memorandum - harvard university

Memorandum

Date: 26 April 2006 To: Mr. Robert G. Fata From: Andrew T. Sarawit and Frank W. Kan Project: 060091 − MMTI Subject: Analysis of MMT Telescope Optical Support Structure and Instrument Rotator for

Binospec Spectrograph In 1995, SGH performed a study to evaluate the gravity-induced distortions of the instrument mounting flange and wide-field corrector mounting flange using a finite element model of the MMT OSS that included the wide-field corrector mounting flange, the instrument rotator support flange, a representation of the bearing flexibility, and the instrument mounting flange. The regions of the OSS model near the instrument rotator were refined. A 3,000 lb instrument with a center of gravity at Z = -62.1 in. with respect to vertex of the primary was analyzed. An overall moment stiffness of the bearing of 109 ft-lb per radian was used in the model. The results of the study were summarized in two Memorandums dated 1 June 1995 and 7 July 1995. We understand that the new Binospec spectrograph is being designed and will have a maximum weight of 6,000 lb with a center of gravity at Z = -87.73 in.

1. PURPOSE

The purpose of this study is to perform structural analysis of MMT telescope optical support structure and instrument rotator to predict the rigid body motions and mounting flange distortions for new Binospec spectrograph.

2. SCOPE OF WORK

The scope of this study is as follows: 1. Review information and drawings of the new Binospec spectrograph and its mounting

flange.

2. Review and correct the existing finite element model (Model 1 – Telescope with existing instrument).

3. Modify the existing finite element model to include the weight and center of gravity of the new Binospec spectrograph and its mounting flange (Model 2 – Telescope with new Binospec spectrograph).

4. Perform analyses for gravity load at zenith and horizon pointing.

Memo to Mr. Robert G. Fata - 2 - 26 April 2006

5. Summarize the following results:

• Tables showing displacements at the focal plane and at the corrector with respect to the optical axis due to gravity load at zenith and horizon pointing,

• Plots of out-of-plane (∆z) and out-of-round (∆r) distortions of the instrument rotator support flange, bearing outer and inner races, instrument mounting flange, and wide-field corrector mounting flange for gravity face side minus gravity face up, and

• Tables summarizing order of magnitude stresses in the OSS near the instrument rotator, instrument rotator support flange, bearing outer and inner races, and the instrument mounting flange due to gravity load at zenith and horizon pointing.

3. REFERENECES

• SAO figures and drawings of Binospec spectrograph, weight and center of gravity location, main mounting flange and support truss attached as Appendix A.

• SGH Memorandum to Mr. Dan Fabricant at SAO dated 1 June 1995.

• SGH Memorandum to Mr. Dan Fabricant at SAO dated 7 July 1995.

4. FINITE ELEMENT MODELS

We reviewed the existing finite element model used in the 1995 study. We found some discrepancies in the weight and center of gravity of the wide-field corrector and some inaccuracies in the way the displacements and rotations of the primary mirror vertex were calculated. We corrected the existing finite element model with existing instrument (Model 1 – Telescope with existing instrument) and re-ran the analyses. We then modified the model to include the weight and center of gravity of the new Binospec spectrograph and its mounting flange (Model 2 – Telescope with new Binospec spectrograph) and repeated the analyses.

4.1 Model 1 – Telescope with Existing Instrument

After reviewing the existing finite element model used in the 1995 study, we found that the weight and center of gravity of the wide-field corrector were changed. We also found that the displacements and rotations of the primary mirror vertex were calculated based on the weighted average of the displacements of the lower workpoints of the hardpoint platform. These lower workpoints were on the structural points on the back of the mirror cell. The hardpoint platform was not in the model. We modified the existing finite element model with the following changes: • Change in weight and center of gravity of the wide-field corrector from the existing

1,000 lb with a center of gravity at Z = -12 in. with respect to vertex of the primary to 1,200 lb with a center of gravity at Z = -15.87 in. (see Figure 2 in Appendix A).


• Change in location of focal plane from the existing of Z = -70 in. to Z = -70.67 in. (see Figure 2 in Appendix A).

• Change in method of calculating the displacements and rotations of the primary mirror vertex. We improved the calculation method by adding the hardpoint platform into the model. The displacements and rotations of the primary mirror vertex were rigidly linked to the displacements of the upper workpoints of the hardpoint platform.

4.2 Model 2 – Telescope with New Binospec Spectrograph

We modified Model 1 to account for the changes related to the new Binospec spectrograph: • Change in weight of the instrument from the existing 3,000 lb with a center of gravity at

Z = -62.1 in. to 6,000 lb with a center of gravity at Z = -87.73 in. (see Figure 2 in Appendix A).

• Change in instrument mounting flange cross section: overall height from 7 in. to 5 in., overall width from 10 in. to 5 in., and vertical leg thickness from 0.5 in. to 0.75 in. (see Sheet 2 in Appendix A).

• Change in the way of attaching the instrument weight to the mounting flange. We modified the interpolation element (RBE3) so that the instrument weight will be transmitted to the mounting flange at discrete locations. A spherical coordinate system was used for the output coordinate system of the instrument mount flange nodes. The circumferential and meridian displacements at selected nodes were linked by RBE3 element to the concentrated mass to match the structural action of the support truss (see Appendix A). The weights of the three electronic boxes were modeled by concentrated masses that were attached via RBE3 elements to the mounting flange. The mounting flange was re-meshed to accommodate the locations of the working points of the support truss.

Figures 1 and 2 show the isometric view of the overall finite element model and area near the instrument rotator for Model 2.

5. RESULTS

We performed analyses for gravity load at zenith and horizon pointing using Models 1 and 2 described above. Figures 3 through 6 show the deflected shape of Model 2 for gravity load at zenith and horizon pointing, respectively. The coordinates and the computed gravity deflections at the wide-field corrector mounting flange (nodes 642 through 650) and at the instrument mounting flange (nodes 8301 through 8365 for Model 1 and nodes 8301 through 8397 for Model 2) are shown in Tables 1 and 2 for Models 1 and 2 respectively. The gravity displacements of the corrector and focal point with respect to the optical axis are also included in these tables. The optical axis is defined by the displacements and rotations of the primary mirror at its vertex.


