U.S. patent number 3,701,521 [Application Number 05/007,306] was granted by the patent office on 1972-10-31 for means for making a multi-facet substantially paraboloidal collimator.
This patent grant is currently assigned to TRW Inc., Redondo Beach, CA (U.S. corp.). Invention is credited to Allan D. LeVantine.
United States Patent |
3,701,521 |
|
October 31, 1972 |
MEANS FOR MAKING A MULTI-FACET SUBSTANTIALLY PARABOLOIDAL
COLLIMATOR
Abstract
A light reflecting collimator having a substantially
paraboloidal surface and being formed of a plurality of juxtaposed
facets each having a substantially paraboloidal surface. A method
for making such a collimator of a plurality of facets each having a
substantially paraboloidal surface on individual plates and each
facet formed on each plate being defined by two paraboloidal radii
lying in orthogonal planes.
Inventors: |
Allan D. LeVantine (Tarzana,
CA) |
Assignee: |
TRW Inc., Redondo Beach, CA (U.S.
corp.) (N/A)
|
Family
ID: |
21725399 |
Appl.
No.: |
05/007,306 |
Filed: |
January 12, 1970 |
Current U.S.
Class: |
269/48; 29/283;
269/49; 269/154; 269/292; 269/909 |
Current CPC
Class: |
G02B
5/08 (20130101); F21S 8/006 (20130101); F21V
7/048 (20130101); F21V 5/008 (20130101); F21V
5/007 (20130101); B24B 13/015 (20130101); Y10T
29/53991 (20150115); Y10S 269/909 (20130101) |
Current International
Class: |
B24B
13/00 (20060101); B24B 13/015 (20060101); G02B
5/08 (20060101); B23q 003/18 (); B25b 011/02 ();
B23p 021/00 () |
Field of
Search: |
;269/48,49,154,266,292,321W ;72/379,390 ;29/283 |
References Cited
[Referenced By]
U.S. Patent Documents
Primary Examiner: Wayne A. Morse, Jr.
Attorney, Agent or Firm: Gerald Singer Alfons Valukonis
Daniel T. Anderson
Parent Case Text
This application is a division of my application Ser. No. 656,093,
now U.S. Pat. No. 3,494,231.
Claims
1. A jig for making a facet of a paraboloidal collimator
comprising: a. a base member having top and bottom surfaces; b.
said top surface being formed of steps extending from a central
apex downwardly toward opposite sides, symmetrically to nadir outer
edge positions; c. said steps extending in a longitudinal direction
relative to an axis of a transverse curve formed by a line
extending on the outer edges of said steps, wherein the depth of
each step from the apex is determined from the equation: where dh
is the depth of each step, C is the transverse distance normal to
said axis from the central apex to each step edge, arbitrarily
selected, R.sub.c is a radius to be used to cut a spherical surface
in an outer face of a plate to be secured on said jig for making
said facet and the first parabolic radius extending in one of two
orthogonal planes for defining the finished facet, and R.sub.s is a
second parabolic radius for defining the finished facet in the
other of said orthogonal planes; and d. means for securing a flat
workpiece to said top surface for deforming the same to have an
approximately cylindrical cross section.
Description
In the prior art paraboloidal collimators have been generally small
and formed as a single element. In a solar simulator, for example,
where a relatively large reflecting collimator is required, it
would be very expensive to form the structure of a single element
in that the material used is relatively rigid and heavy, and the
paraboloidal surface would have to be ground into it. This would be
an obviously difficult and time-consuming effort. By forming a
substantially paraboloidal surface on a plurality of relatively
small sections, great savings of time and expense have been
accomplished. The invention provides a substantial simplification
over that which would normally be used for grinding and polishing a
surface of the required contour. This is especially true for
producing the required surface upon a metal plate, such as aluminum
which is used in solar simulators. In the manufacture of four
collimators for a solar simulator, using the present invention,
approximately three quarters of a million dollars was saved over
what the cost of grinding true paraboloidal surfaces would have
been.
It is the object of the invention to provide a method for producing
a surface on a flat metal or other relatively rigid plate, such as
glass, defined by two radii of curvature in orthogonal planes.
Another object of the invention is to provide a jig for making a
facet of a substantially paraboloidal collimator.
It is still another object of the invention to provide a method for
making a collimator having a substantially paraboloidal surface
formed of a plurality of paraboloidal facets upon individual
plates, each facet being defined by two paraboloidal radii in
orthogonal planes.
