SNAP Telescope Metering Structure Analysis

# Executive Summary

A baseline design has been developed for the SuperNova/Acceleration
Probe (SNAP) telescope structure, which, combined with the optical
elements, forms the optical telescope assembly (OTA). Finite element
modal and stress analyses have been performed to evaluate and refine the
design. These analyses validate the baseline design as a viable
configuration.

On-orbit performance goals include the ability to maintain precise and
well-controlled spatial relations between all the optical components,
subject to thermal variations and the influence of attitude control and
other spacecraft accelerations. This goal is to be met with a minimum of
mass and with a minimum of obscuration of the field of view.
Additionally, the support structure must survive the launch acceleration
and vibration environment.

The dynamic influences on optics positioning and alignment are minimized
and launch loads are tolerated by making the structure stiff. Thermal
distortion effects are minimized by employing materials with near-zero
coefficients of thermal expansion, in combination with active thermal
control of the structure. Mass may be traded for stiffness to some
extent, with the optimal balance to be determined subject to refined
spacecraft requirements.

Figure 1 shows a schematic view illustrating the light paths of the SNAP
Telescope. As currently envisioned, the SNAP telescope employs a
three-mirror anastigmat (TMA) configuration^1,2,3^. The concave primary
mirror and convex secondary mirror are on a common axis, and the folding
flat mirror folds the image 90 degrees toward the concave tertiary
mirror, which projects the image through a hole in the folding flat
mirror onto the flat focal plane.

The current mechanical design configuration is illustrated in Figures 2
and 3 and is summarized in Table 1. The predominant structural material
used throughout is a quasi-isotropic layup of M55J carbon fiber/cyanate
ester, with very low in-plane coefficients of thermal expansion. The
primary, secondary, and tertiary mirrors are assumed to be lightweighted
ULE glass, while the folding flat mirror is silicon carbide. The design
has a fundamental natural frequency of 39 hertz. Its total mass is
around 497kg, consisting of 147kg of structure supporting 350kg of dead
load. Launch load strength safety factors for the telescope structure
itself are nearly 40.

Information on the SNAP mission and science are available at the SNAP
home page, http://snap.lbl.gov.

## ![](media/image1.png){width="6.375in" height="2.4451388888888888in"}Figure 1-Schematic of SNAP Optics

![](media/image2.wmf)

**Figure 2-Telescope design configuration**

![](media/image3.wmf)

**Figure 3-Telescope design configuration**

![](media/image4.jpeg){width="6.29375in" height="5.822222222222222in"}

**Table 1-Summary of FEA Model**

# Description of the model

Figures 2 and 3 illustrate the complete OTA model. Table 1 lists
particulars of the model. The entire OTA is supported on six carbon
fiber struts mounted to a perfectly rigid base. These struts will
actually mount to the spacecraft assembly, but for this study, the OTA
is analyzed independently.

The OTA support struts mount to the triangular bench, 200mm thick,
approximately 2m long each side, comprised of face sheets, perimeter and
eggcrating made from 2mm thick sheets of carbon fiber. Figures 4 and 5
show the internal structure of the bench. Moisture absorption in cyanate
ester matrix materials raises concerns for both optical surface
contamination and dimensional stability. Published water diffusion data
suggest a maximum lamina thickness of approximately 2mm for a one-month
post launch dry-out period, which is consistent with SNAP commissioning
plans.

The secondary mirror assembly (SMA) support structure mounts to the
corners of the bench. It is comprised of three legs and a shroud, all
constructed of 2mm thick carbon fiber. The base of each leg includes a
larger base section, outside the field of view of the telescope. The
thinner portions of the legs obscure part of the field of view and are
therefore as narrow as practical. To minimize the effects of stray light
from the side faces of the legs, they taper from a width of 38mm on the
side facing the primary mirror to 19mm on the opposite side. Figure 6
illustrates this taper and shows bulkheads within the leg sections that
raise the frequency of drumhead modes of the sides of the legs. The legs
are 250mm deep. The SMA itself is represented by a mass dummy supported
on six struts (not shown here).

Because of geometric constraints, the SMA support structure must attach
to the bench after the primary mirror is installed. Therefore, it may be
a bolt-on assembly.

