cure the UV curable liquid
being used quick:Ly enough to be practical. The source 26
is arranged so it can be programmed to be turned off and
on, and to move:, such that the focused spot 27 moves
across the surfa~~e 23 ~of the liquid 22. Thus, as the spot
27 moves, it cures the liquid 22 into a solid, and "draws"
a solid pattern on the surface in much the same way a
chart recorder or plotter uses a pen to draw a pattern on
paper.
The light source 26 for the presently preferred
embodiment of a stereolithography system is typically a
helium-cadmium ultraviolet laser such as the Model 4240-N
HeCd Multimode Laser, made by Liconix of Sunnyvale,
California.
In the system of FIG. 12, means may be provided to
keep the surface 23 at. a constant level and to replenish
this material after an object has been removed, so that
the focus spot 27 will remain sharply in focus on a fixed
focus plane, thus insuring maximum resolution in forming
a high layer along the working surface. In this regard,
it is desired to shape the focal point to provide a region
of high intensity right at the working surface 23, rapidly
diverging to low intensity and thereby limiting the depth
of the curing process to provide the thinnest appropriate
cross-sectional laminae for the object being formed.
The elevator platform 29 is used to support and hold
the object 30 being formed, and to move it up and down as
required. Typically, after a layer is formed, the object
30 is moved beyond th.e level of the next layer to allow
the liquid 22 to flow into the momentary void at surface
23 left where the solid was formed, and then it is moved
back to the correct level for the next layer. The
requirements for the elevator platform 29 are that it can
134089
33
be moved in a programmed fashion at appropriate speeds,
with adequate precision, and that it is powerful enough to
handle the weight of the object 30 being formed. In
addition, a manual fine adjustment of the elevator
platform position is useful during the set-up phase and
when the object is being removed.
The elevator platform 29 can be mechanical,
pneumatic, hydraulic, or electrical and may also be
optical or electronic feedback to precisely control its
position. The elevator platform 29 is typically
fabricated of either glass or aluminum, but any material
to which the cured plastic material will adhere is
suitable.
A computer c:ontrol.led pump (not shown) may be used to
maintain a constant level of the liquid 22 at the working
surface 23. Appropriate level detection system and
feedback network:, well known in the art, can be used to
drive a fluid pump or a liquid displacement device, such
as a solid rod (riot shown) which is moved out of the fluid
medium as the elfwator platform is moved further into the
fluid medium, to offset changes in fluid volume and
maintain constant fluid level at the surface 23.
Alternatively, the source 26 can be moved relative to the
sensed level 23 ;end automatically maintain sharp focus at
the working surface 23. All of these alternatives can be
readily achieved by appropriate data operating in
conjunction with the computer control system 28.
After the three-dimensional object 30 has been
formed, the elevator platform 29 is raised and the object
is removed from the platform for post processing.
As will be apparent from FIG. 13 of the drawings,
there is shown an alternate configuration of a
stereolithograph.y system wherein the UV curable liquid 22
or the like floats on a heavier UV transparent liquid 32
which is non-miscible. and non-wetting with the curable
liquid 22. By way of' example, ethylene glycol or heavy
water are suitable for the intermediate liquid layer 32.
34
In the system of FIG. 12, the three-dimensional object 30
is pulled up from the liquid 22, rather than down and
further into the liquid medium, as shown in the system of
FIG. 11. _
The UV light source 26 in FIG. 13 focuses the spot 27
at the interface between the liquid 22 and the
non-miscible intermediate liquid layer 32, the UV
radiation passing through a suitable W transparent window
33, of quartz or the like, supported at the bottom of the
container 21. The curable liquid 22 is provided in a very
thin layer over the non-miscible layer 32 and thereby has
the advantage of limiting layer thickness directly rather
than relying solely upon adsorption and the like to limit
the depth of curing since ideally an ultrathin lamina is
to be provided. Hence, the region of formation will be
more sharply defined and some surfaces will be formed
smoother with the system of FIG. 5 than with that of FIG.
12. In addition, a sm<~ller volume of UV curable liquid 22
is required, and the substitution of one curable material
for another is easier.
The new an~3 improved stereolithographic method and
apparatus has many advantages over currently used methods
for producing plastic objects. The method avoids the need
of producing tooling drawings and tooling. The designer
can work directly with the computer and a
stereolithographic device, and when he is satisfied with
the design as displayed on the output screen of the
computer, he can fabricate a part for direct examination,
information defining t:he object being specially processed
to reduce curl and distortion, and increase resolution,
strength and accuracy of reproduction. If the design has
to be modified, it can be easily done through the
computer, and then another part can be made to verify that
the change was corrects. If the design calls for several
parts with interacting design parameters, the method
becomes even more useful because all of the part designs
can be quickly changed and made again so that the total
~~~~~9U
assembly can be made and examined, repeatedly if
necessary.
A~ter the design is complete, part production can
begin immediately, so 'that the weeks and months between
5 design and production .are avoided. Ultimate production
rates and parts cost:a should be similar to current
injection molding costs for short run production, with
even lower labor cos>ts than those associated with
injection molding. Injection molding is economical only
10 when large numbers of identical parts are required.
Stereolithography is particularly useful for short run
production because the need for tooling is eliminated and
production set-u;p time is minimal. Likewise, design
changes and custom parts are easily provided using the
15 technique. Because of the ease of making parts,
stereolithography can allow plastic parts to be used in
many places whey<~ metal or other material parts are now
used. Moreover, it allows plastic models of objects to be
quickly and economically provided, prior to the decision
20 to make more expensive metal or other material parts.
It will be apparent from the foregoing that, while a
variety of stereolithoc~raphic systems have been disclosed
for the practice of the present invention, they all have
in common the concept of drawing upon a substantially
25 two-dimensional surface: and extracting a three-dimensional
object from that surface.
The present invention satisfies a long existing need
in the art for a CAD and CAM system capable of rapidly,
reliably, accurately and economically designing and
30 fabricating threfa-dimensional plastic parts and the like,
and reducing strE~ss and curl.
An embodim<:nt o:E the multi-pass curl reduction
technique described earlier will now be described. In
this embodiment, a layer of liquid resin is incrementally
35 cured to a particular depth through multiple passes of a
UV laser beam over the resin such that the layer does not
adhere to an adjacent already-cured layer below on the
.134089(!
36
first pass. Instead, adhesion is achieved at a later
pass, and in fact, add. itional passes after adhesion has
been achieved are: possible to achieve even more adhesion.
For example, for a layer thickness of 20 mils, adhesion
will be achieved when enough passes have been made to
incrementally cure the layer down to 20 mils. However,
even after adhesion ha;s been achieved, additional passes
can be made to cause the layer to penetrate another 6 mils
into the already-cured layer below to achieve even greater
adhesion betwen the la}~ers. As a result, a cure depth of
26 mils is achieved even though the layer thickness may
only be 20 mils.
Multi-pass i-educe:~ curl in two ways. First, multi
pass cures a layer incrementally, and enables the top
portions of a layer to ~~ure without transmitting stress to
previously cured layers. With reference to Figure 14a,
when layer 100 is cured in a single pass, the resin making
up the layer will simultaneously shrink and adhere to
layer 101, causing stress to be transmitted to this layer.
The result is that, unless layer 101 is somehow anchored
to resist the transmittal of stress, both layers will curl
upwards as illustrated in Figure 14b. If layer 100 were
cured on multiple passes, on the other hand, it could be
cured without transmiti~ing a significant amount of stress
to layer 101. With reference to Figure 15a, through
multi-pass, layer 100 could be cured almost to the point
of adhering to layer 101, but separated from it by
distance 102, which could be on the order of a few mils.
Then, in a subsequent pass, the layers would be adhered to
one another, but since the amount of resin which is cured
on the final pass is ;mall, there will be less shrinkage
on the final pass compared with a single pass; and
therefore less stress transmitted to the lower layer.
The second way mufti-pass reduces curl is that when
the adhesion pa~~s is made, the resin being cured on the
adhesion pass will be sandwiched in between a rigid
already-cured layer below, and the rigid already-cured
37
portion of the present: layer above. With reference to
FIG. 15b, the curing ~of this resin will simultaneously
introduce stresses to both the upper and lower cured
layers, which will tend to cancel each other out. For
example, lower layer 101 will tend to bend upwards, while
upper layer 100 will tend to bend downwards as indicated.
The result is that they>e effects will tend to offset each
other as the force tending to curl layer 101 upwards will
be counter-balanced by the rigidity of the already-cured
portion of layer 100, whereas the force tending to curl
layer 100 downwards will be counter-balanced by the
rigidity of lower. layer 101.
A possible embodiment of multi-pass is to provide
only two passes for a. given layer, with adhesion (and
possible over-curing to penetrate into the next layer for
better adhesion) occurring on the second pass. In this
embodiment, it is preferable to cure a layer on a first
pass so it is a close as possible, i.e. within 1 mil, to
the bottom layer, which layer is then adhered to the
bottom layer on i=he second pass.
A preferred embodiment of multi-pass is to provide
more than two passes, i.e. four or five passes, for a
given layer, such that after the first pass, an
incremental amount of the uncured gap between the layers
is incrementally cured on subsequent passes until a gap of
only about two to three mils remains. Then, in a
subsequent pass, the remaining two to three mil gap is
cured, and adherence is achieved.
In deciding whether to implement multi-pass with only
3o two passes, or with more than two passes, it is important
to consider the precision with which the cure depth for
a given layer can be estimated and/or controlled. If the
cure depth can only be estimated with a precision of two
to three mils, for example, then in the two-pass
embodiment, there is a danger that adherence will be
achieved on th~s first pass, which would defeat the
purposes of using multi-pass in the first instance, and
134080
38
would also result: in curl. Of course, there is a danger
than in the preferred. multi-pass embodiment described
above, that adherence could be achieved before the desired
pass (which desired pass may not be the final pass if
over-curing into the next layer is effectuated) because of
the imprecision in estimating cure depth, but this is much
less of a problem. than in the two pass case, since in the
pass during which adherence takes place, only a very small
amount of resin will typically be cured, and only a very
small amount of stress will therefore be transmitted to
the lower layer. In th~~ two pass case, on the other hand,
in general, a large amount of liquid resin will be cured
on the first pass, so that adherence during this pass can
result in a large amount of curl since the stress
transmitted to the lower layer depends on the amount of
resin cured when adherence takes place. The reason why a
lot of resin wil:1 be cured on the first pass in the two
pass case is that, as discussed earlier, it is important
in this embodiment to try to cure down to within a few
mils of the layer below on the first pass, so that in the
second pass, when adherence is achieved, only a small
amount of resin caill be cured. Therefore, on the first
pass, a large volume of resin will typically be cured with
the aim of curing to within a few mils of the lower layer.