The out-of-plane (∆z) and out-of round (∆r) distortions of the four rings at the instrument support (the instrument rotator support flange, the outer race, the inner race, and the instrument mounting flange) and the wide-field corrector mounting flange for gravity face side minus gravity face up are shown in Figures 7 and 8 for Model 1 and Figures 9 and 10 for Model 2. The peak-to-peak distortions are given in the following table:

Peak-to-peak distortions (mil) Model 1 Model 2 Component

∆z ∆r ∆z ∆r Instrument rotator support flange 0.8 1.8 1.0 2.2 Bearing outer race 0.8 1.9 1.0 2.3 Bearing inner race 0.3 0.7 0.5 1.9 Instrument mounting flange 0.3 0.8 0.5 2.2 Wide-field corrector mounting flange 0.2 0.2 0.2 0.2

In order to ensure that the ring distortion for gravity face side minus gravity face up is a good measure of the actual behavior, the gravity face side and gravity face up distortions of the four rings and the wide-field corrector mounting flange are plotted separately in Figures 11 through 14 for Model 1 and Figures 15 through 18 for Model 2. The plots show that the gravity face side distortion is almost orthogonal to the gravity face up distortion and the gravity face up distortion is the dominant term. Peak stresses in the OSS near the instrument rotator and the four rings at the instrument support due to gravity load at zenith and horizon pointing are given in the following table:

Peak stress (ksi) Model 1 Model 2 Component

Face up Face side Face up Face side OSS near the instrument rotator 2.2 0.4 2.5 0.8 Instrument rotator support flange 1.0 0.3 1.1 0.5 Bearing outer race 1.0 0.4 1.3 0.8 Bearing inner race 0.2 0.1 0.9 0.9 Instrument mounting flange 0.3 0.1 1.1 0.9

The stresses in the bearing inner and outer races reported in the above table are results of the overall structural actions (hoop and bending). The effect of the bearing preload and the local stresses resulting from the rollers are not included. Contour plots of the stresses in the instrument rotator support flange and adjacent region are shown in Figures 19 and 20 for Model 1 and Figures 21 and 22 for Model 2.

6. DISCUSSION

The results of Model 1 are very similar to the results of the 1995 study except the displacement of the primary mirror vertex in the Y-direction. This is due to the inclusion of hardpoint platform which should be more accurate.


The results of Models 1 and 2 show the following effects of the increase in instrument weight and shift in instrument center of gravity: • The relative displacement of the focal point with respect to the optical has increased;

the relative ∆z displacement for face up gravity increases from -3.94 mil to -4.92 mil and the relative ∆y displacement for face side gravity increases from -1.14 mil to -2.90 mil.

• The magnitudes of the distortions of the four rings at the instrument support have increased as expected. The shapes of the distortions have also changed because of the inclusion of the structural action of the support truss of the instrument.

• The relative radial displacements between the outer race and the inner race of the bearing have changed. However, the maximum relative radial displacement for gravity load at zenith pointing gravity remains at similar magnitude (1.0 mils for Model 1 from Figure 14 and 0.9 mils for Model 2 from Figure 18).

• Stresses in the OSS near the instrument rotator and the four rings at the instrument support have increased but remain small and acceptable.

The change of instrument weight and center of gravity will require adding or removing permanent counterweights since the motorized counterweight will not have the required capacity.

We contacted Avon Bearings regarding the static strength, fatigue life, and the stiffness of the instrument rotator bearing. In summary, the bearing has a minimum static safety factor of 6.5, a minimum theoretical L-10 life of 235,700 hours at 4 rpm continuous, and a moment stiffness of 6.72 x 1010 in.-lb per radian with 0.0005 in. preload. The details of report from Avon Bearings are included in Appendix B.

O:\DATEFILE\2006\Kan\FWK05-M-emb.doc

Table 1 – Coordinates and Gravity Deflections – Model 1

060091 MMT Instrument Rotator and Corrector Cell SupportAnalysis: Model 1 - Telescope with Existing Instrument

Location of Grid

Grid ID R θ Z X Y Z

Corrector Cell Support Flange

642 19.91 -90 -20.43 0.0000 -19.9100 -20.4300643 19.91 -67.5 -20.43 7.6192 -18.3944 -20.4300644 19.91 -45 -20.43 14.0785 -14.0785 -20.4300645 19.91 -32.259 -20.43 16.8368 -10.6269 -20.4300646 19.91 -16.175 -20.43 19.1219 -5.5464 -20.4300647 19.91 22.5 -20.43 18.3944 7.6192 -20.4300648 19.91 45 -20.43 14.0785 14.0785 -20.4300649 19.91 67.5 -20.43 7.6192 18.3944 -20.4300650 19.91 90 -20.43 0.0000 19.9100 -20.4300

Corrector CG997 0.0000 0.0000 -15.8700

Corrector CG on Optical Axis987 0.0000 0.0000 -15.8700

Instrument Support Flange

8301 34.25 -90 -57.44 0.0000 -34.2500 -57.44008303 34.25 -84.375 -57.44 3.3571 -34.0851 -57.44008305 34.25 -78.75 -57.44 6.6818 -33.5919 -57.44008307 34.25 -73.125 -57.44 9.9423 -32.7752 -57.44008309 34.25 -67.5 -57.44 13.1069 -31.6429 -57.44008311 34.25 -61.875 -57.44 16.1453 -30.2058 -57.44008313 34.25 -56.25 -57.44 19.0283 -28.4778 -57.44008315 34.25 -50.625 -57.44 21.7280 -26.4756 -57.44008317 34.25 -45 -57.44 24.2184 -24.2184 -57.44008319 34.25 -39.375 -57.44 26.4756 -21.7280 -57.44008321 34.25 -33.75 -57.44 28.4778 -19.0283 -57.44008323 34.25 -28.125 -57.44 30.2058 -16.1453 -57.44008325 34.25 -22.5 -57.44 31.6429 -13.1069 -57.44008327 34.25 -16.875 -57.44 32.7752 -9.9423 -57.44008329 34.25 -11.25 -57.44 33.5919 -6.6818 -57.44008331 34.25 -5.625 -57.44 34.0851 -3.3571 -57.44008333 34.25 0 -57.44 34.2500 0.0000 -57.44008335 34.25 5.625 -57.44 34.0851 3.3571 -57.44008337 34.25 11.25 -57.44 33.5919 6.6818 -57.44008339 34.25 16.875 -57.44 32.7752 9.9423 -57.44008341 34.25 22.5 -57.44 31.6429 13.1069 -57.44008343 34.25 28.125 -57.44 30.2058 16.1453 -57.44008345 34.25 33.75 -57.44 28.4778 19.0283 -57.44008347 34.25 39.375 -57.44 26.4756 21.7280 -57.44008349 34.25 45 -57.44 24.2184 24.2184 -57.44008351 34.25 50.625 -57.44 21.7280 26.4756 -57.44008353 34.25 56.25 -57.44 19.0283 28.4778 -57.44008355 34.25 61.875 -57.44 16.1453 30.2058 -57.44008357 34.25 67.5 -57.44 13.1069 31.6429 -57.44008359 34.25 73.125 -57.44 9.9423 32.7752 -57.44008361 34.25 78.75 -57.44 6.6818 33.5919 -57.44008363 34.25 84.375 -57.44 3.3571 34.0851 -57.44008365 34.25 90 -57.44 0.0000 34.2500 -57.4400

Focal Point975 0.0000 0.0000 -70.6700

Focal Point on Optical Axis974 0.0000 0.0000 -70.6700

Table 1 – Coordinates and Gravity Deflections – Model 1 (cont.)


