U.S. patent application number 14/051810 was filed with the patent office on 2015-04-16 for apparatus and method for forming three-dimensional objects using a curved build platform.
This patent application is currently assigned to Global Filtration Systems, a dba of Gulf Filtration Systems Inc.. The applicant listed for this patent is Global Filtration Systems, a dba of Gulf Filtration Systems Inc.. Invention is credited to Ali El-Siblani, Alexandr Shkolnik, Chi Zhou.
Application Number | 20150102531 14/051810 |
Document ID | / |
Family ID | 52809030 |
Filed Date | 2015-04-16 |
United States Patent
Application |
20150102531 |
Kind Code |
A1 |
El-Siblani; Ali ; et
al. |
April 16, 2015 |
APPARATUS AND METHOD FOR FORMING THREE-DIMENSIONAL OBJECTS USING A
CURVED BUILD PLATFORM
Abstract
An apparatus and method for making a three-dimensional object
from a solidifiable material using a linear solidification device
is shown and described. In certain examples, the linear
solidification device includes a laser diode that projects light
onto a scanning device, such as a rotating polygonal mirror or a
linear scanning micromirror, which then deflects the light onto a
photohardenable resin. As a result, the linear solidification
device scans a line of solidification energy in a direction that is
substantially orthogonal to the direction of travel of the laser
diode. In other examples, the linear solidification device is a
laser device array or light emitting diode array that extends in a
direction substantially orthogonal to the direction of travel of
the array.
Inventors: |
El-Siblani; Ali; (Dearborn
Heights, MI) ; Shkolnik; Alexandr; (Los Angeles,
CA) ; Zhou; Chi; (Amherst, NY) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
Global Filtration Systems, a dba of Gulf Filtration Systems
Inc. |
Dearborn Heights |
MI |
US |
|
|
Assignee: |
Global Filtration Systems, a dba of
Gulf Filtration Systems Inc.
Dearborn Heights
MI
|
Family ID: |
52809030 |
Appl. No.: |
14/051810 |
Filed: |
October 11, 2013 |
Current U.S.
Class: |
264/401 ;
425/174 |
Current CPC
Class: |
B29L 2031/7739 20130101;
B29L 2031/772 20130101; B29C 64/135 20170801; B29C 64/245 20170801;
B33Y 10/00 20141201; B29C 64/241 20170801 |
Class at
Publication: |
264/401 ;
425/174 |
International
Class: |
B29C 67/00 20060101
B29C067/00 |
Claims
1. An apparatus for making a three-dimensional object from a
solidifiable material, comprising: a solidification energy source;
a source of the solidifiable material; a build platform movable
along a build axis, wherein the build platform has a
cross-sectional profile when viewed along a cross-sectional axis
direction perpendicular to the build axis, and the cross-sectional
profile includes a curved surface.
2. The apparatus of claim 1, wherein the curved surface has a
substantially constant radius of curvature.
3. The apparatus of claim 1, wherein the build platform has an
upper surface and a lower surface, the lower surface is between the
solidification energy source and the upper surface, and the lower
surface is the curved surface.
4. The apparatus of claim 3, wherein the lower surface is curved in
a direction along a travel axis perpendicular to the build axis and
the cross-sectional axis.
5. The apparatus of claim 3, wherein the lower surface has
direction of curvature and a mid-point along the direction of
curvature, the lower surface includes a sagittal line extending
along the cross-sectional axis at the of the mid-point along the
direction of curvature, and during an object building operation,
the sagittal line traverses a trochoidal path.
6. The apparatus of claim 5, wherein during an object building
operation, the solidifiable material is solidified into a plurality
of layers, following the solidification of each layer a
partially-solidified exposed object surface is formed, and during
the object building operation solidification occurs exclusively at
positions along the exposed object surface that lie at a constant
distance along the build axis from the solidification energy
source.
7. The apparatus of claim 5, wherein an exposed surface of the
object attached to the build platform defines a tangent plane
perpendicular to the build axis and a tangent line defined by the
intersection of the tangent plane and the exposed surface of the
object, and during the object building operation the tangent line
moves along the travel axis direction in coordination with the
solidification energy source.
8. The apparatus of claim 7, wherein during an object building
operation the solidification energy source projects solidification
energy to solidify the solidifiable material into a plurality of
layers comprising the three-dimensional object, each layer has a
layer thickness, and following the solidification of each layer the
build platform moves along the build axis such that the sagittal
line moves away from the solidification energy source along the
build axis by a distance equal to the layer thickness.
9. The apparatus of claim 1, wherein the build platform has a lower
surface spaced apart from an upper surface along the build axis,
the upper surface is between the solidification energy source and
the lower surface, and the upper surface is the curved surface.
10. The apparatus of claim 9, wherein the upper surface is curved
in a direction along a travel axis direction perpendicular to the
build axis and the cross-sectional axis direction.
11. The apparatus of claim 1, wherein during an object building
operation the solidification energy source moves along a travel
axis as it projects solidification energy along the build axis.
12. The apparatus of claim 11, wherein during a single layer
solidification operation during which the solidification energy
source projects solidification energy to solidify the solidifiable
material, the build platform moves along the travel axis direction
and along the build axis.
13. The apparatus of claim 12, wherein during the single layer
solidification operation the build platform moves simultaneously
along the travel axis and along the build axis.
14. The apparatus of claim 11, wherein during an object building
operation, the solidification energy source moves along the travel
axis and projects solidification energy along the build axis and in
a scanning pattern along the cross-sectional axis direction.
15. The apparatus of claim 14, wherein during an object building
operation, the build platform rotates about an axis of rotation
parallel to the cross-sectional axis direction as the
solidification energy source projects solidification energy along
the cross-sectional axis direction.
16. The apparatus of claim 1, wherein the curved surface has a
direction of curvature and a mid-point along the direction of
curvature, the curved surface includes a sagittal plane defining a
sagittal line extending along the cross-sectional axis at the of
the mid-point along the direction of curvature, and during a single
layer solidification operation, the build platform rotates about
the axis of rotation from a first angular orientation to a second
angular orientation as the sagittal line travels a distance
.DELTA.x along the travel axis direction, and the distance .DELTA.x
is related to the first and second angular positions as follows:
.DELTA.x=a[o.sub.R1-o.sub.R2]+b[sin(2.pi.-o.sub.R1)-sin(2.pi.-o-
.sub.R2)] wherein, .DELTA.x=change in position of the sagittal line
along the travel axis from a first position x.sub.1 to a second
position x.sub.2; o.sub.R1=the angle of rotation of the build
platform when the sagittal line is at the first travel axis
position x.sub.1 relative to a reference angular orientation at
which the sagittal plane is parallel to the build axis;
o.sub.R2=the angle of rotation of the build platform when the
sagittal plane is at the second travel axis position x.sub.2
relative to the reference angular orientation; a=the length of the
radius of curvature of the curved surface of the build platform;
and b=the distance between the sagittal line and the center of a
circle of radius a defined by the curved surface along the radial
direction of the circle.
17. The apparatus of claim 16, wherein the during a single layer
solidification operation, the sagittal line moves a distance
.DELTA.z along the build axis as the build platform rotates about
the axis of rotation from the first angular orientation to the
second angular orientation, and the distance .DELTA.z is related to
the first and second angular orientations as follows:
.DELTA.z=b[cos(2.pi.-o.sub.R1)-cos(2.pi.-o.sub.R2)] wherein,
.DELTA.z=the distance traveled by the sagittal line along the build
axis from a first position z.sub.1 to a second position z.sub.2;
o.sub.R1=the angle of rotation of the build platform when the
sagittal line is at the first build axis position z.sub.1 relative
to a reference angular orientation at which the sagittal plane is
parallel to the build axis; o.sub.R2=the angle of rotation of the
build platform when the sagittal line is at the second build axis
position z.sub.2 relative to the reference angular orientation;
a=the length of the radius of curvature of the curved surface of
the build platform; and b=the distance between the sagittal line
and the center of a circle of radius a defined by the curved
surface along the radial direction of the circle.
18. The apparatus of claim 15, wherein during the single layer
solidification operation, the build platform simultaneously rotates
about the axis of rotation, moves along the build axis, and moves
along the travel axis direction.
19. The apparatus of claim 1, wherein the cross-sectional profile
of the build platform perpendicular to the cross-sectional
direction axis is a circular segment.
20. The apparatus of claim 1, wherein during an object building
operation, the solidification energy source projects solidification
energy to the solidifiable material as the solidification energy
source moves in a first direction along a travel axis and does not
project solidification energy to the solidifiable material as it
moves in a second direction along the travel axis, wherein the
first direction along the travel axis is opposite the second
direction along the travel axis.
21. The apparatus of claim 1, further comprising a linear
solidification device comprising the solidification energy source,
wherein the linear solidification energy source projects energy
along the cross-sectional axis direction.
22. The apparatus of claim 21, wherein the linear solidification
device comprises rotating energy deflector in optical communication
with the solidification energy source.
23. The apparatus of claim 1, further comprising a build platform
travel axis translation motor, a build platform build axis
translation motor, and a build platform rotation motor, wherein
during a single layer solidification operation, the build platform
travel axis translation motor, the build platform build axis
translation motor, and the build platform rotation motor are each
operated so that an axis of rotation of the build platform rotation
motor traverses a trochoidal path.
24. The apparatus of claim 1, wherein during the formation of a
single object layer, the build platform is rotated at a constant
angular speed about an axis of rotation.
25. The apparatus of claim 24, wherein the curved surface has a
direction of curvature and a mid-point along the direction of
curvature, the curved surface includes a sagittal plane defining a
sagittal line extending along the cross-sectional axis at the of
the mid-point along the direction of curvature, and during the
formation of a single object layer, the sagittal line moves along
the travel axis at a speed that is related to the constant angular
speed at which the build platform rotates about the axis of
rotation in accordance with the following relationship:
dx/dt=.omega.(a-b[cos(.omega.t)]) wherein, dx/dt is the velocity of
the sagittal line along the travel axis (mm/sec); .omega.=angular
rotational velocity of the build platform (radians/sec); a=the
length of the radius of curvature defined by curved build platform
surface (mm); and b=the distance between the center of a trochoidal
circle defined by the radius of curvature of the curved build
platform surface and the sagittal line along the radial direction
of the circle (mm); and t=time (sec) required for a trochoidal
circle of radius a to rotate at the angular rotational velocity
.omega. from a reference position at which the sagittal plane is
parallel to the build axis to the current angular orientation of
the sagittal plane.
26. The apparatus of claim 25, wherein during the formation of a
single object layer, the sagittal line moves along the build axis
at a speed that is related to the constant angular speed at which
the build platform rotates about the axis of rotation in accordance
with the following relationship: dz/dt=b.omega.[sin(.omega.t)]
wherein, dz/dt is the velocity of the sagittal line along the build
axis (mm/sec); .omega.=angular rotational velocity of the build
platform (radians/sec); b=the distance between the center of a
trochoidal circle defined by the radius of curvature of the curved
build platform surface and the sagittal line along the radial
direction of the circle (mm); and t=time (sec) required for a
trochoidal circle of radius a to rotate at the angular rotational
velocity .omega. from a reference position at which the sagittal
plane is parallel to the build axis to the current angular
orientation of the sagittal plane.
27. An apparatus for making a three-dimensional object from a
solidifiable material, comprising: a solidification energy source
that moves along a travel axis; a source of the solidifiable
material; a build platform that moves along the travel axis while
rotating about an axis of rotation perpendicular to the travel axis
during the formation of a single object layer.
28. The apparatus of claim 27, wherein the solidification energy
source moves along the travel axis as the build platform moves
along the travel axis during the formation of a single object
layer.
29. The apparatus of claim 27, wherein during the formation of a
single object layer, the build platform moves along a build axis
perpendicular to the travel axis as the build platform moves along
the travel axis and rotates about the axis of rotation.
30. The apparatus of claim 27, wherein the build platform has a
cross-sectional profile when viewed along a cross-sectional axis
perpendicular to the build axis and the travel axis, and the
cross-sectional profile includes a curved surface that is curved
along the travel axis.
31. The apparatus of claim 30, wherein the curved surface has a
mid-point and a sagittal line extending along the cross-sectional
axis direction at the mid-point, and during the formation of a
single object layer, the sagittal line traverses a trochoidal path
along the travel axis.
32. The apparatus of claim 27, wherein during an object building
operation, the solidifiable material is solidified into a plurality
of layers, following the solidification of each layer an exposed
object surface is formed, and the build platform is manipulated
such that solidification energy is only transmitted to the
solidifiable material when the exposed object surface at the travel
axis position of the solidification energy source is at a fixed
distance from the solidification energy source along the build
axis.
33. The apparatus of claim 27, wherein during an object building
operation, the solidification energy source moves along the travel
axis and projects solidification energy in a scanning pattern along
a cross-sectional axis parallel to the axis of rotation of the
build platform.
34. The apparatus of claim 27, wherein during an object building
operation the solidification energy source projects solidification
energy to the solidifiable material as the solidification energy
source moves in a first direction along the travel axis and does
not project solidification energy to the solidifiable material as
it moves in a second direction along the travel axis, wherein the
first direction along the travel axis is opposite the second
direction along the travel axis.
35. The apparatus of claim 27, further comprising a build platform
travel axis translation motor, a build platform rotation motor, and
a build platform build axis translation motor, wherein during the
formation of a single object layer, the build platform travel axis
translation motor, the build platform rotation motor, and the build
platform build axis translation motor are operated such that an
axis of rotation of the build axis rotation motor traverses a
trochoidal path.
36. A method of making a layer of a three-dimensional object on a
build platform from a solidifiable material, wherein the build
platform has a curved surface and a sagittal line lying on the
curved surface, the method comprising: providing a solidification
energy source; moving the solidification energy source along a
travel axis; moving the build platform along the travel axis and
along a build axis; rotating the build platform about an axis of
rotation; and selectively supplying solidification energy from the
solidification energy source to the solidifiable material along a
scanning axis direction.
37. The method of claim 36, further comprising traversing the
sagittal line in a trochoidal path.
38. The method of claim 36, further comprising traversing the axis
of rotation in a trochoidal path.
39. The method of claim 36, wherein build platform has a curved
surface with a radius of curvature of length a, the step of moving
the solidification energy source along the travel axis comprises
moving the solidification energy source along the travel axis at a
velocity v.sub.x, and the step of rotating the build platform about
the axis of rotation comprises rotating the build platform at an
angular velocity .omega. in accordance with the following
relationship: .omega.=(1/a)v.sub.x wherein, .omega.=angular
velocity (radians/sec); a=the length of the radius of curvature
(mm); and v.sub.x=velocity of the solidification energy source
along the travel axis (mm/sec).
40. The method of claim 39, wherein the step of moving the build
platform along the travel axis comprises moving the build platform
along the travel axis at a travel axis velocity that varies with
the angular velocity .omega..
41. The method of claim 39, wherein the step of moving the build
platform along the build axis comprises moving the build platform
along the build axis at a build axis velocity that varies with the
angular velocity .omega..
42. The method of claim 36, wherein the step of rotating the build
platform about an axis of rotation comprises rotating the build
platform from a first angular orientation to a second angular
orientation.
43. The method of claim 42, wherein the step of moving the build
platform along the travel axis comprises moving the build platform
by a distance along the travel axis that varies with the first
angular orientation and the second angular orientation.
44. The method of claim 42, wherein the step of moving the build
platform along the build axis comprises moving the build platform
by a distance along the build axis that varies with the first
angular orientation and the second angular orientation.
45. A method of making a three-dimensional object comprising a
removable support section and a finished object section from a
solidifiable material, wherein the removable support section and
the finished object section are at adjacent locations along a build
axis, the method comprising: forming the removable support section
on a curved surface of a build platform, wherein the curved surface
defines a sagittal plane parallel to the build axis, the removable
support section has a build platform contacting surface and a
finished object contacting surface; forming the finished object
section such that the finished object section has a base connected
to the finished object contacting surface of the removable support
section, and the base of the finished object section is planar.
46. The method of claim 45, wherein the base of the finished object
section includes a surface that faces the curved surface of the
build platform, and the spacing between the finished object base
and the curved surface of the build platform varies along the width
of the build platform.
47. The method of claim 45, wherein the base of the removable
support section is discontinuous.
48. The method of claim 45, wherein the build platform is curved
along a direction perpendicular to the build axis.
49. The method of claim 45, further comprising removing the
removable support section from the build platform.
50. The method of claim 45, further comprising separating the
finished object section from the removable support section.
Description
FIELD
[0001] The disclosure relates to an apparatus and method for
manufacturing three-dimensional objects, and more specifically, to
an apparatus and method for forming three-dimensional objects using
a build platform that is curved and/or which moves in multiple
dimensions as solidification energy is supplied to a solidifiable
material.
DESCRIPTION OF THE RELATED ART
[0002] Three-dimensional rapid prototyping and manufacturing allows
for quick and accurate production of components at high accuracy.
Machining steps may be reduced or eliminated using such techniques
and certain components may be functionally equivalent to their
regular production counterparts depending on the materials used for
production.
[0003] The components produced may range in size from small to
large parts. The manufacture of parts may be based on various
technologies including photo-polymer hardening using light or laser
curing methods. Secondary curing may take place with exposure to,
for example, ultraviolet (UV) light. A process to convert a
computer aided design (CAD) data to a data model suitable for rapid
manufacturing may be used to produce data suitable for constructing
the component. Then, a pattern generator may be used to construct
the part. An example of a pattern generator may include the use of
DLP (Digital Light Processing technology) from Texas
Instruments.RTM., SXRD.TM. (Silicon X-tal Reflective Display), LCD
(Liquid Crystal Display), LCOS (Liquid Crystal on Silicon), DMD
(digital mirror device), J-ILA from JVC, SLM (Spatial light
modulator) or any type of selective light modulation system.
[0004] In certain known methods of making a three-dimensional
object, the object is progressively formed as a series of sections
on a build platform in a direction along a build axis. After each
section is formed, its exposed surface is contacted with fresh
solidifiable material which is then solidified in a pattern
corresponding to object data that defines the size and shape of the
three-dimensional object. In certain processes, the solidifiable
material is an uncured or partially cured polymeric resin, and the
fresh solidified material is supplied between the solidified
exposed surface of the partially-formed object and a solidification
substrate. The solidification substrate planarizes the exposed
surface of fresh solidifiable material to ensure that a given
solidification energy will solidify the material to the same depth
along the exposed surface. Following solidification, however, the
newly solidified material must be separated from the solidification
substrate. In some cases this is done by increasing the distance
between the build platform and the solidification substrate.
However, many known build platforms are substantially planar, and
the interface between the solidified exposed surface and the
solidification substrate defines an area that must be separated. As
the interface area increases, so do the required separation forces.
If the separation force is too great, the object can break. As a
result, in many known three-dimensional object manufacturing
methods the build area (the total exposed surface area of the
object(s) perpendicular to the build axis) must be limited to
regulate the separation force, which reduces either the number
and/or surface area of the objects that can be built during an
object building process. Thus, a need has arisen for an apparatus
and method for making three-dimensional objects which addresses the
foregoing issues.
BRIEF DESCRIPTION OF THE DRAWINGS
[0005] The disclosure will now be described, by way of example,
with reference to the accompanying drawings, in which:
[0006] FIG. 1 is a side cross-sectional, schematic view of a system
for making a three-dimensional object with a planar build platform
that moves only along a build (z) axis during an object building
operation;
[0007] FIG. 2 is a detailed perspective view of a modified portion
of the system of FIG. 1 with a build platform having a curved lower
surface and which is translatable along a travel axis and build
axis and rotatable about an axis of rotation;
[0008] FIG. 3 is a top plan view of the system of FIG. 2;
[0009] FIG. 4 is a side elevational view of the system of FIG.
2;
[0010] FIG. 5 is a bottom plan view of the system of FIG. 2;
[0011] FIGS. 6A-6F are schematic views of the build platform and
linear solidification device of the system of FIG. 2 in various
positions along the travel axis as the linear solidification device
moves in a first direction (FIGS. 6A-6C) and a second direction
(FIGS. 6D-6F) along the travel axis;
[0012] FIG. 6G is a schematic view of two rotational positions of
the build platform of the system of FIG. 2 used to illustrate the
rotational relationship between the movement of a point on a
trochoidal circle and the rotational orientation of the build
platform;
[0013] FIG. 6H is a schematic view of a build platform with a
partially formed object built thereon in a first position along a
travel axis and in a first rotational orientation about an axis of
rotation during an object building operation;
[0014] FIG. 6I is a schematic view of a build platform with a
partially formed object built thereon in a second position along a
travel axis and in a second rotational orientation about an axis of
rotation during an object building operation;
[0015] FIG. 7A is a rear perspective view of an exemplary linear
solidification device comprising a solidification energy source and
a rotating energy deflector;
[0016] FIG. 7B is a front perspective view of the linear
solidification device of FIG. 7A with a portion of the housing
removed;
[0017] FIG. 7C is a schematic view of a first alternate version of
the linear solidification device of FIG. 7A in which the housing is
removed and which includes a solidification energy synchronization
sensor;
[0018] FIG. 7D is a schematic view of a second alternate version of
the linear solidification device of FIG. 7A in which the housing is
removed and which includes dual solidification energy sources and a
solidification energy sensor;
[0019] FIG. 8A is an exploded perspective view of a film assembly
that can be used as a solidifiable material container in the system
of FIG. 2;
[0020] FIG. 8B is a side elevational view of the film assembly of
FIG. 8A;
[0021] FIG. 8C is a perspective view of the film assembly of FIG.