For a 20 mil layer i~hickness, this requires that the
first pass penetrate approximately 18-19 mils towards the
layer below, which represents a much larger volume of
liquid resin.
In the preferred multiple pass embodiment, on the
other hand, it :is not necessary for the first pass to
bring the layers to within a few mils of each other.
Instead, a wider gap can be left after the first pass, and
it will be left up to subsequent passes to bring the
layers to within a few mils of each other, and ultimately
adhere. Therefore, if adherence takes place at all before
the desired pass, it will surely not take place on the
first pass, when a large amount of liquid resin will be
~3~089~U
39
cured, but will only take place on a later pass when only
a relatively sma:Ll volume of liquid resin will be cured.
Also, according to Beer's law (discussed below), much less
penetration of the cure depth will typically be achieved
on a subsequent pass compared to a first pass, even if the
exposure of the LJV lasEar is kept the same on each pass.
Imprecision in estimating cure depth is due to many
sources. In general, the cure depth depends
logarithmically on the exposure from the W laser, which
l0 means that doubling or tripling the exposure will not
double or triple the cure depth, but will increase it much
less than this.
This relationship (between exposure and cure depth)
can theoreticall~~ be deascribed in the form of an equation
known as Beer's Law, which is as follows: If = Ia a - °x
where If is the intensity of the W light at a distance X
into the liquid, Io is t:he intensity of the W light at the
liquid surface, cc is a proportionality constant, and X is
the distance into the liquid at which the intensity If
is measured. Therefore, in principle, the increase in
cure depth for a given pass can be determined based on the
accumulated exposure of the previous passes and the
incremental exposure which will be applied on the given
pass.
Due to several practical "real-world" considerations,
however, the increase in cure depth may not obey Beer's
Law exactly. 1?first, due to an effect known as the
"lensing ef fect, " the estimated cure depth based on Beer' s
Law in a multi-pass implementation will under-estimate the
actual cure depth achieved by approximately two to three
mils. The results is that adhesion may be achieved sooner
than expected.
The lensing effect will occur because cured resin
from previous paws will act as a lens, since the cured
13~~~3~0
resin has a diff-_erent index of refraction compared with
the liquid resin. In ;a mufti-pass implementation, during
the intermediate passes, the laser beam will pass through
the resin which has already been cured on previous passes,
5 and the cured r~asin, as mentioned above, will act as a
lens, and will Eocus the UV laser light, causing it to
achieve a greater cur.=_ depth penetration than predicted
using Beer's Law.
The lensing effect can be illustrated with respect to
10 FIG. 16, in which, compared to previous Figures, like
elements are id.entifi.ed with like reference numerals.
FIG. 16a shows cured resin 103 produced by a single pass
of the UV laser at a particular exposure. The cure depth
achieved is identified as T~.
15 FIG. 16b shows the cured resin produced by multiple
passes of the UV laser beam, where the increase in the
cure depth at .each pass is identified with reference
numerals 103a, 103b, 103c, and 103d, respectively. If it
is assumed that: the sum of the incremental exposures
20 applied at each pass equals the exposure applied in the
single pass of FIG. 16a, based on Beer's Law, it would be
expected that TZ would equal T~. However as illustrated,
because of the i.ensinc~ ef fect, Tz will be greater than T~
by an increment .indicated as T3, which will be on the order
25 of 2-3 mils.
Another reason, for imprecision is due to bleaching of
the photoinitiat:or component of the resin (a/k/a "photo-
bleaching"), which can occur as the resin is exposed many
times through the multiple passes~of the UV light.
30 Because of photo-bleaching, less UV light will be absorbed
by the photoinitiator than predicted, with the result that
the laser light will penetrate deeper into the resin than
predicted.
A third reason for imprecision is variations in the
35 intensity of the light produced by the laser, which, in
turn, are caused by power fluctuations in the output of
the laser.
i ~,
~34~~90
41
For example, a lacer presently used in the SLA-250,
a commercial stereolithography apparatus manufactured by
3D Systems, Inc., has a continuous power output of
approximately ~20 mW. Because of power fluctuations, the
laser output may be punctuated by 16-28 mW power bursts.
In the SLA-250, the laser beam is directed to step across
the surface of the liquid resin in incremental steps, and
to then remain stationary for a given time period after
each step. The e:~cposur~e for the laser on an infinitesimal
l0 part of the liquid sur:Eace will be directly proportional
to the laser output power multiplied by the step period
divided by the step size. In other words, for a given
laser output power, the exposure to the resin can be
increased either by increasing the step period or
decreasing the step size. Therefore, the fluctuations in
laser output power wil)L show up directly as fluctuations
in exposure, with the result that the cure depth may vary
by a few mils from what is expected because of these
fluctuations.
In sum, the combined impact of the lensing effect,
the bleaching of i:.he photoinitiator, and power
fluctuations of the laser output result in imprecision in
estimating cure depth, so that, as a practical matter, it
is preferable to implernent multi-pass with more than two
passes.
Another possible embodiment of mufti-pass is to keep
the laser exposure on each pass uniform. In many
instances, however, uniform exposure on each pass will not
be possible because of the impact of Beer's Law, according
to which uniform increments of exposure at each pass will
not lead to uniform increments in cure depth. Instead,
much more will be cured on the first pass than on
subsequent passer. For example, it is entirely possible
for a first pass to cure 90% of the layer thickness, for
a second pass to cure 90% of the uncured gap which remains
left over after the first pass, and for a third pass to
cure 90% of the remaining uncured gap left over after the
1340~~U
42
second pass, etc. The result is that with uniform
exposure, a layer may adhere only after two passes, with
the additional passes :resulting in even more adherence
between the layers. As a result, in general, an
embodiment where non-uniform exposures are possible on the
various passes wi:L1 be preferable.
Several examples will now be provided showing the
advantage of providing the option of non-uniform exposures
on the various passes. These examples all assume that the
desired layer thickness; is 20 mils, that each layer is
over cured so that: it penetrates 6 mils an adjacent, lower
layer, that a cure depth of 26 mils will be achieved
through an accumulated exposure level of 1, and that the
doubling of the exposure will result in a 4 mil
incremental increase in t:~ cure depth. Based on these
assumptions, the following relationship between cure depth
and exposure level results:
Cure depth Accumulated Exposure
26 mils 1
22 mils 1/2
18 mils 1/4
14 mils 1/8
10 mils 1/16
In all the examples, it will be assumed that the
accumulated exposure from all the passes will be 1, so
that the cure depth, after all the passes have taken
place, will be 26 mils:. The number of passes, and the
incremental exposure at each pass are the variables
changed in the examples. Therefore, in the examples,
exposure refers i~o the incremented exposure applied on a
particular pass, not the accumulated exposure applied up
to and including this pass.
The first set of examples are for a two-pass
embodiment of mu:Lti-paws.
~~~~~9J
43
Example 1.) Two passes, uniform exposure
ass eXposure cure depth
1 1/2 22 mils
2 1/2 26 mils
Since this example (which shows a uniform exposure at
each pass of 1/2) will achieve a cure depth of 22 mils on
the first pass, which is greater than the layer thickness
of 20 mils, it is note a preferable implementation of
multi-pass because the layer will adhere on the first
pass.
Example 2.) Two passes non-uniform exposure
ass eXQosure cure depth
1 1/4 18 mils
2 3/4 8 mils
Since the cure depth on the first pass is only 18
mils, this example is an acceptable implementation.
Example 3.) Two passes non-uniform exposure
ass exposure cure depth
1 1/8 14 mils
2 7/8 12 mils
Since the cure depth on the first pass is only 14
mils, this example is also an acceptable implementation.
A comparison of Examples 2.) and 3.) indicates that
Example 2.) may b<~ preferable since the top layer is cured
closer to the bottom layer after the first pass, so that
on the second pas:, when adherence occurs, less resin will
have to be cured. In fact, if cure depth could be
precisely estimated on the first pass, the optimum
solution would require the exposure on the first pass to
be in the range o:E 1/4-:L/2, which would leave even less of
a gap between the layers after the first pass. However,
because of the impre~~ision in estimating cure depth
discussed above, it is preferable for the exposure on the
first pass to be c:Loser to 1/4 rather than 1/2.
Therefore, Example 2.) is a preferred implementation
compared with Example a.).
The next set: of examples are for three passes.
44
Example 411 Three passes, uniform exposure
ass ex~~osure cure depth
1 1/3 19.7 mils
2 1/3 23.7 mils
3 1/3 26 mils
As indicated, this example may not an acceptable
implementation because adhesion occurs on the second pass,
and in addition, due to the degree of imprecision
involved, because' some adhesion may, in all likelihood,
occur on the firsts pass since the 19.7 mil cure depth is
so close to the layer i=hickness of 20 mils. Since there
is a significant danger that adhesion may occur on the
first pass, when the amount of liquid resin which is cured
is great, this example is not a preferred embodiment of
multi-pass.
Example. 51 Three passes, non-uniform ext~osure
ass exposure cure depth
1 1/4 18 mils
2 1/~4 22 mils
3 1/:? 26 mils
In this example, since the cure depth after the
second pass is 22 mils, adherence will occur on the second
pass, which may not be acceptable if adherence is desired
on the third pasts. On the other hand, because the first
pass achieved a cure depth of 18 mils, the amount of
plastic being cured during the second pass is not great,
so the cure introduced by adherence on the second pass is
not likely to be dramatic.
Examples 6!) Three passes, non-uniform exposure
ass exposure cure depth
1 1/4 18 mils
2 1/8 20.3 mils
3 5/8 26 mils
Since the cure depth after the second pass is 20.3
mils, there with probably be some adhesion after the
second pass, although the amount of resin being cured on
the second pass will be small since the first pass is
45
estimated to have achieved a cure depth of 18 mils. In
addition, because of the imprecision ~n estimating cure
depth, it is possible that adherence will not occur at all
on the second pass..
Example 7.) Three passes, non-uniform exposure
ass expC~sure cure depth
1 1/4 18 mils
2 1/lE~ 19.3 mils
3 11/1.6 26 mils
Since the cure depth after the second pass is only
19.3 mils, this ea:ample is an acceptable implementation,
although there may be some adhesion after the second pass
because of the imprecision of estimating cure depth.
