Download MAESTRO Primary Structure Allowable Deflections

MAESTRO Primary Structure Allowable Deflections
Scott Mathews
Steward Observatory – Technical Division
November 14, 2003
Contents
Introduction ......................................................................................................................... 3
Structural Configuration ..................................................................................................... 3
Optical Truss ................................................................................................................... 4
Optics Can (Collimator) .............................................................................................. 4
Injection Optics Assembly .......................................................................................... 6
Grating ........................................................................................................................ 6
Dewar .......................................................................................................................... 6
Interface Structure (weldment) ................................................................................... 7
Analysis Procedure ............................................................................................................. 8
Finite Element Model ..................................................................................................... 8
Assumptions.................................................................................................................... 8
Uncertainty Factors ......................................................................................................... 9
Unit Displacement Cases .................................................................................................... 9
Deflection due to Change in Temperature ........................................................................ 10
Deflection due to Gravity.................................................................................................. 10
Sidereal Analysis .......................................................................................................... 10
Change in Elevation Angle – Ry Rotation .................................................................... 10
Change in Elevation Angle – Rx Rotation.................................................................... 11
Change in De-rotation Angle – Rz Rotation ................................................................. 11
Worst-case Combinations ................................................................................................. 11
Lens Aberrations ............................................................................................................... 12
Rigid Body Motion ........................................................................................................... 12
Page 2 of 12
Introduction
MAESTRO is a new MMT echellette spectrograph, which will be mounted to the
telescope at the f5 Cassegrain interface. The primary structure supporting the
MAESTRO optical components must meet optical tolerances that allow for
fabrication, assembly, and alignment errors, gravitational deflection, and
deflections due to changes in environmental conditions, primarily humidity and
temperature.
An optical tolerance analysis defines an overall motion budget that must be met
for the system to perform within specification. By using the optical tolerances
parametrically, i.e. defining them as maximum “allowables”, the design of the
primary structure is completed so that the aberrations and rigid body motions of
the optical elements are maintained within budget.
Moreover, the overall budget must be partitioned to allocate a sufficient amount
for the alignment of the optical system, which can be affected by the method of
alignment, the design of the mechanical components, and the tolerances they are
fabricated to. The amount of the motion budget left over defines the requirements
of the primary structure for stiffness and deformation due to humidity and
temperature.
In fact, the definition of the alignment procedure and primary structure is a
synergistic process, in which trade-offs are evaluated to arrive at the best possible
combination of process and configuration to meet performance specifications. In
this light, it was concluded that a high-stiffness, thermally stable primary structure
could be designed and fabricated with enough precision to allow for the
implementation of an alignment process deemed most suitable and utilized the
maximum possible allocation of the optical tolerance budget.
Thus, a set of structural deflections were defined as the allowable maximum, from
which detailed designed of the mechanical subsystem would be based. This
report describes the configuration of the primary structure, the structural
deflection analysis, and the allowable deflections that were derived.
Structural Configuration
The MAESTRO primary structure consists of a lightweight, high-stiffness, low
thermal growth optical bench, which is attached quasi-kinematically to the
telescope on a steel interface structure. In this fashion, motion of the relatively
massive telescope structure is effectively de-coupled from the optical system. By
providing up to three channels of active control, additional accuracy of the optical
system can be maintained by negating systematic changes in the shape of the
structure during an observation run.
Page 3 of 12
The optical bench incorporates a space frame supporting the main optical
components – injection optics assembly collimator, prism, grating, and dewar.
The telescope interface structure is a steel weldment that mounts to the rotator
ring flange on the telescope. The optical bench is attached to the interface
structure with ten flexure fittings that allow for radial growth of the rotator flange
without loading the optical bench.
Optical Truss
The optical truss is a triangular section, space frame built from graphite/fiberglass/epoxy hybrid tubing bonded together with aluminum fittings. Intermediate
support structure providing the mounting points for the optical components within
the space frame is built from honeycomb sandwich material. The honeycomb
sandwich is made using 1” thick phenolic core and .030” thick facesheets (six
plies of AS4 graphite/epoxy). The optical truss is shown in Figure 1.
Aluminum fitting
Composite tube
Honeycomb sandwich
bulkhead
Figure 1. Optical Truss (space frame)
Optics Can (Collimator)
The optics can contains the six lenses arranged as three singlets and one triplet
numbered 1 through 6 from forward to aft with respect to the injection optics.
Page 4 of 12
Each lens is potted into an aluminum cell with RTV. The dimensions of the RTV
bonds are sized to a-thermalize the lenses in the cells, while supporting the lens
weight and allowing for a nominal 3% volumetric expansion of the RTV material
due to humidity. Lens cells 2 through 6 are stacked together, with aluminum
spacers between that can be machined to provide optimal de-spacing between the
lenses. Lenses 4, 5 and 6 form a triplet, with oil filling the interstitial spaces
between lenses 4 and 5, and lenses 5 and 6. Lens 1 is a focusable, and is therefore
mounted in a translating stage. Furthermore, the lens 1 stage is mounted to the
other five lenses using an Invar shell so that the pistoning of lens 1 with respect to
lens 2 due to temperature is minimized.