8A in an assembled configuration;
[0022] FIG. 9 is a graphical depiction of three-dimensional object
data for use in illustrating a method of making a three-dimensional
object using a linear solidification device;
[0023] FIG. 10 is a graphical representation of sliced data
representative of the three-dimensional object of FIG. 9;
[0024] FIG. 11A is a graphical representation of object
cross-section strip data corresponding to one of the slices of a
three-dimensional object shown in FIG. 10;
[0025] FIG. 11B is a top plan view of a source of solidifiable
material comprising a build envelope and lateral offset
regions;
[0026] FIG. 11C is a top plan view of the source of solidifiable
material of FIG. 11B with the object cross-section strip data of
FIG. 1A mapped onto the build envelope;
[0027] FIG. 11D is a table depicting exemplary sets of string data
which correspond to the object cross-sectional strip data of FIG.
11C;
[0028] FIGS. 12A and 12B are a flow chart depicting an exemplary
method of making a three-dimensional object using a curved build
platform that moves in multiple dimensions during an object
solidification operation;
[0029] FIG. 13 is a cross-sectional view of the build platform of
FIG. 2 with an attached object comprising a finished object section
and a removable support section built using the system of FIG. 2;
and
[0030] FIGS. 14A and 14B are a flow chart depicting another
exemplary method of making a three-dimensional object using a
curved build platform that moves in multiple dimensions during an
object solidification operation.
[0031] Like numerals refer to like parts in the drawings.
DETAILED DESCRIPTION
[0032] The Figures illustrate examples of an apparatus and method
for manufacturing a three-dimensional object from a solidifiable
material. Based on the foregoing, it is to be generally understood
that the nomenclature used herein is simply for convenience and the
terms used to describe the invention should be given the broadest
meaning by one of ordinary skill in the art.
[0033] The apparatuses and methods described herein are generally
applicable to additive manufacturing of three-dimensional objects,
such as components or parts (discussed herein generally as
objects), but may be used beyond that scope for alternative
applications. In a first aspect, the system and methods generally
include a build platform having a surface that is curved along a
travel axis direction. The travel axis is defined by the movement
of a source of solidification energy that solidifies a solidifiable
material into a three-dimensional object based on object data. In a
second aspect, the systems and methods include a build platform
that moves in multiple dimensions as solidification energy is
supplied to a solidifiable material. In certain examples, the build
platform is curved along the travel axis and rotates about an axis
of rotation that is perpendicular to the travel axis and build axis
as the build platform moves along the travel axis and build axis in
correspondence with the movement of a linear solidification device
along the travel axis.
[0034] In accordance with one implementation, the solidifiable
material is solidified on the most recently formed exposed surface
of the three-dimensional object along a line that extends along the
length of the build platform. The line is located at a position
along the build platform width (and the travel axis) which
corresponds to a rotational orientation between a sagittal plane of
the build platform and the build axis. The sagittal plane is a
plane of symmetry along a curved surface of the build platform on
which a three-dimensional object is built. The intersection of the
sagittal plane and the curved surface defines a sagittal line
extending along the length of the build platform and
perpendicularly to the plane defined by the travel axis and build
axis.
[0035] In certain preferred examples, the build platform is
manipulated so that the build platform sagittal line and the axis
of rotation of the build platform travel in trochoidal paths in the
plane defined by the travel axis and the build axis. The trochoidal
paths are defined by a trochoidal circle having a radius equal to
the radius of curvature of the build platform's curved surface. In
the same or other examples, the trochoidal paths of the sagittal
line and the axis of rotation change with the addition of each
layer of solidified material to the partially formed
three-dimensional object. In the same or other examples, the
relationship between the rotation of the build platform relative to
a reference rotational orientation (at which the plane tangent to
the sagittal line is perpendicular to the build axis) and the
positions of the sagittal line and the axis of rotation along the
travel axis change with the addition of each layer of solidified
material to the partially-formed three-dimensional object. In
certain preferred examples, the operation of motors that translate
and rotate the build platform is adjusted so that a point of
interest that is fixed relative to the build platform moves in a
trochoidal path during object solidification and object separation
operations.
[0036] In preferred examples, the solidified material at the
exposed surface of the object following the addition of a new layer
is separated from a solidification substrate or a film such that
the separation forces at any one time are concentrated along a line
extending along the length of the build platform. Because the
instantaneous separation forces are concentrated along a line, the
force required to separate a given surface area of the object from
the solidification substrate is reduced relative to techniques in
which separation occurs within an area. As a result, separation
forces do not limit, or at least play a significantly reduced role
in determining, the maximum possible area of the object
perpendicular to the build axis (i.e., the axis along which the
layers are sequentially solidified).
[0037] FIG. 1 depicts a simplified, schematic view of a system 40
for making a three-dimensional object 59 from a solidifiable
material 50. System 40 includes a housing 54 used to support a
solidifiable material container 48, a linear solidification device
42, and a build platform 44. Solidifiable material container 48
comprises sidewalls 62 and a bottom that comprises a rigid or semi
rigid solidification substrate 52 that is transparent and/or
translucent with a film 55 coating adhered to its upper surface.
FIG. 1 is provided to illustrate the basic arrangement and
relationship of the linear solidification device 42, housing 54,
solidifiable material container 48, and build platform 44. However,
in FIG. 1, build platform 44 is configured to move only in the
build (z) axis direction by virtue of its operative connection to a
build axis translation motor (not shown in FIG. 1) and its sliding
engagement with a vertical rail support member 58 (which is shown
in simplified form in FIG. 1). In contrast to the system of FIG. 1,
the build platforms of the present disclosure, as described below,
are configured to move in multiple dimensions during an object
building operation. In one preferred example, the build platforms
described herein are configured to translate along a travel (x)
axis, translate along a build (z) axis, and rotate about an axis of
rotation R.sub.x perpendicular to the travel (x) and build (z)
axis. In the same or other examples, the build platforms described
herein include an object contact surface that is curved along the
build platform's width direction. In certain illustrative
embodiments, the curvature defines a radius of curvature that is
substantially constant, or more preferably, constant within
standard machining tolerances. In FIG. 1, object 59 includes a
build platform contact surface 60 that is adhered to build platform
44. As explained further below, in certain examples, the object 50
comprises a finished object section and a removable object section,
wherein the build platform contact surface 60 of object 59 is part
of the removable support section.
[0038] Solidification substrate 52 is held in frame sections 67a
(not shown in FIG. 1) and 67b so as to be positioned over opening
56 in the upper surface 51 of housing 54. During an object building
process an exposed surface 64 of the partially-completed
three-dimensional object 59 is immersed in solidifiable material 50
so that a desired layer thickness of solidifiable material is
provided between the exposed object surface 64 and the film 55
coated on the solidification substrate 52. Solidification energy
(e.g., UV or visible light) is projected upwardly along the build
axis (z) direction through the solidification substrate 52 and film
55 to solidify the desired layer thickness of solidifiable material
in contact with the film 55.
[0039] As discussed herein, a solidifiable material 50 is a
material that when subjected to energy, wholly or partially
hardens. This reaction to solidification or partial solidification
may be used as the basis for constructing the three-dimensional
object. Examples of a solidifiable material may include a
polymerizable or cross-linkable material, a photopolymer, a photo
powder, a photo paste, or a photosensitive composite that contains
any kind of ceramic based powder such as aluminum oxide or
zirconium oxide or ytteria stabilized zirconium oxide, a curable
silicone composition, silica based nano-particles or
nano-composites. The solidifiable material may further include
fillers. Moreover, the solidifiable material my take on a final
form (e.g., after exposure to the electromagnetic radiation) that
may vary from semi-solids, solids, waxes, and crystalline solids.
In one embodiment of a photopolymer paste solidifiable material, a
viscosity of between 10000 cP (centipoises) and 150000 cp is
preferred.
[0040] When discussing a photopolymerizable, photocurable, or
solidifiable material, any material is meant, possibly comprising a
resin and optionally further components, which is solidifiable by
means of supply of stimulating energy such as electromagnetic
radiation. Suitably, a material that is polymerizable and/or
cross-linkable (i.e., curable) by electromagnetic radiation (common
wavelengths in use today include UV radiation and/or visible light)
can be used as such material. In an example, a material comprising
a resin formed from at least one ethylenically unsaturated compound
(including but not limited to (meth)acrylate monomers and polymers)
and/or at least one epoxy group-containing compound may be used.
Suitable other components of the solidifiable material include, for
example, inorganic and/or organic fillers, coloring substances,
viscosity-controlling agents, etc., but are not limited
thereto.
[0041] When photopolymers are used as the solidifiable material, a
photoinitiator is typically provided. The photoinitiator absorbs
light and generates free radicals which start the polymerization
and/or crosslinking process. Suitable types of photoinitiators
include metallocenes, 1,2 di-ketones, acylphosphine oxides,
benzyldimethyl-ketals, .alpha.-amino ketones, and .alpha.-hydroxy
ketones. Examples of suitable metallocenes include Bis (eta
5-2,4-cyclopenadien-1-yl)Bis[2,6-difluoro-3-(1H-pyrrol-1-yl)phenyl]titani-
um, such as Irgacure 784, which is supplied by Ciba Specialty
chemicals. Examples of suitable 1,2 di-ketones include quinones
such as camphorquinone. Examples of suitable acylphosphine oxides
include bis acyl phosphine oxide (BAPO), which is supplied under
the name Irgacure 819, and mono acyl phosphine oxide (MAPO) which
is supplied under the name Darocur.RTM. TPO. Both Irgacure 819 and
Darocur.RTM. TPO are supplied by Ciba Specialty Chemicals. Examples
of suitable benzyldimethyl ketals include
alpha,alpha-dimethoxy-alpha-phenylacetophenone, which is supplied
under the name Irgacure 651. Suitable .alpha.-amino ketones include
2-benzyl-2-(dimethylamino)-1-[4-(4-morpholinyl)phenyl]-1-butanone-
, which is supplied under the name Irgacure 369. Suitable
.alpha.-hydroxy ketones include 1-hydroxy-cyclohexyl-phenyl-ketone,
which is supplied under the name Irgacure 184 and a 50-50 (by
weight) mixture of 1-hydroxy-cyclohexyl-phenyl-ketone and
benzophenone, which is supplied under the name Irgacure 500.
[0042] The apparatuses and methods described herein may include a
solidification substrate, such as rigid or semi-rigid, transparent
and/or translucent substrate 52, against which a solidifiable
material is solidified as an object 59 is built from the
solidification material. Alternatively, and as shown in FIG. 1, the
substrate 52 may have a film 55 on its upper surface so that the
solidifiable material 50 solidifies against film 55. The
solidification substrate 52 facilitates the creation of a
substantially planar surface of solidifiable material 50 which is
exposed to energy provided by linear solidification device 42. The
substantially planar surface improves the accuracy of the build
process.
[0043] The bottom of solidifiable material container 48 is a
substantially rigid or semi-rigid transparent and/or translucent
substrate 52 that receives solidification energy from linear
solidification device 42 and transmits the received solidification
energy to solidifiable material 50. Solidification substrate 52 is
substantially permeable to the energy supplied by linear
solidification device 42. In certain examples, it is preferred that
the energy from linear solidification device 42 pass through
solidification substrate 52 without a significant diminution in
transmitted energy or a significant alteration of the energy
spectrum transmitted to the solidifiable material 50 relative to
the spectrum that is incident to the lower surface of
solidification substrate 52. In the case where the energy from
linear solidification device 42 is light (including non-visible
light such as UV light), solidification substrate 52 is preferably
substantially translucent to the wavelength(s) of light supplied by
linear solidification device 42.
[0044] One example of a rigid or semi-rigid solidification
substrate 52 is a translucent float glass. Another example is a
translucent plastic. A variety of different float glasses and
plastics may be used. Exemplary plastics that may be used include
transparent acrylic plastics supplied by Evonik under the name
Acrylite.RTM.. The term "translucent" is meant to indicate that
substrate 52 is capable of transmitting the light wavelengths
(including non-visible light such as UV light) necessary to
solidify the solidifiable material and that the intensity of such
wavelengths is not significantly altered as the light passes
through substrate 52. In the case of photopolymers, a
photoinitiator is commonly provided to start the
polymerization/cross-linking process. Photoinitiators will have an
absorption spectrum based on their concentration in the
photopolymer. That spectrum corresponds to the wavelengths that
must pass through solidification substrate 52 and which must be
absorbed by the photoinitiator to initiate solidification. In one
example wherein solidification energy source 112 is a blue laser
light diode, Irgacure 819 and Irgacure 714 photoinitiators may
preferably be used.
[0045] Referring to FIG. 2 a more detailed view of modified portion
of system 40 of FIG. 1 is provided with a portion of the housing 54
removed. The system of FIG. 2 provides a build platform 44 that is
curved along its width and along a an axis of travel (the travel
axis or "x" axis) along which linear solidification device 42 moves
during an object solidification operation and during an object
separation operation. The system of FIG. 2 also provides a build
platform 44 that is movable in multiple dimensions during an object
solidification operation and an object separation operation.
Specifically, build platform 44 can translate in the travel (x)
axis direction and build (z) axis direction as well as rotate about
an axis of rotation R.sub.x parallel to the y axis.
[0046] The system of FIG. 2 includes two frame sections 67a and 67b
which are spaced apart from one another in the travel (x) axis
direction and which hold solidification substrate 52 within opening
56 (FIG. 1) in the upper surface 51 of housing 54. As shown in the
figure, build platform 44 includes a lower surface 46 that is
curved along its width and the travel (x) axis and which is the
object contacting surface of the build platform 44. In preferred
examples, the lower surface 46 has a substantially constant radius
of curvature that is preferably constant within standard machining
tolerances. When build platform 44 is viewed along the y-axis, the
lower surface 46 defines an arc. The upper surface of build
platform 44 comprises end portions 47a and 47b which are spaced
apart from one another along the travel (x) axis and which are
separated by a center recessed portion 49. The end portions 47a and
47b each have corresponding recesses 45a and 45b, which are spaced
apart from center recessed portion 49 along the travel (x) axis. A
build platform rotational motor 86 is supported by a rotational
motor platform 53 that is attached to the end portions 47a and 47b
of build platform 44 by suitable fasteners 101a, 101b, 101c (not
shown) and 101d (not shown).
[0047] In the example of FIG. 2, build platform rotational motor 86
is disposed within a build platform holder 61. Build platform
holder 61 comprises a rear wall 75 connected on each of its ends to
side walls 81a and 81b. Sidewalls 81a and 81b are spaced apart from
one another along the travel (x) axis and slope downward along the
build (z) axis in a direction along the y axis moving away from the
rear wall 75. Build platform rotational motor 86 is disposed in a
recess created by rear wall 75 and sidewalls 81a and 81b. The build
platform holder 61 also includes base portions 95a and 95b which
lie in a plane parallel to the x-y plane on top of the rotational
motor platform 53. Fasteners 103a-d (only 103a and 103d are shown)
attach the base portions 95a and 95b of the build platform holder
61 to slides (not visible) attached to the underside of the build
platform holder base portions 95a and 95b. The slides include
grooves that face inwardly toward one another along the travel (x)
axis. As shown in FIG. 4, the rotational motor platform 53 includes
a pair of engaging projections 157a and 157b (not shown) that can
be slidably inserted into the grooves. Handle 99 is operative to
tighten the slides and pull them closer to the underside of the
base portions 95a and 95b, thereby locking the build platform 53
into place. Rotational motor platform 53 includes handles 57a and
57b which are spaced apart from one another and on opposite sides
of build platform rotational motor 86 along the travel (x) axis.
The assembly defined by the rotational motor platform 53 and the
build platform 44 can be slidably inserted into the grooves of the
slides and releasably connected to the base portions 95a and 95b of
build platform holder 61 by using handle 99.
[0048] Build platform rotational motor 86 is connected to a
mounting flange 89 which is in turn connected to cylindrical gear
box 91. Build platform rotational motor 86 has an axis of rotation
that defines the axis of rotation R.sub.x of build platform 44
(FIG. 2). Cylindrical gear box 91 is connected to a junction cover
93 through an opening in the rear wall 75 of build platform holder
61. Build platform holder 61 operatively connects build platform
rotational motor 86 to build platform 44 so that when build
platform rotational motor 86 rotates about rotational axis R.sub.x,
the build platform holder 61 also rotates, causing the rotational
motor platform 53 and build platform 44 to rotate therewith.
Mounting flange 89 and junction cover 93 also rotate with build
platform rotational motor 86. Level sensor 123 (FIG. 4) is provided
to detect the level of solidifiable material in solidifiable
material container 43 and feedback the detected level to a level
control system that supplies solidifiable material to container
43.
[0049] As mentioned previously, build platform 44 has a lower
surface 46 that is curved along the platform width and along the
travel (x) axis. In preferred examples, the lower surface 46
defines a cylindrical segment with a radial direction parallel to
the x-z plane and a length parallel to the y-axis. In preferred
examples, the mid-point of lower surface 46 of build platform 44
(i.e., the location that is equidistant from the edges of the end
portions 47a and 47b of the build platform 44) defines a sagittal
plane that bifurcates the lower surface 46 into two equal halves
and which intersects the lower surface 46 at a line 79 extending
along the y-axis (referred to as the "sagittal line" hereinafter).
The sagittal line 79 is parallel to the rotational axis R.sub.x and
traverses a trochoidal path during object building operations and
object separation operations (i.e., during the separation of the
most recently solidified exposed surface of the object from a
solidification substrate or film that the solidifiable material
solidifies against).
[0050] As indicated previously, in the example of FIGS. 2-5, build
platform 44 is configured to move in multiple dimensions during an
object solidification operation and an object separation operation.
In addition to rotating about the rotational axis R.sub.x, build
platform 44 is configured to translate along the travel (x) axis
during object solidification operations and object separation
operations. Travel axis translation motor 80 (FIGS. 2-4) is
provided to translate build platform 44 along the travel (x) axis.
Cables 139 are provided to supply power to travel axis translation
motor 80.
[0051] As shown in FIGS. 2-3, travel axis translation motor 80 is
connected to and rotates ball screw 82 when motor 80 is energized.
Ball screw 82 engages complementary threads in threaded nuts 85a
and 85b (not shown). Threaded nuts 85a and 85b are mounted on
opposite sides of a travel axis carriage 83 and are spaced apart
from one another along the travel (x) axis direction. Travel axis
carriage 83 includes a through-bore which allows ball screw 82 to
pass from one side of the carriage 83 to another side along the
travel (x) axis. The threaded engagement of ball screw 82 and the
threaded nuts 85a and 85b causes the travel axis carriage 83 to
translate along the travel (x) axis as the ball screw 82 rotates
about its longitudinal axis.
[0052] Build platform rotational motor 86 is operatively connected
to build platform travel axis translation motor 80 so that when the
travel axis translation motor 80 is energized, the build platform
44 translates along the travel (x) axis as the travel axis carriage
83 translates along the travel (x) axis direction. The build
platform rotational motor 86 also translates along the travel (x)
axis when travel axis translation motor 80 is energized. In the
example of FIGS. 2-5, travel axis carriage 83 is connected to build
platform holder 61 by a series of rods or posts (not shown). The
rods are positioned on either side of the junction cover 93 along
the travel x-axis and have lengths along the y-axis. In certain
preferred examples, the travel axis carriage 83 does not rotate as
the build platform rotational motor 86 rotates. In accordance with
such examples, the rods are of sufficient length to maintain a
y-axis gap between the junction cover 93 and the travel axis
carriage 83 so that the junction cover 93 can rotate relative to
the travel axis carriage 83.
[0053] Travel axis carriage 83 is vertically supported on first
linear slide 90a and a second linear slide 90b (not shown) spaced
apart from first linear slide 90a along the build (z) axis. The
linear slides 90a and 90b are attached to a vertical mounting plate
71 that is attached to a build axis support assembly 70. Linear
bearings 94 and 96 are mounted on a surface of travel axis carriage
83 and slidingly engage linear slides 90a and 90b. A lower pair of
linear bearings (not shown in FIG. 2) engages the second linear
slide (also not shown). Thus, rotation of ball screw 82 causes the
travel axis carriage 83 to translate along the travel (x) axis as
the linear bearings 94 and 96 slidingly engage the linear slide 90a
(and as another pair of linear bearings engages slide 90b). Pillow
blocks 84a and 84b include pressed ball bearings and are provided
to improve the stability of the ball screw 82 and travel axis
carriage 83. Pillow blocks 84a and 84b do not rotate with the ball
screw 82. Instead, the ball screw 82 rotates relative to the pillow
blocks 84a and 84b. As the foregoing indicates, energizing both
travel axis translation motor 80 and build platform rotational
motor 86 causes the build platform 44 to translate in the travel
(x) axis direction while simultaneously rotating about the
rotational axis R.