However, even if there were some adhesion on the second
pass, the amount of res_Ln being cured on the second pass
will not be great, the first pass having already achieved
a cure depth of 18 mils.
Example 8.) Three gasses, non-uniform exposure
ass exgC~sure cure depth
1 1/16 10 mils
2 1/lE~ 14 mils
3 14/1.6 26 mils
This example is an acceptable implementation since
the cure depth after the second pass is only 14 mils.
However, a 6 mil thick volume of resin will have to be
cured on the third pass when adhesion occurs, which can
introduce a significant amount of curl. Therefore,
Example 7.) is a preferable implementation, since much
less resin will have to be cured on the third pass.
In sum, the above examples demonstrate that non-
uniform exposure levels on the various passes is
preferable to an implementation which requires uniform
exposure levels on the various passes, since, in many
instances, uniforrl exposures will result in adhesion too
early. Also, the above examples were provided for
illustrative purp~~ses only, and are not intended to be
limiting.
~~~osoo
46
A consideration in choosing exposure levels for the
multiple passes i;s to avoid downward curl, a problem that
can occur on a given pass if the cure depth achieved in
previous passes is so small, that the curing of the liquid
resin that takes place on later passes will cause the
resin cured on the previous passes to bend downwards. In
fact, if downward bending is large enough, then adhesion
to the lower layer can occur sooner than expected, which
as described above, can introduce even more stress into
the part by introducing upward curl of the bottom layer.
This problem will be particularly acute if the incremental
cure depth at Each pass is uniform since, in this
instance, the cured re:~in from the previous passes will
(except for the first pass) be relatively thin, and
therefore more easily bent by the curing during the later
passes.
In addition, the amount of downward bending will be
dependent on the amount of resin which is cured during the
later passes, since the: more resin which is cured on the
later passes, the more stress which is transmitted to the
resin cured by the earlier passes. However, particularly
where multi-pass :is imp:Lemented with more than two passes,
the amount of resin cured during the later passes may be
relatively small, so that the downward bending problem may
be alleviated by this type of implementation.
The problem of downward bending can be illustrated
with reference to FIG. 17a, in which compared with the
previous Figures,, like references numerals are used to
identity like com,ponenta.
As indicai~ed, in a particular multi-pass
implementation, bottom layer 101 is already cured, and
layer 100 is being cured by multiple passes during which
incremental amounts of liquid resin, identified by
reference numerals 104x, 104b, and 104c, respectively, is
cured. As shown, when resin 104c is cured, it shrinks and
simultaneously adheres to cured resin 104b, transmitting
stress and, causing downward bending. As indicated, if
130890
- 47 -
the downward bending at the ends of the already-cured portion
of the layer, idESntified by reference numerals 105 and 106
respectively, is great enough, the ends may touch the upper
surface of layer 101, resulting in early adherence.
To alleviatE~ this problem, two solutions are possible.
One solution is i:o increase the thickness of the resin cured
in the early pas;~es, 104a and 104b, respectively, with respect
to that cured during the later passes, 104c, or alternatively,
to decrease the thickness of the resin cured during the later
passes, 104c, compared with that cured during the early
passes, 104a and 104b. This is illustrated in FIG. 17b,
where, as before, compared with previous Figures, like
components are identified with like reference numerals.
Another problem that can occur with multi-pass is
birdnesting, which is a distortion that can occur if there are
significant dela~~s between the multiple passes. The problem
occurs when resin cured on a particular pass is allowed to
float for a long period of time on the surface of the liquid
resin before additional passes adhere this cured resin to the
layer below. If the delay is long enough, the cured resin
floating on the .surface of the resin can migrate about before
it is adhered to the layer below. Birdnesting will be
discussed in more detail below. A particular multi-pass
technique that addresses birdnesting is known as redraw. A
possible solution to the birdnesting problem is to reduce as
much as possible the delays the delays between successive
passes.
.~~4~g9U
- 48 -
The REDRAW c:apabilities and functions reside in the BUILD
program (a/k/a SI1PER in other versions of the software) which
programs are described in detail in co-pending Canadian Patent
Application S.N. 596,825. Briefly, BUILD controls the laser
movement through the u:~e of two other programs, STEREO and
LASER, and it obtains i~he parameters it needs to implement the
numerous REDRAW functions based on information supplied in
either 1.) a .PRM default parameter file in which a user can
specify default F;EDRAW parameters; 2.) a .L layer control file
in which a user can specify REDRAW parameters on a layer by
layer, and vector type by vector type, basis; or 3.) a .R
range control fiJ_e in which a user can specify REDRAW
parameters for a range of layers, and for vector types within
a range. To imp_Lement the REDRAW functions, various command
lines specifying REDRAW parameters are placed in either of
these files simi:Lar to the way that other cure parameters are
defined (as expl<~ined in the above co-pending applications).
The first p.Lace BUILD looks for REDRAW control parameters
is the .L or .R Nile, not both. As indicated above, the .L
file enables a u:~er to specify REDRAW parameters with a high
degree of contro:L. With the .L file, a user can specify
REDRAW parameter; for a particular vector type within a layer
of an object. For example, for a .L file consisting of merged
data for four objects, which data represents 11 different
vector types, th~~ .L file enables 44 different REDRAW
parameters to be specified for each layer. In sum, the .L
file provides layer by layer control of multi-pass.
~3~U~9U
- 48a -
The .R file is designed for those applications whether
the layer by layer control allowed by the .L file is not
needed. Instead of providing layer by layer control, the .R
file provides co:ztrol on a range-by-range
13~D~9~
49
basis, where a range represents any number of adjacent
layers.
The REDRAW parametcars can be placed into the .R file
using a user interface program known as PREPARE. To place
the REDRAW parameters into the . L file, a standard word
processor type line ediltor is used.
If BUILD requires any REDRAW parameters which it is
unable to obtain from either the .L or .R files, then it
will seek them from the .PRM default parameter file.
REDRAW parameters can be placed in these files by use of
the PREPARE program.
The first REDRAW command is RC ##, where RC is a
mnemonic for Redraw Count. This command specifies the
number of passes that the laser beam will make over each
vector of a cross--section, i.e., the number of passes for
a particular layer. The number of passes specified can
range from 1 to 10.
The second REDRAW command is RD . where RD is a
mnemonic for Redraw Delay. This command specifies the
length of time the laser will wait at the beginning of
each pass. As mentioned earlier, the laser beam moves
across the surface of the resin in steps followed by
delays at each step. The delay at each step is known as
the Step Period, which is identified with the mnemonic SP,
and the command for specifying a particular value of SP is
the command SP ##, where the value chosen is in units of
10 microseconds. The value of RD can be specified as any
number in the range of 0 to 65,535, which number
represents the delay in units which are multiples of the
SP value. Thus, an RD of 10 represents a delay of ten
times the value specified for SP. In general, the RD
command is not used much, and the standard value is 0.
The RD command is similar to the JD command (which
mnemonic stands for Jump Delay).
Note that the JD and RD commands are both
necessitated by t:he inability of the software running on
the PROCESS computer (which software controls the rotation
~~~~~90
of the dynamic mirrors, and hence the movement of the
laser beam across. the liquid resin) to take account of the
time it takes for the laser beam to jump from a first
vector to another vector, after it has drawn the first
5 vector. After the laser beam has been directed to sweep
out a particular vector, the software will direct the beam
to start drawing out another vector, perhaps beginning at
a different location than the end of the previous vector,
and will then simultaneously begin counting down the time
10 for the laser to step through the vector as if the beam
were instantaneously situated at the beginning of the next
vector. In many instances, the PROCESS computer will
begin the counting while the laser beam is still jumping
to the beginning of the vector. When the laser finally
15 gets to the right location, the PROCESS computer will
immediately position it at the location it has counted
down to, with the result that the first part of the vector
may be skipped over and left uncured.
The effect can be illustrated with the help of FIGS.
20 21a and 21b. FIG. 21b illustrates cross-section 105 of an
object, and assoc:fated vectors 106a, 106b, 106c, 106d, and
106e spanning the surface of the cross-section, which
vectors represent the movement of the laser beam as it
cures the liquid plastic that forms the cross-section.
25 The dotted lines betwe~=_n the head and tails of successive
vectors is the movement of the laser as it jumps from one
vector to another, and it is the jumping time for these
jumps that causes the problem mentioned above.
The effect of the jumping time is illustrated in FIG.
30 21b, in which .Like Elements are identified with like
reference numerals compared with FIG. 21a. The jumping
time results in an area, identified with reference numeral
107 in FIG. 21b, which is left uncured.
The use of JD and RD is designed to get around this
35 problem. The delay specified by these commands is the
time the PROCES~~ computer is directed to wait, after it
has cured a particular vector, before it begins stepping
~3~fl89U
51
through the next vector. In the context of REDRAW, RD is
the time the PROCE:~S computer is directed to wait after it
has completed a pass o~ner a particular area, before it
begins a next pass over that area. By causing the PROCESS
computer to wait, the stepping through can be delayed
until the laser beam is positioned properly.
As mentioned earlier, JD and RD are rarely used, and
the reason for this is illustrated in FIG. 21c. FIG. 21c
illustrates a technique known as the "zig-zag" technique
which is now implemented in the software to reduce the
travel distance and hence jumping time between successive
vectors. As illustrated, successive vectors 106a, 106b,
106c, 106d, and 106e, instead of all pointing in the same
direction as indicated in FIGS. 21a and 21b, are caused to
alternate directions, as illustrated in FIG. 21c. The
direction of these vectors indicates the movement of the
laser beam on the surface of the resin as it traces out
these vectors. The result is that jumping time is
dramatically reduced, making it frequently unnecessary to
use the JD command. Thi:~ technique is also implemented in
REDRAW, so that the laser beam will be caused to alternate
directions every time it: passes over a particular area in
multi-pass. As a result, it is also frequently
unnecessary to use the RD command.
The third REL)RAW command is RS , where RS is the
mnemonic for Redraw Size:. It was recognized early on that
a problem with sovme forms of multi-pass was birdnesting,
and to alleviate this problem, the RS command was added to
enable long vectors in ~~ given cross-section to be broken
up into smaller mini-vectors so that multi-pass could be
performed on each mini-vector before proceeding on to the
next mini-vector. By choosing an appropriate size for the
mini-vector, cured resin from the early passes could more
rapidly be adhered to t:he layer below than if the entire
vector were drawn on a given pass. The RS command
specifies the length of the mini-vector into which the
vectors of the cross-section are divided.
