Sloan Digital Sky Survey Telescope Technical Note 19980413
Virtually the entire rear surface of the 2.5-m telescope primary support structure is covered by the Cassegrain instrument rotator. It supports the SDSS camera and the spectrographs. For spectroscopy, a plug-plate cartridge is mounted on the rotator in lieu of the camera. The cartridge mates to the same pseudo kinematic mounting surfaces that locate the camera and is coupled directly to the instrument rotator bearing that is mounted to the primary mirror cell. Consequently, the deformation of its mounting surface during operation is expected to be inconsequential.
The spectrograph mounting is another matter. A fiber slit head assembly, on either side of each cartridge, is inserted into a socket in the corresponding spectrograph during the mounting process. Each fiber slit head is spring loaded against kinematic mounting surfaces within the spectrograph socket. As a result, some motion of the spectrograph with respect to the cartridge is acceptable during operation, e.g., due to varying gravity loads. We have specified no more than +/-0.030" of relative motion at the spectrograph socket opening between the cartridge and the spectrograph due to the deformation of the instrument rotator. This applies for elevation angles from zenith to horizon and for any rotator angle.
The existing instrument rotator has several shortcomings that are corrected in the current design.
The instrument rotator consists of three modules.
Finite Element Analysis (FEA) is used to determine the amount of distortion the ring girder will experience from the weight of the spectrographs as it and they move about both the altitude and rotator axes.
All components are steel. The drawings show a front, cross-sectional and back view of the rotator (Figure 1, Figure 2 and Figure 3 respectively). The drawing is accompanied by a DXF file that is dimensionally accurate. The major components appear on different layers of the CAD drawing in DXF format. Dimensions may be taken from this file.
Figure 1: Instrument rotator front view.
Figure 2: Instrument rotator section.
Figure 3: Instrument rotator back view.
Dimensional stability of the spectrographs is a high priority, i.e., the deformation of the instrument rotator due to changing loads and the differential thermal expansion of the spectrographs and instrument rotator should not apply significant forces to the spectrographs. Consequently, attachments of the spectrographs to the instrument rotator are made with linear bearings (dry polymer-lubricated journal bearings) that decouple one force component and all three moment components over small angles. They allow differential expansion of each spectrograph with respect to the instrument rotator, e.g., due to the difference of the thermal expansion coefficients of the aluminum spectrograph and the steel instrument rotator, carry large loads and are robust.
Each spectrograph is attached at three points indicated by a pair of bolt holes (1.5" separation) circumscribed by the 4" diameter circle that indicates a raised mounting pad that is machined coplanar with the other mounting points (Figure 1). The linear bearings at the extreme y locations allow translation in y; those at the extreme x locations allow translation in x. This is indicated by the orientation of the bolt hole pairs in the figure. Each bearing allows translation in the direction normal to the line connecting the bolt hole pair.
In the front and section AA views (Figure 1 and Figure 2), the spectrographs are represented by two point masses attached by weightless struts to the mounting pads. This model was used to determine the forces applied to the spectrograph mounting points for each load case. In-plane forces calculated from this model are larger than are likely to be present at the actual attachments and are conservative. The results are not much affected since the rotator has high in-plane stiffness.
The deflection of the model and stresses were calculated for three load cases.
To summarize the constraints:
The displacements are shown in Figure 4, Figure 5 and Figure 6. These figures are linked to animations of the deflections that are exaggerated so as to be apparent (to view, click on the figure). Stresses in the model are low as compared to the yield strength of low carbon steel, i.e., 30000 psi. For example, the maximum stress for case 1 was 2390 psi. Low stresses are to be expected in a design where stiffness rather than strength is the more stringent criterion.
Figure 4: Load case 1 (axial gravity). An animation of the deformation is available. Displacements in z, the axial direction, are in inches.
Figure 5: Load case 2 (axial gravity).
Figure 6: Load case 3 (transverse gravity).
A similar model was used to analyze a flat circular annular plate, fixed on the outer edge and guided axially on the inner edge (Table 24, Case 1f, Warren C. Young, Roark's Formulas for Stress and Strain, 6th Edition, McGraw-Hill, New York, 1989, p. 402.) The material properties and overall geometry were the same as in the rotator model. The details were different. The annular plate was 0.125 inches thick whereas the rotator is a hollow weldment with stiffeners and holes.
The deflection of the inner edge of the annular plate model was -0.093 inches. That calculated with formulas in Young was -0.096 inches. This agreement is more than adequate for our purposes.
The maximum axial displacement range of the instrument rotator is a bit under 0.016" (case 1). The other cases give similar but smaller values (the maximum for case 3 should be doubled to get the range since the rotator has an angular range of more than 360°). Obviously, this is an upper limit on the differential axial displacement of the three mounting points for each spectrograph. The spectrograph socket opening is 19.00" below the spectrograph mounting points. On the instrument rotator, the mounting points have a maximum extent of 15.95" by 62.97". Consequently, a differential axial displacement of the mounting points causes a lateral displacement of the socket opening of similar or smaller magnitude. This implies that all motions of the spectrograph socket opening due to variations in gravity loads are expected to have a range of less than 0.016", well within the value specified in the introduction. The calculated stresses in the model are low compared to the yield strength of low carbon steel.
Yet to be added to the design is a cylindrical mounting surface for an optical encoding system. This addition is not expected to affect the deflection of the rotator or change its geometry significantly. The surface will likely be added near the R35.6" inner surface of the ring girder. About 224" of tape will be required at this radius.