[0054] In certain examples, build platform 44 is also translatable
along the build (z) axis while translating along the travel (x)
axis and rotating about the rotational axis R. As shown in FIG. 4,
a build axis motor 125 is operatively connected to build platform
44 to cause the build platform 44 to translate along the build (z)
axis when build axis motor 125 is energized. In the particular
exemplary system of FIGS. 2-5, the build axis motor 125 is
energizable to cause both the build platform rotational motor 86
and the travel axis translation motor 80 to translate along the
build (z) axis. Vertical mounting plate 71 (FIG. 2) is attached to
build axis support assembly 70 by suitable fastening mechanisms.
The build axis support assembly 70 includes a vertical end supports
72a and 72b placed in facing opposition to one another and spaced
apart from one another along the travel (x) axis. Vertical end
supports 72a and 72b are also attached to respective linear bearing
mounting brackets 73a and 73b, each of which is attached to two
respective linear bearing 78a/78c and 78b/78d (only 78a and 78b are
visible in FIG. 2). The linear bearings 78a-78d slidingly engage
vertical rails 76a and 76b mounted on vertical rail support member
58. In the example of FIGS. 2-5, the vertical mounting plate 71 on
which the translation motor linear slides 90a and 90b (not shown)
are mounted is attached to the vertical end supports 72a and 72b in
order to connect the vertical mounting plate 71 to the build axis
support assembly 70. Vertical end supports 72a and 72b are
connected to another via horizontal support member 74. A lower end
of travel switch 68a is mounted on the vertical rail support member
58 as is an upper end of travel switch 68c which is spaced apart
from the lower end of travel switch along the build (z) axis. A
contact 68b is attached to vertical end support 72a and moves along
with the vertical end support 72a in response to the operation of
build platform build axis motor 125. Thus, as the build platform 44
moves along the build (z) axis in the upward direction, the contact
68b will eventually reach and make contact with switch 68c, thereby
generating a signal indicating that the end of travel has been
reached in the upward direction along the build (z) axis. This
signal can be provided to a controller or microcontroller operating
motor 125 to reverse its operation so that the build platform 44
moves in the downward build (z) axis direction thereafter. As the
build platform 44 moves along the build (z) axis in the downward
direction, the contact 68b will eventually reach and make contact
with lower end of travel switch 68a, thereby generating a signal
indicating that the end of travel has been reached in the downward
direction along the build (z) axis. The signal can be provided to a
controller or microcontroller operating motor 125 to reverse its
operation so that build platform 44 moves in the upward build (z)
axis direction thereafter.
[0055] Although not shown in detail in the figures, build axis
motor 125 is configured similarly to translation axis motor 80.
Build axis motor 125 is connected to a ball screw 77 via the motor
shaft and a coupling (not shown). Ball screw 77 is connected to
first pillow block 133 which is packed with ball bearings that
allow the ball screw 77 to rotate about its longitudinal axis
relative to pillow block 133 (FIG. 4). Ball screw 77 also extends
through second pillow block 135a which is also packed with ball
bearings and relative to which ball screw 77 also rotates about its
longitudinal axis. Threaded nut 135b is internally threaded and
engages external threads of ball screw 77 such that when ball screw
77 rotates, threaded nut 135b translates along the build (z) axis.
Threaded nut 135b is operatively connected to build axis support
assembly 70 so that when the build axis motor 125 is energized,
ball screw 77 rotates, causing the threaded nut 135b and build axis
support assembly 70 to translate along the build (z) axis.
[0056] When the build axis motor 125 is energized, the build axis
support assembly 70 and travel axis translation motor 80 translate
along the build (z) axis. In addition, the build platform
rotational motor 86, build platform holder 61, rotational motor
platform 53 and build platform 44 translate along the build axis
when build axis motor 125 is energized. Thus, the build platform
travel axis translation motor 80, build platform rotational motor
86, and build platform build axis translation motor 125 provide
three independent degrees of freedom for build platform 44,
allowing it to simultaneously translate along the travel (x) and
build (z) axes as it rotates about the rotational axis R.
[0057] Referring now to FIGS. 4 and 5, during an object building
operation, linear solidification device 42 moves along the travel
(x) axis as it selectively projects solidification energy upward
along the build (z) axis and progressively along the scanning (y)
axis. In certain examples, the linear solidification device 42
selectively projects solidification energy upward along the build
axis and progressively along the scanning (y) axis only while it
moves in a first direction along the travel (x) axis. The linear
solidification device 42 then moves in a second direction along the
travel (x) axis that is opposite the first direction without
projecting solidification energy. In certain preferred examples,
the movement of the linear solidification device 42 in the second
direction along the travel (x) axis occurs during an object
separation operation wherein the most recently solidified exposed
surface 64 of object 59 (see FIG. 1) is separated from
solidification substrate 52 (or film 55 if provided). When the
linear solidification device 42 moves in the first direction along
the travel (x) axis, it selectively supplies solidification energy
to regions along the scanning (y) axis and upward along the build
(z) axis in a manner that corresponds to data that represents the
three-dimensional object being built. At the same time, or in other
examples, the linear solidification device 42 moves in a
coordinated fashion with the build platform 44, and in particular,
with a tangent line (TL) of the build platform 44. As illustrated
in FIGS. 6A-6I and described further below, the tangent line TL
extends along the length (y-axis) direction of the build platform
44. However, the tangent line TL is not at a fixed location along
the width (x-axis) of the build platform 44. Rather, it is a line
located at the travel (x) axis position at which the lower build
platform surface 46 (or the exposed object surface 64 if portions
of the object have been formed on surface 46) is at the lowest
build (z) axis position z.sub.min. When no object is present on the
build platform, the tangent line TL is defined by the intersection
of a plane that is tangent to the lower build platform surface 46
and perpendicular to the build (z) axis. When a portion of the
object is present on the build platform, the tangent line TL is
defined by the intersection of a plane that is tangent to the
exposed surface of the partially-formed object and perpendicular to
the build (z) axis. In accordance with this definition, the tangent
line TL remains perpendicular to the travel (x) and build (z) axes
and moves along the travel (x) axis during an object build
operation and during an object separation operation. In certain
preferred examples, the tangent line TL moves along the travel axis
at the same travel axis velocity (v.sub.x) as the linear
solidification device 42. In the same or other examples, the travel
(x) axis position of the linear solidification device 42 remains
aligned with the travel (x) axis position of the tangent line TL as
the linear solidification device 42 moves along the travel (x)
axis. In preferred examples, the coordinated movement of the
tangent line TL and the linear solidification device 42 during a
solidification operation causes solidification to occur in a linear
pattern along the tangent line TL. In the same or other preferred
examples, separation of a recently solidified object section from a
solidification substrate during an object separation process occurs
substantially, or preferably only, along the tangent line TL. As a
result, the instantaneous separation forces required to separate a
layer of a three-dimensional object from a solidification substrate
are reduced relative to methods and systems in which the
instantaneous separation forces occur along an area. Exemplary
techniques of providing object data are described further below
with respect to FIGS. 9-10 and 11A-11D.
[0058] FIG. 5 depicts the underside of the system of FIG. 2 and
components for translating linear solidification device 42 along
the travel (x) axis. Linear solidification device translation motor
88 is connected to shaft 108. Shaft 108 is connected to pulleys 111
and 105 which are spaced apart from one another along the y-axis.
Pulley mounting brackets 107 and 129 are attached to the underside
of the housing upper surface 51 and rotatably mount corresponding
pulleys 111 and 105. Brackets 115 and 131 mount pulleys 119 and 127
to the underside of upper surface 51 of housing 54. Pulleys 119 and
127 are spaced apart from one another along the y-axis. Pulley 111
is spaced apart from pulley 127 along the travel (x) axis. Pulley
105 is spaced apart from pulley 119 along the travel (x) axis.
Linear solidification device 42 is attached to a transverse support
member 63. Transverse support member 63 is connected to timing belt
brackets 106 and 104 as well as to linear bearings (not shown) that
slidingly engage linear slides (not shown) mounted on the underside
of upper surface 51. When motor 88 is energized, shaft 108 rotates
about its longitudinal axis causing pulleys 105 and 111 to rotate.
The rotation of pulleys 105 and 111 causes timing belts 100 and 102
to circulate and pulleys 119 and 127 to rotate. As the timing belts
100 and 102 circulate, the linear solidification device transverse
support member 63 moves along the travel (x) axis, and the linear
bearings (not shown) connected to transverse support member 63
slidingly engage linear slides positioned between the timing belts
100 and 102 and the underside of housing upper surface 51. Fan 123
(FIG. 5) is also provided to dissipate any heat generated during
the solidification process.
[0059] As mentioned previously, in certain preferred examples of
the system 40, build platform 44 has a lower surface 46 that is in
the shape of a partial cylinder with a radial direction parallel to
the x-z plane and a length direction parallel to the x-y plane.
When viewed along the scanning (y) axis, the lower surface 46 and
its end points define a circular segment as shown in FIGS. 6A-6F in
which the lower surface 46 is curved along the width dimension of
the build platform 44 and along the travel (x) axis direction. A
sagittal plane bisects the lower surface 46 into two halves and
intersects the lower surface 46 along sagittal line 79. Lower
surface 46 preferably has a substantially constant radius of
curvature, or more preferably, a constant radius of curvature
within standard manufacturing tolerances.
[0060] As best seen in FIG. 2, the actual upper surface of the
build platform may not be planar and may, for example, include
recesses such as recesses 45a and 45b and center recessed portion
49. However, for purposes of understanding the movement of the
build platform 44 using the methods described herein, it is
convenient to describe the cross-sectional view of the build
platform 44 when viewed along the y-axis by defining a circular
segment in which the ends of the lower surface 46 are connected by
a planar surface 47 (which may be imaginary) as shown in FIGS.
6A-6F. As indicated above, it is also convenient to define a
sagittal line 79 (which appears a point when build platform 44 is
viewed along the y-axis) that extends along the lower surface 46 in
the scanning (y) axis direction at the mid-point along the
direction of curvature of the lower surface 46. A plane tangent to
the sagittal line 79 would therefore also be parallel to the planar
upper surface 47 that can be defined for build platform 44.
[0061] As mentioned previously, during object building and/or
object separation operations, the build platform 44 moves along the
travel (x) axis and rotates about a rotational axis R.sub.x
parallel to the y-axis. In one particular implementation, the build
platform moves such that fixed points on the build platform, such
as the sagittal line 79, traverse trochoidal paths in the x-z plane
during the formation and separation of each layer of solidified
material. In addition, other points that remain fixed in space
relative to the build platform will also traverse trochoidal paths.
For example, the rotational axis R.sub.x defined by rotational
motor 86 will traverse trochoidal paths in the x-z plane during
object solidification and separation processes. A "trochoid" is a
curve described by a point that is fixed in space relative to a
circle (the "trochoidal circle") as the circle rolls along a planar
surface. In accordance with the implementation, the sagittal line
79 and the rotational axis R.sub.x traverse specific, and
respective trochoidal paths during the solidification of each layer
used to form three-dimensional object 59, but the respective
trochoidal paths of both sagittal line 79 and rotational axis
R.sub.x will vary between different layers of the three-dimensional
object. In the same or other implementations, movement of the
tangent line TL along the travel (x) axis is based on the movement
of the linear solidification device 42 along the travel (x) axis.
In a preferred example, the angular speed of rotation .omega. of
the rotational motor 86 about rotational axis R.sub.x, and hence,
the angular speed of rotation .omega. of sagittal line 79 about
rotational axis R.sub.x are held constant during an object
solidification process and/or an object separation process. In the
same or other examples, the angular speed of rotation .omega.
corresponds to the velocity v.sub.x of the linear solidification
device 42 along the travel (x) axis and the radius of curvature of
the lower build platform surface 46. In preferred examples, the
tangent line TL and the linear solidification device 42 remain
aligned along the travel (x) axis as the linear solidification
device 42 moves along the travel (x) axis. During the formation of
the first layer of a three-dimensional object, the tangent line TL
will intersect the lower surface 46 of build platform 44 (FIGS.
6A-6C). During the formation of subsequent layers, the tangent line
TL will intersect the exposed surface of the most recently formed
object layer (FIGS. 6H and 6I).
[0062] In addition, in certain examples, as the linear
solidification device 42 moves along the travel (x) axis, the build
platform 44 is manipulated so that the portion of the exposed
surface of the object being formed which was most recently
solidified lies at a constant distance along the build (z) axis
from the linear solidification device 42 (.DELTA.z.sub.fixed in
FIGS. 6H and 6I) and from the bottom of solidifiable material
container 48. This configuration provides for a consistent
thickness of unsolidified solidifiable material, and therefore, a
consistent thickness of solidified material for each layer that is
formed.
[0063] FIGS. 6A-6F depict an example of a build platform 44 that
moves in multiple dimensions during an object solidification and an
object separation process. As the figures indicate, the radius of
curvature of the lower surface 46 of build platform 44 defines a
trochoidal circle (not shown) having a center C and a radius a that
equals the distance between Center C and the sagittal line 79. The
build platform 44 is manipulated to simulate the rolling of the
trochoidal circle on a tangent plane perpendicular to the build (z)
axis. In FIGS. 6A-6C, the tangent line TL is defined by the
intersection of the tangent plane and the lower surface 46 of the
build platform 44 because no solidified object has yet been formed
on the lower build platform surface 46. However, in general, the
tangent plane is tangent to the most recently formed exposed
surface of the three-dimensional object and perpendicular to the
build (z) axis, and the tangent line is the intersection of the
tangent plane with that most recently formed exposed surface. See
FIGS. 6H and 6I.
[0064] As the figures indicate, the tangent line TL moves in
alignment with the linear solidification device 42 in a first
direction along the travel (x) axis during an object solidification
process (FIGS. 6A-6C). The tangent line TL also moves in alignment
with the linear solidification device 42 in a second direction
along the travel (x) axis during an object separation process
(FIGS. 6D-6F). However, the alignment of the linear solidification
device 42 and the tangent line TL are not critical during an object
separation process. Nevertheless, it is often convenient to program
a control computer or microcontroller that guides the movement of
linear solidification device 42 and build platform 44 so that the
linear solidification device 42 and tangent line TL remain aligned
along the travel (x) axis direction regardless of whether
solidification or separation is occurring.
[0065] In FIGS. 6A-6C, the sagittal line 79 and axis of rotation
R.sub.x move in first respective trochoidal paths in the x-z plane.
In FIGS. 6D-6F (which depict the movement after a first layer of
the three-dimensional object is formed), the sagittal line 79 and
axis of rotation R.sub.x move in second respective trochoidal paths
in the x-z plane (the first layer of solidified material is not
visible in FIGS. 6D-6F but would be present on the lower surface 46
of build platform 44). In FIGS. 6A and 6F, the linear
solidification device 42 is at a first build axis boundary within a
build envelope (described further below with respect to FIG. 11B).
In FIGS. 6C and 6D, the linear solidification device 42 is at a
second build axis boundary within the build envelope. The first and
second build axis boundaries are spaced apart along the travel (x)
axis and define the maximum travel (x) axis dimension of the
three-dimensional object which can be constructed. Thus, sagittal
line 79 and rotational axis R.sub.x move along the travel (x) axis,
the build (z) axis, and rotate in the x-z plane during the object
solidification process of FIGS. 6A-6C the object separation process
of FIGS. 6D-6F.
[0066] In order to describe the build platform 44 movement in
accordance with this example, it is convenient to define a
trochoidal circle having a radius equal to the radius of curvature
of the build platform lower surface 46. The trochoidal circle is
considered to roll along the tangent plane that intersects the
exposed object surface at the tangent line (see FIGS. 6H and 6I).
If x represents the position of the fixed point along the planar
surface and z represents the distance of the point from the surface
as the circle rolls, the x and z positions relative to a starting
position at 0, 0 which is in contact with the tangent plane surface
(i.e., x=0 and z=0 is a point on the circle to which the plane
along which the circle rolls is tangent) can be described as
follows:
x=ao-b sin(o) (1)
z=a-b cos(o) (2) [0067] where, [0068] a=the length of the radius of
the trochoidal circle; [0069] b=the distance between the point of
interest that is fixed relative to the trochoidal circle and the
center of the trochoidal circle in the radial direction; and [0070]
o is the angle of rotation from a starting angle of 0 when x and z
are 0.
[0071] In certain preferred examples, the movement of build
platform 44 is based on a trochoidal path in which the radius of
curvature a remains constant during the build process while the
distance b changes during the build process. In certain preferred
examples, after each layer of the three-dimensional object is
built, the build platform 44 is elevated in the build (z) axis
direction by an amount equal to the layer thickness, thereby
reducing the value of b by an amount equal to the layer thickness
(.DELTA.b).
[0072] The movement of any point that lies at a fixed distance b
from the center C of the trochoidal circle can be described using
equations (1) and (2). For purposes of understanding the motion of
build platform 44 it is convenient to describe the movement of the
rotational axis R.sub.x defined by the rotational motor 86 and the
sagittal line 79. In equations (1) and (2), the movement of each of
these lines R.sub.x and 79 (which appear as points when viewed in
cross-section, as in FIGS. 6A-6F), will be based on the radius a
defined by the radius of curvature of the lower build platform
surface 46. In addition, the values of b used for both the sagittal
line 79 and the rotational axis R.sub.x will change by a layer
thickness (.DELTA.b) with the formation of each layer. However, the
initial values of b will differ. With respect to the sagittal line
79, the initial value of b will equal the radius of curvature a of
the lower build platform surface 46. With respect to rotational
axis R.sub.x, the initial value of b will equal the difference
between the length of radius a and the distance d between the
rotational axis R.sub.x and the sagittal line 79 in the radial
direction defined by lower build platform surface 46. Thus, during
the formation of a given layer of solidifiable material, the values
of b applicable to the rotational axis R.sub.x and the sagittal
line 79 will remain constant. However, they will not be the same.
Instead, the value of b for the rotational axis R.sub.x will be
smaller than the value of b for the sagittal line 79 by an amount
equal to the distance between the rotational axis R.sub.x and the
sagittal line 79 along the radial direction defined by the lower
build platform surface 46. The value of the radius of curvature a
is the same for the sagittal line 79 and the rotational axis
R.sub.x and remains constant throughout the process of making a
three-dimensional object.
[0073] Referring again to FIGS. 6A-6F, it is convenient to define a
reference rotational orientation of the build platform 44 as the
orientation at which a plane tangent to lower surface 46 at
sagittal line 79 is perpendicular to the build (z) axis and
parallel to the x-y plane as illustrated in FIGS. 6B and 6E.
Equations (1) and (2) are defined for a trochoidal circle that
rolls along a plane (the "tangent plane") that is perpendicular to
the build (z) axis and tangent to the most recently formed exposed
surface of the three-dimensional object (or for the first layer,
the plane that is perpendicular to the build (z) axis and tangent
to the lower build platform surface 46). In the reference
orientation, the sagittal plane is parallel to the y-z plane and
perpendicular to the x-y plane. Equations (1) and (2) are based on
a trochoidal circle that rolls from a starting point at which the
center C of the trochoidal circle and the rotational axis R.sub.x
define a line that is parallel to the build (z) axis. A trochoidal
circle starting at that position would roll in the clock-wise
direction by 2.pi. radians to reach the reference rotational
orientation of FIG. 6B. As a result, when build platform 44 is in
the reference rotational orientation, the angle o in equations (1)
and (2) is 360 degrees or 2.pi. radians because the point of
interest (e.g., the sagittal line 79 or rotational axis R.sub.x) is
rotated 360.degree. Or radians) from the reference position.
[0074] As the linear solidification device 42 moves a distance
.DELTA.x.sub.LD in the travel (x) axis direction, the tangent line
TL moves by the same amount (.DELTA.x.sub.TL) via the operation of
build platform travel axis translation motor 80. The angular
rotation of the build platform about rotational axis R.sub.x can be
related to the distance .DELTA.x as follows:
.DELTA.o=-(1/a).DELTA.x.sub.TL (3) [0075] where, [0076]
.DELTA.o=o.sub.2-o.sub.1 is the change in the angle of rotation of
the sagittal plane on which rotation axis R.sub.x and sagittal line
79 lie as the tangent line TL moves a distance .DELTA.x.sub.TL
along the travel (x) axis; and [0077]
.DELTA.x.sub.TL=x.sub.2-x.sub.1 is the change in travel (x) axis
position of the tangent line TL, which also equals the change in
travel (x) axis position of linear solidification device 42.
[0078] In equation (3), .DELTA.x.sub.TL is positive when moving in
a first direction (e.g., left to right in FIGS. 6A-6C) along the
travel (x) axis and negative when moving in a second direction
(e.g., right to left in FIGS. 6D-6F) along the travel (x) axis.