Loading Case 1: Gravity at zenith (Face up)

Grid ID ∆r ∆θ ∆z ∆x ∆y ∆z


642 -2.45E-04 1.50E-20 -1.61E-02 0.00E+00 2.45E-04 -1.61E-02643 -2.68E-04 -3.54E-05 -1.61E-02 -1.35E-04 2.34E-04 -1.61E-02644 -3.49E-04 -4.99E-05 -1.62E-02 -2.82E-04 2.11E-04 -1.62E-02645 -3.99E-04 -4.02E-05 -1.61E-02 -3.59E-04 1.79E-04 -1.61E-02646 -4.53E-04 -5.75E-06 -1.61E-02 -4.37E-04 1.21E-04 -1.61E-02647 -3.57E-04 7.68E-05 -1.59E-02 -3.59E-04 -6.58E-05 -1.59E-02648 -2.73E-04 6.11E-05 -1.60E-02 -2.36E-04 -1.50E-04 -1.60E-02649 -2.28E-04 2.90E-05 -1.58E-02 -1.14E-04 -2.00E-04 -1.58E-02650 -2.30E-04 -1.41E-20 -1.57E-02 0.00E+00 -2.30E-04 -1.57E-02

Corrector CG997 0.00E+00 2.55E-06 -1.60E-02

Corrector CG on Optical Axis987 0.00E+00 2.35E-03 -1.19E-02

Displacement of Correct CG with respect to Optical Axis997-987 0.00E+00 -2.35E-03 -4.16E-03


8301 -4.04E-04 2.48E-20 -1.61E-02 0.00E+00 4.04E-04 -1.61E-028303 -3.99E-04 4.34E-05 -1.61E-02 4.12E-06 4.01E-04 -1.61E-028305 -3.86E-04 8.67E-05 -1.61E-02 9.67E-06 3.96E-04 -1.61E-028307 -3.61E-04 1.28E-04 -1.60E-02 1.79E-05 3.83E-04 -1.60E-028309 -3.23E-04 1.67E-04 -1.60E-02 3.04E-05 3.62E-04 -1.60E-028311 -2.72E-04 2.02E-04 -1.60E-02 4.98E-05 3.35E-04 -1.60E-028313 -2.06E-04 2.32E-04 -1.60E-02 7.80E-05 3.00E-04 -1.60E-028315 -1.26E-04 2.54E-04 -1.59E-02 1.16E-04 2.58E-04 -1.59E-028317 -3.20E-05 2.66E-04 -1.59E-02 1.66E-04 2.11E-04 -1.59E-028319 7.04E-05 2.68E-04 -1.58E-02 2.25E-04 1.63E-04 -1.58E-028321 1.76E-04 2.60E-04 -1.58E-02 2.91E-04 1.19E-04 -1.58E-028323 2.77E-04 2.37E-04 -1.58E-02 3.56E-04 7.85E-05 -1.58E-028325 3.65E-04 2.04E-04 -1.57E-02 4.16E-04 4.88E-05 -1.57E-028327 4.36E-04 1.63E-04 -1.57E-02 4.65E-04 2.95E-05 -1.57E-028329 4.75E-04 1.14E-04 -1.57E-02 4.88E-04 1.89E-05 -1.57E-028331 4.86E-04 6.18E-05 -1.57E-02 4.90E-04 1.39E-05 -1.57E-028333 4.71E-04 1.02E-05 -1.56E-02 4.71E-04 1.02E-05 -1.56E-028335 4.24E-04 -3.55E-05 -1.57E-02 4.25E-04 6.20E-06 -1.57E-028337 3.57E-04 -7.53E-05 -1.57E-02 3.65E-04 -4.15E-06 -1.57E-028339 2.77E-04 -1.07E-04 -1.57E-02 2.96E-04 -2.25E-05 -1.57E-028341 1.88E-04 -1.26E-04 -1.57E-02 2.22E-04 -4.43E-05 -1.57E-028343 1.01E-04 -1.35E-04 -1.57E-02 1.53E-04 -7.15E-05 -1.57E-028345 2.11E-05 -1.36E-04 -1.57E-02 9.30E-05 -1.01E-04 -1.57E-028347 -4.28E-05 -1.27E-04 -1.58E-02 4.72E-05 -1.25E-04 -1.58E-028349 -9.05E-05 -1.12E-04 -1.58E-02 1.52E-05 -1.43E-04 -1.58E-028351 -1.21E-04 -9.36E-05 -1.57E-02 -4.28E-06 -1.53E-04 -1.57E-028353 -1.33E-04 -7.53E-05 -1.57E-02 -1.13E-05 -1.52E-04 -1.57E-028355 -1.32E-04 -5.66E-05 -1.57E-02 -1.22E-05 -1.43E-04 -1.57E-028357 -1.20E-04 -3.88E-05 -1.57E-02 -1.01E-05 -1.26E-04 -1.57E-028359 -1.07E-04 -2.66E-05 -1.57E-02 -5.53E-06 -1.10E-04 -1.57E-028361 -9.19E-05 -1.59E-05 -1.57E-02 -2.35E-06 -9.32E-05 -1.57E-028363 -7.86E-05 -6.75E-06 -1.56E-02 -9.88E-07 -7.89E-05 -1.56E-028365 -7.61E-05 -4.66E-21 -1.56E-02 0.00E+00 -7.61E-05 -1.56E-02

Focal Point975 0.00E+00 1.19E-04 -1.58E-02

Focal Point on Optical Axis974 0.00E+00 1.50E-03 -1.19E-02

Displacement of Focal Point with respect to Optical Axis975-974 0.00E+00 -1.38E-03 -3.94E-03



Loading Case 2: Gravity at horizon (Face side)



642 3.71E-03 -2.27E-19 -1.19E-03 0.00E+00 -3.71E-03 -1.19E-03643 3.42E-03 -1.41E-03 -1.13E-03 3.26E-06 -3.70E-03 -1.13E-03644 2.60E-03 -2.61E-03 -9.30E-04 -2.38E-06 -3.69E-03 -9.30E-04645 1.96E-03 -3.12E-03 -7.71E-04 -6.32E-06 -3.68E-03 -7.71E-04646 1.01E-03 -3.53E-03 -5.39E-04 -1.02E-05 -3.68E-03 -5.39E-04647 -1.42E-03 -3.39E-03 5.31E-05 -1.35E-05 -3.68E-03 5.31E-05648 -2.62E-03 -2.60E-03 3.75E-04 -1.36E-05 -3.69E-03 3.75E-04649 -3.43E-03 -1.41E-03 5.91E-04 -1.13E-05 -3.71E-03 5.91E-04650 -3.72E-03 -2.28E-19 6.50E-04 0.00E+00 -3.72E-03 6.50E-04

