tmt.opt.pre.07.060.rel01 hps-280001-0105 – volume-5 – october 24-25 2007 – slide 1 tmt m1...

TMT.OPT.PRE.07.060.REL01 HPS-280001-0105 – Volume-5 – October 24-25 2007 – Slide 1

TMT M1 Segment Support Assembly (SSA) Preliminary Design Review (PDR)

Volume-5: FLEXURES

Pasadena, CaliforniaOctober 24-25, 2007

Contributors to the development effort:from IMTEC

RJ Ponchione, Eric Ponslet, Shahriar Setoodeh, Vince Stephens, Alan Tubb, Eric Williams

from the TMT ProjectGeorge Angeli, Curt Baffes, Doug MacMynowski, Terry Mast, Jerry Nelson, Ben

Platt, Lennon Rodgers, Mark Sirota, Gary Sanders, Larry Stepp, Kei Szeto

TMT ConfidentialThe Information herein contains Cost Estimates and Business Strategies Proprietary to the TMT Project and may be

used by the recipient only for the purpose of performing a confidential internal review of the TMT Construction Proposal. Disclosure outside of the TMT Project and its External Advisory Panel is subject to the prior written approval

of the TMT Project Manager.

* Note: HYTEC, Inc. merged with IMTEC Inc. in March 2007.


ContentsSSA Flexures - Design/Analysis– Design Load Combinations– Central Diaphragm (Lateral Support)

Requirements / GoalsDesign descriptionComponent sizingFactor of Safety Summary

– Rod-Type Flexures (Axial Support)Requirements / GoalsDescription

– Mirror support rod flexures (27 ea)– Whiffletree Pivots (12 ea)– Actuator Rod Flexures (3 ea)

Component Design Loads & SizingFactor of Safety Summary

– Lateral Guide FlexureRequirements / GoalsDesign descriptionComponent sizingFactor of Safety Summary


DESIGN LOAD COMBINATIONS

Flexures


Central DiaphragmDesign Load Combinations:– Sources: DRD, Project Meetings, and Engineering Judgment

Load events are linear combination of multiple load inputs:SSA Design Load Combinations

WH Non-Observing Survival5 Handling4 Transportation3

Observing Fault1 Vertical Lateral Vertical Lateral Vertical Lateral Vertical Lateral Coating

Operational Lateral g's 1.0 1.0 0 1.4 0 3.0 0 3.0 0 0 1.0

Operational Axial g's 1.0 1.0 1.4 1.0 3.0 1.0 3.0 1.0 0 0 1.0

Thermal2 DT, °C 30 40 40 40 45 45 45 45 45 45 35

Transportation Lateral g's 0 0 0 0 0 0 0 0 0 10.0 0

Transportation Axial g's 0 0 0 0 0 0 0 0 10.0 1.0 0

WH Combined Zernike 1.00 0.00 1.00 1.00 1.00 1.00 1.00 1.00 0.1 0.1 0.0

WH Hard Stop 0.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.0 0.0 0.0Notes: 1) Warping harness controller failure, drives actuators against hard-stops.

Assumed to all occur simultaneously, in worst combination.2) Worst case DT from stress-free assembly temperature: 15-25C.3) Assume segment inverted. Mass of SSA (without reference frame) resting on segment. Warping harness lightly preloaded during shipment to prevent rattling.4) Handling: 3.0g quasi-static load factor per L. Stepp 9/7/075) Seismic/Survival: 3.0g quasi-static seismic load per DSL 9/7/07

Controlling for Diaphragm & Lateral Guide Flexure

SSA TEMPERATURE EXCURSIONS, Deg C.SSA Assembly Figuring or

(Stress Free Temp.) Observing Non-observing Survival Handling Transportation Coating1

Max Temp 25 5 35 40 50 50 50

Min Temp 15 -5 -15 -20 -20 -20 10

Max +DT 20 25 35 35 35Max -DT -30 -40 -45 -45 -45 -15Notes: 1) Per 9/27/2007 Videoconference, Coating and Figuring temperatures shall be limited to 50C max to protect adhesive.