Sagittal plane angles of rotation o that are counter-clockwise from
the tangent line TL and the y-z plane are positive, and sagittal
plane angles of rotation o that are clockwise from the tangent line
TL and the y-z plane are negative. As mentioned above, the angle o
is the angle of rotation of a trochoidal circle defined by the
radius of curvature a of the lower build platform surface 46
relative to a starting position at which the sagittal plane is
perpendicular to the tangent plane that defines the tangent line
TL. It is convenient to define the angular position of the sagittal
line 79 and the rotation axis R.sub.x relative to the build
platform reference positions of FIGS. 6B and 6E, in which the plane
tangent to the sagittal line 79 is perpendicular to the build (z)
axis. In the reference orientation of FIGS. 6B and 6E,
o=360.degree.=2.pi. radians. Thus, the angle of rotation (in
radians) relative to the reference orientation can be defined as
follows:
o.sub.R=2.pi.-o (4) [0079] where, [0080] o is the angular rotation
of a trochoidal circle of radius a from a starting position at
which the sagittal plane of the build platform 44 is perpendicular
to the tangent plane on which the trochoidal circle rolls.
[0081] In equation (4), angular positions that are counterclockwise
from the tangent line TL and the y-z plane are positive, while
those that are clockwise from the tangent line TL and the y-z plane
are negative. Thus, in FIG. 6A o.sub.R is positive, while in FIG.
6C, o.sub.R will have a negative value.
[0082] A change in the relative angular orientation o.sub.R can be
defined as follows:
.DELTA.o.sub.R=o.sub.R2-o.sub.R1 (5) [0083] where, [0084] o.sub.R2
is a second rotational orientation relative to the reference
rotational orientation of FIGS. 6B and 6E and o.sub.R1 is a first
rotational orientation relative to the reference rotational
orientation of FIGS. 6B and 6E.
[0085] The build platform 44 is rotated about rotational axis
R.sub.x (FIG. 2) via the operation of build axis rotation motor 86
such that the rotational orientation of the sagittal plane on which
sagittal line 79 and rotation axis R.sub.x lie changes by an amount
.DELTA.o in accordance with equation (3) and an amount
.DELTA.o.sub.R in accordance with equation (5). As it rotates from
the rotational orientation of FIG. 6A, the build platform 44
eventually reaches the reference rotational orientation of FIG. 6B.
As the linear solidification device 42 continues to move in the
travel (x) axis direction, the build platform 44 continues to
translate along the travel (x) axis and to rotate about the
rotational axis R.sub.x until reaching the rotational orientation
of FIG. 6D, at which point the linear solidification device 42 has
completed its traversal of the build envelope 342 (FIG. 11B) in the
travel (x) axis direction. As FIGS. 6A-C indicate, at each position
along the travel (x) axis, the linear solidification device 42
remains aligned with the minimum build axis position (z.sub.min)
defined by the tangent line TL (which appears as a point in FIGS.
6A-6C because the length of the line is along the y-axis). During
the formation of the first layer of the three-dimensional object,
the linear solidification device 42 remains aligned with the part
of the build platform lower surface 46 that has the lowest build
(z) axis position, z.sub.min. During the formation of subsequent
layers, the linear solidification device 42 remains aligned with
the portion of the exposed object surface that has the lowest build
(z) axis position, z.sub.min (FIGS. 6H and 6I). In preferred
examples, the minimum build axis position z.sub.min of the
trochoidal circle defined by the radius of curvature a of the lower
build platform surface 46 is maintained at a fixed distance from
the bottom of the solidifiable material container 48 during an
object building operation, which ensures that the thickness of
unsolidified solidifiable material at the location of
solidification remains constant during the formation of each part
of a layer and each layer of an object. In the same or other
examples, the spacing along the z-axis between the linear
solidification device 42 and the most recently solidified exposed
surface 64 of the object 59 (FIG. 1) is also held constant.
[0086] In FIGS. 6D-6F, the motion of the build platform 44 is
reversed and the build platform travels in a second direction along
the travel (x) axis that is opposite the first direction in which
it travels in FIGS. 6A-6C. In the example of FIGS. 6D-6F, linear
solidification device 42 does not supply solidification energy to
the solidifiable material 50 when traveling in the second
direction. FIGS. 6D-6F define a separation operation (although the
object is not visible) in which solidified object material is
separated from the solidification substrate 52 and film 55. Because
of the trochoidal path of sagittal line 79, the separation forces
at each moment are concentrated along tangent line TL of the
trochoidal circle. Because the separation forces are concentrated
along a line instead of a larger surface area of the object being
built, separation forces will not tend to limit the x-y area of the
object that can be built.
[0087] Referring to FIGS. 6H and 6I, the linear solidification
device 42 is depicted in two different rotational orientations and
two different locations along the travel (x) axis. The trochoidal
circle defined by the radius of curvature of the lower surface 46
of build platform 44 is shown in dashed lines and labeled as "TC."
The solidified object 59 is shown on the build platform 49. As the
figures indicate, the exposed surface 64 of the most recently
formed object layer lies on the circumference of trochoidal circle
TC. The linear solidification device 42 remains aligned along the
travel (x) axis with the tangent line TL, which is located at the
minimum build (z) axis position of the trochoidal circle on which
the most recently formed, exposed object surface 64 lies. The
trochoidal circle rolls on the plane (the tangent plane) that is
perpendicular to the build (z) axis and tangent to the most
recently solidified, exposed object surface 64. The tangent line TL
is defined by the intersection of the exposed object surface 64 and
the tangent plane.
[0088] In FIGS. 6H and 6I, the initial value of b for the
trochoidal point of interest (e.g., the sagittal line 79 or
rotational axis R.sub.x) has been reduced by the number of layers
comprising object 59 multiplied the thickness of the layers (which
is the same for all layers comprising the object in this particular
example). The trochoidal circle rotates in a clockwise direction on
the tangent plane from an initial rotational orientation in FIG. 6H
at which the sagittal plane (a plane through the center C of the
trochoidal circle that symmetrically divides the lower build
platform surface 46 into two sections) is oriented at an angle
o.sub.R1 relative to the build (z) axis to a subsequent rotational
orientation at which the sagittal plane is oriented at an angle
o.sub.R2 relative to the build (z) axis.
[0089] Equations (1) and (2) can be modified to use the angular
rotation relative to the non-rotated position of FIGS. 6B and 6E
(i.e., to use o.sub.R) and to calculate the distance that the
sagittal line 79 travels along the travel (x) axis as the sagittal
line 79 is rotated from a first angular position o.sub.R1 to a
second angular position o.sub.R2 as follows:
.DELTA.x=a[o.sub.R1-o.sub.R2]+b[sin(2.pi.-o.sub.R1)-sin(2.pi.-o.sub.R2)]
(6) [0090] wherein, [0091] .DELTA.x=change in position of the
sagittal line 79 along the travel (x) axis from a first position
x.sub.1 to a second position x.sub.2; [0092] o.sub.R1=the angle of
rotation of the build platform 44 when the sagittal line is at the
first position x.sub.1 relative to a reference rotational
orientation (FIGS. 6B and 6E) in which the sagittal plane is
parallel to the y-z plane and perpendicular to the x-y plane;
[0093] o.sub.R2=the angle of rotation of the build platform 44 when
the sagittal line is at the second position x.sub.2 relative to the
reference angular orientation (FIGS. 6B and 6E) in which the
sagittal plane is parallel to the y-z plane and perpendicular to
the x-y plane; [0094] a=the length of the radius of curvature of
lower surface 46 of the build platform 44; [0095] b=the distance
between the sagittal line 79 and the center of the circle of radius
a along the radial direction.
[0096] In equation (6), the center of the circle of radius a
remains at a fixed position along the build (z) axis during the
formation of each layer of a three-dimensional object. Thus, the
value of a will remain constant for the formation of each layer,
and the initial value of b for sagittal line 79 will equal the
length of radius a. Each subsequent value of b will be one layer
thickness less than the previous value of b. When the build
platform 44 is rotated counter-clockwise relative to the x-y plane,
the sagittal plane will be rotated counterclockwise relative to the
tangent line TL and the y-z plane, and o.sub.R will be positive
(FIGS. 6A and 6F). When the build platform 44 is rotated clock-wise
relative to the x-y plane, the sagittal plane will be rotated
clockwise relative to the tangent line TL and the y-z plane, and
o.sub.R will be negative (FIGS. 6C and 6D).
[0097] Equation (6) can be modified to describe the trochoidal path
of other fixed points of interest. For example, the equation can be
used to describe the travel (x) axis path of the rotation axis
R.sub.x. In that case, the value of b would be the distance from
the center of the trochoidal circle of radius a to the axis of
rotation R.sub.x along the radial direction. The length of a will
again equal the length of the radius of curvature of lower build
platform surface 46 during the formation of each layer of the
three-dimensional object.
[0098] In certain examples of making a three-dimensional object
herein, the values of .DELTA.x calculated from equation (6) are
used to guide the movement of the build platform travel axis
translation motor 80. As indicated in FIG. 2, the build platform
travel axis translation motor 80 is configured so that the movement
of ball screw 82 by a certain amount .DELTA.x along the travel (x)
axis causes the axis of rotation R.sub.x to move by the same amount
along the travel (x) axis. When the system is configured in this
manner, it is preferable to calculate the trochoidal path of the
rotational axis R.sub.x not the sagittal line 79 so that the value
of .DELTA.x obtained from equation (6) can be directly used to
guide the operation of build platform travel axis translation motor
80. Thus, in preferred examples, the trochoidal point of interest
lies on the intersection of rotational axis R.sub.x and the axis of
translation of build platform travel axis translation motor 80.
[0099] FIG. 6G illustrates the relationship between the angle of
rotation .DELTA.o.sub.R of the sagittal plane relative to the y-z
plane and the rotation of the build platform 44 relative to the
non-rotated reference orientation of FIG. 6B. The sagittal plane
bifurcates the lower build platform surface 46 and includes the
center C of the trochoidal circle as well as the sagittal line 79
and the rotation axis R. The build platform 44 is shown in the
reference (non-rotated) orientation in solid lines and in a rotated
orientation in dashed lines. The build platform rotates about the
rotational axis R.sub.x such that the upper surface 47 of the build
platform 44 is rotated by an amount .DELTA.o relative to the
reference orientation. As the figure illustrates, the change in
rotational position of the build platform relative to the x-y plane
(.DELTA.o) equals the angle of rotation (o.sub.R) of the sagittal
plane (on which rotation axis R.sub.x and sagittal line 79 lie)
relative to the y-z plane. Thus, the angle of rotation predicted by
the equations of a trochoid can be used to determine the rotation
of the rotational motor 86.
[0100] If the sagittal line 79 traverses a trochoidal path in the
x-z plane, equation (2) can be modified to determine the change in
build (z) axis position of the sagittal line as the build platform
rotates from one angular position relative to the reference
position (FIGS. 6B and 6E) to another angular position relative to
the reference position:
.DELTA.z=b[cos(2.pi.-o.sub.R1)-cos(2.pi.-o.sub.R2)] (7) [0101]
wherein, [0102] .DELTA.z=the distance traveled by the sagittal line
79 along the build (z) axis from an initial position to a second
position, wherein the distance upward along the build (z) axis and
away from the solidifiable material container 43 is defined as
being positive; [0103] o.sub.R1=the angle of rotation of the build
platform (in radians) relative to a non-rotated reference position
(FIGS. 6B and 6E) in which the sagittal plane is parallel to the
y-z plane and perpendicular to the x-y plane; [0104] o.sub.R2=the
angle of rotation of the build platform (in radians) relative to a
non-rotated reference position (FIGS. 6B and 6E) in which the
sagittal plane is parallel to the y-z plane and perpendicular to
the x-y plane; [0105] a=the length of the radius of curvature of
lower surface 46 of build platform 44; and [0106] b is the distance
between the sagittal line 79 and the center of the circle of radius
a along the radial direction.
[0107] In equation 7, the center of the circle of radius a remains
at a fixed position along the build (z) axis during the formation
of each layer of a three-dimensional object. Thus, the value of a
remains constant during the formation of each layer of the
three-dimensional object, and initial value of b for the sagittal
line 79 will equal the radius a. Each subsequent value of b will be
on layer thickness less than the previous value of b. As with
equation (6), when the build platform 44) is rotated
counter-clockwise relative to the x-y plane, the sagittal plane
will be rotated counterclockwise relative to the tangent line TL
and the y-z plane, and the value of o.sub.R in equation (7) will be
positive (FIGS. 6A and 6C). When the build platform 44 is rotated
clock-wise relative to the x-y plane, the sagittal plane will be
rotated clockwise relative to the tangent line TL and the y-z
plane, and the value of o.sub.R in equation (7) will be negative
(FIGS. 6C and 6D).
[0108] As with equation (6), equation (7) can be modified to
determine the change in the rotational axis R.sub.x position as the
build platform rotates from o.sub.R1 to o.sub.R2. In that case, the
initial value of b would equal the difference between the length of
radius a and the distance between the axis of rotation R.sub.x and
the sagittal line 79 in the radial direction. In preferred
implementations, the trochoidal point of interest used in equation
(7) is selected so that the calculated value of .DELTA.z equals the
distance of translation of ball screw 77 along the build (z) axis
so that the calculated value of .DELTA.z can be used to guide the
operation of build platform build axis motor 125. In the system of
FIGS. 2-5, the axis of translation of the build platform build axis
translation motor 125 is perpendicular to a plane in which the
rotational axis R.sub.x and the axis of translation of build axis
translation motor 80 lie. Thus, the trochoidal path of rotational
axis R.sub.x would preferably be used to calculate .DELTA.z in
equation (7) and then to guide the movement of the build platform
build axis motor 125.
[0109] Referring again to FIG. 6G, the radius a used in equations
(1) to (4) is the radius of curvature of the lower surface 46 of
the build platform 44. The radius a can be determined from the
sagittal height h defined by the lower surface 46 and the width w
of the build platform along the direction of curvature (i.e., the
width w is the chord length defined by lower surface 46):
a=(h.sup.2+0.25w.sup.2)/2h (8) [0110] where, [0111] h=the sagittal
height h defined by the lower surface 46; [0112] w=the width of the
build platform 44 defined by the width of the lower surface 46.
[0113] In FIG. 6A, the sagittal line 79 is at an initial position
corresponding to the position of linear solidification device 42 at
which solidification may first begin along the travel axis (i.e.,
linear solidification device 42 and tangent line TL are at the
build envelope border 343 of FIG. 11B as discussed further below).
At this initial position, the upper surface 47 and the plane
tangent to the sagittal line 79 are rotated counter-clockwise by an
angle o.sub.R relative to the reference orientation of FIG. 6B. The
angle o.sub.R is also the angle of rotation of the trochoidal
circle of radius a in the orientation of FIG. 6A relative the
orientation of FIG. 6B. Thus, in FIG. 6A, o.sub.R is positive and
equals 2.pi.-o.
[0114] In FIG. 6B, the build platform 44 is in the non-rotated
orientation at which o.sub.R is zero and o=2.pi.. The position of
tangent line TL along the travel (x) axis is the mid-point of the
build envelope 342 length in the travel (x) axis direction (FIG.
11B). In FIG. 6C, the build platform 44 has completed its traversal
in the travel (x) axis direction. The value of o.sub.R is negative
in the orientation of FIG. 6C and equals 2.pi.-o.
[0115] As discussed previously, the system 40 of FIGS. 1-5 includes
a linear solidification device 42. The linear solidification device
42 may be configured in a number of ways. In certain examples, the
linear solidification device 42 progressively exposes portions of
the solidifiable material to solidification energy in a scanning
(y) axis direction as the linear solidification device 42 device
moves along the travel (x) axis direction. In other examples, a
generally, or preferably substantially, linear pattern of
solidification energy is applied in a single exposure along one
direction as the device moves in another direction. The
solidification energy may comprise electromagnetic radiation. The
electromagnetic radiation may include actinic light, visible or
invisible light, UV-radiation, IR-radiation, electron beam
radiation, X-ray radiation, laser radiation, or the like. Moreover,
while each type of electromagnetic radiation in the electromagnetic
spectrum may be discussed generally, the disclosure is not limited
to the specific examples provided. Those of skill in the art are
aware that variations on the type of electromagnetic radiation and
the methods of generating the electromagnetic radiation may be
determined based on the needs of the application. In preferred
embodiments, linear solidification device 42 includes a linear
scanning device, and solidification energy is "scanned" in a
scanning direction that defines a scanning axis (i.e., the y-axis)
as the linear solidification device 42 moves in a direction along
the travel (x) axis. Preferably, the linear solidification device
42 is not itself moved in the y-direction as this occurs. The
sequential linear scans in the scanning axis direction may be
referred to as "linear scanning operations" herein.
[0116] An example of a linear solidification device 42 is depicted
in FIGS. 7A and 7B. Linear solidification device 42 comprises a
solidification energy source 112, a scanning device, and a housing
110. In FIGS. 7A and 7B, the linear solidification device 42 is
depicted upside down relative to the orientation of FIGS. 1-5. In
FIGS. 1-5, the solidifiable material is above the linear
solidification device 42 along the build (z) axis so that the
linear opening 114 is positioned between the rotating energy
deflector 113 and the solidification substrate 52 along the build
(z) axis.
[0117] In the embodiment depicted in FIGS. 7A and 7B, the scanning
device is a rotating energy deflector 113. In other examples of a
linear solidification device 42, the scanning device is a laser
scanning micromirror that is used in place of rotating energy
deflector 113. Thus, it should be understood throughout that a
laser scanning micromirror may be used in place of a rotating
energy deflector 113 in the exemplary embodiments described
herein.
[0118] Suitable laser scanning micromirrors include
magnetically-actuated MOEMS (micro-opto-electromechanical systems)
micromirrors supplied under the name LSCAN by Lemoptix SA of
Switzerland. A linear scanning micromirror comprises a silicon chip
with a fixed part and a movable mirror part. The mirror is
electrically or magnetically actuated to tilt relative to the fixed
part to a degree that corresponds to the actuating signal. As the
mirror tilts, received solidification energy is scanned via
deflection from the tilting mirror. Thus, the degree of tilt or
tilt angle corresponds to the position along the scanning (y) axis
at which the deflected solidification energy strikes the surface of
the solidifiable material.
[0119] Linear solidification device housing 110 is a generally
polygonal structure. As depicted in FIGS. 7A and 7B, housing 110
has an open face, but the face may instead be closed. Rotating
energy deflector 113 is spaced apart from solidification energy
source 112 along both the z-axis and the y-axis, and may be
slightly offset from solidification energy source 112 along the
x-axis as well. Rotating energy deflector 113 is rotatably mounted
to housing 110 so as to rotate substantially within a plane that
may preferably be oriented substantially perpendicularly to the y-z
plane. Solidification energy source port 66 is provided for
mounting solidification energy source 112 (e.g., a laser diode)
such that it is in optical communication with at least one facet
116a-116f of rotating energy deflector 113 at one time. Lens 117
(described further below) is spaced apart and below from rotating
energy deflector 113 in the height (z-axis) direction and is
located above housing linear opening 114 in FIG. 7B but below
linear opening 114 when installed in system 40, as indicated by
FIGS. 1 and 4.
[0120] Motor 118 is mounted on a rear surface of housing 110 and is
operatively connected to rotating energy deflector 113. Motor 118
is connected to a source of power (not shown). When motor 118 is
energized, rotating energy deflector 113 rotates in the y-z plane,
bringing the various facets 116a-116f sequentially into optical
communication with solidification energy source 112. A control unit
(not shown) may also be provided to selectively energize motor 118,
solidification energy source 112 and/or motor 88. Either or both of
motors 88 and 118 may be stepper or servo motors. In certain
examples, either or both of the motors 118 and 88 are driven by
continuous energy pulses. In the case of motor 118, in certain
preferred embodiments, it is driven by continuous energy pulses
such that the timing of each pulse corresponds to a fixed
rotational position of a facet 116(a)-(f) of rotating energy
deflector 113. As the motor is pulsed, each of the facets
116(a)-(f) will sequentially come into optical communication with
solidification energy source 112, and the particular facet 116a-f
that is in optical communication with solidification energy source
112 will have a fixed rotational position that corresponds to the
timing of the pulse.
[0121] In certain implementations, the rotational position of
rotating energy deflector 113 may repeatably correspond to the
timing of each energy pulse of motor 118 without being known by the
operator. The fixed association of the motor 118 energy pulse and
the rotational position of the facets 116a-116f allows the motor
pulse timing to be used to synchronize the transmission of a
synchronization solidification energy signal from solidification
energy source 112 so that a synchronization solidification energy
signal is issued for each facet 116(a)-(f) at some defined
rotational position while it is in optical communication with
solidification energy source 112.
[0122] In certain implementations, it is desirable to provide a
y-axis scanning speed (i.e., a speed at which solidification energy
moves along the exposed surface of the solidifiable material) that
is significantly greater than the travel (x) axis speed at which
the linear solidification device 42 moves. Providing this disparity
in y-axis and x-axis speeds helps to better ensure that the scanned
energy pattern is linear and orthogonal to the travel (x) axis,
thereby reducing the likelihood of object distortion. In certain
examples, the scanning speed in the y-axis direction is at least
about 1000 times, preferably at least about 2000 times, more
preferably at least about 4000 times, still more preferably at
least about 6000 times, and even more preferably at least about
8000 times the speed of movement of linear solidification device 42
along the travel (x) axis. In one example, linear solidification
device 42 moves at a speed of about 1 inch/second along the travel
(x) axis, and the y-axis scanning speed is about 10,000
inches/second. Increasing the scanning speed relative to the speed
of movement of linear solidification device 42 along the travel
axis increases the resolution of the scanning process by increasing
the number of scan lines per unit of length along the travel (x)
axis.