1~~~8~U
52
As discussed earlier, the laser beam moves in steps,
and the step size is identified by the mnemonic SS. The
command for specifying the step size is SS ##, where the
number specified ~~an range from 0 to 65,538 bits, where a
bit represents approximately .3 mil (the actual tranlation
is 3560 bits per inch). AS a result, a particular pass
can proceed over a distance which can range from a minimum
of approximately .3 mila to a maximum of approximately 20
inches.
The units of RS are: multiples of SS . For example, an
SS of 2, and an RS of lc)00, indicates that each pass will
draw 2000 bits of vector information before jumping back
to make additional passes. Alternatively, with an SS of
8, and an RS of 1000, then 8000 bits of vector information
will be drawn bef~~re beginning another pass.
The last REDRAW command is a command for providing a
different laser exposure value for each pass. This is
accomplished by specifying a different SP value for each
pass, since as indicated earlier, the exposure is directly
proportional to Sl?. ThE~ format of the command is SP ,
, . . . . depending on the number of passes. The
value of SP is in units of 10 acs, and in addition, each SP
can range in value from approximately 5-15 to
approximately 4000-6500.
As mentioned earlier, for a given layer of an object,
different REDRAW parameters can be specified for each
vector type in th~~t layer using the .L file. In addition,
all the REDRAW commands will be completed for a particular
vector type, before REDRAW commands for the next vector
type are expected..
A typical command line in the .L file might appear as
follows: 920, LB1, "F;C 3; RD 0; RS 1000; SP 250, 150,
1000; SS 2." This command indicates that at the layer of
a first object located 920 vertical bits from the bottom,
that for the layer boundary vectors for that object,
identified by the mnemonic LB1, 3 passes will be performed
for each boundary vector (indicated by the REDRAW command
U
- 53 -
RC 3), each pass will draw 2000 bits of a boundary vector
(indicated by the commands SS 2 and RS 1000) before proceeding
on to the next pass, and the SP values for the first, second,
and third passes, respectively, will be 250, 150, and 1000.
A typical command in a .R file might appear as follows:
LB1, "RC 3; RD 0; RS 1000; SP 250, 150, 1000; SS 2" which
command is identical to that specified above for the .L file,
except that no layer specification is provided, since this
command will apply to <~11 layers within a specified range. A
command in the .FARM default parameter would look similar to
this.
A sample report showing the format of the .L file is
shown in FIG. 18. As illustrated, only vectors for a first
object are repre:~ented,, and REDRAW commands can be specified
for each vector type within a layer of that object. The
vector types and their associated mnemonics are as follows:
LB la~~rer boundary
LH la~~er crosshatch
NFDB ne<~r-flat down-facing skin boundary
NFDH near-flat down-facing skin cross hatch
NFUB near-flat up-facing skin boundary
FB flat down-facing skin boundary
FDF flat down-facing skin fill
NFDF near flat down-facing skin fill
NFUF near flat up-facing skin fill
FUB flat up-facing skin boundary
FUF flat up-facing skin fill
134U89U
- 54 -
The various vector types are described in more detail in
Canadian Patent Application S.N. 596,825. Briefly, boundary
vectors are used to tr<~ce the perimeter of each layer, cross
hatch vectors are' used to trace the internal portion of each
layer surrounded by the layer boundary, and skill fill vectors
are used to trace' any outward surfaces of the object. They
are traced in the: following order: boundary, cross-hatch, and
skin.
FIG. 19 is ~~ samp.le report showing the format of the .R
file. As indicated, t'.ne format is similar to that for the .L
file, except that. the specification of REDRAW parameters is
only possible for a particular vector type within a range of
layers.
In FIG. 19, the REDRAW commands for a particular range
are framed by the' mnemonics #TOP and #BTM, and in addition,
the range of layers to which the REDRAW commands apply are
provided in the .Line before the #TOP mnemonic.
For the fir:~t block of REDRAW commands in FIG. 19, the
range specified :is 920, 920, which indicates that the range
specified for thc~ first block of REDRAW commands is the one
layer located at 920 SLICE units from the bottom (assuming
CAD/CAM units of inches, and a desired resolution of 1,000,
the SLICE units will be mils. The difference between the
CAD/CAM and SLICE reference scales is described in more detail
in Canadian Patent Application S.N. 596,825. This is because
the beginning an~3 ending points of the range are identical:
920 mils. The ending point of the range could just as well
~3~~18~~0
- 54a -
have been specif_Led as any other value in the CAD/CAM
reference scale, in which case, the block of commands would
apply to all layers in the specified range.
FIG. 20 illizstrat~~s default parameters listed in a .PRM
file, which parameters will be used if they are not specified
in either the .L or .R files. As indicated, default
parameters can be specified for each object (assuming more
than one object is being built at the same time), and for each
object, can be further specified for each vector type within
any layer of than object. For example, the default parameters
specified for thE= layer boundary vectors of the first object
are as follows: LB1, "RD 1; RS 300; RC 1; SP 20; JD 0; SS 8."
This command line=_ is interpreted as follows: the default
value for
~~4os~u
Redraw Delay is 1 (representing 200 acs gi.ven the default
SP value of 20), i:or Redraw Size is 300 (representing 2400
bits or approximately '720 mils, given the default SS of
8), for Redraw Count i~a 1 (indicating single pass, i.e.,
5 layer boundary vectors are not to be multi-passed), for
Step Period is 20 (repr<asenting 200 ~s), for Jump Delay is
0 (indicating this command is not being used), and for
Step Size is 8 (representing 8 bits or approximately 2.4
mils). Since t:he default value for RC is 1, this
10 indicates that unless multi-pass is specified in either
the .L or .R files for the layer boundary vectors, it
will not be provided for these vectors.
As is evident from the above description, the commer
cial embodiment of REDRAW utilizes a technique known as
15 the "short vector" technique, whereby any vector is
divided up into a sequence of short mini-vectors, and the
entire vector is mufti-passed by successively multi-
passing each of the mini-vectors. The objective of the
short vector technique is to eliminate the problem of
20 birdnesting, a problem which could occur if multi-passing
were attempted on the full length of vectors as a whole,
especially long vectors. In this instance, the plastic
cured during the early passes will be floating quite
awhile on the surface of the liquid resin before they
25 would be adhered to the lower layer through curing from
subsequent, add itional passes. As a result, this cured
plastic can move before it is finally adhered to the layer
below, a problem which can manifest itself as a distortion
in the final pari~, which distortion resembles a birdnest,
30 and hence is called birdnesting.
It has been found that if the short mini-vectors are
made too small, that another problem crops up, which is
the downward bending or bowed down effect, discussed
earlier with reference to FIGS. 17a and 17b, according to
35 which the cured plastic from the early passes is caused to
bow downwards from the shrinkage of the plastic below it
cured during th,e later passes. As a result of this
0
56
effect, adherence takes place too early, and upward curl
then results. The problem manifests itself in the form of
a scalloped appearance of the surface of the part.
Several approaches are possible to alleviate the
birdnesting and bowed down effects mentioned above.
First, boundary vectors are the only vectors where
birdnesting may result from their being drawn through
multiple passes since they are typically drawn in
isolation from thae other vectors, and do not therefore
have anything to adhere to when they are drawn. Hatch
vectors, on the other hand, are usually drawn after the
border vectors hare been drawn, and they therefore adhere
to the cured plastic from the border vectors when they are
drawn, even if they are drawn in multiple passes. Skin
and near-flat skin vectors also are typically drawn after
the border and hatch vectors are drawn, and may adhere to
the cured plastic from i:hese vectors when they are drawn.
In addition, the spacing between these vectors is typic-
ally very small (appro:Kimately 1-4 mils, compared to a
spacing of approximately 30-100 mils for hatch vectors),
so that adherence will also take place with cured plastic
from adjacent skin and :near flat skin vectors.
Thus, one solution to the birdnesting problem is to
only mufti-pass ithe hatch vectors, and not the border
vectors. All the hatch vectors could be mufti-passed, or
alternatively, only a percentage of the hatch vectors
could be mufti-parsed. Even if the hatch vectors did have
a bowed down appearance from the mufti-passing, this would
not affect the outer appearance of the part. This
solution is feasible in the commercial embodiment of
REDRAW described above, since the use of the .L, .R, or
.PRM files all allow mufti-pass to be implemented only for
selected vector types. Thus, REDRAW could only be
provided for the hatch vectors.
Another solution is to mufti-pass all vector types,
but to use other techniques such as Web Supports or
Smalley's to eliminate birdnesting. Web Supports are
13~ 08f9U
_ 57 _
described in more detail in Canadian Patent Application S.N.
596,837. Smalle;r's ar~~ described in more detail in Canadian
Patent Application 596,850.
A third solution is to use a two pass implementation of
multi-pass so that the cured plastic from the first pass will
be adhered on the' second pass, and will therefore only be
floating for a short while. The disadvantage is that as
mentioned earlier, more than two passes is beneficial for
dealing with the imprecision in estimating cure depth. This
disadvantage cou:Ld be alleviated by only two pass
multi-passing thc~ border vectors (where birdnesting is a
problem), but mu:Lti-passing with more than two passes for the
remainder of the vectors.
A fourth po:~sible solution is to isolate the use of
multi- pass to those areas of the part having critical volume
features, that i:~ areas that are most susceptible to
distortion, such as cantilevered sections of a part. These
areas can be iso:Lated through the use of the .R file, which
can be used to specify a range of cross sections to which
multi-pass is to be applied.
An important aspect of REDRAW is the ability to specify
different SP values (and hence different exposures) for
different passes. As discussed earlier, it is frequently
necessary to specify different exposure values for the
different passes in order to prevent adhesion from occurring
earlier than desired. Preferably, the SP values should be
chosen so that o:n the first pass, a large percentage of the
gap between layers is cured, leaving an uncured area which is
cured on successive passes, and which area has a thickness in
the range of
13~0~9U
58
only 1-5 mils depending on the layer thickness and
tolerances possib:Le. Tlhe preferred size of the gap will
depend on the layer thickness as follows:
Laver thickness Uncured sap
20 mils 1-5 mils
mils 1-3 mils
5 mils 1-2 mils
As can be seen, the size of the uncured gap remaining
after the first pass can increase with the layer thick
10 ness. This is bE>_cause the greater the layer thickness,
the more plastic that will be cured on the first pass,
which plastic will. be less susceptible to downward bending
from the shrinking of the plastic in the uncured gap as it
is cured.
