ANALYSIS OF THE STRUCTURE OF THE KECK TELESCOPE

The Keck Telescope, currently in fabrication, is to be installed near the peak of Mauna Kea on the island of Hawaii. On completion, it will be the world's largest optical telescope, with a 10 meter diameter (equivalent) mirror. For the sake of comparison, we note that the diameter of the mirror of the Hale Telescope measures five meters.

Many novel features are incorporated into the design of the Keck Telescope. The mirror itself is segmented, and consists of 36 hexagonal (in plane) elements. Its figure is maintained during observing by continually measuring relative positions of the segments and adjusting as required with the aid of an elaborate system of actuators which are capable of controlling translations in the direction of the optical axis (z-axis), and rotations of each segment about the x- and y-axis. Thus, the stiffness involving these three degrees of freedom of motion is the "electronic stiffness." The remaining three degrees of freedom of motion are controlled by providing adequate traditional structural stiffness. The concept of a segmented mirror was proposed by J. Nelson of the University of California and the Lawrence Berkeley Laboratory (LBL), the initiator of the project and currently the project scientist.

A segmented mirror possesses several advantaged over a monolithic mirror. These include much lower weight (the Keck mirror is only 7.5 cm thick), ease of transportation, and ease of removal and replacement required for realuminizing without loss of observing time. The segmented mirror technology is totally new, and much research went into its development and testing.

Primary mirror array.

The structure of the Keck Telescope also represents a departure from traditional design. It consists of two principal parts: the tube and the yoke. The yoke rotates in azimuth and supports the tube which rotates about the elevation axis. Thus, the Keck is an altitude-azimuth telescope. Both the yoke and the tube were designed as space frame structures to be as light as practical, consistent with the requirement that the figure of the mirror be maintained during observing. Thus, we attempted to optimize the distribution of weight in the structure in the sense of placing material where it contributed the most toward a reduction in the image motions, and toward an increase in the dynamic stiffness.

These efforts at optimization proved successful in that the total weight of the Keck Telescope, including the primary and all instrumentation, is approximately 270 tons. For comparison, the equivalent weight of the Hale Telescope, with the mirror half the size of Keck's, is approximately 550 tons. Perhaps even more striking is a comparison of the 7.5 meter altitude-azimuth telescope currently being designed in Japan: its weight is over 400 tons, while its mirror is only 75% the diameter of the Keck Telescope.

The writer has been involved with the design of the structure of the Keck Telescope since 1980, when the first conceptual schemes were prepared. From the outset, the structure was conceived as a space frame, with the tube a three-dimensional equivalent of the traditional Cerrurian truss. Of particular interest is the mirror cell which directly supports the primary mirror and all the associated instrumentation. In traditional telescopes the mirror cell weights several times the weight of the mirror itself. In the Keck Telescope, because of its geometry (i.e., because it is a space frame structure), the mirror cell weights approximately 40% of the weight of the primary. As noted, the mirror cell was extensively optimized, as were the yoke and other parts of the structure.

FEA computer model of the Keck Telescope.

Initial analyses were performed with the aid of the SAP IV finite element-based software developed by E. Wilson and his associates at U.C. Berkeley and implemented on a CDC 7400 computer at LBL. Final design was performed using the Algor Supersap software implemented on both IBM PC/AT at the writer's office, and on VAX 8650 at LBL. The AT was connected via a telephone modem to the VAX.

It may be of some interest to discuss the reasons why Supersap was selected for the design work. The fact that it is based on an early version of SAP IV was helpful, since we were quite familiar with the latter, and, thus, the need for mastering yet another software did not arise. It was most important to us that Supersap implementations for both the AT and VAX were available, since both had to be used - essentially all of the model-definition work was done on the AT, while the actual running of the files was accomplished on a much larger and faster VAX. Finally, the pre- and post-processing facilities of Supersap, such as TDraw, Substruct, POSTD, etc., made the modeling work tractable. TDraw in particular was absolutely indispensable. Without it, the task of constructing the computer model would be much more difficult, and the task of evaluating results impossible.

Tube to horizon - gravity deflections magnified 1000 times.

Dynamic response - mode shape associated with rotation of the structure about azimuth, f = 8.33 Hz.

Computer model of the Keck Telescope (side elevation - angle to zenith 40o).

For the sake of historical accuracy we should note that many details of the implementation of Supersap on the AT were initially not fully worked out at the time we first started using it in the fall of 1984. For quite a long time we functioned, in effect, as a beta station, learning as we went. Fortunately, the staff at Algor were exceptionally cooperative in removing any quirks brought to their attention, with Blaine Myers at the forefront of the effort. We were also most fortunate in being able to rely on the assistance of C. Stoll of the Keck project science staff and LBL in installing, debugging, and generally making possible the use of Supersap on the VAX. It can be safely said that without Cliff Stoll the project could not have been completed as quickly as it was.

Our analytical effort involved many models: a model of the complete structure, a model of one-half of the structure (i.e., those portions of the structure located at x equal to or greater than zero), and many models of various portions of the total system. Some interesting statistics regarding the complete model are cited below.

• Number of Elements: plate (type 6) 4178, beam (type 2) 2845, other (type 7) 146
• Total Number of Elements: 7529
• Number of Nodes: 4525
• Number of Degrees of Freedom: 26,153
• Bandwidth (after optimization): 2226
• Static Run Time on VAX 8650: 20.8 hours
• Dynamic Run Time (12 modes, half-model): 30 hours
• Disc Space Required: in excess of one gigabyte

Thus, it is fair to say that from the computation point of view, analysis of the structure of the Keck Telescope presented problems as unique as the very challenging problems of the design itself.

Some of the results are presented in the figures throughout this case history. All of these figures were generated using TDraw, and printed on a laser printer driven by the VAX.

Dynamic response of the lower tube and mirror cell - mode shape associated with translation along elevation axis, f = 10.85 Hz.

At this point, the structure is being fabricated, and it is to be erected within the already completed observatory dome near the peak of Mauna Kea in the early part of 1989. In the meantime, the primary mirror segments are being cast and polished, and will be shipped to the mountain as they become ready. Hopefully, the telescope will be fully ready for service by 1990-1991.

The Keck Telescope is owned by the California Association for Research in Astronomy (CARA), a joint venture of the University of California and the California Institute of Technology. Managing the project for CARA is G. Smith who heads a staff of a number of professionals expert in various disciplines involved in the operation. H. Boesgaard is the observatory dome and telescope structure manager. The structure itself was designed in the writer's office in San Francisco.

FEA computer model of the Keck Telescope.

Copyright © 1988 Algor, Inc. All rights reserved.