[0123] The scanning speed (in number of scans per unit time) at
which solidification energy is progressively applied to selected
areas of a solidifiable resin along the scanning (y) axis
corresponds to the rotational speed of rotating energy deflector
113 multiplied by the number of facets 116a-f. In certain examples,
the rotational speed is from about 1,000 to about 10,000 rpm,
preferably from about 2,000 to about 8,000 rpm, and more
[0124] In certain preferred examples, and as shown in FIG. 7B, lens
117 is provided between the rotating energy deflector 113 and a
bottom surface of housing 110 to focus deflected solidification
energy and transmit it through linear opening 114 and toward the
solidifiable material. In the example of FIG. 7B, lens 117 is
preferably a flat field lens. In certain examples, the lens 117 is
a flat field lens that is transparent to violet and ultraviolet
radiation. In additional examples, the lens 117 also has a focal
distance that is longer on the ends of the lens relative to the
middle (referring to the y-axis scanning direction along which the
lens length is oriented) to compensate for different solidification
energy beam travel distances from the rotating energy deflector 92
to the solidifiable material. In certain implementations, lens 117
includes an anti-reflective coating such that the coated lens
transmits at least 90%, preferably at least 92%, and more
preferably at least 95% of the incident light having a wavelength
ranging from about 380 nm to about 420 nm. In one example, lens 98
transmits at least about 95% of the incident light having a
wavelength of about 405 nm. Suitable coatings include single layer,
magnesium difluoride (MgF.sub.2) coatings, including ARSL0001 MgF2
coatings supplied by Siltint Industries of the United Kingdom.
[0125] In one preferred embodiment, solidification energy source
112 is a laser diode that emits light in the range of 380 nm-420
nm. A range of 390 nm-410 nm is preferred, and a range of from 400
nm to about 410 nm is more preferred. The laser power is preferably
at least about 300 mW, more preferably at least about 400 mW, and
even more preferably, at least about 450 mW. At the same time, the
laser power is preferably no more than about 700 mW, more
preferably no more than about 600 mW, and still more preferably no
more than about 550 mW. In one example, a 500 mW, 405 nm blue-light
laser is used. Suitable blue light laser diodes include 405 nm, 500
mW laser diodes supplied by Sanyo.
[0126] Rotating energy deflector 113 deflects solidification energy
that is incident upon it toward flat field lens 117. Rotating
energy deflector 113 preferably rotates in a rotation plane as
linear solidification device 42 moves along the travel (x) axis. In
certain examples, the rotation plane is substantially perpendicular
to the travel axis (i.e., the rotation plane is the y-z plane). In
certain examples, rotating energy deflector 113 rotates at a
substantially constant rotational speed. In other examples, the
linear solidification device 42 moves at a substantially constant
speed along the travel (x) axis. In further examples, the rotating
energy deflector 113 rotates at a substantially constant rotational
speed and the linear solidification device 42 moves along the
travel (x) axis at a substantially constant speed.
[0127] When solidification energy source 112 is a light source,
rotating energy deflector 113 is preferably a rotating light
deflector capable of deflecting visible or UV light. In one
exemplary embodiment, rotating energy deflector 113 is a polygonal
mirror having one or more facets 116a, b, c, etc. defined around
its perimeter. In the example of FIG. 7B, rotating energy deflector
113 is a hexagonal mirror having facets 116a to 116f. Each facet
116a-116f has at least one rotational position, and preferably
several, at which it will be in optical communication with
solidification energy source 112 to receive light projected
therefrom. As the rotating energy deflector 113 rotates,
solidification energy (e.g., visible or ultraviolet light) will be
deflected along the length of each facet 116a-f in succession. At
any one time, one of the facets 116a-116f will receive and deflect
solidification energy. As the facet changes its rotational
position, the angle of incidence of the solidification energy with
respect to the facet will change, altering the angle of deflection,
and therefore, the scanning (y) axis location at which the
deflected solidification energy strikes the solidification
substrate 52 and the solidifiable material 50 above it (FIG. 1).
Thus, each rotational position of rotating energy deflector 113
corresponds to a position along the scanning (y) axis at which
solidification energy may be projected at a given time. However,
for a given number of rotating energy deflector 113 facets F, there
will be F rotational positions that each correspond to a particular
position along the scanning axis direction. As will be discussed in
greater detail below, one or more controllers or microcontrollers
may be provided to regulate the movement of the build platform 44,
solidification energy source 112, rotating energy deflector 113,
and motor 88 that traverses the linear solidification device 42
across the solidifiable material.
[0128] In certain examples, the maximum length of scan along the
scanning (y) axis will correspond to the full length of an
individual facet 116a-116f. That is, as the light progressively
impinges on the entire length of any one facet 116a-116f, the
deflected light will correspondingly complete a full scan length in
along the scanning (y) axis. The number of facets 116a, 116b, etc.
on the rotating energy deflector 113 will correspond to the number
of y-axis scans that are performed for one complete revolution of
rotating energy deflector 113. In the case of a hexagonal mirror,
six y-axis scans will occur for every complete rotation of rotating
energy deflector 113. For rotating energy deflectors that maintain
a constant rotational direction (e.g., clockwise or
counterclockwise), the scans will be uni-directional along the
y-axis. Put differently, as light transitions from one facet 116a
to another 116b, the scan will return to its starting position in
the y-axis, as opposed to scanning back in the opposite direction.
However, other rotating energy deflector configurations may be used
including those in which the rotating energy deflector 113 rotates
in two rotational directions to produce a "back and forth" scan in
the y-axis direction.
[0129] In the system 40 of FIGS. 1-5, linear solidification device
42 is positioned underneath rigid or semi-rigid solidification
substrate 52 and moves in a first direction along the travel (x)
axis to solidify solidifiable material 50 (FIG. 1). Lens 117 is
located vertically (z-axis) above rotating energy deflector 113 and
vertically (z-axis) below linear opening 114 (FIGS. 5a and 5b). As
linear solidification device 42 translates along the travel (x)
axis, solidification energy is selectively projected upward along
the build (z) axis and progressively scanned in the scanning (y)
axis direction to selectively solidify certain locations along a
generally--and preferably substantially--linear scanning path (as
dictated by the shape of the three-dimensional object at a given
travel (x) axis position). Whether a given y-axis location on the
solidifiable material will receive solidification energy depends on
whether solidification energy is being supplied by the
solidification energy source 112 as the facet 116a-116f that is in
optical communication with solidification energy light source
reaches the rotational position corresponding to that y-axis
location.
[0130] Referring to FIG. 7C, and alternate embodiment of linear
solidification device 42 of FIGS. 7A and B is depicted. In FIG. 7C,
housing 110 is removed. As shown in the figure, solidification
energy source 112 is in optical communication with one facet
116(a)-(f) of rotating energy deflector 113 at any one time as
rotating energy deflector 113 rotates in the y-z plane (i.e., the
plane orthogonal to the direction of movement of linear
solidification device 42 along the travel (x) axis). In this
embodiment, one or more solidification energy focusing devices is
provided between solidification energy source 112 and rotating
energy deflector 113. In the example of FIG. 7C, the one or more
focusing devices comprises a collimator 137 and a cylindrical lens
120.
[0131] Collimator 137 is provided between solidification energy
source 112 and cylindrical lens 120. Cylindrical lens 120 is
provided between collimator 137 and rotating energy deflector 113.
Collimator 137 is also a focusing lens and creates a round shaped
beam. Cylindrical lens 120 stretches the round-shaped beam into a
more linear form to allow the beam to decrease the area of impact
against rotating energy deflector 113 and more precisely fit the
beam within the dimensions of one particular facet 116(a)-(f).
Thus, solidification energy transmitted from solidification energy
source 112 passes through collimator 137 first and cylindrical lens
120 second before reaching a particular facet 116(a)-(f) of
rotating energy deflector 113.
[0132] In certain preferred examples, collimator 137 and/or
cylindrical lens 120 transmit at least 90%, preferably at least
92%, and more preferably at least 95% of the incident light having
a wavelength ranging from about 380 nm to about 420 nm. In one
example, collimator 137 and cylindrical lens 120 transmit at least
about 95% of the incident light having a wavelength of about 405
nm. In the same or other examples, solidification energy source 112
comprises a laser diode having a beam divergence of at least about
five (5) milliradians, more preferably at least about six (6)
milliradians, and sill more preferably at least about 6.5
milliradians. At the same time or in other examples, the beam
divergence is no more than about nine (9) milliradians, preferably
no more than about eight (8) milliradians, and still more
preferably not more than about 7.5 milliradians. In one example,
the divergence is about 7 milliradians. Collimator 137 is
preferably configured with a focal length sufficient to collimate
light having the foregoing beam divergence values. Collimator 137
is preferably configured to receive incident laser light having a
"butterfly" shape and convert it into a round beam for transmission
to cylindrical lens 120.
[0133] In certain examples, collimator 137 has an effective focal
length that ranges from about 4.0 mm to about 4.1 mm, preferably
from about 4.0 mm to about 4.5 mm, and more preferably from about
4.01 mm to about 4.03 mm. In one example, collimator 137 is a
molded glass aspheric collimator lens having an effective focal
length of about 4.02 mm. One such collimator 137 is a Geltech.TM.
anti-reflective coated, molded glass aspheric collimator lens
supplied as part number 671TME-405 by Thorlabs, Inc. of Newton,
N.J. This collimator is formed from ECO-550 glass, has an effective
focal length of 4.02 mm, and has a numerical aperture of 0.60.
[0134] In certain examples, collimator 137 and/or cylindrical lens
120 are optimized based on the specific wavelength and beam
divergence characteristics of solidification energy source 112. In
one example, collimator 137 and/or cylindrical lens 120 are formed
from a borosilicate glass such as BK-7 optical glass. In certain
preferred examples, collimator 137 and/or cylindrical lens 120 are
coated with an anti-reflective coating such that the coated
collimator 137 and coated cylindrical lens 120 transmit at least
90%, preferably at least 92%, and more preferably at least 95% of
the incident light having a wavelength ranging from about 380 nm to
about 420 nm. Suitable anti-reflective coatings include magnesium
difluoride (MgF2) coatings such as the ARSL0001 MgF2 coating
supplied by Siltint Industries of the United Kingdom.
[0135] In certain examples of a linear solidification device 42,
the solidification energy defines a spot (which may or may not be
circular) at the point of impingement on the solidifiable material.
The angle of incidence between the solidification energy and the
solidifiable material will vary with the rotational position of a
given facet 116(a)-(f) relative to the solidification energy source
112. The spot dimensions and shape will also tend to vary with the
angle of incidence. In some cases, this variation in spot size
and/or spot dimensions can produce uneven solidification patterns
and degrade the accuracy of the object building process. Thus, in
certain examples, one or more lenses are provided between rotating
energy deflector 113 and the solidifiable material 50 (FIG. 1) to
increase the uniformity of the spot size and/or dimensions as the
rotational position of rotating energy deflector 113 changes. In
certain examples, the one or more lenses is a flat field lens 117
(FIGS. 7A and 7B). In other examples (FIG. 7C), the one or more
lenses is an F-Theta lens (126 or 130 in FIG. 7C). In other
examples, and as also shown in FIG. 7C, the one or more lenses is a
pair of F-Theta lenses 126 and 130. The F-Theta lenses 126 and 130
are spaced apart from one another and from the rotating energy
deflector 113 along the build (z) axis. First F-Theta lens 126 is
positioned between second F-Theta lens 130 and rotating energy
deflector 113 along the build (z) axis. Second F-Theta lens 130 is
positioned between first F-Theta lens 126 and the solidifiable
material 50 (as well as between first F-Theta lens 126 and linear
114, not shown in FIGS. 7C-D) along the build (z) axis.
[0136] First F-Theta lens 126 includes an incident face 128 and a
transmissive face 134. Incident face 128 receives deflected
solidification energy from rotating energy deflector 113.
Transmissive face 134 transmits solidification energy from first
F-Theta lens 126 to second F-Theta lens 130. Similarly, second
F-Theta lens 130 includes incident face 136 and transmissive face
138. Incident face 136 receives solidification energy transmitted
from transmissive face 134 of first F-Theta lens 126, and
transmissive face 138 transmits solidification energy from second
F-Theta lens 130 to housing linear opening 114 (not shown in FIGS.
7C-7D) and to the solidifiable material 50.
[0137] In certain implementations of the linear solidification
device 42 of FIG. 7C, first F-Theta lens 126 has a refractive index
that is less than that of second F-Theta lens 130. The relative
difference in refractive indices helps reduce laser beam scattering
losses. At the same time or in other implementations, the radius of
curvature of first F-Theta lens transmissive face 134 is less than
the radius of curvature of second F-Theta lens transmissive face
138. Suitable pairs of F-Theta lenses are commercially available
and include F-Theta lenses supplied by Konica Minolta and HP. In
certain embodiments, the F-Theta lenses 126 and 130 are preferably
coated with an anti-reflective coating. The anti-reflective coating
is used to maximize the amount of selected wavelengths of
solidification energy that are transmitted through F-Theta lenses
126 and 130. In one example, the anti-reflective coating allows the
coated F-Theta lenses 126 and 130 to transmit greater than 90
percent of the incident solidification energy having a wavelength
between about 325 nm and 420 nm, preferably greater than 90 percent
of the incident solidification energy having a wavelength between
about 380 nm and about 420 nm, more preferably greater than about
92 percent of the incident solidification energy having a
wavelength between about 380 nm and about 420 nm, and still more
preferably greater than 95 percent of the incident solidification
energy having a wavelength between about 380 nm and about 420 nm.
In one specific example, the coated F-theta lenses transmit at
least about 95% of the incident light having a wavelength of about
405 nm (i.e., blue laser light). In other preferred embodiments,
collimator 137, and cylindrical lens 120 are also coated with the
same anti-reflective coating. Suitable anti-reflective coatings
include magnesium difluoride (MgF2) coatings such as the ARSL001
coating supplied by Siltint Industries of the United Kingdom.
[0138] In certain examples, linear solidification device 42 may
comprise multiple solidification energy sources. In some
implementations, the linear solidification device 42 may include
multiple solidification energy sources that provide solidification
energy of the same wavelength, and the device 42 may transmit a
single beam of solidification energy to the solidifiable material.
In other implementations, the device 42 may include solidification
energy sources of different wavelengths and selectively transmit
solidification energy of only one of the wavelengths to a
solidifiable material. This implementation may be particularly
useful when a three-dimensional object is built using multiple
solidifiable materials each of which solidifies in response to
solidification energy of different wavelengths (e.g., because their
photoinitiators are activated by different wavelengths of
solidification energy).
[0139] Referring to FIG. 7D, an alternate version of linear
solidification device 42 (with the housing removed) is depicted in
schematic form. The linear solidification device 42 is the same as
the one depicted in FIG. 7C with two exceptions. First, the linear
solidification device 42 of FIG. 7D includes two solidification
energy sources 112a and 112b. In the specific embodiment of FIG.
7D, solidification energy sources 112a and 112b transmit
solidification energy of substantially the same wavelength. In some
cases, the use of such multiple solidification energy sources 112a,
112b is desirable in order to increase the power of the
solidification energy transmitted to the solidifiable material. The
power of the solidification energy can affect the rate of
solidification, which in turn may limit the maximum speed of travel
of the linear solidification device 42 in the x-axis direction. In
order to solidify, for example, a given volume of a solidifiable
resin, the volume must receive sufficient solidification energy
(e.g., in Joules). The solidification energy received by a given
volume of solidifiable material is a function of the power (e.g.,
in Watts) of the solidification energy and the time of exposure of
the volume of solidifiable material. As a result, as the power is
reduced, the rate of travel of the linear solidification energy
device 42 must be reduced to ensure that sufficient solidification
energy is received at each location along the direction of travel
(i.e., x-axis) of linear solidification energy device 42. Put
differently, at a desired solidification depth along the build axis
(z-axis), increasing the power of the solidification energy
increases the rate at which the linear solidification device 42 can
be traversed in the x-axis direction, and hence, the speed of an
object build process.
[0140] The second difference between the linear solidification
energy devices 42 of FIGS. 7C and 7D is the inclusion of prisms
121a and 121b in FIG. 7D. The linear solidification energy device
42 of FIG. 7D is intended to combine solidification energy from
both sources 112a and 112b into a single beam for delivery to the
solidifiable material. The single beam preferably has a power that
is at least 1.5 times, preferably at least 1.7 times, and more
preferably at least 1.95 times the average power of the individual
solidification energy sources 112a and 112b. Each solidification
energy source 112a and 112b transmits its respective solidification
energy to a respective prism 121a and 121b. The prisms 121a and
121b receive incident solidification energy at a first angle and
deflect the energy to produce transmitted solidification energy
beams at a second (different) angle that allows the individual
beams to be combined in a single beam. It is believed that the
individual beams combine ahead of cylindrical lens 120, after which
the solidification energy is received by rotating energy deflector
113 and ultimately transmitted to the solidifiable material in the
same manner described previously with respect to FIG. 7C.
[0141] As mentioned previously, the linear solidification device 42
of FIGS. 7C and 7D also includes a solidification energy sensor
122, which may be an optical sensor. Suitable optical sensors
include photodiodes. One exemplary photodiode that may be used is a
404 nm, 500 mW photodiode supplied by Opnext under the part number
HL40023MG.
[0142] Solidification energy sensor 122 generates a signal upon
receipt of solidification energy. Mirror 132 is provided and is in
optical communication with rotating energy deflector 113 such that
when each facet 116a-f of rotating energy deflector 113 receives
solidification energy from solidification energy source 112 while
at a particular rotational position (or range of positions) in the
y-z plane, the energy will be deflected toward mirror 132 (as shown
by the dashed lines in FIG. 7C). Similarly, when the scanning
device used in linear solidification device 42 is a linear scanning
micromirror, a particular tilt angle or range of tilt angles will
cause received solidification energy to be deflected toward mirror
132. The solidification energy then reflects off of mirror 132
along a path that is substantially parallel to the scanning axis
(y-axis) between first F-Theta lens 126 and second F-Theta lens 130
to sensor 122. Sensor 122 may be operatively connected to a
computer to which it will transmit the signal generated upon
receipt of solidification energy. The signal may be stored as data
and/or used in programs associated with a solidification energy
source controller (not shown). An example of a line scanning
synchronization method that makes use of the generated sensor
signal is described below.
[0143] In certain examples, sensor 122 is used to determine the
beginning of a line scanning operation along the scanning axis
(y-axis) direction. However, in certain cases using the
solidification energy sources described herein, the intensity of
the solidification energy transmitted by solidification energy
source 112 may be higher than desired, thereby reducing the
sensitivity of sensor 122 due, at least in part, to the presence of
scattered and ambient light. As a result, in some implementations a
filter 124 is provided between sensor 122 and mirror 132 along the
path of travel of solidification energy from mirror 132 to sensor
122. Filter 124 preferably reduces the intensity of electromagnetic
radiation received by sensor 122 without appreciably altering its
wavelength(s). Thus, in one example filter 124 is a neutral density
filter. One such suitable neutral density filter is a 16.times.
neutral density filter supplied by Samy's Camera of Los Angeles,
Calif. under the part number HDVND58. In certain implementations,
sensor 122 is used to synchronize a timer that serves as a
reference for linear scanning operations. In such cases, the
exposure of sensor 122 to scattered or ambient light may cause
synchronization errors. Thus, filter 124 is preferably configured
to ensure that only direct solidification energy from
solidification energy source 112 is received by sensor 122.
[0144] Referring again to FIG. 1, container 48 is configured to
retain a volume of solidifiable material in its interior and to
receive solidification energy through its bottom surface.
Solidifiable material is periodically dispensed into container 48
as the level of solidifiable material drops due to the
solidification of the solidifiable material into the
three-dimensional object. In one example, container 48 comprises a
basin with silicone side walls and a bottom comprising
solidification substrate 52 and a protective film 55 adhered
thereto. In one example, the film 55 is a monofluoroalkoxy (MFA)
film. In another example, a basin comprising a transparent
resilient bottom and resilient side walls is used as container 48.
In certain implementations, both the transparent resilient bottom
and the resilient side walls are formed from the same or different
silicone polymers. In other implementations, the bottom of silicone
basin is adhered to a solidification substrate such as a rigid or
semi-rigid glass or plastic that is transparent and/or translucent.
In another implementation, a basin comprising non-resilient acrylic
side walls and a resilient silicone bottom is used. In another
example, the bottom of the basin is defined by a rigid or
semi-rigid transparent solidification substrate 52 that is
connected to side walls formed of a resilient or plastically
deformable polymeric material. In a further example, the substrate
52 may be coated with a resilient transparent material, such as a
silicone, that extends only a portion of the way to the side walls,
leaving a peripheral gap around the coating and between the coating
and the sidewalls. In yet another example, the substrate 52 may be
coated with a resilient transparent material that extends all the
way to the side walls. A non-resilient material such as a
transparent non-resilient film may also be provided as a layer on
top of the resilient bottom between the resilient bottom and the
build platform 44.
