SMA Technical Memo Number 130

Dynamic Effects of Elevation Counterweights

William N. Davis , SAO Central Engineering

January 7, 1999

Summary:

The SMA finite element model of a complete antenna was updated to the current elevation counterweight design, and balanced about the azimuth axis. Frequencies and modeshapes were calculated over the full range of elevation angle positions. The first mode, tipping about the elevation axis, shows a frequency variation from 7hz at zenith, to a maximum of 8.3hz at ~40^o elevation, to 6.9hz at 10^o elevation. A static analysis was also performed to determine the motion of mirror 3 as a function of elevation angle.

Discussion:

The SMA Antenna model is shown in Figure 1. The counterweighted reflector was modified to have a balanced weight of 23960 lbs. The mass distribution of the mount was modified to a balanced weight of 87874 lbs. This is about 7% less than the predicted balanced weight of 93349 lbs. by George Nystrom, however there are some design changes in progress on the cabin and environmental control unit which will affect the total mass and its distribution. Since the lower modes are primarily influenced by the reflector mass, elevation counterweights and the stiffness of the drivescrew, the results given here should not vary significantly with the mount mass or its distribution. We will update this model once the final cabin design is completed to verify this opinion. The reflector was rotated through elevation angles from 10^o above horizon to zenith, and the first 6 mode frequencies are plotted as a function of elevation angle in Figure 2.

Figure 1 - SMA Antenna Finite Element Model

Figure 2 - Frequencies vs. Elevation Angle

Typical modeshapes are presented for 60^o elevation, modes 1-6

Mirror 3 is also included in this model. The co-ordinate system used for mirror 3 motions is shown in Figure 3. The optical axis of the reflector is +Y and the elevation axis is the Z axis. The gravity deformations of the node representing the center point of mirror 3 are plotted as a function of elevation angle in Figure 4 (translations) and Figure 5 (rotations).

Figure 3 - Model Co-ordinate System for M3 Motions

Figure 4 - M3 Displacements vs. Elevation Angle

Figure 5 - M3 Rotations vs. Elevation Angle

Conclusions:

The analysis results are documented here, and the impact on optical performance will be determined by other project personnel.