1

HELMRI Primary Support

• General Requirements– OD = 1.7 m (66.929 inches)

– Thickness = 10.16 cm (4.0 inches)

– Rsph = 7.7 m (303.149 inches)

– Lateral Support: 14° tilt during testing, try to use tangent rods.

2

Axial Support, Starting Point … Nelson 36 point

• Nelson predicts 6.54 nm-rms with 36 support points

drc = 0.01745

Diameter 66.929 inches Weight = 1294.69 Lbs D = 74702886Thickness 4 inches u = 5.577417density 0.092 Lb/in^3 K = 5.5modulus 1.32E+07 psi Gamma= 1.89E-03mu = 0.24N = 36 Surf rms = 1.80E-07 inches = 4.58 nm-rms

Row Radius Clocking Number Load/ptinches degrees Lbs

1 8.597 0.00 6 36.0572 19.312 15.18 6 39.1003 19.312 44.82 6 39.1004 29.549 9.76 6 33.4255 29.563 30.00 6 34.6766 29.549 50.24 6 33.425

Total = 1294.69

Uniform Support forces are preferable

Use three rings, round off angles

3

• Nelson 36 point support, simplified somewhat1

X Y

Z

HELMRI Primary 120 deg Segment, Axial Support Optimization60° sector model used for optimizing actuator locations (with uniform support forces).

4

• Initial Deformation (Simplified Nelson Support)– 7.87 nm-rms

5

FEM results, all support forces identical

• Results of row positioning iterations:– FEM results use 120% of glass density

• 5.84/1.2 = 4.87 nm-rms compared to 4.58 nm-rms Nelson optimized value.

Surface Focus CoefTRIAL R1 R2 R3 nm-rms waves

1 8.6 19.3 29.5 7.872 8 19.3 30 6.063 8.3 19.3 30.2 64 8.3 19.3 30.5 5.93 0.625 8.3 19.3 30.8 5.87 0.736 8.3 19.3 31.2 5.84 0.90

Nelson 4.58 nm-rms

6

• Result at trial 6, 5.84 nm-rms

7

Full Mirror Model

• Full model is based on case 4– Slightly more rms distortion than cases 5 or 6 but less power.

8

– The full mirror model.

1

X Y

Z

HELMRI Primary, Axial and Lateral Loads

9

Full Mirror Analysis Results

• 1 g Z, Surface is 5.88 nm-rms

10

1 g Lateral on 3 tangent rods

• 1 g lateral load, 219 nm-rms (would be 53 nm-rms at 14°)

11

1 g lateral on strap (uniform radial support force)

• 1 g gives 47 nm-rms surface (14° tilt gives 11.4 nm-rms)

Gravity vector

Supported edge

12

Net Performance

• Mirror support force errors.– Actuator error force magnitudes:

• Pneumatic rolling diaphragm MMT f/5 axial units (passive):– Fr, Ft ~ 0.007*Fax = 0.31 lbs– Fax ~ 0.27 Lbs– Mr, Mt ~ 0.016*Fax = 0.71 in-lbs– Mz ~ 0.8 in-lbs

• Active actuators (closed loop on figure optional) can reduce axial error force to 0.07 Lbs or less.

– Random error effects (random distribution) shown on next slide.– Systematic and low order effects are probably worse:

• Systematic force distributions can be caused by:– Cell deflection (print through)– Temperature change– Friction and movement.

• Low order effects:– Probability of random forces having a significant astigmatic or other low

order component is quite good.