[0145] In a further example, solidifiable material container 48 may
comprise a film assembly 148 disposed above solidification
substrate 52. As best seen in FIGS. 8A-C, film assembly 148
comprises a film 154 and one or more frames, which in the
embodiment of FIGS. 8A-8C includes an inner frame 150 and an outer
frame 152. As best seen in FIGS. 8A-C, in one example, outer frame
152 of film assembly 148 is a generally rigid and rectangular
structure shaped to cooperatively engage inner frame 150. Inner
frame 150 is a generally rigid and rectangular structure which
includes an upper lip 151 that projects outwardly around the
perimeter of inner frame 150. Outer frame 152 fits underneath upper
lip 151. In certain examples, the outer edge of lip 151 and the
outer perimeter of outer frame 152 are substantially flush with one
another and define a substantially continuous outer surface. Film
154 is preferably secured between the inner frame 150 and outer
frame 152. In one example, the outer periphery of film 154 is
secured between the underside of the inner frame lip 151 and the
upper surface of outer frame 152.
[0146] In addition, through-holes 158 (FIG. 8A) formed on the upper
surface of inner frame upper lip 151 are alignable with
complementary holes 156 (FIG. 8A) formed on the upper surface of
outer frame 152, allowing fasteners such as screws, bolts, etc. to
secure outer frame 152 to inner frame 150. Thus, in certain
examples, the fasteners are selected to minimize the amount of
leakage in the area between inner frame lip 151 and the upper most
surface of outer frame 152. In other examples, portions of the
inner frame area may be filled with a suitable resin blocking agent
such as a cured resin. Suitable cured resins include silicones and
epoxies.
[0147] Together, film 154, outer frame 152, and inner frame 150
define a film assembly 148 that is securable to the upper surface
51 of housing 54 (FIG. 1) and which is mounted on solidification
substrate 52. In certain embodiments, it is contemplated that film
assembly 148 will be replaced periodically due to the stress on
film 154. Thus, film assembly 148 is preferably releasably secured
to housing 54 to facilitate replacement of film assembly 148. In
such implementations, film 154 is not adhered to solidification
substrate 52, but rather, is tightly stretched across it to enable
the film 154 to stretch in the build (z) axis direction relative to
solidification substrate 52. However, in other implementations, the
film 154 may be adhered to the solidification substrate 52.
[0148] In certain embodiments, film 154 is configured to provide a
relieved area that reduces or minimizes the likelihood of vacuum
formation between film 154 and rigid or semi-rigid solidification
substrate 52. In such embodiments, a portion of film 154 includes a
relieved area (not shown) defined by mircotextures or grooves in
its lower surface (i.e., the surface facing rigid or semi-rigid
solidification substrate 52 along the build (z) axis). The relieved
area lies above rigid or semi-rigid solidification substrate 52
while also extending beyond the perimeter of rigid or semi-rigid
solidification substrate 52. In certain examples, film assembly 148
has a width in the scanning (y) axis direction which is longer than
the width (in the scanning axis direction) of rigid or semi-rigid
solidification substrate 52. The variation in width creates a gap
between the edge of rigid or semi-rigid solidification substrate 52
and the inner surface of inner frame 150, creating a leak path from
the atmosphere to the portion of the relieved area of film 154
lying above and in facing opposition to rigid or semi-rigid
solidification substrate 52, thereby minimizing the likelihood of
vacuum formation between film 154 and rigid or semi-rigid
solidification substrate 52.
[0149] Film 154 is preferably a homopolymer or copolymer formed
from ethylenically unsaturated, halogenated monomers.
Fluoropolymers are preferred. Examples of suitable materials for
protective film 154 include polyvinylidene fluoride (PVDF),
ethylenchlorotrifluoroethylene (ECTFE), ethylenetetrafluoroethylene
(ETFE), polytetrafluoroethylene (PTFE), perfluoroalkoxy (PFA), and
modified fluoroalkoxy (a copolymer of tetrafluoroethylene and
perfluoromethylvinylether, also known as MFA). Examples of suitable
film 154 materials include PVDF films sold under the Kynar.RTM.
name by Arkema, ECTFE films sold under the Halar.RTM. name by
SolvaySolexis, ETFE films sold under the Tefzel.RTM. name by
DuPont, PFA films sold under the Teflon.RTM.-PFA name by DuPont,
and MFA films sold under the name Nowofol. MFA and Teflon.RTM.
films are preferred.
[0150] In certain implementations, a portion of the solidifiable
material within the area defined by the travel (x) and scanning (y)
axes will be capable of receiving solidification energy from linear
solidification device 42. This portion may be defined as the "build
envelope." FIGS. 11B and 11C depict a top plan view of a region of
solidifiable material 50 which includes a build envelope 342. The
build envelope 342 defines the maximum area of solidification, and
therefore, the maximum three-dimensional object area in the x-y
plane (i.e., the travel axis/scanning axis plane). As shown in
FIGS. 11B and 11C, in certain cases the linear solidification
device 42 is movable along the travel (x) axis through a total
distance that equals the sum of a build envelope 342 length L and
two offset distances, .delta..sub.L and .delta..sub.R. The offset
distances .delta..sub.L and .delta..sub.R respectively represent
the distance from the left end-of-travel (EOT) position of linear
solidification device 42 to the left-hand side build envelope
boundary 343 and the distance from the right-hand side EOT position
to the right-hand side build envelope boundary 345. In certain
examples, the offset distances, .delta..sub.L and .delta..sub.R are
provided to ensure that the linear solidification device 42 has
time to achieve a substantially constant speed along the travel (x)
axis before any solidification of solidifiable material will begin
(i.e., before build envelope 342 is reached). In certain examples,
the movement of the linear solidification device 42 at a constant
travel (x) axis speed avoids the necessity of directly measuring
the travel axis position at any given moment because it allows a
motor movement parameter for linear solidification device motor 88
(FIG. 5) to provide an indirect indication of travel axis position.
In one particular example suitable for servo and stepper motors,
the motor movement parameter is a number of motor steps. In certain
examples, .delta..sub.L and .delta..sub.R are equal.
[0151] In accordance with one method of using the system 40 of
FIGS. 1-5, linear solidification device 42 is traversed in a first
direction along the travel (x) axis by virtue of its operative
connection to linear solidification device translation motor 88
(FIG. 5). Solidification energy may be is selectively projected
from the linear solidification device 42 though the solidification
substrate 52 once the linear solidification device 42 reaches the
edge 343 of the build envelope 342 and until linear solidification
device 42 reaches edge 345 of the build envelope 342. In certain
preferred examples herein, solidification of the solidifiable
material only occurs while the linear solidification device 42 is
moving in one direction along the travel (x) axis, and separation
of the solidified material from the film 55 and solidification
substrate 52 occurs when the linear solidification device 42 moves
in the opposite direction along the travel (x) axis.
[0152] In certain examples, as rotating energy deflector 113
rotates, solidification energy source 112 will selectively project
light in accordance with data that represents the object being
built. At a given location along the travel (x) axis, some scanning
(y) axis locations may be solidified and others may not, depending
on the shape of the object being built. One way of selectively
projecting light to the solidifiable material is to selectively
activate the solidification energy source 112 depending on the
travel (x) axis location of the linear solidification device 42 and
the rotational position of the facet 116a-f that is in optical
communication with the solidification energy source 112. While each
facet 116a-116f will have a full range of locations along its
length at which solidification energy may be received from
solidification energy source 112, it will not necessarily be the
case that each such facet location will receive solidification
energy during any individual scan performed by that facet. Thus, by
(directly or indirectly) coordinating the activation of
solidification energy source with the rotational position of a
given facet 116a-116f, solidification energy can be selectively
provided to only those locations along the y-axis where
solidification is desired.
[0153] The number of linear scans that can be performed within a
given linear distance along the travel (x) axis may depend on
several variables, including the rotational speed of rotating
energy deflector 113, the number of facets F on the rotating energy
deflector 113, and the speed of movement of the linear
solidification device 42 along the travel (x) axis direction. In
general, as the speed of movement of the linear solidification
device 42 increases along the travel (x) axis, the number of linear
scans per unit of travel axis length decreases. However, as the
number of facets on the rotating energy deflector 113 increases or
as the rotational speed of the rotating energy deflector 113
increases, the number of linear scans per unit of travel axis
length increases. Thus, for a given build envelope distance L along
the travel axis in units such as millimeters, the maximum number of
line scanning operations that can be performed may be calculated as
follows:
N.sub.max=(L/S)*(RPM/60)*F (9) [0154] where, [0155]
N.sub.max=maximum number of line scanning operations along the
travel (x) axis within the build envelope; [0156] L=desired length
of the build envelope along the travel (x) axis (mm); [0157]
S=speed of movement of linear solidification device 42 along the
travel axis (mm/sec); [0158] RPM=rotational frequency of rotating
energy deflector 113 (revolutions/minute); and [0159] F=number of
facets on the rotating energy deflector 113.
[0160] Each linear scan can then be assigned a linear scan index n
(which can also be called a string index when sets of data strings
are used as object layer data) ranging from a value of 0 to
N.sub.max-1. Equation (9) can also be used to calculate an actual
number of line scanning operations needed for a given part length
along the travel (x) axis. In that case, L would be the desired
length of the part along the travel (x) axis and N.sub.max would be
replaced by N, which would represent the total number of line
scanning operations used to form the part.
[0161] When the linear solidification device 42 is moving at a
constant speed S along the travel (x) axis, a motor movement
parameter such as a number of motor steps for linear solidification
device translation motor 88 may be correlated to the build envelope
length L and used to define a variable W which equals a number of
motor steps/L. A microcontroller unit associated with system 40 can
then use the number of motor steps to indirectly determine the
number of a linear scan (or string index as described further
herein) position of the linear solidification device within the
build envelope in accordance with the following equation:
scan index n=((number of steps from boundary)/(W)(S))*(RPM/60)*F
(10)
[0162] In equation (10), the number of steps from the boundary
refers to the number of motor steps counted starting at build
envelope boundary 343 and moving from left to right or starting at
build envelope boundary 345 and moving from right to left. A
particular three-dimensional object layer having a length along the
travel (x) axis may be formed by a number of linear scans performed
within build envelope 342.
[0163] In certain examples, a host computer associated with system
40 will assign scan index numbers or string data index numbers by
scaling the part to the build envelope size and assigning a scan
index number n based on the total number of possible scans
N.sub.max in the build envelope 342. The scan index numbers n will
then be correlated to a number of motor steps as set forth in
equation (7). This relationship depends, in part, on the accuracy
of the value W which is the ratio of the number of steps required
for the linear solidification device 42 to traverse the build
envelope length L along the travel (x) axis (FIG. 11B) divided by
L. In some cases, W may deviate from the value predicted by
geometry of the mechanical devices used to move the linear
solidification device 42 (i.e., the value predicted by the gear
ratio for motor 76, the rotational speed of motor 76, and the
pulley diameter of pulleys 82a and 82b). In that case, it may be
desirable to adjust the value of W. In certain examples, test parts
are built and measured to determine the extent to which the actual
value of W is offset from the predicted value, and the offset is
used to provide a corrected value of W.
[0164] As indicated previously, the systems for making a
three-dimensional object described herein may include a control
unit, such as a microcontrol unit or microcontroller, which
contains locally stored and executed programs for activating the
motor 88 for translating linear solidification device 42 along the
travel (x) axis, the motor 80 for translating build platform 44
along the travel (x) axis, the motor 86 for rotating build platform
44 about axis of rotation R.sub.x, and the motor 125 (FIG. 4) for
translating build platform 44 along the build (z) axis, as well as
for selectively activating solidification energy source 112. In
certain examples, the systems include a host computer that
processes three-dimensional object data into a format recognized by
the microcontroller unit and then transmits the data to the
microcontroller for use by the microcontroller unit's locally
stored and executed programs. As used herein, the term
"microcontroller" refers to a high-performance, programmable
computer memory system used for special tasks. In certain examples,
the microcontrollers described herein include an integrated circuit
chip having a microprocessor, a read only memory (ROM), interfaces
for peripheral devices, timers, analog to digital and digital to
analog converters, and possibly other functional units.
[0165] In certain examples, a linear solidification controller (not
shown) selectively activates and deactivates solidification energy
source 112 of linear solidification device 42, at least in part,
based on the position of linear solidification device 42 along the
travel (x) axis. The position along the travel (x) axis may be
directly detected or may be indirectly determined by other
variables (e.g., a number of motor steps). In one implementation
discussed further below, an end of travel sensor 346 (FIGS. 11B and
C) is used along with a motor movement parameter to indirectly
determine the travel (x) axis position.
[0166] In one implementation, the linear solidification controller
is a microcontroller or solidification energy source controller
(not shown) which is operatively connected to solidification energy
source 112 to change the energization state of solidification
energy source 112 by selectively activating and deactivating it. In
additional examples, the controller selectively activates the
solidification energy source 112, at least in part, based on shape
information about the three-dimensional object being built. In
further examples, the controller selectively activates the
solidification energy source 112 based on the position of linear
solidification device 42 along the travel (x) axis (or based on
another variable that correlates to the position such as a number
of motor steps for motor 88) and based on shape information about
the object being built which varies with the travel (x) axis
position. On a given exposed surface of solidifiable material, the
specific x, y locations that will receive the solidification energy
will be dependent on the y-axis profile of the object being built
at the given x-axis location of solidification energy source 112
and rotating energy deflector 113.
[0167] In certain examples, the shape information about the object
being built is provided as three-dimensional object shape
information which mathematically defines the shape of the object in
three-dimensional space. The three-dimensional object data is then
sliced or subdivided into object layer data preferably along a
dimension that corresponds to a build (z) axis along which the
build platform 44 moves relative to the solidifiable material
container 48. The object layer data may comprise information that
mathematically defines the shape of the object in a plane
orthogonal to the build axis (i.e., the x-y plane). Thus, in one
example wherein the build axis is referred to as the z-axis, each
set of object data layer may comprise x and y coordinates that
define the shape of the object cross-section at a given z-axis
position. Exemplary methods of providing and using object data to
drive the solidification process are described further below.
[0168] Referring again to FIGS. 7C-D and 11B, in certain
implementations, linear solidification device 42 is positioned
within the build envelope 342 such that mirror 132 is located
immediately proximate scanning-axis build envelope boundary 344. In
such implementations, the receipt of solidification energy by
sensor 122 (FIGS. 7C-D) indicates that a line scanning operation
may begin immediately thereafter because if the solidification
energy source 112 remains activated and if rotating energy
deflector 113 continues to rotate, solidification energy will be
transmitted to the solidifiable material at the scanning axis build
envelope boundary 344 immediately after it is transmitted to mirror
132. Therefore, sensor 122 can be used to indicate the beginning of
a line scanning operation for each facet 116(a)-116(f). As
mentioned previously, when solidification energy source 112 remains
activated while rotating energy deflector 113 completes a single
revolution, a number of linear scanning operations will be
completed along the scanning (y) axis which equals the number of
the rotating energy deflector's 113 facets 116(a)-(f).
[0169] In those cases where sensor 122 is used to indicate the
beginning of a line scanning operation, it is useful to briefly
activate solidification energy source 112 at a specific moment at
which the transmitted solidification energy will be received by
mirror 132. The brief activation of solidification energy source
112 may be coordinated or synchronized with an actuating signal
sent to the scanning device used in linear solidification device
114. For example and as mentioned previously, in certain cases
motor 118 is energized by a constant frequency pulse, the timing of
which corresponds to a fixed rotational position for the particular
facet 116(a)-(f) that is in optical communication with
solidification energy source 112. Therefore, through a process of
trial and error a lag time may be determined between the leading or
trailing edge of the motor pulses and the receipt of solidification
energy by sensor 122. More specifically, the source of
solidification energy 112 can be selectively activated at a number
of times relative to the leading or trailing edge of the pulse to
determine which lag time results in the generation of a
solidification energy sensor signal by sensor 122. In one preferred
embodiment, the solidification energy source 112 is activated at or
within a specified time following the trailing edge of the energy
pulse used to drive motor 118.
[0170] In certain cases, the sensor 122 may be unnecessary because
a specified lag time relative to the energization pulses that drive
motor 118 will reliably indicate when a line scanning operation is
about to begin (assuming solidification energy source 112 remains
activated). However, in some examples, the pulses cannot be used to
reliably indicate when a line scanning operation is about to begin
within the desired degree of precision. For example, the facets
116(a) to 116(f) of rotating energy deflector 113 may not be
perfectly or consistently planar. In that case, the scanning (y)
axis position of solidification energy may not correlate well with
the rotational position of rotating energy deflector 113. In
addition, heat generated by solidification energy source 112 can
cause slight variations in the path of the solidification energy
toward the solidifiable material and the angle of incidence at
which it strikes the solidifiable material. Thus, sensor 122
assists in better determining the time at which a line scanning
operation may begin (or is about to begin if the solidification
energy source 112 remains activated). This is particularly helpful
when object data is stored as time values because the time values
can be reliably correlated to specific positions along the scanning
axis direction relative to the scanning axis boundary 344 of build
envelope 342 (FIG. 11B). In certain examples, a timer is set to
zero when sensor 122 generates a synchronization signal, and the
object data is specified as time values at which the energization
state of solidification energy source 112 is changed relative to
the zero time value.
[0171] In accordance with certain implementations of the
three-dimensional object manufacturing processes and apparatuses
described herein, a method of representing object data for use in
controlling the action of linear solidification device 42 is
illustrated in FIGS. 9-11D. Typical file types used to generate
object data include STL (Stereo Lithography) files or other CAD
(Computer Aided Drafting) files commonly translated for rapid
prototyping systems into formats such as SLC, CLI slice data files
or voxelized data files which may include data formats such as BMP,
PNG, etc. However, any data input type may be used and converted
internally to create the image data used by the linear
solidification device 42. The object data corresponds to the energy
pattern supplied by linear solidification device 42 and may be
generated by a control unit or by an external source or device
(e.g., a network or storage device).
[0172] As an exemplary three-dimensional object, a simple cylinder
300 is shown in FIG. 9. Locations on or within the cylinder can be
characterized by x, y, and z-axes as shown. In certain linear
solidification device implementations, the intensity and duration
of solidification energy supplied at a particular x, y location
cannot be varied. As a result, those locations in the x, y plane
which receive solidification energy will solidify to substantially
the same depth. Particularly in such implementations, it can be
useful to perform a data "slicing" operation in which a computer
representation of the three-dimensional object is sliced to create
a plurality of sections in the build axis (z-axis) direction, each
representing a uniform depth across at all points across the x-y
plane. Each such section may mathematically correspond to or be
represented by an object layer data set. One exemplary illustration
of such slices is graphically depicted in FIG. 10. As shown in FIG.
10, a data representation of the object 300 can be further
represented as a plurality of build axis (z-axis) slices 302.sub.i,
wherein the total number of slices n is substantially equal to the
height of the object as built divided by the depth of
solidification provided by linear solidification device 42. The
slices 302.sub.i may be represented mathematically by object layer
data sets in which each layer is defined by x, y coordinates
representing its contours and a z-axis value representing its
location along the build axis, with .DELTA.z values between
adjacent slices representing the thickness of the layer.
[0173] Each object layer data set may be represented graphically as
a plurality of strips having a length along the scanning axis
(y-axis) direction and a width along the x-axis direction, with the
strips being arranged width-wise along the x-axis direction.
Referring to FIG. 11A, a view taken along the vertical (z-axis)
direction of a graphical representation of an individual object
data slice 302, is provided. The individual slice 302, may be
represented as a plurality of adjacent strips 304.sub.j, which is
represented as m strips. The dashed line is not part of the data
representation, but is provided to show the generally circular
shape defined by strips 304.sub.j. In the example of FIG. 11A, the
strips have a width corresponding to the direction of movement of
the linear solidification device 42 along the travel (x) axis and
length corresponding to a direction other than the direction of
linear solidification device 42 movement (y-axis). In the specific
example of FIG. 11A, the strip length direction is substantially
perpendicular to the x-axis direction.
[0174] Each strip 304.sub.j graphically depicts a data
representation (preferably provided in a form that is readable by a
computer processor) of those locations of solidifiable material
that will be solidified in the y-axis direction for a given x-axis
location. The locations may also be defined relative to build
envelope boundaries such as the scanning axis boundary 344 and the
travel (x) axis boundaries 343 and 345 of FIG. 11B. The control
unit (not shown) receives data indicating the location of
solidification energy in the x-axis direction, for example, as
indicated by the position of linear solidification device 42 in the
x-axis direction. The control unit also receives the data
representation (strips 304j) and directly or indirectly associates
each strip 304.sub.j with a travel (x) axis position in the build
envelope 342 defined within the exposed surface of the solidifiable
material. Thus, a position within a strip of the data
representation corresponds to a position on the exposed surface of
the solidifiable material.
[0175] In FIG. 11A x.sub.0 corresponds to the position of the
linear solidification device 42 at which solidification will begin.