The inner baffle mounts to the center of the bench. It is modeled as a
simple carbon fiber tube, with the mass of the baffle blades rolled into
the mass of the tube.

Below the bench is the lower optics bay, which consists of 2mm thick
carbon fiber outer walls and bulkheads, to which are mounted the lower
optical elements---tertiary mirror, folding flat mirror, and instrument
(focal plane/focal plane shield/spectrograph).

Three startracker mass representations are mounted to the anti-sunward
side of the bench. The startrackers are baselined in this model as Ball
Aerospace CT-602's with light shades.

The SIRU (inertial reference unit) mass dummy is mounted to the lower
side of the bench. It has the mass and size of a Northrop Grumman
SIRU-Dual String model.

The focal plane is a hexagonal mass dummy, mounted on six struts to the
lower optics bay. The 10mm thick focal plane shield is in turn
kinematically mounted to the focal plane using another six struts. The
spectrograph is integrally installed on the focal plane.

The primary, folding flat, and tertiary mirrors are each modeled using
plate elements, with material properties set to simulate thick,
lightweighted parts. These components are intended primarily to be mass
representations in the telescope model. More detailed baseline designs
for each of the telescope's four mirrors have been developed and studied
independently. The mirror studies are discussed separately in the tech
note, SNAP-TECH-05007.doc.

![](media/image5.wmf)

**Figure 4-Telescope cutaway view**

![](media/image6.jpeg){width="3.5625in" height="4.039583333333334in"}

**Figure 5-Bench eggcrating**

![](media/image7.wmf)

**Figure 6-Slice through SMA support leg showing taper**

# 

# Performance goals and results

For a Delta IV Medium launch vehicle, minimum natural frequencies for
primary structures are 27 Hz axial and 10 Hz lateral, and the minimum
natural frequency for secondary structures is 35 Hz, regardless of
orientation. Maximum quasi-static accelerations are 6.5g axial and 2g
lateral^4^.

Figures 7 through 10 illustrate the first four vibration modes of the
design. Natural frequencies are all 39 Hz and higher. The first, second,
and fourth modes are dominated by compliance of the SMA support
structure, while the third exhibits some bench deformations. The fourth
mode is a fundamentally rotational mode, which should not be strongly
excited under launch conditions. The first predominantly axial mode has
a frequency of 68 Hz.

Due to compliance of the spacecraft, natural frequencies of the OTA
installed on the spacecraft will be lower than when it is mounted
rigidly, as in this study. A sufficiently stiff spacecraft and high OTA
natural frequencies will ensure that the structure meets launch vehicle
frequency requirements. Preliminary studies with provisional spacecraft
designs have shown that the frequency requirements described above can
be met with ample margins.

The intent of this study is to analyze the telescope structure itself.
The mirrors, instrument, and other payload items, along with their
respective support struts are not modeled in detail, and stresses in
these elements are not examined in this model. Under quasi-static
accelerations of 6.5 g axial or 2 g lateral, worst-case principal
stresses in the carbon fiber telescope structure show a factor of safety
of 37 against material failure. This indicates that designing for high
natural frequencies results in an extremely strong structure.

![](media/image8.jpeg){width="3.1166666666666667in"
height="4.589583333333334in"}

**Figure 7-First Mode, 39 Hz**

![](media/image9.jpeg){width="2.834722222222222in"
height="4.095138888888889in"}

**Figure 8-Second Mode, 40 Hz**

![](media/image10.jpeg){width="3.0104166666666665in" height="4.43125in"}

**Figure 9-Third Mode, 44 Hz**

![](media/image11.jpeg){width="3.895138888888889in" height="4.1125in"}

**Figure 10-Fourth Mode, 44 Hz**

# Conclusion

A baseline design for the SNAP telescope structure has been developed
and shown to meet basic launch requirements. Input from industry is
warranted to further examine many issues, including manufacturability,
integration, and spacecraft interactions.

## REFERENCES

1.  M. Lampton, et al, "SNAP Telescope" SPIE **4849** pp.215-226, 2002.

2.  M. Lampton, et al, "SNAP Telescope: an Update" SPIE **5166** pp.
    113-123, 2004.

3.  M. Sholl, et al, "SNAP Telescope" SPIE **5487-73**, in press 2004.

4.  Boeing Delta IV Payload Planners Guide, October 2000.