It is a further object of the invention to provide a collimator
having a substantially paraboloidal surface and formed of a
plurality of juxtaposed facets each having a paraboloidal
surface.
Further objects and advantages of the invention may be brought out
in the following part of the specification wherein small details
have been described for the competence of disclosure, without
intending to limit the scope of the invention which is set forth in
the appended claims.
Referring to the accompanying drawings, which are for illustrative
purposes:
FIG. 1 is a diagrammatic view of portions of a solar simulator
employing paraboloidal collimators made according to the
invention;
FIG. invention; is a side cross-sectional and diagrammatic view of
a central row of facets of a collimator illustrating portions of
the parabola geometry as they relate to the invention:
FIG. 2A is an enlarged view of the center facet shown in FIG.
2;
FIG. 3A is a side diagrammatic view illustrating the geometry of a
paraboloid as it relates to the center point of a specific
off-center facet of the collimator according to the invention;
FIG. 3B is a plan view of a collimator, viewed along lines parallel
to the axis of the parabola, projected from FIG. 3A;
FIG. 3C is a true view of the facet whose center point and a
tangent thereto is illustrated in FIG. 3A, viewed normal to the
tangent plane;
FIG. 4 is a side-elevational view of a jig for forming a facet
according to the invention;
FIG. 5 is a diagrammatic view illustrating the geometry from which
the jig calculations are determined for a single facet of a known
parabola;
FIG. 6 is a plan view of the jig shown in FIG. 4 with the facet
plate, shown in FIG. 3C, positioned thereon;
FIG. 7 is a plan view of the jig and plate shown in FIG. 6 with
fill-in pieces arranged around the plate for obtaining a continuous
mill cut on the face of the plate;
FIG. 8 is a side-elevational view of the facet plate, shown in FIG.
3C, in position for cutting the edges of the plate; and
FIG. 9 is a fragmentary view of a collimator illustrating means for
securing the various facets together.
DESCRIPTION OF THE PREFERRED EMBODIMENTS
Referring to FIG. 1, there are shown portions of a solar simulator,
generally indicated as 10, diagrammatically illustrated. The solar
simulator is comprised of a plurality of light sources and their
collectors, generally indicated at 11, in optical alignment with an
input mosaic lens 12, output mosaic lens 13 and an aligning lens
14. The beams produced by the light sources, after passing through
the lenses, are reflected by an off-axis, substantially
paraboloidal collimator 17, comprised of nine substantially
paraboloidal facets 18, each defined by two radii of curvature in
orthogonal planes. The parallel light rays 19 are reflected
downwardly from the collimator parallel to a center line 20 of a
test chamber, not shown. The test chamber has four other
collimators 23, 24 and 25, forming reflective portions of a total
solar simulator apparatus.
The facets 18 are made from aluminum alloy plates and are suspended
in a nearly horizontal position from a rigid thermally stabilized
rack, generally indicated as 26 in FIG. 9. The rack is constructed
of tubular members running generally horizontally with respect to
the collimator and fluid is circulated through the tubular members
to thermally stabilize the structure. The tubular members are
adjustable to provide means to properly align each facet so as to
form the substantially paraboloidal collimator. Thermal
stabilization of the rack eliminates the possibility of any
movement of aligned facets when the space simulation chamber is
under a vacuum and having liquid nitrogen in the panels lining the
walls of the chamber.
In FIG. 2 there is shown a cross-sectional view of the collimator
17 illustrating the reflective faces of the facets 18A, 18B and 18C
on a predetermined parabolic curve 29. The parabola 29 has an axis
30 and a focus point F. In designing the solar simulator, it was
determined that the center point 31 of the collimator should be
off-axis, an angle equal to 28, specifically 26.degree., the angle
being formed by the parabolic axis and the line 33 from the focus
to the center point 31. As is known, in a parabola a line 32 drawn
normal to a tangent 35, as shown in FIG. 2A, to the point 31,
intersects the parabolic axis at an angle .theta., half of 2
.theta.. Similarly, the lines 32 and 33 also form an angle equal to
.theta..
In any paraboloid a line, such as 32, has the length of a radius
R.sub.s in a plane perpendicular to the face of the drawing. The
radius R.sub.s defines the curvature of the paraboloid at point 31
in the aforesaid plane. A second radius R.sub.c, longer than
R.sub.s as indicated by the extension 32B of the line 32, is in the
plane of the face of the drawing, normal to the plane of the radius
R.sub.s, and together the two radii in the respective orthogonal
planes determine the surface of a facet as 18B at the point 31.