2) Observing temperatures 0+/-5C differs from optical analysis temperature (9+/-4C). 0+/-5C used for structural analysis to envelope all sites.


CENTRAL DIAPHRAGM

Flexures

Requirements / GoalsRequirements / Goals

Design descriptionDesign description

Component sizingComponent sizing

Factor of Safety Summary Factor of Safety Summary


Central DiaphragmDesign Approach:– Central diaphragm supports segment, reacting lateral gravity load

– Low expansion metal diaphragm bonded directly to mirror:No de-coupling flexures (low cost & compact)

Single machined part– no bonds, welds, or brazed joints that would interfere with the low CTE goal

Mirror has central pocket to position diaphragm in optimal location– minimize later print-thru

Material: Invar (or Inovar)– INOVAR (from IMPHY Alloys, France) is high-purity, low-Carbon version of Invar

Results in lower CTE and greater temporal stability compared to regular Invar

CTE = 0.65 PPM/C vs. 1.3 PPM/C for regular Invar

Note: we do not rely on the lower CTE, but hope to build it into the design

0.250 mm thick epoxy bondline


Requirements & Goals

Requirements & Goals– Minimize diaphragm outside diameter:

Best optical performance & lowest cost

– Minimize piston stiffness:Decouple axial and lateral supports

– Lateral strength characteristics:Linear response through 1.5g static (no buckling during observing)

Elastic behavior – post buckled – to 4.5g static (3.0g * 1.5 FOS)

– Torsional load characteristics:Stiffness to achieve >8 Hz first clocking mode

Strength sufficient for robustness in handling

– Flexure ID governed by Torsional goals:(60mm center hub) [See backup slide]

– 130mm Flexure OD chosen as compromise between size vs. stiffness:Prefer smallest OD and pocket bore

Need compliance to decouple axial support


Requirements & Goals

Requirements & Goals, Cont.– Buckling controls design:

we choose ~2.0g nominal static buckling capacity – elastic behavior to 4.5g. (3.0 g with 1.5 FOS)

– Other characteristics result from these decisions

Design Load Case– Mass of mirror segment subject to lateral gravity

1g Lateral Load: Fr = 9.81 * 154.3kg = 1519 N


Diaphragm Trade StudyFlat Diaphragm

Stress Relieving Diaphragm

Design Trade-off– Two central diaphragm designs considered:

Traditional Flat diaphragm

Stress reducing diaphragm (Convolution and slotted rim)

– Optical performance analysis guided down-select:Flat diaphragm optical performance:

– Lateral surface error: ~9.2nm RMS

– Thermal distortion surface error = ~2.4nm RMS /C

Stress reducing diaphragm optical performance:– Lateral surface error: ~16nm RMS

– Thermal distortion surface error = ~1.0nm RMS/C

JPL PSS analysis showed flat diaphragm to be better overall:

– Prefer less high-spatial-frequency lateral distortion

– Can tolerate more low-spatial-frequency thermal distortion.


Diaphragm Trade Study

Optical Performance ComparisonFlat Invar Diaphragm Stress Relieving Invar Diaphragm

PV = 153. nmRMS = 9.22 nm

PV = 19.7 nm/◦C

RMS = 2.4 nm/◦C

PV = 252.4 nmRMS = 15.6 nm

PV = 4.4 nm/◦C

RMS = 0.98 nm/◦C

Note: Units are surface error

FOR REFERENCE:

LATEST PREDICTIONS DIFFER SLIGHTLY

(See Volume 3 for Latest P

rediction)


Design Overview

Overview: Cross-Section View

Mirror Segment

Moving Frame

Diaphragm

Adhesive Bond:Diaphragm to Glass

Adhesive layer

Slide Repeated from Vol-1


Design Details

Diaphragm Material: Invar (Inovar)– E = 130 GPa (18.85E6 psi)

– Fty = 260 MPa (37.7 ksi) typical

– = 1.3 ppm/C

150mm

60mm

130mm

Flexure region Hub: 8.5mm thk.