Corrector CG997 0.00E+00 -3.90E-03 -2.78E-04

Corrector CG on Optical Axis987 0.00E+00 -3.61E-03 4.85E-04



8301 2.47E-03 -1.51E-19 -1.93E-03 0.00E+00 -2.47E-03 -1.93E-038303 2.46E-03 -2.41E-04 -1.92E-03 1.56E-06 -2.47E-03 -1.92E-038305 2.44E-03 -4.80E-04 -1.90E-03 4.30E-06 -2.48E-03 -1.90E-038307 2.39E-03 -7.17E-04 -1.85E-03 9.03E-06 -2.50E-03 -1.85E-038309 2.33E-03 -9.48E-04 -1.79E-03 1.60E-05 -2.52E-03 -1.79E-038311 2.25E-03 -1.17E-03 -1.71E-03 2.52E-05 -2.54E-03 -1.71E-038313 2.14E-03 -1.39E-03 -1.62E-03 3.56E-05 -2.56E-03 -1.62E-038315 2.02E-03 -1.60E-03 -1.52E-03 4.62E-05 -2.57E-03 -1.52E-038317 1.87E-03 -1.79E-03 -1.40E-03 5.58E-05 -2.59E-03 -1.40E-038319 1.69E-03 -1.97E-03 -1.28E-03 6.26E-05 -2.59E-03 -1.28E-038321 1.50E-03 -2.12E-03 -1.15E-03 6.51E-05 -2.60E-03 -1.15E-038323 1.28E-03 -2.26E-03 -1.02E-03 6.28E-05 -2.60E-03 -1.02E-038325 1.04E-03 -2.38E-03 -8.75E-04 5.45E-05 -2.60E-03 -8.75E-048327 7.92E-04 -2.47E-03 -7.31E-04 4.05E-05 -2.60E-03 -7.31E-048329 5.27E-04 -2.54E-03 -5.84E-04 2.16E-05 -2.59E-03 -5.84E-048331 2.53E-04 -2.58E-03 -4.36E-04 -9.53E-07 -2.59E-03 -4.36E-048333 -2.51E-05 -2.59E-03 -2.87E-04 -2.51E-05 -2.59E-03 -2.87E-048335 -3.02E-04 -2.57E-03 -1.37E-04 -4.87E-05 -2.59E-03 -1.37E-048337 -5.74E-04 -2.53E-03 1.29E-05 -6.97E-05 -2.59E-03 1.29E-058339 -8.35E-04 -2.46E-03 1.62E-04 -8.59E-05 -2.59E-03 1.62E-048341 -1.08E-03 -2.36E-03 3.10E-04 -9.64E-05 -2.60E-03 3.10E-048343 -1.31E-03 -2.24E-03 4.55E-04 -1.00E-04 -2.59E-03 4.55E-048345 -1.52E-03 -2.10E-03 5.97E-04 -9.77E-05 -2.59E-03 5.97E-048347 -1.71E-03 -1.94E-03 7.33E-04 -8.98E-05 -2.58E-03 7.33E-048349 -1.87E-03 -1.76E-03 8.63E-04 -7.77E-05 -2.57E-03 8.63E-048351 -2.01E-03 -1.57E-03 9.85E-04 -6.30E-05 -2.55E-03 9.85E-048353 -2.13E-03 -1.36E-03 1.10E-03 -4.77E-05 -2.52E-03 1.10E-038355 -2.22E-03 -1.15E-03 1.19E-03 -3.33E-05 -2.50E-03 1.19E-038357 -2.29E-03 -9.26E-04 1.28E-03 -2.11E-05 -2.47E-03 1.28E-038359 -2.35E-03 -7.00E-04 1.34E-03 -1.19E-05 -2.45E-03 1.34E-038361 -2.39E-03 -4.69E-04 1.39E-03 -5.70E-06 -2.43E-03 1.39E-038363 -2.40E-03 -2.35E-04 1.42E-03 -2.12E-06 -2.42E-03 1.42E-038365 -2.41E-03 -1.48E-19 1.43E-03 0.00E+00 -2.41E-03 1.43E-03

Focal Point975 0.00E+00 -1.91E-03 -2.69E-04

Focal Point on Optical Axis974 0.00E+00 -7.67E-04 4.85E-04


Table 2 – Coordinates and Gravity Deflections – Model 2

060091 MMT Instrument Rotator and Corrector Cell SupportAnalysis: Model 2 - Telescope with New Binospec Spectrograph

Location of Grid

Grid ID R θ Z X Y Z


642 19.91 -90 -20.43 0.0000 -19.9100 -20.4300643 19.91 -67.5 -20.43 7.6192 -18.3944 -20.4300644 19.91 -45 -20.43 14.0785 -14.0785 -20.4300645 19.91 -32.259 -20.43 16.8368 -10.6269 -20.4300646 19.91 -16.175 -20.43 19.1219 -5.5464 -20.4300647 19.91 22.5 -20.43 18.3944 7.6192 -20.4300648 19.91 45 -20.43 14.0785 14.0785 -20.4300649 19.91 67.5 -20.43 7.6192 18.3944 -20.4300650 19.91 90 -20.43 0.0000 19.9100 -20.4300

Corrector CG997 0.0000 0.0000 -15.8700

Corrector CG on Optical Axis987 0.0000 0.0000 -15.8700


8301 33.5666 -90 -57.2931 0.0000 -33.5666 -57.29318303 33.5666 -86.25 -57.2931 2.1954 -33.4947 -57.29318305 33.5666 -82.5 -57.2931 4.3813 -33.2794 -57.29318307 33.5666 -78.75 -57.2931 6.5485 -32.9216 -57.29318309 33.5666 -75 -57.2931 8.6877 -32.4228 -57.29318311 33.5666 -71.25 -57.2931 10.7896 -31.7852 -57.29318313 33.5666 -67.5 -57.2931 12.8454 -31.0115 -57.29318315 33.5666 -63.75 -57.2931 14.8461 -30.1050 -57.29318317 33.5666 -60 -57.2931 16.7833 -29.0695 -57.29318319 33.5666 -56.25 -57.2931 18.6486 -27.9096 -57.29318321 33.5666 -52.5 -57.2931 20.4341 -26.6302 -57.29318323 33.5666 -48.75 -57.2931 22.1320 -25.2367 -57.29318325 33.5666 -45 -57.2931 23.7352 -23.7352 -57.29318327 33.5666 -41.25 -57.2931 25.2367 -22.1320 -57.29318329 33.5666 -37.5 -57.2931 26.6302 -20.4341 -57.29318331 33.5666 -33.75 -57.2931 27.9096 -18.6486 -57.29318333 33.5666 -30 -57.2931 29.0695 -16.7833 -57.29318335 33.5666 -26.25 -57.2931 30.1050 -14.8461 -57.29318337 33.5666 -22.5 -57.2931 31.0115 -12.8454 -57.29318339 33.5666 -18.75 -57.2931 31.7852 -10.7896 -57.29318341 33.5666 -15 -57.2931 32.4228 -8.6877 -57.29318343 33.5666 -11.25 -57.2931 32.9216 -6.5485 -57.29318345 33.5666 -7.5 -57.2931 33.2794 -4.3813 -57.29318347 33.5666 -3.75 -57.2931 33.4947 -2.1954 -57.29318349 33.5666 0 -57.2931 33.5666 0.0000 -57.29318351 33.5666 3.75 -57.2931 33.4947 2.1954 -57.29318353 33.5666 7.5 -57.2931 33.2794 4.3813 -57.29318355 33.5666 11.25 -57.2931 32.9216 6.5485 -57.29318357 33.5666 15 -57.2931 32.4228 8.6877 -57.29318359 33.5666 18.75 -57.2931 31.7852 10.7896 -57.29318361 33.5666 22.5 -57.2931 31.0115 12.8454 -57.29318363 33.5666 26.25 -57.2931 30.1050 14.8461 -57.29318365 33.5666 30 -57.2931 29.0695 16.7833 -57.29318367 33.5666 33.75 -57.2931 27.9096 18.6486 -57.29318369 33.5666 37.5 -57.2931 26.6302 20.4341 -57.29318371 33.5666 41.25 -57.2931 25.2367 22.1320 -57.29318373 33.5666 45 -57.2931 23.7352 23.7352 -57.29318375 33.5666 48.75 -57.2931 22.1320 25.2367 -57.29318377 33.5666 52.5 -57.2931 20.4341 26.6302 -57.29318379 33.5666 56.25 -57.2931 18.6486 27.9096 -57.29318381 33.5666 60 -57.2931 16.7833 29.0695 -57.29318383 33.5666 63.75 -57.2931 14.8461 30.1050 -57.29318385 33.5666 67.5 -57.2931 12.8454 31.0115 -57.29318387 33.5666 71.25 -57.2931 10.7896 31.7852 -57.29318389 33.5666 75 -57.2931 8.6877 32.4228 -57.29318391 33.5666 78.75 -57.2931 6.5485 32.9216 -57.29318393 33.5666 82.5 -57.2931 4.3813 33.2794 -57.29318395 33.5666 86.25 -57.2931 2.1954 33.4947 -57.29318397 33.5666 90 -57.2931 0.0000 33.5666 -57.2931