The optics can is mounted to the space frame with flexures, which decouples
thermal expansion of the optics can with respect to the support structure. The
configuration of the optics can is shown in Figure 2.
Lens 6 cell
Lens 5 cell
Invar extension shell
Lens 4 cell
Lens 3 cell
Lens 2 cell
Lens 1 stage
Figure 2. Optics Can Assembly
Page 5 of 12
Injection Optics Assembly
A lens doublet, which converts the f5 focus to f3, a removable slit mounted on a
slide, a shutter, and a fold mirror mounted in a single stiff housing comprise the
injection optics assembly. By packaging these components together their
alignment with respect to each other is more easily maintained, and alignment of
the injection optics assembly with respect to the optics can assembly is more
easily facilitated. The injection optics assembly mounts to the forward bulkhead
of the space frame.
Grating
The grating is kinematically supported in a rigid cell made of Invar clad,
honeycomb sandwich material. Kinematic support is provided by six flexures,
which allow for motion of the grating decoupled from its support structure, and
precise alignment of the grating to the rest of the optical system. The grating cell
is itself mounted on a box structure attached to the space frame. Tilt of the
grating is provided in about two axes parallel to the principal axes of the grating
surface. A gross tilt about one axis is provided to provide initial alignment of the
blaze pattern on the detector plane prior to an observation. Fine tilt adjustments
about both axes are actively controlled to maintain the position of the blaze
pattern during the observation.
Dewar
The dewar is mounted aft of the injection optics assembly, opposite lens 1 of the
collimator. The dewar is supported on a tube sub-frame within the main optical
truss. This configuration provides support of the dewar weight directly into the
optical truss hardpoints, so that the influence the dewar motions with respect to
the rest of the optical system – primarily the injection optics – are minimized.
The dewar sub-frame also allows for easy access to the dewar and for its
alignment and removal.
The complete optical bench showing the location of the primary optical
components is depicted in Figure 3.
Page 6 of 12
Dewar sub-frame
tubes
Dewar
Injection optics
assembly
Optics can
support structure
Optics can
assembly
Prism
Optics can
support flexures
Grating
Grating cell
Grating cell
support box
Figure 3. Optical Bench Assembly
Interface Structure (weldment)
The interface structure is a steel weldment fabricated from 10”x 4” steel tubing.
It bolts to the telescope rotator flange at eight points, and includes fittings that
attach to ten upper aluminum fittings of the optical bench space frame. The
optical bench attach fitting include flexures, which are oriented in a radial pattern
about the optical telescope centerline. The flexures allow radial expansion and
shrinkage of the telescope and interface structures without distorting the optical
bench. The interface structure is shown in Figure 4.
Figure 5. Interface Structure (steel weldment)
Page 7 of 12
Analysis Procedure
Deflections are estimated using a finite element model of the entire mechanical
structure, which is loaded with gravity loads and thermal gradients to produce
structural deflections. The finite element model was created using I-deas
parametric modeling software
Finite Element Model
The finite element model (FEM) uses a combination of thin shell and beam
elements to represent the structure and its load paths. The entire optical bench,
optical component support structures, and interface weldment is included in the
FEM representation. Up to 60,000 degrees of freedom are defined, depending on
boundary conditions. The FEM is shown in Figure 5.
+X
+Y
+Z
Figure 5. Finite-element Model (in I-DEAS MS 9m3)
Assumptions
It is assumed that all deflections are linearly elastic. Composite tubes are
modeled as quasi-isotropic linear beams rigidly attached at their intersection
points. Honeycomb sandwich structures are modeled as plane-stress orthotropic
thin shells with appropriate bending and transverse shear factors to represent the
stiffness properties of the sandwich construction. Optical elements are modeled
Page 8 of 12
as lumped masses positioned at their centers of gravity (CG), and constrained to
the elastic elements representing their attachment structures. Therefore, it is
important to note that the deflections of the CG positions are intended to represent
rigid body motions of the optical elements, and note aberrations that might be
caused by deformation of the glass.
Uncertainty Factors
Uncertainty factors are used to provide sufficient analytical margin to the
structural deflection estimates. Mass densities of elements are adjusted
corresponding to the level of detail in the design, so that actual component mass is
enveloped by analytical (modeled) mass. Density factors range from 1.05 to 1.50.
Fitting factors are used to account for the flexibility of mechanical joints, which
are typically not modeled in detail for practical considerations. This is especially
important for bonded joints, which can represent a significant amount of the
overall flexibility of an elastic structure. Fittings factors range from 1.00 to 1.20.
An overall factor is applied to account for other miscellaneous uncertainties, and
this is reduced as the design matures. Currently a factor of 1.10 is applied to the
gravity vector for the gravitational load cases.
Margin is provided in the thermal deflections by assuming higher than actual
changes in temperature. Currently, the assumed change in temperature is 2F per
hour, which is over four times the specified maximum for the MMT.