Rim: 3mm thk.

Information repeated from Vol-1


Analysis Overview

Analysis Cases– Axial (Piston) load (1N unit load applied)

Linear-elastic small deflection analysis– we expect operational deflections of diaphragm to be on the order of microns

– Lateral (Radial) load (1g dead weight applied: 1519N)Linear-elastic small deflection analysis

Eigenvalue buckling

Nonlinear buckling load-deflection analysis– Determine post-buckling behavior to 4.5g

– Torsional load (1N-m unit load applied to central hub)Linear-elastic small deflection analysis

– Assess torsional stiffness and segment clocking natural frequency

Eigenvalue buckling– assess susceptibility to damage due to handling loads (no significant torsional loads

anticipated)

– Thermal Mismatch (DT = 1◦C Unit Case)Linear-elastic small deflection analysis

Eigenvalue buckling analysis– CTE mismatch between glass and diaphragm can result in diaphragm buckling


Analysis Methodology

Typical analysis results– Lateral load: Nonlinear analysis

1g (linear)

2.7g (initial buckling)

4.5g (remains elastic)

Lateral Load-Deflection

1g 2g 3g 4g

Note: Deflections magnified 50x


Diaphragm Axial Radial Radial Stiffness, N/micronThickness Stiffness Bucking Nonlinear Stress Analysis Results, ksi Nonlinear Results

mm N/m x103Pcr (g's) 1.0 g 2.0 g 3.0 g 4.5 g Linear Secant Tan at 4.5g

0.25 15.20 0.83 5.9 20.0 27.4 41.0 168 116 1000.30 25.60 1.42 5.0 10.0 25.5 34.5 198 141 1170.35 39.37 2.20 4.3 8.6 22.1 32.1 226 178 1440.38 47.60 2.67 4.0 8.1 12.1 30.5 241 199 1560.40 56.50 3.20 3.8 7.6 11.4 28.1 254 224 162

Yield 37 37 37 37

Diaphragm flexure dimensions: OD=130mm, ID=60mm, thickness varied. Material: Invar E=130 GPa

Diaphragm Stress vs. g-load

0

5

10

15

20

25

30

35

40

45

1.0 g 1.5 g 2.0 g 2.5 g 3.0 g 3.5 g 4.0 g 4.5 g

Lateral g load

Str

ess

, ks

i

Invar Yield Strength

0.250mm thick

0.300mm thick

0.350mm thick

0.375mm thick

0.400mm thick

Stiffness and Buckling Capacity vs. Thickness

0

10

20

30

40

50

60

0.25 0.30 0.35 0.40

Thickness, mm

Ax

ial

Sti

ffn

ess

, N

/m x

10^

3

0.0

1.0

2.0

3.0

4.0

5.0

6.0

Ra

dia

l B

uck

lin

g L

oad

, g

's

Axial Stiffness

Radial Bucking

Thickness Sizing Study

Nonlinear analysis performed to select thickness:– 0.350mm chosen as nominal thickness (0.350+/-0.025mm)

NominalDesign


Analysis Summary

FEA Results– Considering diaphragm thickness tolerance (+/-0.025mm)

AXIAL PERFORMANCE RADIAL PERFORMANCEStress, per N Applied Load 1g Stress, MPa (psi) Buckling

Stiffness Diaphragm Max Bond Stress, Pa (psi) Stiffness Diaphragm Max Bond Stress LoadN/m s

vm, MPa (psi) speel

s1

tmax N/m (Hz) s

vms

peels

1t

max N (g's)

Nominal Thickness: 0.350mm 3.76E+04 2.60 3838 4034 5859 2.26E+08 29.7 0.510 0.995 0.916 3235(377) (0.56) (0.58) (0.85) (192) (4307) (74) (144) (133) (2.13)