Focal Point975 0.0000 0.0000 -70.6700

Focal Point on Optical Axis974 0.0000 0.0000 -70.6700



Loading Case 1: Gravity at zenith (Face up)



642 -3.29E-04 2.02E-20 -1.74E-02 0.00E+00 3.29E-04 -1.74E-02643 -3.44E-04 -1.54E-05 -1.75E-02 -1.46E-04 3.12E-04 -1.75E-02644 -4.10E-04 -1.79E-05 -1.75E-02 -3.03E-04 2.77E-04 -1.75E-02645 -4.55E-04 -5.30E-06 -1.75E-02 -3.88E-04 2.38E-04 -1.75E-02646 -5.05E-04 3.19E-05 -1.75E-02 -4.76E-04 1.71E-04 -1.75E-02647 -3.76E-04 1.15E-04 -1.75E-02 -3.91E-04 -3.76E-05 -1.75E-02648 -2.77E-04 8.85E-05 -1.75E-02 -2.58E-04 -1.33E-04 -1.75E-02649 -2.27E-04 4.12E-05 -1.73E-02 -1.25E-04 -1.94E-04 -1.73E-02650 -2.32E-04 -1.42E-20 -1.72E-02 0.00E+00 -2.32E-04 -1.72E-02

Corrector CG997 0.00E+00 6.87E-05 -1.74E-02

Corrector CG on Optical Axis987 0.00E+00 2.57E-03 -1.26E-02



8301 -8.59E-04 5.26E-20 -1.74E-02 0.00E+00 8.59E-04 -1.74E-028303 -8.44E-04 6.86E-05 -1.74E-02 1.32E-05 8.47E-04 -1.74E-028305 -7.99E-04 1.35E-04 -1.74E-02 2.96E-05 8.10E-04 -1.74E-028307 -7.44E-04 2.02E-04 -1.74E-02 5.32E-05 7.69E-04 -1.74E-028309 -6.50E-04 2.65E-04 -1.74E-02 8.73E-05 6.96E-04 -1.74E-028311 -5.19E-04 3.20E-04 -1.75E-02 1.36E-04 5.95E-04 -1.75E-028313 -3.57E-04 3.65E-04 -1.75E-02 2.01E-04 4.69E-04 -1.75E-028315 -1.94E-04 3.87E-04 -1.75E-02 2.61E-04 3.45E-04 -1.75E-028317 -4.06E-05 3.99E-04 -1.75E-02 3.25E-04 2.35E-04 -1.75E-028319 9.85E-05 4.01E-04 -1.75E-02 3.88E-04 1.41E-04 -1.75E-028321 2.22E-04 3.95E-04 -1.74E-02 4.49E-04 6.42E-05 -1.74E-028323 3.45E-04 3.81E-04 -1.74E-02 5.14E-04 -7.90E-06 -1.74E-028325 4.69E-04 3.59E-04 -1.73E-02 5.86E-04 -7.79E-05 -1.73E-028327 5.92E-04 3.29E-04 -1.73E-02 6.62E-04 -1.43E-04 -1.73E-028329 7.09E-04 2.91E-04 -1.73E-02 7.39E-04 -2.01E-04 -1.73E-028331 8.25E-04 2.38E-04 -1.72E-02 8.19E-04 -2.60E-04 -1.72E-028333 9.34E-04 1.79E-04 -1.72E-02 8.98E-04 -3.12E-04 -1.72E-028335 1.03E-03 1.12E-04 -1.72E-02 9.72E-04 -3.54E-04 -1.72E-028337 1.10E-03 3.96E-05 -1.72E-02 1.03E-03 -3.85E-04 -1.72E-028339 1.15E-03 -4.35E-05 -1.73E-02 1.07E-03 -4.10E-04 -1.73E-028341 1.16E-03 -1.29E-04 -1.73E-02 1.09E-03 -4.25E-04 -1.73E-028343 1.14E-03 -2.14E-04 -1.73E-02 1.08E-03 -4.32E-04 -1.73E-028345 1.08E-03 -2.96E-04 -1.74E-02 1.03E-03 -4.35E-04 -1.74E-028347 9.74E-04 -3.73E-04 -1.74E-02 9.47E-04 -4.36E-04 -1.74E-028349 8.15E-04 -4.41E-04 -1.74E-02 8.15E-04 -4.41E-04 -1.74E-028351 6.08E-04 -4.97E-04 -1.74E-02 6.39E-04 -4.56E-04 -1.74E-028353 3.63E-04 -5.38E-04 -1.74E-02 4.30E-04 -4.86E-04 -1.74E-028355 9.73E-05 -5.39E-04 -1.74E-02 2.01E-04 -5.10E-04 -1.74E-028357 -1.53E-04 -5.23E-04 -1.74E-02 -1.25E-05 -5.44E-04 -1.74E-028359 -3.74E-04 -4.90E-04 -1.74E-02 -1.96E-04 -5.85E-04 -1.74E-028361 -5.53E-04 -4.45E-04 -1.74E-02 -3.41E-04 -6.23E-04 -1.74E-028363 -7.09E-04 -3.83E-04 -1.74E-02 -4.67E-04 -6.57E-04 -1.74E-028365 -8.25E-04 -3.11E-04 -1.75E-02 -5.59E-04 -6.82E-04 -1.75E-028367 -8.93E-04 -2.34E-04 -1.75E-02 -6.13E-04 -6.91E-04 -1.75E-028369 -9.11E-04 -1.53E-04 -1.75E-02 -6.30E-04 -6.77E-04 -1.75E-028371 -8.92E-04 -6.98E-05 -1.75E-02 -6.24E-04 -6.40E-04 -1.75E-028373 -8.14E-04 1.06E-05 -1.75E-02 -5.83E-04 -5.68E-04 -1.75E-028375 -6.84E-04 8.41E-05 -1.75E-02 -5.14E-04 -4.59E-04 -1.75E-028377 -5.08E-04 1.47E-04 -1.76E-02 -4.26E-04 -3.13E-04 -1.76E-028379 -3.22E-04 1.77E-04 -1.76E-02 -3.27E-04 -1.70E-04 -1.76E-028381 -1.44E-04 1.95E-04 -1.76E-02 -2.41E-04 -2.67E-05 -1.76E-028383 1.77E-05 2.02E-04 -1.76E-02 -1.73E-04 1.05E-04 -1.76E-028385 1.54E-04 1.98E-04 -1.75E-02 -1.24E-04 2.18E-04 -1.75E-028387 2.71E-04 1.80E-04 -1.75E-02 -8.36E-05 3.15E-04 -1.75E-028389 3.74E-04 1.55E-04 -1.74E-02 -5.28E-05 4.01E-04 -1.74E-028391 4.56E-04 1.23E-04 -1.74E-02 -3.18E-05 4.71E-04 -1.74E-028393 5.14E-04 8.68E-05 -1.74E-02 -1.90E-05 5.21E-04 -1.74E-028395 5.48E-04 4.42E-05 -1.73E-02 -8.25E-06 5.50E-04 -1.73E-028397 5.59E-04 3.43E-20 -1.73E-02 0.00E+00 5.59E-04 -1.73E-02