13

Random Error Force Effects, Preliminary

• nm-rms P-V, waves Error nm-rms P-Vsurface surface Number Force waves

1 g Z 5.88 0.055 1 1 5.88 0.055 1 g y 219.18 1.879 0 0.24 0.00 0.0001g y strap 47.16 0.483 1 0.24 11.41 0.117 1 Lb Fr at an outer actuator rmax = 100.00 0.66 0.007 18 0.31 0.86 0.010 1 Lb Ft at an outer actuator rmax = 100.00 0.60 0.007 18 0.31 0.79 0.009 1 Lb Fz at an outer actuator rmax = 100.00 15.57 0.130 18 0.27 17.84 0.149 1 in-Lb Mr at an outer actuat rmax = 100.00 0.68 0.007 18 0.71 2.04 0.020 1 in-Lb Mt at an outer actuat rmax = 100.00 0.30 0.004 18 0.71 0.92 0.011 1 in-Lb Mz at an outer actuat rmax = 100.00 0.04 0.000 18 0.8 0.12 0.001 1 Lb Fr at an inner actuator rmax = 100.00 0.69 0.006 6 0.31 0.52 0.004 1 Lb Ft at an inner actuator rmax = 100.00 0.70 0.006 6 0.31 0.53 0.004 1 Lb Fz at an inner actuator rmax = 100.00 2.80 0.028 6 0.27 1.85 0.018 1 in-Lb Mr at an inner actuat rmax = 100.00 0.31 0.002 6 0.71 0.54 0.004 1 in-Lb Mt at an inner actuat rmax = 100.00 0.31 0.002 6 0.71 0.53 0.004 1 in-Lb Mz at an inner actuat rmax = 100.00 0.02 0.000 6 0.8 0.04 0.000 1 Lb Fr at an intermediate ac rmax = 100.00 0.35 0.003 12 0.31 0.38 0.004 1 Lb Ft at an intermediate ac rmax = 100.00 1.00 0.008 12 0.31 1.07 0.008 1 Lb Fz at an intermediate ac rmax = 100.00 7.93 0.064 12 0.27 7.41 0.060 1 in-Lb Mr at an intermediate rmax = 100.00 0.58 0.005 12 0.71 1.43 0.011 1 in-Lb Mt at an intermediate rmax = 100.00 0.17 0.001 12 0.71 0.41 0.003 1 in-Lb Mz at an intermediate rmax = 100.00 0.01 0.000 12 0.8 0.02 0.000

1 sigma astigmatism (Fz)10.14 1 0.27 2.74 0.0221 sigma 3 theta (Fz) 4.86 1 0.27 1.31 0.0101 sigma spherical (Fz) 1.14 1 0.27 0.31 0.002

23.70 0.210

Net Surface

Zenith pointing, net surface =

Lateral on tangent rods not included

Axial force errors are the major contributors

14

Effect of using a force loop to control axial force

nm-rms P-V, waves Error nm-rms P-Vsurface surface Number Force waves

1 g Z 5.88 0.055 1 1 5.88 0.055 1 g y 219.18 1.879 0 0.24 0.00 0.0001g y strap 47.16 0.483 1 0.24 11.41 0.117 1 Lb Fr at an outer actuator rmax = 100.00 0.66 0.007 18 0.31 0.86 0.010 1 Lb Ft at an outer actuator rmax = 100.00 0.60 0.007 18 0.31 0.79 0.009 1 Lb Fz at an outer actuator rmax = 100.00 15.57 0.130 18 0.07 4.62 0.039 1 in-Lb Mr at an outer actuat rmax = 100.00 0.68 0.007 18 0.71 2.04 0.020 1 in-Lb Mt at an outer actuat rmax = 100.00 0.30 0.004 18 0.71 0.92 0.011 1 in-Lb Mz at an outer actuat rmax = 100.00 0.04 0.000 18 0.8 0.12 0.001 1 Lb Fr at an inner actuator rmax = 100.00 0.69 0.006 6 0.31 0.52 0.004 1 Lb Ft at an inner actuator rmax = 100.00 0.70 0.006 6 0.31 0.53 0.004 1 Lb Fz at an inner actuator rmax = 100.00 2.80 0.028 6 0.07 0.48 0.005 1 in-Lb Mr at an inner actuat rmax = 100.00 0.31 0.002 6 0.71 0.54 0.004 1 in-Lb Mt at an inner actuat rmax = 100.00 0.31 0.002 6 0.71 0.53 0.004 1 in-Lb Mz at an inner actuat rmax = 100.00 0.02 0.000 6 0.8 0.04 0.000 1 Lb Fr at an intermediate ac rmax = 100.00 0.35 0.003 12 0.31 0.38 0.004 1 Lb Ft at an intermediate ac rmax = 100.00 1.00 0.008 12 0.31 1.07 0.008 1 Lb Fz at an intermediate ac rmax = 100.00 7.93 0.064 12 0.07 1.92 0.015 1 in-Lb Mr at an intermediate rmax = 100.00 0.58 0.005 12 0.71 1.43 0.011 1 in-Lb Mt at an intermediate rmax = 100.00 0.17 0.001 12 0.71 0.41 0.003 1 in-Lb Mz at an intermediate rmax = 100.00 0.01 0.000 12 0.8 0.02 0.0001 sigma astigmatism (Fz) 10.14 1 0.07 0.71 0.0061 sigma 3 theta (Fz) 4.86 1 0.07 0.34 0.0031 sigma spherical (Fz) 1.14 1 0.07 0.08 0.0006

14.2 0.14

Net Surface

Zenith pointing, net surface =

Lateral on tangent rods not included

Axial force errors have been reduced to 0.07 Lbs

15

Customer Support Arrangement

• 1 g z uniform support forces, 6.4 nm-rms surface

16

Customer Support Arrangement

• 1 g z optimized axial support forces, 3.8 nm-rms surface

17

1 g Z (Z is normal to C/L of mirror)