After the first pa=ss, the SP for the remaining passes
should preferably be chosen to effectuate a 1-2 mil
increase in cure depth per pass. As a result, during the
pass when adherence takes place, only a very small amount
of plastic will be cured, with the result that the stress
introduced by th~~ shrinkage of the plastic during this
pass will be minimal, stress which would otherwise be
transmitted to th.e cured portion of the layer above, and
to the cured layer below.
Several examples of the dashed line, bent line, and
secondary structure techniques will now be described.
FIGS. 22a-22f illustrate an example which combines the
technique of using secondary structures and rivets to
connect rails. In all these Figures, like components are
identified with like reference numerals. Figure 22a shows
a side view of layers 107a, 107b, and 107c, which are
shown stacked on top of: each other. As shown, the layers
have been cured :in isolation from each other in order to
reduce curl by eliminating the ability of the layers to
transmit stress t.o one another while they are being cured.
As indicated, though, <j problem with curing the layers in
isolation from one another is that the final part will be
very weak, as there is nothing holding the layers
1~~~89t~
59
together. As a result, a secondary structure must be
added to connect to the layers.
Each layer in FIG. 22a is actually comprised of two
lines in paral_Lel, <~nd a top view of a layer is
illustrated in FIG. 22b, which shows layer 107b as
consisting of lines 107b(1) and 107b(2) in parallel. As
shown, the lines for a given layer have also been cured in
isolation from each other to reduce curl, and they must
also be connected by some form of secondary structure in
order to provide struci:.ure to the part.
FIG. 22b is a top view of layer 107b, which
illustrates secondary structure 108a, 108b, 108c, 108d,
and 108e, for connecting the lines of a particular layer,
in this case, lines 107b(1) and 107b(2) of layer 107b. In
addition, as will be seen, the secondary structure also
connects the lines of adjacent layers together, in this
case, lines 107b(1) and 107b(2) are respectively connected
to lines 107c(1) and 107c(2) by the secondary structure.
This is illustrated in FIG. 22c, which shows a side view
of the lines of layer 107b stacked on top of the lines for
layer 107c, and conne~~ted by secondary structure 108a,
108b, 108c, 108d, and :L08e.
The secondary structure has two aspects to it, and
comprises supporting lines of lower exposure and an area
of higher exposure known as rivets for connecting support
lines from adjacent layers together. This is illustrated
in FIGS. 22d and 22e. As indicated in FIG. 22e, the
secondary structure for layer 107b comprises, in part,
connecting support lines 108a(1), 108b(1) 108c(1), 108d(1)
and 108e(1) of lower exposure than lines 107b(1) and
107b(2) making up the layer (as a result of which the
support lines have a lower cure depth than the lines
making up the layer). In addition, the support lines are
used to connect t:he lines making up a layer, in this case
lines 107b(1) and 10'7b(2) of layer 107b. Also, the
secondary structure is comprised, in part, of areas of
higher exposure known as rivets. In FIG. 22e, these are
13~~89iJ
identified as 108,(2), 108b(2), 108c(2), 108d(2), and
108e(2), respectively, which rivets are areas of heavier
exposure than either the support lines or the lines making
up a layer, the result of which is that the rivets have a
5 cure depth which penetrates down to and adheres to the
support lines of an adjacent layer. This is illustrated
in FIG. 22d, which shows the rivets connecting the support
lines for layers 107b and 107c.
An important aspects of rivets is illustrated in FIGS.
10 23a-23c, in which like components are indicated with like
reference numerals. If lines on different layers are
connected by rivet,, then, in certain instances, it may be
important to keep the diameter of the rivets smaller than
the width of the lines. This, in turn, will be
15 accomplished by k:eepinc~ the exposure used to create the
rivets low enough so that this condition does not occur.
FIG. 23a illustrates a line with rivets 109,, 109b, and
109c, where the ~liamet~er of the rivets is much smaller
than the width of the line. FIG. 23b illustrates a line
20 where the diameter of the rivets is larger than those in
FIG. 23a. FIG. 2:3c illustrates a line where the diameter
of the rivets is even larger than the width of the line.
Keeping the diameter of the rivets smaller than the
width of the lines is only important when the lines form
25 the outer surface of a layer of the part. In this
instance, it is important to keep the rivet diameter
smaller than the :Line width so that the outward surface of
the part remains smooth. If the lines being riveted are
support lines in 'the interior of the object, it may not be
30 necessary to keep the diameter of the rivets smaller than
the width of the lines,. In fact, in this instance, as
illustrated in FIGS. ;?2b and 22e, the diameter of the
rivets can be greater than the width of the support 1 fines .
This aspect of rivets is illustrated in more detail
35 in FIGS. 24a-24d, in which like components are identified
with like reference numerals.
61
FIG. 24a illustrates a part comprising layers 107a,
107b, and 107c respectively, which layers are connected to
adjacent layers by means of rivets 109a(2) and 109b(2)
(for connecting layer 107a to 107b), and by means of
rivets 108a(2) and 108b(2) (for connecting layer 107b to
107c).
A top view of rivets 108a(2) and 108b(2) is
illustrated in FIG. 24b. If line 107b makes up the outer
surface of the fivnished part, then if the diameter of the
rivets is greater: than the width of the line, a rough
outer surface will be introduced.
Three techniques a re possible for alleviating this
problem. One technique mentioned earlier is simply to
reduce the size of the diameter of the rivets. A second
technique, illusi=rated in FIG. 24c, is to offset the
rivets from the surface 110 of the line forming the outer
surface of the finished part so that the rivets do not
extend beyond the plane of the surface. A third
technique, illustrated in FIG. 24d, and which is discussed
in detail above, is to introduce support lines, and then
rivet only the support Lines together. In fact, the above
techniques can be combined. FIG. 24d shows lines 107b(1)
and 107b(2) connected by lower exposure support lines,
which support lines are connected to support lines of
adjacent layers by rivets 108a(2) and 108b(2). In
addition, line :107b(1) is connected to a line of an
adjacent layer by means of rivets llla(2) and lllb(2), and
line 107b(2) is <~onnected to a line of an adjacent layer
by means of rivets 110a(2) and 110b(2). If either of
these lines forma the outer surface o,f the part, then as
discussed above, the diameter of the rivets cannot be too
large, or if it ~_s, the rivets must be offset towards the
interior of the part so they do not extend beyond the
plane of the out~ar surface of the part.
Note that in FIG. 24d, parts have been successfully
built where the distance 112 between lines on the same
layer is in the :range ~of 40 to 300 mils, and in addition,
62
where lines on succes>sive, adjacent layers are also
separated by this. dist;~nce. However, other examples are
possible, either by separating the lines by more or less
than this range, and the above range is provided for
illustrative pur~roses only, and is not intended to be
limiting.
FIGS. 25a-25c illustrate another example of using a
secondary structure to connect lines. In these Figures,
like components are identified with like reference
numerals. As shown in FIG. 25a, successive structures
113a, 113b, 113c, and 113d are drawn, wherein each
structure, as illustrated in FIG. 25c has a portion
113a(1) made with relatively low exposure, and another
portion 113a(2) made with higher exposure. Moreover, as
illustrated in FIG. 25a,, the exposure chosen to make the
higher exposure portior.~ should be such that successively
stacked high expo:~ure portions, 113a(2) and 113c(2) in the
Figure, barely touch. l.n fact, successful parts have been
made using this t.echnic;ue where successive high exposure
portions are within 40-300 mils of each other, but this
range is provided. for illustrative purposes only, and is
not intended to be limiting.
Note that lower Exposure portions from successive
layers, 113a(1) a:nd 113Jo(1) in the Figure, overlap, and it
is necessary to rivet these overlapping portions together
so that successive layers adhere to one another. This is
illustrated in F_CG. 25b, which shows rivets 116a, 116b,
and 116c holding together overlapping lower exposure
portions from successive layers, 113a(1) and 113b(1) in
the Figure. Note that the outer surfaces 114 and 115 of
the part are farmed from the stacking of the higher
exposed portions from successive layers, surface 114 being
made up, in part,, of stacked portions 113a and 113c, and
surface 115 being made up, in part, of stacked portions
113b and 113d.
Note that all the curl reduction techniques described
above reduce curl through one of three ways: 1.) reducing
I3~089~
63
stress; 2.) resisting stress; and 3.) relieving stress.
An example of 1.) is multi-pass where successive layers
are cured through multiple passes so that when they do
adhere, only a small amount of stress will be transmitted
to adjacent layers. An example of 2.) is the multi-pass
technique whereby as much of a layer as possible is cured
on the first pass, so that this portion of the layer will
be strong to both resist downward curling, and to resist
the layer below from upward curling. An example of 3.) is
dashed or bent lines, where stress is actually transmitted
from one layer t:o another, but breaks or bends act to
relieve the stress.
The appropriate curl reduction technique for a given
application will involve a trade-off between structural
strength and curl. In general, the higher the structural
strength required for a particular application, the more
curl.
FIGS. 26a-2E~c illustrate a part made with different
curl reduction techniques. FIG. 26a shows the part made
with dashed lines, FIG. 26b shows bent lines, and FIG. 26c
shows a part made: using the secondary structure technique
described above with respect to FIGSs. 25a-25c. With
respect to FIG. 26a, parts have been successfully built
where the length of the solid portions of a line,
identified with reference numeral 117a in the Figure,
range from 40 to 300 mils, and where the breaks between
the successive solid portions, identified with reference
numeral 117b in the Figure, were also in the range of 40
to 300 mils. However, these ranges are illustrative only,
and are not meant to be limiting.
With respect to :FIG. 26b, parts have been success-
fully made with bent lines, where the solid portion of a
line, identified wit'.h reference numeral 108a in the
Figure, is in the rang a of 40-300 mils, and in addition,
where the gaps in then line between the solid portions,
identified with reference numeral 118b in the Figure, is
13~089~~
64
also in this range. Agrain, this range is intended to be
illustrative, and not limiting.
With respect to FIG. 26c, parts have been
successfully built where the distance between parallel
lines of a particular layer, identified with reference
numeral 119 in the' Figure, is in the range of 40-300 mils.
The above range is provided for illustrative purposes
only, and other examples are possible.
A problem with the dashed line technique is that
because of the breaks in a line, a bad part surface finish
may result, and in addition, the parts may be flimsy.