Focal Point975 0.00E+00 -1.18E-04 -1.75E-02

Focal Point on Optical Axis974 0.00E+00 1.71E-03 -1.26E-02




Loading Case 2: Gravity at horizon (Face side)



642 4.18E-03 -2.56E-19 -5.70E-04 0.00E+00 -4.18E-03 -5.70E-04643 3.84E-03 -1.58E-03 -5.69E-04 1.38E-05 -4.16E-03 -5.69E-04644 2.92E-03 -2.91E-03 -4.96E-04 1.06E-05 -4.12E-03 -4.96E-04645 2.19E-03 -3.47E-03 -4.60E-04 3.05E-06 -4.10E-03 -4.60E-04646 1.13E-03 -3.93E-03 -4.16E-04 -9.29E-06 -4.09E-03 -4.16E-04647 -1.58E-03 -3.76E-03 -3.32E-04 -2.42E-05 -4.08E-03 -3.32E-04648 -2.92E-03 -2.88E-03 -1.80E-04 -2.88E-05 -4.11E-03 -1.80E-04649 -3.83E-03 -1.56E-03 -4.84E-05 -2.09E-05 -4.14E-03 -4.84E-05650 -4.16E-03 -2.55E-19 -3.02E-05 0.00E+00 -4.16E-03 -3.02E-05

Corrector CG997 0.00E+00 -4.18E-03 -3.37E-04

Corrector CG on Optical Axis987 0.00E+00 -3.72E-03 4.63E-04



8301 4.34E-03 -2.66E-19 -4.05E-04 0.00E+00 -4.34E-03 -4.05E-048303 4.32E-03 -2.91E-04 -4.00E-04 -7.85E-06 -4.33E-03 -4.00E-048305 4.27E-03 -5.80E-04 -3.84E-04 -1.73E-05 -4.31E-03 -3.84E-048307 4.22E-03 -8.71E-04 -3.46E-04 -3.17E-05 -4.31E-03 -3.46E-048309 4.12E-03 -1.16E-03 -2.96E-04 -5.10E-05 -4.28E-03 -2.96E-048311 3.99E-03 -1.44E-03 -2.38E-04 -7.81E-05 -4.24E-03 -2.38E-048313 3.82E-03 -1.71E-03 -1.77E-04 -1.15E-04 -4.18E-03 -1.77E-048315 3.65E-03 -1.95E-03 -9.90E-05 -1.40E-04 -4.13E-03 -9.90E-058317 3.49E-03 -2.19E-03 -5.64E-05 -1.49E-04 -4.12E-03 -5.64E-058319 3.36E-03 -2.41E-03 -5.30E-05 -1.41E-04 -4.13E-03 -5.30E-058321 3.23E-03 -2.63E-03 -8.08E-05 -1.16E-04 -4.17E-03 -8.08E-058323 3.12E-03 -2.84E-03 -1.01E-04 -8.25E-05 -4.22E-03 -1.01E-048325 3.00E-03 -3.05E-03 -1.35E-04 -3.69E-05 -4.27E-03 -1.35E-048327 2.86E-03 -3.25E-03 -1.73E-04 1.34E-05 -4.33E-03 -1.73E-048329 2.71E-03 -3.43E-03 -2.10E-04 6.08E-05 -4.38E-03 -2.10E-048331 2.54E-03 -3.62E-03 -2.42E-04 1.02E-04 -4.42E-03 -2.42E-048333 2.34E-03 -3.79E-03 -2.76E-04 1.36E-04 -4.45E-03 -2.76E-048335 2.12E-03 -3.95E-03 -3.11E-04 1.55E-04 -4.48E-03 -3.11E-048337 1.86E-03 -4.09E-03 -3.43E-04 1.56E-04 -4.49E-03 -3.43E-048339 1.58E-03 -4.22E-03 -3.69E-04 1.43E-04 -4.50E-03 -3.69E-048341 1.27E-03 -4.32E-03 -3.91E-04 1.07E-04 -4.50E-03 -3.91E-048343 9.26E-04 -4.41E-03 -4.13E-04 4.83E-05 -4.50E-03 -4.13E-048345 5.58E-04 -4.47E-03 -4.35E-04 -3.02E-05 -4.50E-03 -4.35E-048347 1.75E-04 -4.50E-03 -4.51E-04 -1.20E-04 -4.51E-03 -4.51E-048349 -2.27E-04 -4.51E-03 -4.59E-04 -2.27E-04 -4.51E-03 -4.59E-048351 -6.40E-04 -4.48E-03 -4.64E-04 -3.46E-04 -4.52E-03 -4.64E-048353 -1.05E-03 -4.43E-03 -4.67E-04 -4.67E-04 -4.53E-03 -4.67E-048355 -1.45E-03 -4.33E-03 -4.72E-04 -5.81E-04 -4.53E-03 -4.72E-048357 -1.82E-03 -4.21E-03 -4.74E-04 -6.69E-04 -4.54E-03 -4.74E-048359 -2.15E-03 -4.06E-03 -4.75E-04 -7.26E-04 -4.54E-03 -4.75E-048361 -2.43E-03 -3.90E-03 -4.77E-04 -7.51E-04 -4.53E-03 -4.77E-048363 -2.68E-03 -3.71E-03 -4.86E-04 -7.60E-04 -4.52E-03 -4.86E-048365 -2.89E-03 -3.52E-03 -4.95E-04 -7.41E-04 -4.49E-03 -4.95E-048367 -3.05E-03 -3.31E-03 -5.01E-04 -6.98E-04 -4.44E-03 -5.01E-048369 -3.17E-03 -3.09E-03 -5.01E-04 -6.37E-04 -4.38E-03 -5.01E-048371 -3.27E-03 -2.86E-03 -5.10E-04 -5.69E-04 -4.30E-03 -5.10E-048373 -3.31E-03 -2.63E-03 -5.26E-04 -4.83E-04 -4.20E-03 -5.26E-048375 -3.32E-03 -2.40E-03 -5.38E-04 -3.88E-04 -4.08E-03 -5.38E-048377 -3.31E-03 -2.17E-03 -5.37E-04 -2.94E-04 -3.94E-03 -5.37E-048379 -3.29E-03 -1.95E-03 -5.50E-04 -2.06E-04 -3.82E-03 -5.50E-048381 -3.26E-03 -1.73E-03 -5.38E-04 -1.35E-04 -3.69E-03 -5.38E-048383 -3.25E-03 -1.51E-03 -4.92E-04 -8.39E-05 -3.58E-03 -4.92E-048385 -3.25E-03 -1.29E-03 -4.11E-04 -5.22E-05 -3.49E-03 -4.11E-048387 -3.25E-03 -1.07E-03 -3.47E-04 -3.00E-05 -3.43E-03 -3.47E-048389 -3.26E-03 -8.57E-04 -2.87E-04 -1.51E-05 -3.37E-03 -2.87E-048391 -3.26E-03 -6.41E-04 -2.35E-04 -6.60E-06 -3.32E-03 -2.35E-048393 -3.26E-03 -4.26E-04 -1.93E-04 -3.16E-06 -3.29E-03 -1.93E-048395 -3.26E-03 -2.13E-04 -1.69E-04 -8.91E-07 -3.27E-03 -1.69E-048397 -3.26E-03 -2.00E-19 -1.61E-04 0.00E+00 -3.26E-03 -1.61E-04