• Optimized Support Forces– Customer geometry

– Zenith Pointing

– Mirror weight = 1590.44 Lbs

Node Row Angle Nominal Trim NetLbs Lbs Lbs

125 inner 30 44.179 -1.027 43.152365 inner 90 44.179 -1.030 43.149605 inner 150 44.179 -1.031 43.148845 inner 210 44.179 -1.027 43.152

1085 inner 270 44.179 -1.030 43.1491325 inner 330 44.179 -1.023 43.156

9 Intermed. 0 44.179 5.826 50.005129 Intermed. 30 44.179 5.178 49.357249 Intermed. 60 44.179 5.838 50.017369 Intermed. 90 44.179 5.177 49.356489 Intermed. 120 44.179 5.835 50.014609 Intermed. 150 44.179 5.179 49.358729 Intermed. 180 44.179 5.834 50.013849 Intermed. 210 44.179 5.176 49.355969 Intermed. 240 44.179 5.837 50.016

1089 Intermed. 270 44.179 5.173 49.3521209 Intermed. 300 44.179 5.846 50.0251329 Intermed. 330 44.179 5.161 49.340

53 outer 10 44.179 -3.343 40.836133 30 44.179 -3.292 40.887213 50 44.179 -3.330 40.849293 70 44.179 -3.345 40.834453 110 44.179 -3.341 40.838533 130 44.179 -3.338 40.841613 150 44.179 -3.285 40.894693 170 44.179 -3.339 40.840773 190 44.179 -3.340 40.839933 230 44.179 -3.341 40.838

1013 250 44.179 -3.337 40.8421093 270 44.179 -3.287 40.8921173 290 44.179 -3.332 40.8471253 310 44.179 -3.348 40.8311413 350 44.179 -3.318 40.861

373 40.854853 40.854

1333 40.854

CONSTRAINED NODES

18

1 g Lateral Loading, Optimized Fr, Ft at 6 Locations

• Surface figure = 9.56 nm-rms, 0.256 P-V

19

Preliminary Performance Evaluation, Telescope

nm-rms P-V, waves Error nm-rms P-Vsurface surface Number Force waves

1 g Z 3.82 0.031 1 1 3.82 0.031 1 g y 9.56 0.256 1 1.00 9.56 0.2561g y strap 47.16 0.483 1 0.24 11.41 0.117 1 Lb Fr at an outer actuator rmax = 100.00 0.66 0.007 18 0.31 0.86 0.010 1 Lb Ft at an outer actuator rmax = 100.00 0.60 0.007 18 0.31 0.79 0.009 1 Lb Fz at an outer actuator rmax = 100.00 15.57 0.130 18 0.07 4.62 0.039 1 in-Lb Mr at an outer actuat rmax = 100.00 0.68 0.007 18 0.71 2.04 0.020 1 in-Lb Mt at an outer actuat rmax = 100.00 0.30 0.004 18 0.71 0.92 0.011 1 in-Lb Mz at an outer actuat rmax = 100.00 0.04 0.000 18 0.8 0.12 0.001 1 Lb Fr at an inner actuator rmax = 100.00 0.69 0.006 6 0.31 0.52 0.004 1 Lb Ft at an inner actuator rmax = 100.00 0.70 0.006 6 0.31 0.53 0.004 1 Lb Fz at an inner actuator rmax = 100.00 2.80 0.028 6 0.07 0.48 0.005 1 in-Lb Mr at an inner actuat rmax = 100.00 0.31 0.002 6 0.71 0.54 0.004 1 in-Lb Mt at an inner actuat rmax = 100.00 0.31 0.002 6 0.71 0.53 0.004 1 in-Lb Mz at an inner actuat rmax = 100.00 0.02 0.000 6 0.8 0.04 0.000 1 Lb Fr at an intermediate ac rmax = 100.00 0.35 0.003 12 0.31 0.38 0.004 1 Lb Ft at an intermediate ac rmax = 100.00 1.00 0.008 12 0.31 1.07 0.008 1 Lb Fz at an intermediate ac rmax = 100.00 7.93 0.064 12 0.07 1.92 0.015 1 in-Lb Mr at an intermediate rmax = 100.00 0.58 0.005 12 0.71 1.43 0.011 1 in-Lb Mt at an intermediate rmax = 100.00 0.17 0.001 12 0.71 0.41 0.003 1 in-Lb Mz at an intermediate rmax = 100.00 0.01 0.000 12 0.8 0.02 0.0001 sigma astigmatism (Fz) 10.14 1 0.07 0.71 0.0061 sigma 3 theta (Fz) 4.86 1 0.07 0.34 0.0031 sigma spherical (Fz) 1.14 1 0.07 0.08 0.0006