Three variants of the techniques are available to
alleviate these problems, which variants are illustrated
in FIGS. 27a-27e, in which like components are identified
with like reference numerals.
The first variant, the "brick and mortar" variant, is
illustrated in FI:G.27a. According to this variant, the
solid portions of a dashed line are analogized to bricks,
and the breaks between successive bricks are filled in
with liquid resin analogized to mortar, which is then
cured with less exposure than the bricks. A problem with
this variant is that if the mortar is subsequently exposed
at the same level as the bricks to improve strength, curl
will be reintroduced.
The second variant is illustrated in FIG. 27b, in
which a dashed line is placed on a solid line. FIG. 27b
shows the order in which the indicated portions are
successively curf~d. ids indicated, the solid layer is
drawn, and then on top of it are drawn spaced bricks, and
then the interst:~ces between the bricks are filled with
mortar, which interstices are then cured, preferably at a
lower exposure than the bricks. An advantage of curing
the bricks on top of the solid layer is so that the solid
layer will be strong to resist upward curl.
The third variant is illustrated in FIG. 27c, which
variant is to offset a dashed line placed over another
dashed line so that th.e solid portions of one line span
~.34o~~u
the breaks in the secondl line. FIG. 27c shows the order
in which the indicated f>ortions are cured. As indicated,
bricks are drawn on one 1_ayer, and then on the next layer,
bricks are also drawn, but offset from those on the first
5 layer, so that the bricks on the second layer span the
interstices betwes:n the bricks on the first layer. A
problem with this technique is that it results in almost
as much curl as if standard solid lines were drawn.
Other variations of the dashed line technique are
10 illustrated in FIGS. 27d and 27e, where the numerals
indicate the order o:E drawing the indicated solid
portions. FIG. 27d showy placing a first dashed line on
a solid line, and a second offset dashed line placed on
the first dashed line. FIG. 27e shows placing several
15 dashed lines on a solid line which are lined up, and then
offsetting successive dashed lines.
The bent line technique illustrated in general in
FIG. 26b, and variants on this technique are illustrated
in FIGS. 28a-28i. As indicated in FIG. 28a, the basic
20 idea of the bent line technique is to relieve the stress
transmitted to a given layer from adjacent layers. With
respect to FIG. 28a, si=ress introduced to portions 118a
and 118b of line :118, are taken up by lateral movement of
these portions into gap 118c. This is because something
25 must give to relieve the stress, and in the example of
FIG. 28a, what gi~~es is the portions 118a and 118b, which
are allowed to move laterally into gap 118c.
Parts have been successfully built with the
dimensions indicated in FIG. 28b, that is with the solid
30 portions of a line in the range of 40 - 300 mils, and the
gaps between the :solid portions also in this range. Other
examples are po:~sible, and the indicated ranges are
intended to be illustrative only, and not limiting. The
size of the ga~~s should preferably be as small as
35 possible, but as a pracaical matter, the size of the gaps
depends on the tcleranc:es possible, because it is crucial
that successive solid portions do not touch. In the
~3~~89f~
66
example of FIG. 28a, it .is crucial that gap 118c is not so
small that solid portions 118a and 118b touch. If they
touch, then curl will result. Therefore, the lower the
possible tolerances, the greater should be the gaps
between successive solid portions of a bent line.
Successful parts have been built with the gaps as small as
40 mils, but smaller gaps are possible. FIG. 28c shows
an example of a bent lire where the gaps are much smaller
than the length of the solid portions.
A benefit of the bent line technique compared with
the dashed line technique, is that bent lines can be much
stronger than dashed lines, and in addition, their stress
resistance can be much greater after a part is built using
bent lines.
FIG. 28d shows a variant of a bent line where the
bends in the line have a triangular shape. Parts have
been successfully built with each triangular bend on the
order of 250 mils (1/4 inch) in length. In addition, the
angle of the vertex oi: each triangular bend, although
indicated at 90° in FIG. 28d, can vary from this. In
fact, if made smaller than this, the resulting line will
resemble that in FIG. 28c, and even more curl can be
eliminated. If the angle is made greater than this, the
bent line will resemble a straight line, and the curl
effect will be more pronounced.
Another variant of a bent line is illustrated in
FIGS. 28e and 28f. As indicated in FIG. 28e, parts have
been successfully built. using bent lines where the bends
in the line have an inverted triangular shape as illus-
trated, and where each bend has in FIG. 28f the dimensions
indicated, that is, a width of 125 mils (1/8 inch), with
the gaps between successive solid portions 40 mils or
smaller, and with the angles of each triangular bend at
45°, 45°, and 90°, respectively. As before, it is crucial
that successive solid portions of a bent line do not
touch. Otherwise, curl will be introduced. Therefore, in
FIG. 28e, the gaps in t:he line should be kept as small as
~~~osoo
67
possible as long as successive solid portions do not
touch. FIG. 28g shows another variant of a bent line
technique where the bends have a trapezoidal shape. Other
examples are possible, and the examples above are intended
to be illustrative only, and are not intended to be
limiting.
As with dashed lines, a part built with bent lines
may have a poor surface finish. To get around this
problem, a bricks and motar variant of bent lines is
possible whereby the gaps in the bent lines are filled
with liquid resin and thereafter partially exposed. As
before with the dashed line, if this resin is cured to the
same exposure as the rest of the line, the curl effect
will be introduced. FIG. 28h illustrates the technique of
filling in the gaps in the line with liquid resin and then
partially exposing the resin in the gaps. The numbers
indicate the order in which the portions shown are cured.
Another variant is, to place a bent line on a solid
line as indicated in FIG. 28i, which has the advantage
that the solid line drawn first resists upward curl. In
addition, to improve the surface appearance, as in FIG.
28h, the gaps in the bent line are filled in with resin
and partially exposed. The order in which the curing
takes place is indicated by the numerals in the Figure.
FIG. 28j il:Lustra!tes another variant where a first
bent line is placed on a solid line, and a second bent
line is placed on the first bent line but offset from the
first bent line :>o that the solid portions of the second
bent line span i=he gaps in the first bent line. The
numerals indicate the order in which the portions
indicated in the Figure are cured.
Implementatuons of the rivet technique for reducing
curl will now be described. An early implementation of
rivets was in the form of programs written in the Basic
Programming Language which programs provided for layers of
a part to be dirEactly acanned by a laser beam without the
intermediate step of reformatting the data describing the
.~3~~~9~J
- 68 -
layers into vectors as described in co-pending Canadian
Application 596,E;25. These layers were scanned so that the
cure depth for each layer was less than that required to cause
adhesion between the layers. The program would then provide
for additional scanning (exposure) of selected areas of each
layer in order to cause adhesion, but only at these selected
areas. It was found that if the number of these areas at
which adhesion w~~s to occur was relatively small, that minimal
distortion and curl would be generated by the adhesion of the
layers. These higher exposure adhesion areas are what is
referred to here as rivets, and although part distortion can
increase as the number of adhesion points increase, it will be
a small effect if the number of adhesion areas is small.
Later implementat_Lons were consistent with the
intermediate step of reformatting the layer data into vectors.
More details about the different vector types are provided in
Canadian Application S.N. 596,825. These implementations
require that individual vector lengths would be small for
those vectors that contribute to adhesion between layers and
that there should be gaps between these vectors. In addition,
it may be accept~~ble to use a large number of adhesion vectors
between layers to insure structural integrity of the part, as
long as these vectors are interior to the outer boundaries of
the part so that any curl that results will not affect surface
accuracy.
Also, these vectors should generally be placed so that
their length is perpendicular to the direction of probable
~.~~089~.~
- 69 -
distortion. For example, on a cantilever, the direction of
these vectors should preferably be perpendicular to the axis
of the cantilever sect_Lon. FIG. 29a illustrates an
undistorted cantilevered section 120, made up of individual
layers 120a, 120b, 120c, 120d, and 120e, which adhere to
adjacent layers a.s shown to make up the overall section. The
cantilevered section i:~ what is commonly referred to as a
rail. As shown, the se=ction is supported by supports 120
which in turn mak=e direct contact with platform 122. The axis
of the section ins also indicated in the Figure.
FIG. 29b ill.ustrat=es the same cantilevered section
reflecting the distortion caused by curl. In the Figure,
compared with FIC~. 29a, like components are identified with
like reference numerals. As shown, the direction of the curl
is upwards, in the samE~ direction as the axis of the
cantilevered sect=ion.
FIG. 29c is a top view of layer 102d of the section
showing the direc=tion of the vectors that contribute to
adhesion between layer 102d and layer 102e. As shown, the
direction of these vectors is all perpendicular to the
direction of dist:ortio:n, and therefore to the axis of the
cantilevered section.
A problem w_~th this early vector-based implementation is
that it depended on the geometry of the part by virtue of its
dependence on the=_ direction of the axis of the part. More
recent vector-ba;~ed implementations have taken a different
approach that provides the dramatic benefits described above
~3~0890
- 69a -
with rivets, but at the same time ensures good structural
integrity without. such a strong dependence on part geometry.
In these early vector-based implementations of rivets,
the mnemonics used to describe the different vector types
differed from that used in Canadian Application S.N. 596,825.
A detailed description of the different vector types is
available in thi~> application. Briefly, boundary vectors are
used to trace the' parameter of a layer, cross hatch vectors
and used to trace the internal portions of a layer, and skin
fill vectors are used too trace any outward surfaces of a part.
They are traced in the following order: boundary,
~3~089U
~0
cross hatch, and :skin fill. The following list shows the
correspondence between these mnemonics:
1). For layer boundary vectors, "Z" was used to
describe these ve~~tors instead of "LB".
2). For layer crosshatch vectors, "X", "Y" and "I"
were used to describe X, Y and 60/120 crosshatch vectors,
respectively. In later implementations, these vectors
were combined together and characterized by the single
mnemonic "LH".
3). For up facin<~ skin boundary vectors, "S" was
used as the single mnemonic to describe both flat and
near-flat boundary vectors. In later implementations,
these vector types were separated out into different
categories characl~erized by the "FUB" and "NFUB" mnemonics
respectively.
4). For up facing skin hatch vectors, "A", "B", and
"J" were used to describe X, Y and 60/120 skin cross hatch
vectors, respectively. Up facing skin hatch vectors have
no counterpart under the mnemonics used in current
implementations.
5). For up facing skin fill vectors, "H" and "V"
were used to describe X and Y skin fill vectors, respect-
ively. Both flat and near flat fill vectors were included
within these mnemonics. In later implementations, X and
Y fill vectors were combined, but the flat and near flat
vectors were separated out. The new mnemonics are
respectively "FUF" and "NFUF".