The increment x.sub.1-x.sub.0 represents the width of
solidification in the x-axis direction provided by linear
solidification device 42. Thus, when linear solidification device
42 is at position x.sub.0, solidification energy source 112 will
supply solidification energy when a facet 116a-f with which it is
in optical communication has a rotational position corresponding to
the y-axis locations in the build envelope 342 where the strip
defined between x.sub.0 and x.sub.1 is present. In the illustrated
embodiments of FIGS. 7A-C, the length of one facet 116(a)-(f) of
rotating energy deflector 113 corresponds to the maximum scannable
y-axis dimension of the build envelope 342, i.e., the maximum
length of solidification in the y-axis direction. However, any
individual strip 304.sub.j may correspond to a y-axis
solidification length less than the maximum scannable y-axis build
envelope dimension.
[0176] As linear solidification device 42 moves along the travel
(x) axis direction within build envelope 342, it will solidify
regions of solidifiable material corresponding to each strip 304j.
Each travel (x) axis location corresponds to a particular strip
304j. In certain embodiments, a linear encoder is operatively
connected to linear solidification device translation motor 88
and/or shaft 108 to determine the travel (x) axis position of
linear solidification device 42.
[0177] The object layer data that is graphically illustrated in
FIG. 11A may be mapped onto a build envelope 342 as shown in FIG.
11C. Each strip 304j may be defined by an x coordinate (or
x-coordinate pairs) and one or more y-coordinates which define the
regions of solidification at the particular x-axis location.
[0178] In certain examples, each strip 304j may be represented by a
corresponding set of string data. In a preferred embodiment, the
set of string data comprises a set of time values. In another
preferred embodiment, the set of string data comprises a string
number n and a set of time values. In certain cases, the string
number n corresponds to a linear scan number. For example, using
equation (9) (described previously) a maximum number of linear
scans (N.sub.max) may be calculated for a build envelope length L,
and each linear scan will have a corresponding string index number
associated with it. For any particular object layer, regions of the
build envelope 342 along the x-axis direction may not be solidified
and may not be scanned. Nevertheless, all regions at which a unique
linear scan may occur in the x-axis direction may be assigned a
string number. Thus, for a given speed of linear solidification
device travel axis translation motor 88, a given number of facets F
of a rotating energy deflector 113 and a given rotational speed of
rotating energy deflector 92, there will be a maximum number of
linear scans N.sub.max within build envelope 342 and a
corresponding number of sets of data strings, each of which may or
may not have actual scan data (object data) in it, depending on
whether any scanning is to occur at its corresponding x-axis
location. In the example of FIG. 11C, thirteen linear scans are
used to form the object layer represented by strips 304j and each
linear scan corresponds to a linear scan index ranging from n to
n+12 and a unique set of string data having a string index ranging
from n to n+12.
[0179] Typical control systems, including microcontrollers, will
have a built in lag time between the time when solidification data
is read and when solidification energy source 112 is toggled to
either an activated or deactivated conditioned. The lag time may be
variable and may cause errors in the dimensions of the
three-dimensional object being built. In one example, a
microcontroller is provided with the systems for making a
three-dimensional object disclosed herein which has a lag time of
no more than about 80 nanoseconds, preferably no more than about 60
nanoseconds, and even more preferably no more than about 50
nanoseconds. The part error can be related to the toggle lag time
as follows:
Error=(L.sub.BE)(RPM)(F)(t.sub.toggle lag)/(60 sec./min.)(0.001
mm/micron) (11) [0180] wherein, [0181] Error is the maximum
variation in the part dimensions (microns) due to the toggle lag
time; [0182] LBE is the build envelope distance in the scanning (y)
axis direction (mm); [0183] RPM is the rotational frequency of the
rotating energy deflector 113 (revolutions/minute); [0184] F is the
number of facets on the rotating energy deflector 113; and [0185]
t.sub.toggle lag is the time required for the microprocessor to
toggle the state of the solidification energy source.
[0186] In certain preferred implementations, the Error is
preferably no more than 90 microns, more preferably no more than
about 90 microns, still preferably no more than about 70 microns,
and even more preferably no more than about 50 microns.
[0187] FIG. 11D provides a table that illustrates exemplary sets of
string data that correspond to the object strips shown in FIG. 11C.
The string indices begin with n=0 at the left-hand border (x.sub.0)
of build envelope 342 and end at a maximum string number N.sub.max
at the right hand border of the build envelope 342. Thus, certain
sets of string data will not have any object data associated with
them because they do not correspond to x-axis locations where
solidification where occur. In FIG. 11D no solidification occurs
prior to string index n=20 and no solidification occurs after the
string index n+12. Thus, there are no entries in the table of FIG.
11D for the x-axis locations at which no solidification occurs
within build envelope 342.
[0188] Each set of string data depicted in FIG. 11D has a start
code which is represented in hexadecimal notation by a series of
eight Fs. Going from left to right, the string index n for the set
of string data is next. Following the string index a series of time
values is provided. Each time value represents a solidification
source energization state event. In one example, the energization
states are ON or OFF. The time values may take a variety of forms.
However, in one implementation they are defined as elapsed times of
a CPU clock in microcontroller unit used to operate the system for
making a three-dimensional object. In one example, the CPU has a
clock speed of 66 MHz and the units of time are CPU ticks. In an
example where the line scanning speed is 1000 lines per second, the
maximum scan length of each line in the scanning axis (y-axis
direction) corresponds to 66,000 ticks. Thus, the set of string
data at n=20 indicates that the solidification energy source 112
will be activated at 22000 ticks and deactivated at 44000 ticks.
The set of string data at n=21 indicates that solidification energy
source 112 will be activated at 20000 ticks and deactivated at
46000 ticks. In a preferred embodiment a timer is provided (such as
a software timer programmed into the microcontroller unit) which is
reset at the beginning of each linear scan, and the beginning of
each linear scan is synchronized to the build envelope scanning
axis boundary 344 using sensor 122 of FIG. 7C in the manner
described previously. Thus, the ticks are defined relative to a
zero starting time when the timer is reset at which point the line
scanning operation is at the scanning axis boundary 344 (FIG.
11B).
[0189] In certain examples, a host computer transmits sets of
string data to a microcontroller unit that operates the system for
producing a three-dimensional object for each possible linear scan
(i.e., for each string ranging from 0 to N.sub.max-1) even though
some of the sets of string data may have no object data (e.g., no
CPU tick values) associated with them because no solidification
occurs at the x-axis location to which they correspond. While this
technique may be used, it consumes excess microcontroller unit
processor capacity involved in reading string data for sets of
string data corresponding to x-axis locations at which no
solidification occurs. Accordingly, in certain examples, only sets
of string data containing object solidification data (e.g., CPU
tick values) are transmitted to the microcontroller unit. In such
cases it is convenient to define a computer memory index m having
values ranging from 0 to one less than the maximum number of
transmitted sets of data strings M.sub.max, where m uniquely
identifies each set of string data transmitted to the
microcontroller unit. In the example of FIG. 11D, there are a total
of N.sub.max sets of string data defined for the entire build
envelope 342 by the host computer. However, only 13 sets of string
data include any object solidification data. Therefore, assuming
that linear solidification device 42 is moving from left to right
in FIG. 11C, the first set of string data transmitted by the host
computer to the microcontroller unit will have a computer memory
index of m=0 and a string index n of 20. The value of the string
index n will correspond to a specific location along the x-axis
within build envelope 342. However, the computer memory index m
will not necessarily so correspond. Thus, the microcontroller unit
need only read 13 sets of data string sets instead of N.sub.max-1
sets of data strings.
[0190] Referring again to FIG. 7C, embodiments of a method for
synchronizing a timer to the position of a scan line within the
build envelope 342 will now be described. The method comprises
activating a solidification energy source, such as source 112,
which is in optical communication with a scanning device, such as a
rotating energy deflector 113 or a linear scanning micromirror. The
scanning device deflects solidification energy received from
solidification energy source 112, and the deflected solidification
energy is received by a solidification energy sensor, such as
sensor 122. In certain examples, a mirror such as mirror 132 is
provided to facilitate the transmission of deflected solidification
energy from the scanning device to sensor 122.
[0191] In accordance with the method, the solidification energy
sensor 122 senses the receipt of solidification energy and
generates a sensing signal that is transmitted to a system
microcontroller. The sensor's receipt of the solidification energy
corresponds to the beginning of a line scanning operation. A timer
is then initialized to a specified value (e.g., zero) based on the
receipt of solidification energy by the sensor.
[0192] An example of the foregoing synchronization method will be
described with reference to FIG. 7C. As illustrated in the figure,
in certain examples, a solidification energy sensor 122, such as a
light sensor, may be used to determine the y-axis location of
solidification energy supplied by linear solidification energy
device 42. In one example, a solidification energy sensor 122 is in
optical communication with rotating energy deflector 113 to receive
solidification energy deflected therefrom. In another example, the
solidification energy sensor 122 is located at one end of housing
110 to indicate when solidification energy projected in the y-axis
direction has reached its end or beginning of travel in the y-axis
direction. In accordance with the example, the solidification
energy sensor 122 is positioned at a location that corresponds to a
maximum solidification energy position in the second direction
(i.e., at a location corresponding to the end of travel in the
y-axis direction). However, the sensor 122 can be located at other
positions, but is preferably at a location at which the length of
solidification energy travel between sensed events is known. In
FIG. 7C, the location of mirror 132 and sensor 122 along with the
depicted clockwise rotational direction of rotating energy
deflector 113 cause the sensing of solidification energy by sensor
122 to correspond to the beginning of a linear scanning
operation.
[0193] In accordance with such examples, a processor operatively
connected to a clock (i.e., a CPU clock) receives the
solidification energy sensor signals from sensor 122 and a timer
operating on the clock units is synchronized to them, allowing an
elapsed time between sensed solidification energy pulses to be
calculated. The y-axis maximum scan length (e.g., the length of
opening 114 or a measured length of solidification energy travel in
the y-axis direction) is determined, and the speed of
solidification energy beam scanning in the y-axis direction is
calculated by dividing the maximum y-axis length of travel by the
elapsed time between pulses:
s=l/.DELTA.t.sub.max (11) [0194] wherein, [0195] s=speed of
solidification energy beam travel in the y-axis direction (e.g.
cm/sec); [0196] l=maximum length of scanning (e.g., cm); and [0197]
.DELTA.t.sub.max elapsed time between sequential sensed
solidification energy signals generated by solidification energy
sensor (e.g., sec).
[0198] By synchronizing the clock to the sensor's receipt of
solidification energy and using the last speed value (or a suitable
averaged value), the position of the solidification energy beam in
the y-axis direction can be calculated:
y=s.DELTA.t (12) [0199] wherein, [0200] y=y-axis position of
solidification energy beam along solidifiable material relative to
the y-axis starting point (e.g., cm); [0201] s=speed of
solidification energy beam travel from formula (1); and [0202]
.DELTA.t=elapsed time from last solidification energy signal from
sensor.
[0203] A linear solidification controller (for example, as
implemented in a microcontroller unit) operatively connected to
solidification energy source 112 can selectively activate and
deactivate solidification energy source 112 to cause solidification
energy to be supplied only when linear solidification device 42 is
at an x location and the rotating energy deflector 113 is at a
rotational position that corresponds to a point on one of the
strips 304.sub.j shown in FIG. 11A. Using formulas (11) and (12),
the linear solidification controller can receive data indicative of
the y-axis position of solidification energy. A linear encoder may
provide the linear solidification controller with travel (x) axis
location information (for linear solidification energy device 42),
allowing the controller to determine the desired y-axis profile at
the determined travel (x) axis location from object data such as
that in FIG. 11A.
[0204] As mentioned previously, the object layer data may also be
converted to a plurality of sets of string data such that each
plurality corresponds to a given layer and position along the build
axis (z-axis). In accordance with such examples, each set of string
data includes a plurality of time values, each of which defines a
time at which the energization state of the solidification energy
source 112 is changes. Preferably, the time values are defined
relative to a zero time that is reset upon the receipt of a
synchronization solidification energy generated when sensor 122
receives solidification energy, as also discussed previously. In
certain examples, the zero time of a CPU counter is set at the
leading edge of the synchronization sensor signal received by
sensor 122.
[0205] Referring again to FIG. 11A, each strip 304.sub.j
corresponds to a continuous region of solidification in the
scanning (y) axis direction. However, depending on the object being
built, this may not be the case. Certain of the strips 304.sub.j
may be discontinuous, thereby defining unconnected sections along
the scanning (y) axis for a given travel (x) axis location. In
certain examples a solidification energy modulator (such as a laser
diode modulator in the case of a laser diode solidification energy
source 112) is provided to selectively activate solidification
energy source 112.
[0206] Referring to FIGS. 12A-B, a method of forming a
three-dimensional object using the system of FIGS. 2-5 will now be
described (with a suitable housing and solidifiable material
container such as housing 54 and solidifiable material container 48
of FIG. 1 also being provided). The method of FIGS. 12A-B is based
on the movement of the rotational axis R.sub.x along trochoidal
paths. In accordance with the method, the build platform 44 is
manipulated so that the linear solidification device 42 and the
tangent line TL remain aligned along the travel (x) axis as the
linear solidification device 42 moves along the travel (x) axis. In
a preferred embodiment, the method is embodied in a set of computer
readable instructions on a non-transitory computer readable medium
which can be executed by a computer processor. At the beginning of
the method, the linear solidification device 42 is preferably
aligned with the lowest line of the build platform lower surface 46
along the build (z) axis, which is the tangent line at the build
axis position z.sub.min, exemplified in FIG. 6A. The sagittal plane
on which the center C, rotational axis R.sub.x, and sagittal line
79 lie is rotated counter-clockwise by o.sub.R, from the tangent
line TL.
[0207] In accordance with the embodiment, at the start of an object
build process, a layer index k is initialized to zero (Step 1010).
In step 1012, the radius of a trochoidal circle is determined based
on the sagittal height h and the width w of the build platform in
accordance with equation (8) above. The radius need not be
calculated during an individual build process, but rather, can be
determined and pre-set in a computer or microcontroller operating
the system. In step 1014 a layer thickness .DELTA.b (microns) is
read. For the first layer, the value of b equals the difference
between the radius a and the distance d measured between the
rotational axis R.sub.x and the sagittal line 79 along the radial
direction. In step 1016, the value of b is set to this value
(a-d).
[0208] In step 1018, the value of o.sub.Ri when linear
solidification device 42 is at the travel (x) axis border 343 (FIG.
11B) is read. The angle o.sub.Ri can also be pre-set in the
computer or microcontroller.
[0209] In step 1020, linear solidification device 42 is advanced in
a first direction along the travel (x) axis to a position within
build envelope 342 (FIG. 11B). As mentioned above, the tangent line
TL is maintained in alignment with the linear solidification device
42 along the travel (x) axis. Therefore, equation (3) can be used
to calculate the change in the angle of rotation of the trochoidal
circle of radius a for a given distance of travel (.DELTA.x.sub.TL)
of the tangent line TL along the travel (x) axis. If the tangent
line moves by an amount .DELTA.x.sub.TL in the positive direction
(to the right in FIGS. 6A-6C), the angular rotation of the
trochoidal circle will change in radians by an amount equal to
-.DELTA.x.sub.TL/a. In step 1024, the new angle of rotation
relative to the reference position of FIGS. 6B and 6E can be
determined as follows:
o.sub.Rj=o.sub.Ri-.DELTA.x.sub.TL/a (13)
[0210] In step 1025 equation (6) is used to calculate distance
.DELTA.x.sub.j that the rotational axis R.sub.x moves along the
travel axis using the initial angle of rotation o.sub.Ri, the
current angle of rotation o.sub.Rj, the radius a and the distance b
between the rotational axis R.sub.x and the center C of the
trochoidal circle. In step 1026, equation (7) is used to calculate
the distance .DELTA.z.sub.j that the rotational axis R.sub.x moves
along the build (z) axis using the initial angle of rotation
o.sub.Ri and the current angle of rotation o.sub.Rj.
[0211] In step 1028, the build platform rotational motor 86 is
operated to rotate the build platform to the current angle of
rotation o.sub.Rj. In step 1030 motor 80 is operated to translate
the rotational axis R.sub.x to the position .DELTA.x.sub.y (i.e.,
the position of rotational R.sub.x along the travel (x) axis
relative to a starting point when the tangent line TL and linear
solidification device 42 are at the build envelope border 343). In
step 1032 motor 125 is operated to translate the rotational axis
R.sub.x to a position .DELTA.z.sub.j (i.e., the build axis position
relative to a starting point when the tangent line TL and linear
solidification device are at the build envelope border 343).
Although depicted as discrete, sequential steps, steps 1028, 1030,
and 1032 may occur simultaneously or substantially simultaneously
so that the build platform 44 moves in multiple dimensions at the
same time or substantially the same time.
[0212] In step 1036, the set of object string data is read for the
travel axis position that is located at .DELTA.x.sub.TL from the
build envelope border 343. In step 1038, solidification energy is
supplied along the scanning (y) axis in correspondence with the set
of string data.
[0213] In step 1040, the method determines whether the linear
solidification device 42 has reached an end of travel (EOT)
position along the first travel (x) axis direction. If it has not,
control transfers to step 1020, and steps 1020 to 1038 are repeated
for the remaining .DELTA.x.sub.TL increments for j=1 to j.sub.max
along the travel (x) axis. If the linear solidification device 42
has reached the end of travel (or in some examples, build envelope
border 345), control transfers to step 1042 in FIG. 12B.
[0214] In step 1042, the linear solidification device 42 is
translated in a second direction along the travel (x) axis. In
certain examples, the linear solidification device 42 may be
translated through the right-hand offset distance .delta..sub.R and
then back to the build envelope border 345 in step 1042. However,
in step 1042 linear solidification device 42 is translated within
build envelope 342 by an amount .DELTA.x.sub.j from build envelope
border 345. In step 1043, the build platform is raised (using build
platform build axis motor 125) by the layer thickness .DELTA.b, and
the value of b is decreased by the layer thickness .DELTA.b.
[0215] In step 1044, the distance of the tangent line TL from the
build envelope border 345 (.DELTA.x.sub.TL) is determined based on
the distance between the linear solidification device 42 and the
build envelope border 345. When moving in the second direction (as
illustrated in FIGS. 6D-6F), the value of .DELTA.x.sub.TL is
negative. In step 1046 the current value of the angle of rotation
o.sub.Rj relative to the reference orientation is determined using
equation (13) from the initial angle of rotation at build axis
border 345 (o.sub.Ri) and the value of .DELTA.x.sub.TL. When moving
in the second direction, .DELTA.x.sub.TL will have a negative
value. As a result the calculated values of o.sub.Rj-o.sub.Ri will
be positive.
[0216] The value of the travel (x) axis position of the rotational
axis R.sub.x relative to its travel axis starting position (i.e.,
the travel (x) axis position of rotational axis R.sub.x when the
tangent line TL and linear solidification device 42 are both at
build envelope boundary 345) is determined in step 1047 from the
values of o.sub.Ri, o.sub.Rj, a, and b using equation (6). The
value of the build (z) axis position of the rotational axis R.sub.x
relative to its starting position (i.e., the build (z) axis
position of the rotational axis R.sub.x when the tangent line TL
and linear solidification device 42 are both at build envelope
boundary 345) is determined in step 1048 using equation (7). In
step 1050 the build axis rotation motor 86 is operated to rotate
the build platform 44 to the angle of rotation o.sub.Rj relative to
the non-rotated reference position of FIG. 6E. In step 1052 the
build platform travel axis translation motor 80 is operated to move
the rotational axis R.sub.x to the position .DELTA.x.sub.j, and in
step 1054 the build platform build axis translation motor 125 is
operated to move the rotational axis R.sub.x to the position
.DELTA.z.sub.j. Steps 1050-1054 may be carried out simultaneously
or substantially simultaneously. In step 1056 the method determines
whether the linear solidification device 42 has reached its end of
travel (EOT) in the second travel (x) axis direction. If not,
control transfers to step 1042, and steps 1042 to 1054 are repeated
for the remaining .DELTA.x.sub.TL increments for j=1 to j.sub.max
along the travel (x) axis. Otherwise, control transfer to step
1058, in which it is determined if the value of the current layer
index k equals the value of the maximum layer index k.sub.max. If
the current layer index k is equal to the maximum layer index
k.sub.max, the three-dimensional object is complete, and the method
ends. Otherwise, the layer index is incremented in step 1059 and
control transfers to step 1020.
[0217] In the method of FIGS. 12A and 12B, the trochoidal position
of the point of interest (the rotational axis R.sub.x) is
recalculated at various increments along the travel (x) axis to
adjust the operation of the build platform travel axis translation
motor 80, build platform rotation motor 86, and build platform
build axis translation motor 125. However, in other exemplary
methods, the speeds of movement of the trochoidal point may be
recalculated at various time increments and used to manipulate the
movement of build platform 44 via motors 80, 86, and 125. One such
exemplary method is illustrated in FIGS. 14A and B. In accordance
with the method, a layer index is initialized to a value of zero in
step 1062. In step 1064, the radius a of a trochoidal circle on
which the lower build platform surface 46 lies is calculated based
on the sagittal height h and the width w of build platform 44.
Alternatively, the radius a can be calculated and stored beforehand
without being calculated for the performance of an individual
object solidification operation. In step 1066 the layer thickness
.DELTA.b is read.