That is, at each such point, there are two radii in orthogonal
planes that define that portion of the surface of a paraboloid. At
locations off the point 31 in the facet 18B, the radii vary
slightly from R.sub.s and R.sub.c, but the size of 18B, as well as
that of the other facets, is selected so that the deviation is
minor so as not to be of any consequence for purposes for the
invention.
At the center 31 of the facet, the two radii defining the
paraboloid can be defined as R.sub.so = (2 F)/cos .theta..sub.o,
where F is the focal length and .theta. is the angle as indicated
above; and R.sub.co = (2 F)/cos.sup.3 .theta..sub.o. The angle
.theta. is determined by the equation, .theta..sub.o =
tan.sup..sup.-1 (U.sub.o /2 F), where U.sub.o is the distance to
the center of the facet from the paraboloid axis. At any other
location the two radii of the paraboloid are:
R.sub.s = (2 F)/cos .theta., R.sub.c = (2 .sup.-1 )/cos.sup.3
.theta. and .theta. = tan.sup..sup.-1 (U/ 2 F), where U is the
distance of another point from the paraboloid axis. Each collimator
facet, according to the invention, is defined by the two radii
R.sub.so and R.sub.co at all points on the facet surface and the
size of the facet must be chosen so that the deviation in the radii
of curvature of the facet from those of a paraboloid for any
location will be small and insignificant.
For example, a typical computation for these variations is
indicated in the following, where F = 19.3 feet, U.sub.o = 10.3
feet, and U = 11.7 feet, then .theta..sub.o = 14.9.degree.,
R.sub.so = 39.9 feet, R.sub.co = 42.75 feet, .theta. = 16.9.degree.
, R.sub.s = 40.35 feet, and R.sub.c = 44.15 feet. However, the
difference in illumination from that of the true paraboloid and the
collimator made according to the invention is 0.043 which is
insignificant for the illumination purposes required. Thus, as a
matter of practice for the collimator according to the invention,
it is sufficiently accurate to treat the radii of each facet for
all points thereon as R.sub.s and R.sub.c, determined at each
center point, the distance from the parabolic axis to the
respective center points being considered to have a value equal to
a respective U. It should be noted that U.sub.max, as shown in
FIGS. 2 and 3B, is predetermined for the collimator in accordance
with the area to be illuminated and is measured from the axis to
the center point of the space simulator above the area
illuminated.
Further, it should be noted that the intersection of the collimator
facets are visible from the test zone of the simulator, the area to
be illuminated, and these intersections block some of the light
coming from the source image, the image appearing across the
intersections on the collimator. This results in a local decrease
of illumination in the test zone, but this decrease is made
insignificant by closely butting the facets.
For each facet, F of the paraboloid being known, in order to
determine the two radii, it is necessary to determine the angle
.theta. from the equation, .theta. = tan.sup..sup.-1 (U/ 2F). The
distance U for each center point may be determined in reference to
FIGS. 3A, 3B, and 3C. In FIG. 3B, the axis 30 of the parabola is
shown as a point, the axis being perpendicular to the surface of
the drawing. The position of a vertical plane or line 36 is
determined with respect to its position to the test zone or area to
be illuminated by the collimator 17. That is, the line 36 extends
from the axis of the parabola to the point U.sub.max, which is
determined to be at the center of a test chamber having a solar
simulator. Stated differently, the collimator is positioned so that
it will provide the proper illumination upon the test zone or
target. Thus, by using the line 36 as a diagonal through the center
of the rectangular collimator its length and angular position are
known.
The collimator in FIG. 3B is shown to be comprised of nine facets,
each two square feet, for example. The individual facets, as well
as the collimator, are square only when viewed along lines parallel
to the parabolic axis. In such an arrangement the center points of
each facet are easily determined as being at the intersection of
the diagonals of known squares. To determine the distance, U.sub.p,
from the point P, the center of the facet 18D, to the axis in the
vertical plane 37 in FIG. 3B and on the drawing surface in FIG. 3A,
it is necessary to determine the length of the lines indicated as X
and Y, the two sides of the right triangle of which U.sub.p is the
hypotenuse. The line X is equal to the length of the diagonal of a
2 foot square and Y is equal to U.sub.max minus the length of a
diagonal and a half of the 2 foot squares. Thus, the angle .theta.
for the point P, shown in FIG. 3A, for the known parabola and the
radii R.sub.s and R.sub.c for the point P may be calculated from
the equations above.