6). For down facing skin boundary vectors, "C" was
used to describe both flat and near-flat boundary vectors,
but in later im~~lementations, these vector types were
separated out and de~~cribed by the "FDB" and "NFDB"
mnemonics, respecaively.
7 ) . For down facing skin hatch vectors, "F" , "G" ,
and "K" were used to characterize X, Y, and 60/120 cross
hatch vectors, rs;spect:ively. In more recent implementa
tions, only down facing near flat skin hatch vectors are
possible, which are described by the mnemonic "NFDH".
~~~0890
- 71 -
8). For facing skin fill vectors, "D" and "E" were used to
distinguish X and Y skin fill vectors respectively. Both flat
and near flat fill vectors were included under these
mnemonics. In later implementations, both X and Y fill vector
types were combined into one mnemonic, however the flat and
near flat vector types were separated out. The new mnemonics
are "FDF" and "Nl?DF", respectively, for the flat and near flat
vector types.
The first a:~pect of the vector-based implementation of
rivets is specifying a critical area of a particular layer or
layers in which rivets will be placed. These critical areas
are specified by creating what is known as a critical box
file. This file contains one or more box specifications
enclosing volumes that will either have their crosshatch
vectors riveted or not scanned at all. An XV placed at the
beginning of a box specification indicates that crosshatch
vectors inside the box will not be scanned. The critical box
file is an ASCII file generated by any convenient text editor
and is given the same name as that of the output files (the .L
and .V files) th<~t will be created by the MERGE program, which
merges .SLI file; for different objects before beginning the
process of tracing out vectors (described in more detail in
Canadian Applicat=ion S.N. 596,823, except it will have the
extension .BOX instead of .L or .V. Briefly, the CAD file for
an object is refs=_rred to as the .STL file for that object. A
program known as SLICE slices or converts the .STL file into
vector-based lay°r data which is placed into an .SLI file for
134p~9U
71a -
the object. MERGE then merges the .SLI file for different
objects to form ~~ .V file containing the merged vector data,
and also a .L fi:Le for control purposes. The BUILD program
then takes the .'J and .L files, and begins tracing out the
vectors. When the MERE program begins to merge its input
Z
72
.SLI files for different objects, it looks for a corres-
ponding .BOX file. I:E this file is found, MERGE then
appends critical area designations onto all layers that
are indicated as requiring them.
Its content: consist of one or more single line
critical box spec:ificat:ions. A single box consists of a
rectangular volume for a particular vector type followed
by its position i.n spac:e. A typical specification might
look like,
"XV,.94,.04,.250,.8.750,.250,.250,4.375,.250,4.375,8
.750"
The XV indicates that this box surrounds a volume to be
riveted.
The 0.94 indicates the location of the bottom of the
box in the same units and reference scale as that used in
the CAD design of the part. If the CAD units are inches,.
the 0.94 indicates th:3t the bottom of the box is .94
inches from the bottom of the CAD space. The 0.04
represents the height of the box in CAD units (inches in
the above example) above the bottom. The next eight
numbers are read as XY pairs that indicate the corners of
the box in CAD units and are based on the location of the
part in space as designated by the CAD system. FIG. 30
shows the format of a typical .BOX file (entitled for
illustrative purposes only as RIVET. BOX), which file
describes two boxes specifying volumes that will be
riveted. The example shows the file as consisting of a
single text line which is wrapped around for printing
purposes only.
Note that a. benefit of the MERGE program is that
different riveting parameters can be specified for differ-
ent subvolumes of an object by placing the different
subvolumes into aeparate .STL files, slicing them separ-
ately into different .SLI files for each subvolume, and
then merging them. This is because different riveting
parameters can be specified for each .SLI file. More
details on the .SLI and .STL file formats are provided in
~~~~8~0
- 73 -
Canadian Applical~ion S.N. 596,825.
An alternative to the use of the .BOX file to control
riveting to specify rivet commands in the .L file which allow
rivets to be coni~rolled on a layer by layer basis, and within
a layer, on a vector type by vector type basis. Another
approach to controlling riveting is to specify default rivet
parameters for particular vector types in the .PRM file.
Briefly, the .PRM file contains default parameters, and if
BUILD cannot find a particular riveting parameter in the .L
file, it will se~~rch the .PRM file for the parameter. The
rivet commands a:re described below.
1.) VC is ;~ mnemonic for Rivet Count, a command which
has an argument ~~f 1 to 7, and which indicates the number of
passes to make w:nen riveting a vector in a layer to an
adjacent layer. The command format is "VC 2" and "VC 5", for
specifying two o:r five passes, respectively.
2.) VR is ~~ mnemonic for Rivet Reduction, which is a
command that can be used to prevent hatch vectors from being
riveted right up tot he point where they contact boundary
vectors since this may cause a deterioration of the surface
finish of the part along with greater distortion. Compared to
the early vector-based implementation of rivets, which was
heavily dependent on the geometry of the part, the use of
cross hatch vectors for riveting provides geometry
independence since hatch vectors, being present at most if not
all layers, will provide layer to layer adhesion. If it were
ever necessary for a particular application to shape riveting
~~~~89~
- 73a -
to a particular part geometry, the use of the .BOX file to
specify critical box configurations, and the specification of
different riveting parameters for different subvolume .SLI
files which are 1=hen merged as described earlier, will provide
the ability to do so.
The VR commend calls for all scans, except for the first
one, to be of the=_ reduced length. In other words, the first
scan is done at Full vector length, and
140890
74
additional scans are reduced by the VR amount. The
command takes an argument that specifies a particular
distance at each end of a vector that will not be riveted,
which argument c:an have a value in the range of 1 to
65535. This argument indicates the number of SS multiples
taken off of each end of the vector before doing the
multiple scans specified by the VC command. Since the
argument for SS is in terms of bits (1 bit is approxi-
mately .3 mil), the argument for VR can be translated into
bits by multiplyW g it by the SS parameter.
3.) VP is a mnemonic for Rivet Period, and is a
command which is similar to SP in that it specifies an
exposure volume for each scan specified by the VC command.
As with REDRAW, where an exposure value could be specified
for each pass, the VI? has an argument for every scan
called for by the VC command. Each argument can take on
a value of appro:~cimately 10 to 6500 in units of lO~CS. A
typical VP command for VC=4 might look like:
"VC 4;VP 40, 50, 60, 70".
This command would be interpreted as follows: The first
scan will be over the entire vector length and will have
an SP of 40. It is likely that this SP value was chosen
such that the cure depth obtained by this scan is slightly
less than the layer thickness. The second scan will be
over a vector whose end points have been displaced by an
amount specified by the VR command and which is drawn
according to an SP of 50. The third scan covers the same
area as the second scan but its drawing speed is based on
an SP of 60. The: fourth scan is identical to the previous
two except for a drawing speed based on an SP of 70., Note
that these rivet. commands are only used on the various
types of crosshatch.
As discussed earlier with respect to the implementa
tion of multi-paas known as REDRAW, the .L file is created
by a standard text editor, and is used by BUILD (or
SUPER, depending on 'the software version) program for
layer to layer control of the curing process. The R.
~~~g~~~~
- 75 -
file, which provides control for a range of layers, is not
available to control riveting for the particular
implementation oj' rivets described here. The .PRM file is
used by BUILD to obtain default riveting parameters when a
particular parameter is not specified in the .L file. In sum,
the .L file is u:~ed to control riveting on a layer by layer
basis, and within a layer, on a vector type by type basis.
The .PRM file is used only in those instances where a critical
riveting parametE~r is not specified in the .L file.
The format of a .L file for use in controlling riveting
is provided in F:LG. 31. As above, the file is named RIVIT.L
for illustrative purposes only, and shows layer 920 with no
rivet parameters specified. Layer 940, on the other hand, has
a number of rivei~ing commands which apply to it, which
commands are framed by the #TOP and #BTM mnemonics. Note that
unlike the RIVET.BOX file, where parameters are specified in
CAD units, parameters in the .L and .PRM files are specified
in SLICE units. CAD units are the units in which an object is
designed on a CA:D system, and are the units associated with
the .STL file for an object. SLICE units are the units into
which the object is sliced into layers by the SLICE program,
and is associated with the .SLI file for that object. For CAD
units in inches, for example, and a desired SLICE resolution
of 1,000, the SLICE units will be in mils. CAD units, SLICE
units and resolution are described in more detail in Canadian
Application S.N. 596,825.
In FIG. 31, the first riveting command line specified for
13~~8~U
- 76 -
layer 940 is "#C~~ XV, 250, 250, 3750, 8750, 250, 8750" where
the mnemonic #CA stand: for Critical Area. This command is
similar to the .E30X file discussed earlier, and specifies a
critical box, within which the cross hatch vectors are either
riveted or not scanned at all. The XV mnemonic indicates that
the cross hatch vector: will be riveted. The next eight
numbers are four XY pa:Lrs (in SLICE units) that describe the
corners of box which makes up the critical area.
The next command :Line for layer 940 is a command which
applies only to "Z" vectors (which are layer boundary vectors,
and as per the table provided earlier, are referred to in
later implementations with the mnemonic "LB"). As indicated,
the command line is "SS 8; SP 100; JD 0: RC 1", which since a
VC command is not: specified, indicates that the layer boundary
vectors are not being :riveted. The next command line for
layer 940 applies only to the "X" vectors (as per the above
table, X cross hatch i;s now combined with Y and 60/120 cross
hatch into the s_ngle mnemonic "LH") and is as follows: "SS
8; SP 100; JD 0; RC 1; VC 2; VR 500; VP 20, 100". The "VC 2"
command specifies a Rivet Count of two passes, where an
exposure of 20 is specified for the first pass, and an
exposure of 100 is spe~~ified for the second pass. Given
exposure units o. 10 ACS, this translates into an exposure of
400 ~,s, and 1,000 ~.s, respectively. The command "VR 500"
indicates that for the second pass, the X cross hatch vectors
will only be rivE=_ted to within 500 SS multiples from where the
cross hatch vectors join the layer boundary vectors. Given an
~3~fl89U
_ 77 _
SS of 8 bits (approxim<~tely 2.4 mils), this translates into an
offset of approximately 1,200 mils (1.2 inches) from the ends.
FIG. 32 shovas an c=xample of a ,PRM file, entitled
SUPER.RPM for il7.ustrative purposes only. The .PRM file is
described in greater dE=_tail in Canadian application Serial No.
