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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 2F 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 1and 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