The radius R.sub.c lies in the plane 37. The radius R.sub.s is in a
plane indicated by the line 38, the latter plane being normal to
the plane 37, the two being the orthogonal planes having the two
radii which define the curvature of the facet 18D. In FIG. 3A, the
tangent line or plane 35' is perpendicular to the line 38 and is
analogous to the tangent 35 in FIG. 2. The facet 18D is projected
in FIG. 3C, as viewed normal to the tangent plane 35'. In this view
the facet 18D is a parallelogram having two long sides and two
short sides and is not a rectangle, the lengths of the sides being
24.5297 and 24.1379 inches, for example.
To determine the values of U and the radii for the other facets,
other than those on the line 36 where the distances to the center
points are either known or obvious by subtracting diagonals or
diagonal portions from U.sub.max, the same method may be used as
that for determining the value of U.sub.p and the radii in the
facet 18D. Thus, for example, to determine the value of U for the
facet 18E, the value of X' is that of half of a diagonal and that
the value of Y' is equal to U.sub.max minus the length of two
diagonals of the squares. Thus, the length of the hypotenuse 41 is
the value for U in the facet 18E and it is in a vertical plane in
FIG. 3B in which its radius R.sub.c extends. For this value of U,
the angle .theta. may be determined in the vertical plane 41 so as
to determine the respective values of R.sub.s and R.sub.c.
From the foregoing, it is clear how the value of U may be obtained
for the other center points of the nine facets. It should be noted
that each of the vertical planes in FIG. 3B, passing through the
axis and a center point, is at a corresponding angle .phi. with the
plane represented by the line 36.
After the radii for the facets are determined, they are used to
determine the configuration of a facet jig 42, shown in FIGS. 4 and
6, on which facet surfaces are formed. There is a separate jig for
each facet depending upon its radii, but the same jig may be used
for corresponding left and right hand facets with respect to line
36. Each jig is generally circular and has a flat bottom 43. The
upper face of the jig is formed so that a facet plate secured
thereon by bolts, extending through holes 44 and 45 and threadedly
engaged in tapped wells in the bottom of the plate, can be deformed
within its elastic limit to mate with a cylindrical arc generally
designated as 47, the arc being formed by the flat bottom base of
the facet when it is secured against the outer edges of each of the
steps as 48 and 49. That is, the arc 47 could be drawn so as to
pass over each of the steps and the apex 50 as well as the opposite
laterally outside nadirs as 51. The steps are spaced at equal
intervals on both sides of the axis of the cylindrical arc 47 or of
the apex of the jig.
The arc 47 is determined for each facet according to its radii
R.sub.s and R.sub.c. Each substantially paraboloidal face on the
facet is formed by cutting a spherical contour on the facet face 53
on a facet as 18D positioned on the jig. The spherical curvature is
determined by the long radius, R.sub.c. That is, the shape of the
concave spherical cut into the facet face has a radius equal to
R.sub.c. When that has been accomplished, the facet is removed from
the jig and it returns to its undeformed shape due to the energy
stored therein when it was deformed on the jig within its elastic
limit. The facet face 53, after being removed from the jig, is no
longer spherical but has a substantially paraboloidal face, defined
by two radii in orthogonal planes. When the facet plate springs
back to its undeformed shape, the second curvature is formed in the
face 53 and its radius is equal to R.sub.s. When the facet is
removed from the jig, its bottom should be flat and if it is not,
it must be cut to be flat. It is then put back on the jig and the
spherical cut is made again. The jig is of sufficient thickness so
that its deflection relative to that of the facet is
insignificant.
The jig is prepared so that the proper radii and the orthogonal
planes will define its substantially paraboloidal surface. The
configuration of the jig is determined in reference to FIG. 5.
There the large arc 54 has a radius R.sub.c and the small arc 55
has a radius R.sub.s. The distance C is the distance laterally
outwardly from the apex 50 for any step edge on the jig, or stated
differently, the distance out from the apex at which a point on the
cylindrical curve 47 will be formed so as to deform the facet
plate. The distance h.sub.s indicates the deformation that is
required to form the arc 55 on the jig at a point C and the
distance h.sub.c indicates the deformation that is required on the
jig to form the arc 54 at a point C on the jig. The distance dh is
the difference in deformation required between the two arcs, or
determined from the right angle triangles in FIG. 5.