596,825, and the only aspects of the example pertaining to
default riveting paramf~ters will be described here. First,
the only default riveting parameters indicated are for the
layer cross hatch vectors for the first object (described in
the Figure by the: mnemonic "LH1", which as per the table
above, in earlier imply=mentations, would have been described
with the mnemonics "X", "Y" or "I", for X, Y or 60/120 cross
hatch, respectively) and for the near flat down-facing skin
vectors for the i:irst object (described in the Figure with the
mnemonic, "NFDH1", which, as per the table, would have been
described in ear7_ier implementations with the mnemonics "F",
"G", and "K", for X, Y, or 60/120 cross hatch, respectively).
The relevant portion of the file is reproduced below:
LH1, "RC 2; SP 20, 80; JD 0; SS 8;
VCR 5; ! rivet count
VR 99; ! rivet reduction
VP 11, 12, 13, 14, 15" ! rivet step amount
periods
NFDH1, "RC 1; SP 176; JDO; SS 2; VC 5; VR 99; VP
11,12, 13, 14, 15"
First, the portion of each line following the "!" is a
comment for read<~bility purposes only. For the layer cross
~3~0890
- 77a -
hatch vectors, th.e default Rivet Count is 5 passes, with an
exposure of 11, 12, 13, 14 and 15 specified for each
respective pass (which given exposure units of 10~s,
translates into exposures of 110, 120, 130, 140, and 150 ~s,
respectively). The default Rivet Reduction amount is 99 SS
multiples, which given the default SS of 8, translates into a
value of 792 bits or approximately 237.6 mils. For the near
flat down-facing skin vectors, the default riveting parameters
are identical to those specified for the layer cross hatch
vectors.
The .V file produced by MERGE is illustrated in FIG. 33.
The file consists of the vectors to be traced for each layer
divided into the various vector types. As indicated, for
layer 920, the XY pair: for the layer boundary vectors
(indicated by the mnemonic "Z1", with "1" denoting the first
and only object) are listed followed by the XY pairs for the
cross hatch vectors (indicated by the mnemonic "X1"). Then,
the layer boundary and cross hatch vectors are listed for
layer 940.
Aspects of meaning the effectiveness of the various
techniques above will now be described in terms of a
diagnostic part called a "quarter-cylinder", which is a type
~.~4~~9~
of part specifically developed in order to measure the
impact on curl of any of: the aforementioned techniques.
'The quarter-cylinder is actually a cantilevered beam
made up of a number of layers which adhere to adjacent
layers to form t:he overall beam. An aspect of the
quarter-cylinder is the measurement of upward (or
vertical) curl, which results from the adhesion of layers
to adjacent layer~~. FIGS. 34(a) and 34(b) provide a side
view of a quarter cylinder which shows the effects of
upward curl. The quarter cylinder comprises cantilevered
beam 120 made up of layers 120a, 120b, and 120c, which are
supported by platform 7.21. FIG. 34a shows the quarter-
cylinder before the e~Efects of upward curl have been
introduced, while FIG. 34b shows the same quarter-cylinder
after the effects of upwerd curl have been introduced.
FIG. 34b illustrates another aspect of upward curl, which
is that as the number of cured layers increases, they
become more effective in resisting the torque produced by
the successively curecl layers. As a result, in the
example of FIG. 34b, by the time layer 120c is cured, the
effects of upward curl have just about disappeared.
It is important to note that a layer may actually be
cured in steps where horizontal, adjacent lines are
successively cured to form the overall layer. When a line
is cured along-side an already cured line, the first line
will shrink and cause. the already-cured line to curl
horizontally depE;nding on the degree of adhesion between
the line. This effect is illustrated in FIGS. 34c and
34d, wherein FIG. 34c illustrates a top view of layer 120a
comprising lines 123a, 123b, and 123c, respectively, while
FIG. 34d shows the effects of horizontal curl on the same
layer. As indicated, as more lines are built, the effects
of horizontal curl become less pronounced since the
already cured lines become better able to resist the
torque exerted by successive lines.
Another aspect of the quarter cylinder is its ability
to measure anoth~sr typ<a of curl known somewhat graphically
13~U~~i~
_ 79 _
as "sneer". Sneer wil:L be explained after the entire
structure of the quarter cylinder has been explained.
A specific e:~ample of a quarter cylinder is
illustrated in F7:G. 35a. As illustrated, the part comprises
upper layers 124, support layer 125, post-layers 126, and base
layer 127. Advantageously, upper layers 124 comprise 25
layers, post-layers 126 comprise 8 layers, base layer 127
comprises 1 layer, and support layer 125 comprises 1 layer.
Other examples are possible, however, and this example is
provided for illustrative purposes only, and is not intended
to be limiting.
As illustrated in FIG. 35b, which illustrates a top
view of the guar>;er cylinder, each advantageously comprises
inner and outer concentric circularly curved rails, 128 and
129, respectivel,~, where the inner rail has a radius of 27 mm
and the outer rail has a radius of 30 mm. As illustrated in
FIG. 35c, the curved rails subtend an angle of 5u/12 radians,
slightly less than 90°.
With reference to FIG. 35a, post layers 126 comprise
post-pairs 126a, 126b, 126c, and 126d, and as illustrated in
FIG. 35c, each post-pair advantageously comprises two posts.
Post-pair 126a, for example, comprises posts 126a(1) and
126a(2), respectively. Also, as shown in FIG. 35(C), ~./4
radians, a little over half, of the concentric arc is
supported by posts, with each post pair advantageously
uniformly spaced by x.%12 radians along the supported portion
of the arc.
.I34089U
- 79a -
With reference to FIG. 35d, the inner and outer
rails of a layer are advantageously connected by 21 uniformly
spaced support lines oi: lower exposure (which are analogous to
cross hatch vectors described in Canadian Application S.N.
596,825, and which therefore, will be known here simply as
cross hatch), where each line is advantageously uniformly
spaced by x,/48 radians. Advantageously, the cross hatch is
exposed at a lower exposure so that the cross hatch for a
given layer does not initially adhere to cross
1~~'D~DD
hatch for an adjacent layer. Finally, as illustrated in
FIG. 35e, starting with the first cross hatch line, the
center of every ether cross hatch on a given layer is
given extra exposure, i.e. riveted, so that it adheres to
5 the cross hatch below at this location. In FIG. 35e,
successive rivets for a particular layer are identified
with reference numerals 130a, 130b, and 130c, respect-
ively. As described eaarlier, the use of rivets is a
technique for reducing upward curl.
10 The part is advantageously built with 10 mil layers,
but the exposure is varied amongst layers to provide
different cure dEpths. This allows the measurement of
curl at different cure depths. The base layer is advan-
tageously given enough Exposure to ensure good adhesion to
15 the elevator plat:Eorm (not shown), which corresponds to a
30 mil cure. Then posts are advantageously given enough
exposure to ensure good adhesion to the previous layer,
which also corresponds i~o a 30 mil cure. The support rail
is advantageously given a 30 mil cure to assure sufficient
20 strength to resist resin currents during dipping. The
rivets are advant.ageoussly .exposed at a cure depth of 30
mils, to ensure )_ayer to layer adhesion of the lines of
the upper layers. The upper lines, both inner and outer,
and the supporting cross hatch lines are advantageously
25 exposed at a varying cure depth, which parameter is varied
to developed a curve of cure depth versus curl for the
particular curl reduction technique used to make a quarter
cylinder. An overall perspective of a quarter cylinder is
provided in FIG. 35f.
30 To measure curl for a particular curl reduction
technique, the cure depth of the lines of the upper layers
can be varied between one or two mils up to 40 mils. At
each cure depth, as illustrated in FIG. 35g, the thickness
of the quarter cylinder is measured at two locations: 1.)
35 at the first rivEa from the unsupported end of the upper
layers, which location is identified with reference
numeral 131 in FIG. 35g, and the thickness at this
~~~~899
81
location is identified as "s" in the Figure; and 2. ) at
the first rivet from the supported end of the upper layer,
which location is identified with reference numeral 132 in
the Figure, and. the thickness at this location is
identified as "f" in the Figure. The curl factor for a
given cure depth is defined as the ratio f/s. The curl
factor for a range of cure depths are computed, and then
plotted against cure depth. After a particular curve is
plotted, the above would be repeated for different curl
reduction techniques, to find the best curl reduction
technique for a particular application. The above
describes the use: of a secondary structure combined with
rivets to reduce curl, but other techniques described
earlier, such as dashed or bent lines, multi-pass, etc.,
are possible to <waluate with this technique. FIG. 35h
illustrates several :such plots for different curl
reduction techniques.
The type of curl known as sneer will now be
described. It should be noted that if a straight
cantilevered bar were u:~ed to measure curl, the effects of
sneer could not be produced or measured. It is only by
curving the layers of the cantilevered sections to form a
quarter cylinder that the effects of sneer will occur.
With respect to FIG. 35d, when inner and outer lines
129 and 128, respectively, are cured, they will shrink by
the same approximate percentage. Since the percentage of
shrink is about the same, the extent to which the radius
of the outer line shrinks will be greater then the extent
to which the inner line shrinks, since for the larger
radius, a greater incremental change is required to
achieve to same percent;3ge change. The result is that the
outer line will t;ransm.it more stress to the surrounding
structure. The presence of the cross hatch will prevent
the relieving of the stress by movement of the outer line
inwards towards the innE~r line. Therefore, to relieve the
stress, the outer line typically moves upwards to produce
the effect known ;~.s sneer. Note that the effect of sneer
~3~~8L9~
82
will be more pronounced i~he larger the radius of the cross
section of the part under examination.
Sneer can be illustrated with the aid of FIGS. 36a
36c, respectively, which illustrates a side, front, and
top view of a particular part having slotted sections
131a, 131b, and 131c. The effects of sneer are
illustrated in FIG. 36d, which shows that the areas of the
part at the outEar radius distort more, and in some
instances, shown at M of 131c in the Figure, the
distortion is so ~~reat as to cause the solid portion of
the part to split. This is indicated with reference
numeral 131d in the Figure.
Therefore, the quarter-cylinder can also be used to
evaluate the impart on sneer of the various techniques
described above.
It will be apparent from the foregoing that, while
particular forms of thE: invention have been illustrated
and described, various modifications can be made without
departing from the spirit and scope of the invention.
Accordingly, it :is not intended that the invention be
limited, except a:~ by t:he appended claims.
