Slit-plate Deflection Testing
Sloan Digital Sky Survey Telescope Technical Note
19960821
Jessica Granderson and R. (French) Leger
University of Washington
Contents
Introduction
The optical fibers that transport light from the images of
astronomical objects in the telescope focal plane to the
spectrographs must be protected and properly positioned. The SDSS
fiber system uses 640 optical fibers organized into 32 harnesses each
containing 20 fibers. One end of the approximately 2m long fiber is
inserted into a hole in an aluminum plug-plate, and the other end is
fed into and supported by a slit-plate. The aluminum slit-plates are
approximately 235mm wide by 308mm wide, and come in thicknesses of
3.175 and 3.607 mm. Each plate has a series of 16 arced slits into
which 16 of the fiber harnesses are placed.
The fiber harnesses and slit-plate will be located on a slit-head
that is to be inserted into each spectrograph. The entire assembly
will change in orientation as the telescope rotates about its two
axes to track the sky. Since the fibers are to be calibrated from a
fixed position, it will be necessary to know how much the slit-plate
deflects under its own weight due to gravity, as well as how much it
deflects under the weight of the fibers and harnesses. The deflection
of two plates of thickness 3.175 and 3.607mm was tested.
Slit-plate Deflection
The slit-head to which the slit-plates are fastened consists of
two L-shaped end piece wedges attached to a base plate. The
slit-plates are attached to the end pieces of the slit-head by a
series of bolts located along two edges of the plate. The location of
the plates is fixed by a set of dowel pins located between the bolts,
that run through the slit-plate and slit-head.
In the initial attempts to measure the deflection of the
slit-plates, some of the plates tested showed signs of buckling. When
the plates were fastened to the slit-head and lightly tapped on one
surface, the dial indicator jumped, showing a change in deflection of
approximately two microns. When the plate was lightly tapped on the
opposite surface, the indicator jumped back to its initial value.
This hysteresis was attributed to buckling caused by overconstraining
the plate. Only two dowel pins along one side of the plate are
necessary to fix the position of the plate when it is bolted down,
however, a series of pins along each side of the plate
had been used.
Since the slit-plate is only one quarter the thickness of the base
plate, exposing the assembly to a temperature gradient would cause
the slit-plate to expand faster than the base plate. Assuming a
maximum temperature difference of 3°C, the fixed slit-plate could
experience up to 3290N (740lb) of compressive force. Considering this
to be the most significant possible source of buckling, the
slit-plate was tensioned to this value during assembly. To prevent
the hysteresis due to overconstraint of the plates, the number of
dowel pins was reduced to two.
To apply tension to the plates one end of the plate was pinned
into place and bolted to the slit-head end pieces. When a force is
applied to the end pieces of the slit-head, the base plate of the
slit-head flexes under the resulting moment. The moment applied to
the slit-head base plate due to 3290N causes the end pieces to
deflect by approximately 1.63mm. The distance between the end pieces
(free of force) was measured with a micrometer, and a force was
applied to the slit-head end pieces until they deflected by the
desired 1.63mm. The force was maintained, and the free end of the
slit-plate was bolted to the slit-head. The applied force caused
flexure of the slit-head base plate, so once the force was removed,
the slit-head relaxed. The slit-plate, which was bolted to the
deformed slit-head, was then placed under tension as it moved with
the slit-head, back to the relaxed state of the slit-head.
To determine the deflection of a slit-plate under gravity, due to
its own weight, a plate was installed into the slit-head that will
mount to the telescope, and the assembly was held in a vertical
position (0°). A micron dial indicator was positioned along one
edge of the underside of the plate (see Figure
2) and zeroed. The plate and slit-head were rotated to horizontal
(90°), and the subsequent deflection of the plate was recorded.
See Figure 1.
The middle slit on the plate is 254mm long, and can be used as an
average length of fiber and harness to be supported by the plate. The
slits can be seen in Figure 2. 254mm of
fibers and harness were found to have a mass of approximately 2.2g.
Since 16 harnesses are supported by the slit-plate 35.2g is estimated
to be the total mass that each plate carries. 40g was used as a
deliberately conservative estimate with which to perform the
deflection experiments. To determine the deflection of the plate due
to the weight of the fibers and harness the indicator was again
placed on the underside of an edge of the plate, and was zeroed at
the 90°postion. The plate was loaded with 40g, and the
corresponding deflection was recorded. One set of data was taken with
the weights placed at the center of the plate. To determine the
maximum possible deflection of the plate, a second set of data was
taken with the 40g positioned on the edge of the plate, directly on
top of the indicator. To obtain more substantial deflections, the
procedure was repeated with 200g. The results are displayed in
Figure 3.
Figure 1: This picture shows the tensioned slit-plate and
slit-head assembly in the horizontal position, and the location of
the indicator that was used to measure the deflection of the plates.
Figure 2: This close-up view shows the position of the dial
indicator along the underside of the edge of the slit-plate, and the
slits into which the fiber harnesses are inserted.
|
Plate
|
Defl. Under Gravity (microns)
|
Defl. Under 40g - Center of Plate (microns)
|
Defl. Under 40g - Edge of Plate (microns)
|
Defl. Under 200g - Center of Plate (microns)
|
Defl. Under 200g - Edge of Plate (microns)
|
|
3.175mm
|
0.0
|
1.0
|
10.3
|
7.3
|
50.7
|
|
3.607mm
|
1.2
|
1.0
|
7.8
|
7.5
|
33.8
|
Figure 3: This table shows the deflection of both slit-plates,
under three different loading configurations. The data displayed are
the average deflections measured over three trials. The standard
deviation of the data is approximately 0.4.
Analysis
24 microns is budgeted for the deflection of the plates under 1 g
acceleration. (1 g is the acceleration on the plate in the horizontal
position of the deflection testing.) The deflection data indicates
that both plates are of suitable stiffness; each deflected to 1
micron under a 40g load placed at the center of the plate. Even when
the plates were loaded along an edge directly above the indicator,
the largest deflection seen under 40g (10.3 microns) was 43 percent
of the budget value. It can be seen from the 200g data that when the
loading was increased by a factor a five the deflections measured
increased proportionately. In the cases for which the deflection of
the two plates measured were significantly different, the thicker
plate deflected less than the thinner plate, as expected.
Conclusion
The experimental data indicate that a plate as thin as 3.175mm
would not deflect more than the 24 micron budget, under the
estimated harness and fiber weight of 40g. In fact, considering that
under an edge-centered point loading, the largest deflection measured
was 10.3 microns, the actual deflection under a distributed 40g load
would be far less than the budget . Regardless of the
thickness of the plate used, it will be necessary to impart a
significant amount of tension on the plates in order to prevent them
from buckling.
In summary, the 3290N force to be applied to the slit-plate was
determined by assuming a maximum delta T of 3°C. The base plate
of the slit-head was modeled as a beam to which a bending moment
applied through a force imposed upon the end pieces. The end pieces
were compressed to a deflection corresponding to 3290N (1.63mm), at
which point the slit-plate was securely bolted to the flexed
slit-head. Releasing the applied force caused the slit-head to relax,
placing the attached slit-plate under 3290N tension. The method by
which the force was applied to the end pieces, and by which the
deflection of the end pieces was measured was quite straightforward,
and can be repeated somewhat quickly and easily. Tensioning the
slit-plates is a viable means by which to prevent the plates from
buckling, and to decrease their total deflection. To prevent
hysteresis caused by overconstraining the plates, only two dowel pins
will be used to position the plate in the future.
Date created: 8/21/96
Last modified: 8/30/96
Jessica Granderson