When the radii are known, dh, the depth of any step downwardly from
the apex 50 on the jig, is determined by selecting an arbitrary
value for C, the distance laterally outwardly perpendicular to the
axis of the jig or cylindrical surface to be formed. The values for
dh are relatively small in the making of a 2 -foot square facet.
For example, where the radii are 482 and 525 inches, and C is 4
inches, dh is equal to 0.0014 inch, and where C is 15.5 inches, dh
equals 0.0204 inch. The jigs also could be made to be concave, in
which the spherical cut would be for the short radius R.sub.s and
the plate would be deflected into the concavity for the spherical
cut.
The various facets are positioned on their respective jigs in
accordance with the relationship of the central plane or line 36
which forms diagonals for the facets 18 A, B and C, and the angle
.phi. for a respective facet. For the facets 18A, B and C, the
angle .phi. is 0, and they are positioned on a jig with their
diagonals, along a plane 36, directly above and parallel to the
axis of the cylindrical arc 47.
The other plates from which the facets are to be made are
positioned on the jigs so that their center points are crossed by
the axis of the arc of the cylinder. In FIG. 6, for example, the
plate 18D is rotated on the jig so that the diagonal 36', parallel
to the reference plane 3b, through its center P forms the angle
.phi. with the cylindrical axis of the jig arc which is in the
position of the line 37 in FIG. 3B. The angle .phi. is determined
for the facet 18D, for example, as indicated in FIG. 3B, by the
equation:
.phi. = tan.sup..sup.-1 (X/Y). For facet 18E, X' and Y' are used to
solve for .phi.. In this situation, as shown in FIG. 6, the angle
.phi. is to the left of the cylindrical axis at the lower part of
the drawing whereas for the facets on the left of the line 36 in
FIG. 3B, the angle .phi. would be formed to the right of the
cylindrical axis.
Prior to fastening the plates to the jigs, the plates being
somewhat larger than a two foot square, they must be milled along
their edges to form a two foot square when viewed along a line
parallel to the parabolic axis. As shown in FIG. 8, this is
accomplished by placing the plate on a support 59 having an upper
surface 60 slanted at an angle .theta. equal to that for the
respective facet as determined by the value of U. Further, the
plate is rotated or positioned with respect to its angle .phi. in
the same manner as it is on the jig with reference to the plane 36
and its corresponding plane, as 37 for facet 18D. A milling cutter
58 is then applied to the outer edges as 61 and 63 of the plate,
and moved to cut a 2 foot square, the cutter being in a position to
make a vertical cut, or stated differently, in a position parallel
to the axis of the parabola. This then makes a two foot square when
viewed from a position parallel to the parabolic axis. When viewed
as indicated in FIG. 3C, the plate, having finished edges, has the
appearance of a parallelogram and not a square. Two of the sides of
the facets as they would be viewed in FIG. 3C, except for the
facets 18A, 18B and 18C, are slightly longer than the other two
sides. The facets 18A, 18B and 18C have respective equal sides, as
24.5297, 24.3026 and 24.1379 inches.
After the edges of a facet plate are cut, the facet is positioned
on its jig as indicated above, and sectors 65 are placed on the
facet as shown in FIG. 7 so that when the spherical surface is cut,
the cut across and around the facet will be continuous as the
cutting tool passes back and forth over the outer edge of the facet
plate.
After the surfaces of the nine facets have been cut and polished
for reflective purposes, they are assembled in their specific
locations as indicated in FIG. 3B and put together to form the
collimator as shown in FIGS. 1 and 9.
It is clear that the foregoing method for making a substantially
paraboloidal collimator from substantially paraboloidal facets is
considerably less expensive in both time and money than the
manufacture of a collimator in one piece formed to have a
paraboloidal or a substantially paraboloidal face.
The invention and its attendant advantages will be understood from
the foregoing description and it will be apparent that various
changes may be made in the form, construction and arrangement of
the parts of the invention without departing from the spirit and
scope thereof or sacrificing its material advantages, the
arrangement hereinbefore described being merely by way of example.
I do not wish to be restricted to the specific forms shown or uses
mentioned except as defined in the accompanying claims, wherein
various portions have been separated for clarity of reading, not
for emphasis.
* * * * *