Sloan Digital Sky Survey Telescope Technical Note 19980713
The SDSS 2.5-m primary mirror is a borosilicate glass casting with a light-weight honeycomb structure. It is supported in a manner similar to the Apache Point Observatory 3.5-m telescope primary. For that mirror, separate systems support the axial and transverse components of the 3.5-m mirror weight vector. The axial support is provided by 78 air pistons. Three different diameters provide three forces with the same air pressure. The 78 pistons are divided into three groups of 26 each. Each group supports a 120° sector of the mirror. The portion of the weight of the mirror that is not supported by the air pistons is sensed by load cells located near the center of each 120° sector. Each load cell controls the air pressure to the pistons in its sector so that the force on the load cell is about 10 N. This force is too small to cause significant distortion of the mirror.
The transverse support is provided by 38 air pistons, supported by cantilevers from the mirror cell, that act on the mirror local center of gravity surface. Each piston pushes on a steel force spreader that, in turn, pushes on four nickel-iron alloy blocks bonded to the mirror ribs. All transverse air pistons are the same diameter. A single load cell senses the unsupported mirror weight and controls the air pressure to the transverse support pistons. The remaining rotational and lateral degrees of freedom are constrained by two links to the mirror cell. With the mirror pointed at the horizon, these are located near the top and bottom edge of the mirror. They are attached to the back of the mirror and act horizontally.
The locations where the transverse mirror support forces should be applied to the mirror are listed in Table 1 and illustrated in Figure 1. They are from model prim93. Only the locations for the upper right quarter of the mirror are given in Table 1. The units are meters. X and Y are measured from the center of the mirror. Z is measured from back surface of back plate of the mirror. The first support on the list is on the x-axis. Only two of these are needed. Four of all the others are needed. A total of 18 are required.
Table 1: Locations of transverse supports. x (m) y (m) z (m) 0.8345 0 0.1526 1.0015 0.289 0.1618 0.668 0.482 0.1521 0.501 0.771 0.1561 0.167 0.964 0.1587
x (m)
y (m)
z (m)
0.8345
0
0.1526
1.0015
0.289
0.1618
0.668
0.482
0.1521
0.501
0.771
0.1561
0.167
0.964
0.1587
Figure 1: CAD drawing showing the 2.5-m primary mirror and the locations of the transverse support posts (black) and axial pneumatic pistons (blue). The transverse supports act on the two vertices in the rib pattern immediately above each post.
Figure 2: Finite element model of 1/4 of mirror. Four views are shown.
Figure 3: Finite element model with the face plate elements removed and the other elements shrunk 20%. The same four views of Figure 2 are shown.
Figure 4: Finite element model. View 3 of Figure 2 is enlarged.
Figure 5: Finite element model node numbers on mirror mid-height surface. The node numbers on the front surface can be obtained by subtracting 2000 from these; those on the back surface by adding 2000.
The finite element model is illustrated in Figure 2, Figure 3 and Figure 4. It is composed of plate bending elements (Ansys shell63). The node pattern on the back plate is shown in Figure 5. The distortion due to the transverse supports with 1 g acceleration, is 74 nm peak to valley (Figure 6). This is a bit less than the previous model, prim13, at 78 nm p-v. As before, the lateral constraints are assumed to apply 5 N to the back of the mirror. The mirror mass is calculated to be 742 kg.
The surface displacement is dominated by local distortion associated with the support forces. This is similar to the results of the analysis of the Apache Point Observatory 3.5-m primary transverse support system ("Design of the Apache Point Observatory 3.5 m Telescope II. Deformation analysis of the primary mirror", W. A. Siegmund, E.J. Mannery, J. Radochia, P.E.Gillett, Proc. of S.P.I.E., 628, 1986). Because of the similar geometry, the results of the detailed local model described in that paper should be applicable to this mirror. However, since this mirror is not as deep as the 3.5-m mirror, the magnitude of the local surface distortion will be somewhat different. The surface structure function for model prim93 indicates that the error budget for the transverse support system design is satisfied (Figure 7). The structure function is calculated for 0.87 g acceleration, i.e., a zenith angle of 60°.
Figure 6: Predicted surface error for model prim93. The error is about 74 nm peak-valley. (The 9 colors in the legend do not correspond to the 9 colors in the plot. However, the maximum and minimum are annotated on the plot and the color order is green, yellow, red, orange, olive, turquoise, cyan, blue, magenta).
Figure 7: Structure function of the surface error. The point at the 100 cm scale should not be taken seriously since this is comparable to the size of the model. The solid line is the error budget for mirror support design.
A transverse support system for the SDSS 2.5-m primary mirror was analysed. A total of 18 transverse supports was found to produce surface distortion of 74 nm peak to valley with 1 g acceleration. The surface structure function corresponding to a zenith angle of 60° is less than that from a r0 = 120 cm atmosphere, the amount allocated to the support design.
Date created: 7/13/95 Last modified: 8/4/98 Copyright © 1998, Walter A. Siegmund Walter A. Siegmund