Unit Displacement Cases
Unit displacement load cases are performed to check that the orientation
displacement coordinate system is understood, and is consistent with the optical
tolerance analysis. The basic coordinate system for all deflection results has its
origin at the center of the slit, per the “Optical Control Assembly”. The X-axis is
the longitudinal axis of the optical bench (see Figure 5); the positive direction is
from the slit to the grating. The Z-axis is the transverse axis of the optical bench
that is perpendicular to the plane of the slit; the positive direction extends from
the slit away from the telescope rotator flange. The Y-axis is defined using the
right hand rule to complete the orthogonal triad. All rotations follow the right
hand rule. Displacements are defined for the CG positions of the primary optical
elements: injection optics doublet; slit; fold mirror; lens1; lens 2; lens 3; lens 4;
lens 5; lens 6; prism; grating and grating cell; dewar window.
Click on the link below to access the “Unit Displacements” Excel workbook.
Page 9 of 12
Deflection due to Change in Temperature
Thermal deflection was calculated for a -10 Rankine change in temperature.
Thermal deflections can be scaled linearly. The thermal deflections are included
with the Ry-Rotation results described in the next section.
Deflection due to Gravity
Gravity deflections were calculated for 29 separate load vectors representing
rotations about the three MAESTRO principal axes. The three separate rotation
load case sets are described below.
Sidereal Analysis
Brian Cuerden completed an analysis describing the range of load vectors that
would be actually possible at the MMT site. It is important to note that maximum
derotation angular rates occur with the telescope pointed near zenith, thus change
in the gravity vector is small for the highest rates of derotator angle change. Also,
the change in elevation angle cannot exceed 12.7 per hour. For MMT, the
observable elevation angle will not exceed 75 from the zenith, however
deflections at the horizon pointing position are included for reference.
An important result of the sidereal analysis is that the maximum change of the
gravity vector is approximately 0.20G during one hour.
Click on the link below to access the “coord2.xls” Excel workbook and review the
sidereal analysis.
D:\Desktop\MAESTRO\coord2.xls
Change in Elevation Angle – Ry Rotation
For this set of load vectors MAESTRO was assumed oriented perpendicular to the
telescope elevation axis. Load vectors were applied for the zenith pointing
position and in increments of 10 of elevation angle to the horizon pointing
position.
Click on the link below to access the “MAESTRO_110103_RY.xls” Excel
workbook.
D:\Desktop\MAESTRO FEM RESULTS\110103\MAESTRO_110103_RY.xls
Page 10 of 12
The worksheet named “results” lists the absolute deflections for the CG positions.
The worksheet named “relative” list relative deflections between the CG
positions. Note that the thermal deflections are included here as the “delta t”
worksheet
Change in Elevation Angle – Rx Rotation
For this set of load vectors MAESTRO was assumed oriented parallel to the
telescope elevation axis. Load vectors were applied for the zenith pointing
position and in increments of 10 of elevation angle to the horizon pointing
position.
Click on the link below to access the “MAESTRO_110103_RX.xls” Excel
workbook.
D:\Desktop\MAESTRO FEM RESULTS\110103\MAESTRO_110103_RX.xls
Change in De-rotation Angle – Rz Rotation
For this set of load vectors MAESTRO, was rotated about the telescope optical
axis with the telescope in the horizon pointing position. Load vectors were
applied for with MAESTRO initially parallel to the elevation axis and rotated in
increments of 22.5 of derotation angle from 0 to 180.
Click on the link below to access the “MAESTRO_110103_RZ.xls” Excel
workbook.
D:\Desktop\MAESTRO FEM RESULTS\110103\MAESTRO_110103_RZ.xls
Worst-case Combinations
Qualitative inspection of the gravity deflections indicate two specific load vectors
produce the maximum deflections from an initial orientation of the telescope in
the zenith position. Assuming the elevation angle cannot be higher than 70, an
rss combination of the 70 Ry-deflections with the 90 Rz- deflections, or the 70
Rx-deflections with the 90 Rz- deflections will produce the worst-case absolute
deflections due to gravity.
Furthermore, it is conservative to rss thermal and gravity deflections to ascertain
total structural deflection during an observation.
Page 11 of 12
Lens Aberrations
The deflections described thus far are rigid body deflections of the optical
components. Brian Cuerden evaluated lens deformations causing aberrations
while sizing the rtv layer dimension for potting the lenses in their respective cells.
These deformations are due to thermal loading, hydrostatic pressure of oil (lenses
4 and 2 only), and volumetric swelling of the rtv caused by humidity. Rigid body
motion of the lenses relative to the cells was determined to be well below 1and
can be neglected.
Click on the link below to access the “Lens-Results.xls” Excel workbook for
reviewing lens aberration due to thermal loading, hydrostatic pressure, and
humidity.
D:\Desktop\MAESTRO\Lens-Results.xls
Rigid Body Motion
The rigid body motions defined by the gravity deflections can be used to evaluate
boresight changes. Furthermore, rigid body motion of the optical bench relative
to the telescope will also occur, which can be approximated by the absolute
deflections of the injection optics CG position.
When evaluating boresight changes of the grating, remember that tilts about the
grating plane principal axes can be actively controlled.
Page 12 of 12