16.5 0.29

Net Surface

net surface =

• Optimized support forces including Fr and Ft at Six OD Locations

20

Optimized Forces, Lateral Loading, 9.56 nm-rms

• Forces at constrained nodes must be derived from equilibrium considerations

Optim F Optim Flateral lateral

Node Row Angle Loading Node Row Angle Loading

125 inner 30 -5.695 53 outer 10 18.446365 inner 90 -11.456 133 outer 30 -1.811605 inner 150 -5.720 213 outer 50 -14.876845 inner 210 5.709 293 outer 70 5.791

1085 inner 270 11.164 453 outer 110 5.1281325 inner 330 5.827 533 outer 130 -14.323

9 Intermed. 0 -0.913 613 outer 150 -2.569129 Intermed. 30 9.976 693 outer 170 19.951249 Intermed. 60 -1.023 773 outer 190 -19.734369 Intermed. 90 19.124 933 outer 230 14.419489 Intermed. 120 -0.652 1013 outer 250 -4.792609 Intermed. 150 9.495 1093 outer 270 5.471729 Intermed. 180 -0.275 1173 outer 290 -5.603849 Intermed. 210 -9.543 1253 outer 310 14.986969 Intermed. 240 0.148 1413 outer 350 -17.684

1089 Intermed. 270 -19.052 140 Fr 30 163.4721209 Intermed. 300 0.387 380 Fr 90 322.8641329 Intermed. 330 -9.436 620 Fr 150 162.656

860 Fr 210 -157.1651100 Fr 270 -316.8601340 Fr 330 -156.826

140 Ft 30 182.612620 Ft 150 -184.664

21

Add Axial Force at Tangent Pads

• 1 g Y, Surface = 3.7 nm-rms, 0.14 P-V

22

Optimized Reaction Forces, Lateral with Fz at Tangent Pads on OD

• Green blocks are forces at constrained DOF’s obtained by summing– Need to confirm these values to verify equilibrium (not done)

Optim F Optim F Optim Flateral lateral lateral

Node Row Angle FzLoading Node Row Angle FzLoading Node Row Angle FzLoading

125 Fz inner 30 -1.973 120 FZ mid. 30 4.956 140 Fr, OD 30 253.605365 Fz inner 90 -3.951 240 FZ mid. 60 4.814 380 Fr, OD 90 506.201605 Fz inner 150 -1.971 53 FZ outer 10 -0.701 620 Fr, OD 150 254.113845 Fz inner 210 1.973 133 FZ outer 30 47.308 860 Fr, OD 210 -253.001

1085 Fz inner 270 3.938 213 FZ outer 50 -6.114 1100 Fr, OD 270 -507.9211325 Fz inner 330 1.971 293 FZ outer 70 -6.897 1340 Fr, OD 330 -252.498

9 FZ mid. 0 0.018 453 FZ outer 110 -6.882 140 Ft, OD 30 20.147129 FZ mid. 30 -4.857 533 FZ outer 130 -6.130 620 Ft, OD 150 -20.092249 FZ mid. 60 -4.939 613 FZ outer 150 47.431 1100 Ft, OD 270 -0.132369 FZ mid. 90 -9.662 693 FZ outer 170 -0.744 140 Fz, OD 30 -30.309489 FZ mid. 120 -4.950 773 FZ outer 190 0.740 380 Fz, OD 90 -60.450609 FZ mid. 150 -4.852 933 FZ outer 230 6.141 620 Fz, OD 150 -30.373729 FZ mid. 180 0.001 1013 FZ outer 250 6.846 860 Fz, OD 210 30.198849 FZ mid. 210 4.826 1093 FZ outer 270 -94.752 1100 Fz, OD 270 60.671969 FZ mid. 240 4.964 1173 FZ outer 290 6.869 1340 Fz, OD 330 30.128

1089 FZ mid. 270 9.692 1253 FZ outer 310 6.1191413 FZ outer 350 0.681 380.00 Ft, OD 90.00 -0.08

8373.00 Fz 90.00 94.44 860.00 Ft, OD 210.00 -20.128853.00 Fz 210.00 -47.18 1340.00 Ft, OD 330.00 20.289333.00 Fz 330.00 -47.03

23

Plan view of optimized lateral forces, 1 g Y

Deviations from radial are expected based on Swesinger’s solution for meniscus mirrors.