Focal Point975 0.00E+00 -4.42E-03 -3.51E-04

Focal Point on Optical Axis974 0.00E+00 -1.52E-03 4.63E-04


Figure 1 – Isometric View of Model 2 – Telescope with New Binospec Spectrograph

Mass of instrument(exclude mounting flange and electronics boxes)

Focal point

Mass of one electronics box

Instrument mounting flange

Instrument rotator bearing

Wide-field corrector CG

Vertex of primary mirror

Optical axis

Mass of instrument(exclude mounting flange and electronics boxes)

Focal point

Mass of one electronics box

Instrument mounting flange

Instrument rotator bearing

Wide-field corrector CG

Vertex of primary mirror

Optical axis

Figure 2 – Isometric View of Model 2 near Instrument Rotator

Figure 3 – Deformed Shape (x500) for Face Up Gravity – Model 2

Figure 4 – Deformed Shape (x500) for Face Up Gravity – Model 2 near Instrument Rotator

Figure 5 – Deformed Shape (x500) for Face Side Gravity – Model 2

Figure 6 – Deformed Shape (x500) for Face Up Gravity – Model 2 near Instrument Rotator

Distortion after removal of rigid body motion for gravity face side minus gravity face up

-0.0008

-0.0006

-0.0004

-0.0002

0

0.0002

0.0004

0.0006

0.0008

-100 -80 -60 -40 -20 0 20 40 60 80 100

Angle (Deg.)

Out

-of-p

lane

( ∆z)

dis

torti

on (i

n.)

Instrument rotator support flange Outer raceInner race Instrument flangeWide-field corrector mounting flange

Figure 7 – Out-of-Plane Distortions – Face Side Gravity Minus Face Up Gravity – Model 1


-0.0018-0.0016-0.0014-0.0012

-0.001-0.0008-0.0006-0.0004-0.0002

00.00020.00040.00060.0008

0.0010.00120.00140.00160.0018

-100 -80 -60 -40 -20 0 20 40 60 80 100

Angle (Deg.)

Out

-of-r

ound

( ∆r)

dis

torti

on (i

n.)


Figure 8 – Out-of-Round Distortions – Face Side Gravity Minus Face Up Gravity – Model 1


-0.0008

-0.0006

-0.0004

-0.0002

0

0.0002

0.0004

0.0006

0.0008

-100 -80 -60 -40 -20 0 20 40 60 80 100

Angle (Deg.)

Out

-of-p

lane

(∆

z) d

isto

rtion

(in.

)


Figure 9 – Out-of-Plane Distortions – Face Side Gravity Minus Face Up Gravity – Model 2


-0.0018-0.0016-0.0014-0.0012

-0.001-0.0008-0.0006-0.0004-0.0002

00.00020.00040.00060.0008

0.0010.00120.00140.00160.0018

-100 -80 -60 -40 -20 0 20 40 60 80 100

Angle (Deg.)

Out

-of-r

ound

(∆

r) di

stor

tion

(in.)


Figure 10 – Out-of-Round Distortions – Face Side Gravity Minus Face Up Gravity – Model 2

Distortion after removal of rigid body motion for gravity face side

-0.0008

-0.0006

-0.0004

-0.0002

0

0.0002

0.0004

0.0006

0.0008

-100 -80 -60 -40 -20 0 20 40 60 80 100

Angle (Deg.)

Out

-of-p

lane

( ∆z)

dis

torti

on (i

n.)


Figure 11 – Out-of-Plane Distortions – Face Side Gravity– Model 1


-0.0018-0.0016-0.0014-0.0012

-0.001-0.0008-0.0006-0.0004-0.0002

00.00020.00040.00060.0008

0.0010.00120.00140.00160.0018

-100 -80 -60 -40 -20 0 20 40 60 80 100

Angle (Deg.)

Out

-of-r

ound

( ∆r)

dis

torti

on (i

n.)


Figure 12 – Out-of-Round Distortions – Face Side Gravity– Model 1

Distortion after removal of rigid body motion for gravity face up

-0.0008

-0.0006

-0.0004

-0.0002

0

0.0002

0.0004

0.0006

0.0008

-100 -80 -60 -40 -20 0 20 40 60 80 100

Angle (Deg.)

Out

-of-p

lane

( ∆z)

dis

torti

on (i

n.)


Figure 13 – Out-of-Plane Distortions – Face Up Gravity– Model 1


-0.0018-0.0016-0.0014-0.0012

-0.001-0.0008-0.0006-0.0004-0.0002

00.00020.00040.00060.0008

0.0010.00120.00140.00160.0018

-100 -80 -60 -40 -20 0 20 40 60 80 100

Angle (Deg.)

Out

-of-r

ound

( ∆r)

dis

torti

on (i

n.)


Figure 14 – Out-of-Round Distortions – Face Up Gravity– Model 1


-0.0008

-0.0006

-0.0004

-0.0002

0

0.0002

0.0004

0.0006

0.0008

-100 -80 -60 -40 -20 0 20 40 60 80 100

Angle (Deg.)

Out

-of-p

lane

(∆

z) d

isto

rtion

(in.

)


Figure 15 – Out-of-Plane Distortions – Face Side Gravity– Model 2


-0.0018-0.0016-0.0014-0.0012

-0.001-0.0008-0.0006-0.0004-0.0002

00.00020.00040.00060.0008

0.0010.00120.00140.00160.0018

-100 -80 -60 -40 -20 0 20 40 60 80 100

Angle (Deg.)

Out

-of-r

ound

(∆

r) di

stor

tion

(in.)


Figure 16 – Out-of-Round Distortions – Face Side Gravity– Model 2


-0.0008

-0.0006

-0.0004

-0.0002

0

0.0002

0.0004

0.0006

0.0008

-100 -80 -60 -40 -20 0 20 40 60 80 100

Angle (Deg.)

Out

-of-p

lane

(∆

z) d

isto

rtion

(in.

