Sloan Digital Sky Survey Telescope Technical Note 19960821
Jessica Granderson and R. (French) Leger University of Washington
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.
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.
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
7.8
7.5
33.8
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.
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