[0218] The initial value of b in equations (6) and (7) is
determined in step 1068 by subtracting the distance d between the
rotational axis R.sub.x and the sagittal line 79 along the radial
direction of the lower build platform surface 46 from the length of
radius a. A timer is initialized to a value of t.sub.initial in
step 1070. In certain examples, the value of t.sub.initial is
selected based on the starting angular orientation of the sagittal
plane when the linear solidification device 42 is at the build
envelope border 343. An exemplary method for selecting the initial
time t.sub.initial is provided below with respect to equation (17).
The time value is then incremented by a selected time increment
.DELTA.t in step 1071.
[0219] Starting at an initial position such as the one depicted in
FIG. 6A, the linear solidification device 42 begins to move at a
constant or substantially constant velocity v.sub.x in a first
direction along the travel (x) axis in step 1072. The build
platform motors 80, 86, and 125 are manipulated to move the tangent
line TL at the same velocity such that the tangent line TL and
linear solidification device 42 remain in alignment along the
travel (x) axis as the linear solidification device 42 moves along
the travel (x) axis.
[0220] If tangent line TL moves at a constant velocity v.sub.TL
along the travel axis, the rate of angular rotation (in radians per
unit second) of the trochoidal circle of radius a can be calculated
using the following equation:
.omega.=do/dt=(1/a)v.sub.TL (14) [0221] where, [0222] v.sub.TL is
the velocity of the tangent line TL along the travel (x) axis
(mm/sec); [0223] a=the radius of curvature of the lower build
platform surface 46 (mm); [0224] .omega.=angular rotational
velocity (radians/sec).
[0225] The angular rotational velocity of the build platform
.omega. about axis of rotation R.sub.x equals the angular
rotational velocity of the sagittal plane (and hence axis of
rotation R.sub.x and sagittal line 79 because they lie in the
sagittal plane) about the center of the trochoidal circle. Because
the tangent line velocity v.sub.TL is constant, the angular
rotational velocity .omega. is also constant. In step 1078, the
velocity of the rotation axis R.sub.x in a direction along the
travel (x) axis at a time t can be determined using the following
equation:
dx/dt=.omega.(a-b[cos(.omega.t)]) (15) [0226] wherein, [0227] dx/dt
is the velocity of the rotation axis R.sub.x along the travel axis
(mm/sec); [0228] .omega.=angular rotational velocity (radians/sec);
[0229] t=time of rotation (sec) of a trochoidal circle of radius a
to rotate from a reference orientation at which the sagittal plane
is parallel to the build axis; [0230] a=the length of the radius of
curvature defined by the lower build platform surface 46 (mm); and
[0231] b=the distance between the center of a trochoidal circle of
radius a defined by the radius of curvature of lower build platform
surface 46 and the rotation axis R.sub.x along the radial direction
of the lower build platform surface 46 (mm).
[0232] Equation (15) can be used to determine the velocity along
the travel (x) axis of any point that is fixed relative to the
center of the trochoidal circle by using the appropriate value of
b. In the case of sagittal line 79, the initial value of b would
equal the radius a. In the case of the rotational axis R.sub.x, the
initial value of b would equal the length of radius a minus the
distance between the rotational axis R.sub.x and the sagittal line
79 in the radial direction of the lower build platform surface
46.
[0233] The velocity of the rotation axis R.sub.x in a direction
along the build (z) axis at time t can be determined using the
following equation:
dz/dt=b.omega.[sin(.omega.t)] (16) [0234] wherein, [0235] dz/dt is
the velocity of the rotation axis R.sub.x along the build (z) axis
(mm/sec); [0236] .omega.=angular rotational velocity (radians/sec);
[0237] t=time of rotation (sec) of a trochoidal circle of radius a
from a reference orientation at which the sagittal plane is
parallel to the build axis; and [0238] b=the distance between the
center of a trochoidal circle of radius a defined by the radius of
curvature of lower build platform surface 46 and the rotation axis
R.sub.x along the radial direction of the lower build platform
surface 46 (mm).
[0239] In equations (15) and (16), the values of dx/dt and dz/dt
are based on a trochoidal circle that rolls at a constant angular
speed .omega. from a starting reference orientation at which t=0
and .omega.t=o=0 when the sagittal plane is parallel to the build
axis. If starting from this reference orientation, the time it
would take to reach the orientation of FIG. 6A may be determined as
follows:
t.sub.initial=(2.pi.-o.sub.Ri)/.omega. (17) [0240] wherein, [0241]
t.sub.initial is the time (sec) required for the trochoidal circle
to rotate from the reference orientation to o.sub.Ri at the angular
rotational velocity .omega.; and [0242] .omega.=angular rotational
velocity (radians/sec).
[0243] Thus, the initial time value t.sub.initial obtained from
equation (17) can be used as an initial time value for an angle
o.sub.Ri between the sagittal plane and the tangent line. The time
values used in equations (15) and (16) can then be related to the
time elapsed since the build platform was in its initial rotational
orientation as follows:
t=t.sub.initial+.DELTA.t (18) [0244] wherein, [0245] t.sub.initial
is as defined for equation (17); and [0246] .DELTA.t is the time
elapsed from a sagittal plane angular orientation of o.sub.Ri.
[0247] In step 1082, the angular velocity of rotational axis
R.sub.x is adjusted to the value .omega. determined in step 1076 by
adjusting the rotational speed of build platform rotational motor
86. In step 1084, the translational velocity of the rotational axis
R.sub.x along the travel (x) axis is adjusted to the value dx/dt
determined in step 1078 by adjusting the operation of build
platform translation axis motor 80. The translational velocity of
the rotational axis R.sub.x along the build (z) axis is adjusted in
step 1086 to the value dz/dt determined in step 1080. Steps
1082-1086 may be carried out simultaneously or substantially
simultaneously.
[0248] In step 1088, solidification energy is supplied along the
scanning (y) axis at the travel (x) axis location of the tangent
line (x.sub.TL) corresponding to the current time value t in
accordance with the corresponding object data string. In accordance
with the method, it is determined whether the linear solidification
device 42 has reached its end of travel (EOT) in the first
direction along the travel (x) axis in step 1090. If it has not,
control transfers to step 1071, the value of the current time t is
incremented by a selected time increment .DELTA.t, and steps
1072-1088 are repeated. Otherwise, control transfers to step 1094
in FIG. 14B.
[0249] FIG. 14A describes an object solidification operation such
as the one illustrated in FIGS. 6A-6C. FIG. 14B describes on object
separation operation in which the most recently solidified layer of
the object is separated from a solidification substrate such as the
substrate 52 in FIG. 1 or from a film such as film 55 on top of the
substrate 52. In step 1094, the linear solidification device 42
advances in a second direction along the travel (x) axis at a
velocity of -v.sub.x. In step 1096 the build platform is raised by
the layer thickness .DELTA.b using build platform build axis
translation motor 125, and the value of b is decremented by the
layer thickness .DELTA.b. A timer is initialized to a value of t in
step 1098 and is then incremented by the selected time increment
.DELTA.t in step 1099. In certain examples, the value of
t.sub.initial is selected based on the starting angular orientation
of the sagittal plane when the linear solidification device 42 is
at the build envelope border 345. An exemplary method for selecting
the initial time t.sub.initial is provided above with respect to
equation (17). As with the object solidification operation of FIG.
14A, in the object separation operation the linear solidification
device 42 is maintained in alignment with the tangent line TL along
the travel (x) axis. However, it is not critical to maintain their
alignment during an operation separation operation.
[0250] In step 1100, the velocity of the tangent line V.sub.TLx is
set equal to the velocity -v.sub.x of the linear solidification
device along the travel (x) axis. The angular velocity .omega.
corresponding to V.sub.TLx is determined in step 1102 using
equation (14). The translational velocity of the rotation axis
R.sub.x along the travel (x) axis is determined in step 1104 with
equation (15). In step 1106, the translational velocity of the
rotation axis R.sub.x along the build (z) axis is determined using
equation (16).
[0251] In step 1108, the build platform rotation motor 86 is
operated to rotate at the angular velocity .omega. determined in
step 1102. The build platform travel axis translation motor 80 is
adjusted in step 1110 to the speed dx/dt determined in step 1104.
The build platform build axis motor 125 is adjusted in step 1112 to
the speed dz/dt determined in step 1106.
[0252] In step 1114, a determination is made as to whether the
linear solidification device 42 has reached its end of travel in
the second direction along the travel (z) axis. If it has not,
control transfers to step 1099 and steps 1099-1112 are repeated.
Otherwise, control transfers to step 1118 in which the current
layer index k is compared to the maximum layer index value
k.sub.max. If the current layer index value k has reached the
maximum value k.sub.max, the object formation is complete, and the
process ends. Otherwise, control transfers to step 1120, and the
layer index is incremented by one. Control then transfers to step
1070 (FIG. 14A) so that the next layer of the object can be
formed.
[0253] In certain preferred examples, three-dimensional objects
produced using the methods and apparatuses described herein
comprise a removable support section and a finished object section.
The removable supports connect the finished object to the build
platform 44 and can be removed from both the build platform 44 and
the finished object so that the finished object is less likely to
be damaged due to separation from build platform 44. In certain
examples, the removable supports have a geometry that facilitates
their separation from the build platform 44 and the finished
object. In the same or other examples, the removable supports are
formed from a solidifiable material different from the solidifiable
material used to form the finished object and may be dissolved in
water or a suitable organic solvent to remove them from the
finished object. The use of removable supports in connection with
the methods and apparatuses described herein beneficially allows
the finished object to be provided with a base that is
substantially planar despite the fact that the lower surfaced 46 of
build platform 44 is curved.
[0254] Referring to FIG. 13 an object 59 is shown attached to the
lower surface 46 of build platform 44 following the completion of
an object building process. The object 59 comprises finished object
section 161, which is a conical structure, and removable support
section 159. Removable support section 159 is removably affixed to
the lower surface 46 of the build platform. As indicated in the
figure, the finished object section 161 includes a substantially
planar base surface 168 spaced apart from a top 170 along the build
(z) axis. Because the illustrated arrangement is from an
"upside-down" build process, the base surface 168 is at a build (z)
axis position that is above that of the top 170. However, once the
object is removed, it would be flipped over to conform to the
original object data on which it is based.
[0255] If the finished object section 161 were built directly on
the build platform lower surface 46, it would not be possible to
create a planar base surface 168 because of the curvature of build
platform lower surface 46. However, the removable support section
159 acts as an interface between the build platform lower surface
46 and the finished object section 161, thereby allowing the
finished object section to be created with a substantially planar
lower surface 168. The removable supports include a discontinuous
lower surface 163 that is defined by the ends of vertical support
runs 162 which are attached to the build platform lower surface 46.
The discontinuous lower surface 163 defines a curved profile when
viewed along the y-axis that has the same degree of curvature as
the build platform lower surface 46. Removable support section 159
may also include a horizontal member 160 to strengthen the support
structure. In the exemplary support structure, the removable
support section 159 contacts the substantially planar base 168 of
the finished object section 161 at discontinuous and spaced apart
locations, thereby reducing the surface area of the interface
between the removable support section 159 and the finished object
section 161. This configuration reduces the separation forces
required to separate the finished object section 161 from the
removable support section 159 as compared to interface structures
with a greater contact surface area. Thus, in one preferred example
of a method of making a three-dimensional object, object data is
provided which comprises removable support data and finished object
data. The removable support data defines removable supports
comprising a build platform interface surface (e.g., discontinuous
lower surface 163 of FIG. 13) that is curved along a width
dimension of the removable supports and the finished object. The
build platform interface surface may be discontinuous. The
removable supports also comprise an object interface surface that
removably adheres to a the finished object. In preferred examples,
the curvature of the build platform interface surface corresponds
to the curvature of a build platform surface.
Example 1
[0256] An example of the trochoidal movement of the rotational axis
R.sub.x as the platform rotates from an initial position to a
non-rotated reference position (at which the plane tangent to the
sagittal line 79 is perpendicular to the build (z) axis) will now
be described with reference to FIGS. 6A-6C and equations (6)-(7).
In accordance with the example, no solidifiable material has yet
been solidified on the lower surface 46. The build platform lower
surface 46 has a radius of curvature of a=25 inches (635 mm) which
is the radius of the trochoidal circle on which the lower build
platform surface 46 lies during the formation of the first object
layer. The distance d from the axis of rotation R.sub.x to the
sagittal line 79 along the radial direction defined by lower build
platform surface 46 is 10 inches (254 mm). Thus, the initial value
of b=a-d=15 inches (381 mm). The starting angular orientation (FIG.
6A) of the build platform 44 relative to the reference orientation
of FIG. 6B when the linear solidification device 42 is at the build
axis border 343 is o.sub.R1=+10.degree.=+.pi./18 radians. With
respect to equation (1), o.sub.1=2.pi.-.pi./18=35.pi./18 radians.
The angular orientation o.sub.R2 at the reference orientation is 0
(i.e., o.sub.2=2.pi. radians). At the initial rotational
orientation of o.sub.R1, the portion of the build platform (i.e.,
the tangent line TL) lying at the lowest position along the build
(z) axis (shown as z.sub.min in FIG. 6A) is at the border 343 of
the build envelope as is the linear solidification device 42.
[0257] The distance that the tangent line TL will travel along the
travel (x) axis as the build platform 44 rotates from o.sub.R1 to
o.sub.R.sup.2 can be calculated using equation (3) as follows:
.DELTA.x.sub.TL=-a(0-o.sub.R1)=635 mm(.pi./18)=110.8 mm=4.36
inches
[0258] The distance that the rotational axis R.sub.x will move as
the tangent line moves the distance .DELTA.x.sub.TL can be
calculated using equation (6) as follows:
.DELTA.x=635 mm[.pi./18-0]+381
mm[sin(2.pi.-.pi./18)-sin(2.pi.)]
.DELTA.x=635 mm(.pi./18)+381 mm[sin(35.pi./18)]
.DELTA.x=110.83 mm-66.16 mm=44.67 mm
Thus, build platform travel axis translational motor 80 will be
operated to translate the rotational axis R.sub.x of rotational
motor 86 by 44.67 mm in order to move the build platform 44 from
the orientation of FIG. 6A to the orientation of FIG. 6B. In the
example of FIGS. 6A-6C, the non-rotated orientation of FIG. 6B
occurs when the linear solidification device 42 is at the mid-point
of the build envelope along the travel (x) axis. Therefore, to move
the build platform from the orientation of FIG. 6B to the
orientation of FIG. 6C, build platform travel axis translation
motor 80 will be operated to translate the rotational axis R.sub.x
by an additional 44.67 mm.
[0259] The movement of the rotational axis R.sub.x along the build
(z) axis as the linear solidification device 42 moves along the
travel (x) axis from the position of FIG. 6A to the position of
FIG. 6B can be determined from equation (7) as follows:
.DELTA.z=381 mm[cos(2.pi.-.pi./18)-cos(2.pi.)]
.DELTA.z=381 mm[cos(35.pi./18)-1]=-5.79 mm
Thus, build platform build axis translation motor 125 will be
operated to move the rotational axis Rx downward by 5.79 mm along
the build (z) axis in order to move the build platform 44 from the
orientation of FIG. 6A to the orientation of FIG. 6B. The build
platform build axis translation motor 125 will be operated to
translate the rotational axis R.sub.x upward by 5.79 mm in order to
move the build platform 44 from the orientation of FIG. 6B to that
of FIG. 6C. In actual operation, the travel axis position .DELTA.x
and the build axis position .DELTA.z would be recalculated at small
rotational angle increments (e.g., .DELTA.o.sub.R=0.1 radians), and
the motors 80 and 125 would be operated to adjust the rotational
axis R.sub.x position along the travel and build axes at each
rotational angle increment in accordance with equations (6) and
(7).
Example 2
[0260] An example of the trochoidal movement of rotational axis
R.sub.x as the platform rotates from an initial position to a
non-rotated reference position (at which the plane tangent to the
sagittal line 79 is perpendicular to the build (z) axis) will now
be described with reference to FIGS. 6A-6C and equations (14)-(16).
In accordance with the example, no solidifiable material has yet
been solidified on the lower surface 46. The build platform lower
surface 46 has a radius of curvature of a=25 inches (635 mm) which
is the radius of the trochoidal circle on which the lower surface
46 lies during the formation of the first object layer. The
distance d from the axis of rotation R.sub.x to the sagittal line
79 along the radial direction defined by lower build platform
surface 46 is 10 inches (254 mm). Thus, the initial value of
b=a-d=15 inches (381 mm). The starting angular orientation (FIG.
6A) of the build platform 44 relative to the reference orientation
of FIG. 6B when the linear solidification device 42 is at the build
axis border 343 is o.sub.R1=+10.degree.=+.pi./18 radians. The
linear solidification device 42 will travel at a constant rate of 1
inch/sec (25.4 mm/sec) from build axis border 343 (FIG. 6A) to the
mid-point of the build envelope along the travel (x) axis (FIG.
6B). The build platform 44 will be manipulated so that the tangent
line TL moves at the same rate as the linear solidification device
42 along the travel (x) axis, i.e., v.sub.TL=25.4 mm/sec. Thus, the
angular velocity .omega. required to obtain the tangent line
velocity v.sub.TL can be calculated from equation (14) as
follows:
.omega.=(1/635 mm)(25.4 mm/sec)=0.04 radians/sec
[0261] As indicated in Example 1, the build envelope length is
2(110.8 mm)=221.6 mm. Thus, the linear solidification device will
travel from the position of FIG. 6A to that of FIG. 6B in 110.8
mm/(25.4 mm/sec)=4.36 sec. The initial time value used in equations
(15) and (16) may be calculated from equation (17) as follows:
t.sub.initial=(2.pi.-.pi./18)/0.04/sec=152.72 sec.
[0262] Thus, the initial velocity of the rotational axis R.sub.x in
along the travel (x) axis when the linear solidification device 42
is at build envelope border 343 (FIG. 6A) can be determined from
equation (15) as follows:
dx/dt=0.04/sec[635 mm-381 mm[cos(0.04/sec.times.152.72 sec)]]
dx/dt=0.04/sec[635 mm-375 mm]=10.39 mm/sec
[0263] Thus, at the initial orientation of FIG. 6A, build platform
travel axis translation motor 80 would be operated to translate the
rotation axis R.sub.x at 10.39 mm/sec along the travel (x) axis.
The initial velocity of the rotational axis R.sub.x in along the
build (z) axis when the linear solidification device 42 is at build
envelope border 343 (FIG. 6A) can be determined from equation (16)
as follows:
dz/dt=381 mm(0.04/sec)[sin(0.04/sec.times.152.72 sec]
dz/dt=381 mm(0.04/sec)[-0.1735]=-2.64 mm/sec
[0264] Thus, at the initial orientation of FIG. 6A, build platform
build axis translation motor 125 would be operated to translate the
rotational axis R.sub.x along the build (z) axis at -2.64 mm/sec.
When the build platform 44 reaches the non-rotated reference
orientation of FIG. 6B, the elapsed time from the starting position
of FIG. 6A can be determined from the angular rotation and the
angular speed as follows:
.DELTA.t=.pi./18/(0.04/sec)=4.36 sec.
[0265] Equation (15) can be used to determine the velocity of the
rotation axis R.sub.x along the travel (x) axis at the orientation
of FIG. 6B as follows:
dx/dt=0.04/sec[635 mm-381 mm[cos(0.04/sec(152.72 sec+4.36
sec))]
dx/dt=10.16 mm/sec
[0266] Equation (16) can be used to determine the velocity of the
rotation axis R.sub.x along the build (z) axis at the orientation
of FIG. 6B as follows:
dz/dt=381 mm(0.04/sec)[sin(0.04/sec)(152.72 sec+4.36 sec))]
dz/dt=0
[0267] Thus, at the non-rotated reference orientation of FIG. 6B,
the build platform travel axis translation motor 80 would be
operated to translate rotational axis R.sub.x along the travel (x)
axis at 10.16 mm/sec. The build platform build axis translation
motor 125 would momentarily have a zero velocity as the motor
changed the direction of translation from the downward direction to
the upward direction. In actual operation, the values of dx/dt and
dz/dt would be calculated at small time increments .DELTA.t (e.g.,
every 0.1 second), and the speeds of motors 80 and 125 would be
adjusted at each increment in accordance with equations (15) and
(16).
[0268] The present invention has been described with reference to
certain exemplary embodiments thereof. However, it will be readily
apparent to those skilled in the art that it is possible to embody
the invention in specific forms other than those of the exemplary
embodiments described above. This may be done without departing
from the spirit of the invention. The exemplary embodiments are
merely illustrative and should not be considered restrictive in any
way. For example, while the systems, methods, and examples
described herein have been illustrated by way of an "upside down"
build process, they are equally applicable to "right-side up" build
processes, including those in which the build platform curved
surface faces upward and the build platform is progressively
immersed downward into a supply of solidifiable material during an
object building process.
[0269] In addition, systems for manufacturing three-dimensional
objects of the type described herein may be configured with a
solidification substrate that is curved and a build platform that
is planar. In such cases, the solidification substrate would pivot
about an axis parallel to the scanning (y) axis as the linear
solidification device 42 moves along the travel (x) axis. The build
platform would translate along the build (z) axis but not along the
travel (x) or scanning (y) axis. The scope of the invention is
defined by the appended claims and their equivalents, rather than
by the preceding description.
* * * * *