)


Figure 17 – Out-of-Plane Distortions – Face Up Gravity– Model 2


-0.0018-0.0016-0.0014-0.0012

-0.001-0.0008-0.0006-0.0004-0.0002

00.00020.00040.00060.0008

0.0010.00120.00140.00160.0018

-100 -80 -60 -40 -20 0 20 40 60 80 100

Angle (Deg.)

Out

-of-r

ound

(∆

r) di

stor

tion

(in.)


Figure 18 – Out-of-Round Distortions – Face Up Gravity– Model 2

Figure 19 – von Mises Stress (psi) in Instrument Rotator Support Flange and Adjacent Region – Face Up Gravity – Model 1

Figure 20 – von Mises Stress (psi) in Instrument Rotator Support Flange and Adjacent Region – Face Side Gravity – Model 1

Figure 21 – von Mises Stress (psi) in Instrument Rotator Support Flange and Adjacent Region – Face Up Gravity – Model 2

Figure 22 – von Mises Stress (psi) in Instrument Rotator Support Flange and Adjacent Region – Face Side Gravity – Model 2

APPENDIX A

INFORMATION FROM SAO

APPENDIX B

INFORMATION FROM AVON BEARINGS

Frank W. Kan

From: Dick Herbst [[email protected]]

Sent: Monday, March 27, 2006 5:38 PM

To: Frank W. Kan

Subject: RE: Bearing for MMT Instrument Rotator

Attachments: R1572A1.DWG; R1572A1-Part1.rtf; R1572A1-Part2.rtf; R1572A1-Part3.rtf; R1572A1-LoadCase1.rtf; R1572A1-LoadCase2.rtf

4/21/2006

Frank, Attached is our drawing (part number R1572A1) of the bearing we made for the MMT Instrument Rotator. Also attached are sheets showing Avon’s general static ratings for the bearing, the bolts, and the gear and two sheets showing static safety factors for the two combined load conditions “6,000 lbs. axial and 17,500 ft-lbs moment” and “6,000 lbs radial and 17,500 ft-lbs moment. As you can see there is more than adequate static capacity for your loading conditions. Finally I ran our Genrol Rolling Element Bearing Analysis Program as you requested to get the following data: Theoretical L-10 life at 4 rpm continuous with applied loading of 6,000 lbs radial and 17,500 ft-lbs moment is 235,700 hrs Theoretical L-10 life at 4 rpm continuous with applied loading of 6,000 lbs axial and 17,500ft-lbs moment is 238,680 hrs Prorated life with each above load cases applied 50% of the time is 237,180 hrs Moment stiffness with .0005 preload and load case 1 applied 6.7208E+10 in-lb / rad Moment stiffness with .0005 preload and load case 2 applied 6.8658E+10 in-lbs / rad Theoretical turning torque 2,280 ft-lbs If there is anything else you need let me know. Also, if you need the raw data and Genrol computer run I can try to send it to you but it is rather long and has a lot of data that is probably of no use to you. Dick

From: Frank W. Kan [mailto:[email protected]] Sent: Monday, March 13, 2006 12:26 PM To: [email protected] Cc: Andrew T. Sarawit Subject: Bearing for MMT Instrument Rotator Dear Mr. Herbst Thank you for talking to me on the phone. As I have mentioned on the phone, Smithsonian Astrophysical Observatory has contacted us to evaluate the effect of a new instrument with larger weight and new CG which results in a larger overturning moment on the bearing. Attached is a pdf file which contains the original bearing specifications. For the new loading, item 2 “15000 pound feet” will increase to “17,500 pound feet” and the rest of the loadings remain unchanged. Please let me know if you can evaluate whether the existing bearing can support the new loading or not. Thanks Frank W. Kan, P.E. Principal Simpson Gumpertz & Heger Inc. Consulting Engineers 41 Seyon Street, Building #1, Suite 500 Waltham, MA 02453 (781) 907-9000 main (781) 907-9233 direct

AVON BEARINGS CORPORATION 1500 Nagle Road Avon, Ohio 44011

CROSS-ROLLER ANALYSIS

Avon Part Number: R1572A1 Customer: Simpson Gumpertz & Heger Inc. Date: 3/24/2006 Reference No.: Application: MMT Instrument Rotator Run By: reh

I. BEARING ANALYSIS:

A. Bearing Description Roll Dia. Eff. Length Pitch Dia. No. of Rollers Contact Angle Bearing IDC (inches) (inches) (inches) Total Row1 Row2 (degrees) (inches) 1.500 1.100 72.070 120 60 60 45.000 -0.0020

B. Bearing Analysis Results Axial Moment Radial 1. Static Ratings: (lbs) (ft-lbs) (lbs)

Frequent Static Loading: 702,184 843,440 280,874 Intermittent Heavy Duty: 1,053,912 1,265,924 421,565 Theoretical Stress Limit: 1,405,945 1,688,775 562,378 ABMA 1990: 2,215,851 2,661,606 886,340

2. L10 Dynamic Capacity (at 1 Million Revolutions)

Radial: 207,249 (lbs) Axial: 518,122 (lbs)

* The above table is intended to indicate the general capacity of this bearing under a single loaded axis and is not intended for any particular application. Contact Avon Bearings Engineering for multi-axis computer analysis of your required loadings.

Friday, March 24, 2006




II. BOLT ANALYSIS:

A. Bolt Description Bolt Bolt Circle Size Number of Diameter (inches) (Holes) (inches)

Inner Race: 0.750 24 72.000 Outer Race: 0.750 32 76.490

B. Bolt Analysis Results

Fatigue Load Intermittent One Time Max Rating Rating Rating (ft-lbs) (ft-lbs) (ft-lbs)

Inner Race: 384,761 641,268 824,671 Outer Race: 545,007 908,344 1,168,131

* The overturning moment capacity of the bolt pattern indicated is based on ASTM Grade 8 bolts and a safety factor as per Avon Spec. No. BES-5-2-070. Please refer to this specification to interpret bolt capacity information.





III. GEAR ANALYSIS

A. Gear Description

Face Pressure Width Gear Tooth Number of Gear Angle (inches) Type Form Teeth Pitch (degrees)

0.500 O FULL DEPTH 312 4.000 20

B. Gear Analysis Results 285 BHN (lbs)

Tangential Tooth Load: 2,080

* Tangential Tooth Load Capacity using the Lewis Equation and Allowable Stress Levels of 25% of Tensile Strength





IV. STATIC LOAD ANALYSIS Condition: 1

A. Load Description

Time Thrust Radial Moment Rotational (Percent) (lbs) (lbs) (ft-lbs) Speed(rpm)

50.000 6,000 0 17,500 4.000

B. Load Analysis Results Static Safety Factor

Frequenct Static Loading: 7.511 Intermittent Heavy Duty: 11.273 Theoretical Stress Limit: 15.039 ABMA 1990: 23.702





IV. STATIC LOAD ANALYSIS Condition: 2

A. Load Description

Time Thrust Radial Moment Rotational (Percent) (lbs) (lbs) (ft-lbs) Speed(rpm)

50.000 0 6,000 17,500 4.000

B. Load Analysis Results Static Safety Factor

Frequenct Static Loading: 6.473 Intermittent Heavy Duty: 9.715 Theoretical Stress Limit: 12.960 ABMA 1990: 20.425


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