Minimum Thickness: 0.325 mm 3.01E+04 2.12E+08 2592(186) (1.71)

Maximum Thickness: 0.375 mm 4.61E+04 2.40E+08 3979(198) (2.62)

TORSIONAL PERFORMANCE THERMAL PERFORMANCEStress per N-m applied load Buckling Stress per deg C Buckling

Stiffness Diaphragm Max Bond Stress, Pa (psi) Load Diaphragm Max Bond Stress, Pa (psi) LoadN-m/rad (Hz) s

vm, MPa (psi) speel

s1

tmax N-m s

vm, MPa (psi) speel

s1

tmax Deg C

Nominal Thickness: 0.350mm 2.29E+05 0.75 50 7764 7761 447 0.413 35200 132400 76533 112(13.2) (108) (0.01) (1.13) (1.13) (59.9) (5.10) (19.20) (11.10)

Minimum Thickness: 0.325 mm 2.14E+05 358 95.8(12.8)

Maximum Thickness: 0.375 mm 2.44E+05 549 113.5(13.6)

Flat Diaphragm: Flexure: OD = 130mm, ID = 60mm M_mirror = 154.8 kg I_mirror = 33.12 kg-m2

Rim: OD = 150mm, ID = 130mm Wt = 1518.6 NBond: 0.250 mm thick Nominal

Adhesive: EA9313E = 296 ksi, = 45 PPM/C, = 0.15


Effect of Thickness Variation

FEA Results for Baseline Design (t=0.350+/-0.025mm)– Nonlinear response – post buckling

– Min, Nominal & Max thickness (machining tolerances)Thickness Diaphragm Max von Mises Stress, MPa

mm 0.0 g 1.0 g 2.0 g 3.0 g 4.0 g 4.5 g

0.325 0 31.9 99.5 157.1 200.3 223.10.350 0 29.7 59.5 147.2 192.1 210.60.375 0 27.9 55.7 126.5 183.7 204.7

Invar Yield Strength: 260MPa

260 260 260 260 260 260

Diaphragm von Mises Stress vs. Lateral g-load

0

50

100

150

200

250

300

0.0 g 0.5 g 1.0 g 1.5 g 2.0 g 2.5 g 3.0 g 3.5 g 4.0 g 4.5 g

g-load

Max

vo

n M

ises

Str

ess

, M

Pa Yield Strength

Min Thk., 0.325mm

Nom. Thk., 0.350mm

Max Thk., 0.375mm


Central Diaphragm - SUMMARYSummary– Flat regular invar diaphragm sized for TMT application:

Design Parameters:– Rim OD=150mm, ID=130mm, 3mm thick

– Flexure OD=130mm, ID=60mm, thickness=0.350+/-0.025mm

– Center Hub 60mm OD x 8.5mm thick

– Material: Invar or Imphy Alloys INOVAR (ultra pure Invar)

– Requirements and goals satisfied:Axial stiffness minimized

– effect on optical performance verified at system level

Lateral:– Linear behavior through 1.7g lateral (with min thickness)

– Elastic through 4.5g lateral (post buckling)

– Bond max shear stress <150 psi at 1g

Sufficient torsional stiffness (12 Hz.) and strength (>350 Nm)

Thermal buckling >95C


ROD TYPE FLEXURES

Flexures


Design descriptionDesign description– Mirror support rod flexures (27 ea)– Whiffletree Pivots (12 ea)– Actuator Rod Flexures (3 ea)




RequirementsRod flexures are required to– have some minimum axial stiffness

– resist column buckling

– have good lateral compliance

– have good strength to resist all anticipated loads

– be corrosion resistant

– be low cost

– be easy to install

We consider all of these factors when making design decisions

System stiffness requirement affects rod-flexure design:– Piston stiffness requirement: 12N/micron - with rigid actuator and mirror cell

wind rejection

The design process is iterative – this is a snapshot


Loads and Factors of SafetyRequirements, cont.– Rod flexures subject to a variety of load conditions as defined previously:

– Required factors of safety (based on engineering judgment)

SSA Design Load CombinationsWH Non-Observing Survival5 Handling4 Transportation3

Observing Fault1 Vertical Lateral Vertical Lateral Vertical Lateral Vertical Lateral Coating

Operational Lateral g's 1.0 1.0 0 1.4 0 3.0 0 3.0 0 0 1.0

Operational Axial g's 1.0 1.0 1.4 1.0 3.0 1.0 3.0 1.0 0 0 1.0

Thermal2 DT, °C 30 40 40 40 45 45 45 45 45 45 35

Transportation Lateral g's 0 0 0 0 0 0 0 0 0 10.0 0

Transportation Axial g's 0 0 0 0 0 0 0 0 10.0 1.0 0

WH Combined Zernike 1.00 0.00 1.00 1.00 1.00 1.00 1.00 1.00 0.1 0.1 0.0

WH Hard Stop 0.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.0 0.0 0.0Notes: 1) Warping harness controller failure, drives actuators against hard-stops.

Assumed to all occur simultaneously, in worst combination.2) Worst case DT from stress-free assembly temperature: 15-25C.3) Assume segment inverted. Mass of SSA (without reference frame) resting on segment. Warping harness lightly preloaded during shipment to prevent rattling.4) Handling: 3.0g quasi-static load factor per L. Stepp 9/7/075) Seismic/Survival: 3.0g quasi-static seismic load per DSL 9/7/07

Design Factors of Safety (Yield and Buckling)WH Non-Observing Survival Handling4 Transportation3

Observing Fault Vertical Lateral Vertical Lateral Vertical Lateral Vertical Lateral Coating

1.50 1.10 1.50 1.50 1.10 1.10 1.10 1.10 1.10 1.10 1.50

Table repeated form slide-4


Flexure Design OverviewDesign Overview– Rod-Type Flexures

Cross-Section ViewPivots

Next Slide

Mirror supportrod flexures


Flexure Design OverviewDesign Overview– Pivots

Triangle-Triangle PivotFlexible Region:1.5mm OD x 20mm longMaterial: 17-4 PH

MF- Large Triangle PivotFlexible Region:3.0mm OD x 45mm longMaterial: 17-4 PH

Moving Frame

Sheet Flexure Mid-Plane

Large Wt Triangle

Small WT Triangle


Flexure Design OverviewDesign Overview– Mirror support Rod Flexure Design

VentHole

VentHole

Mirror

WTTriangle

InvarPuck

Rod Material: 304 CD

Flexible Region:2.1mm OD x 143mm Long

M3 Hex Nut, 3 places

Repeated from Vol-1


Flexure Design OverviewDesign Overview– Actuator Rod Flexure Design

Flexible Region:7.23mm OD x 115mm Long

Knurled

Slide Repeated from Vol-1


Flexure Design OverviewDesign Overview– Rod flexure lengths are constrained by the system design.

The desire for a compact system drove the fundamental layout

– Mirror rods:For buckling controlled design mounted to back surface of mirror, longer is better

– Diminishing returns after 80mm

Length only important because we attach to back-surface

Mid-plane mounting independent of length fro buckling critical

– We choose 143mm for convenience

– Triangle-Triangle PivotsWith nested whiffletree triangles, the available space is limited

Maximum length for this arrangement is 20 mm

– Moving Frame to Large Triangle PivotsLength constrained to 45mm

– Actuator flexureMaximum length is 115 mm with this arrangement


Flexure Design OverviewDesign Overview– Given the System stiffness requirement 12N/micron

– Axial Stiffness budget guides flexure sizingWe desire bending compliance, but require axial stiffness

Balanced design implies maintaining certain axial stiffness values for rod flexures– Triangle-Triangle Pivots: Kaxial > 17 N/micron

– MF to Large Triangle Kaxial > 30 N/micron

– Actuator Flexure Kaxial > 40 N/micron

Number Component Total Total Fraction

In Dia. Length Modulus Stiffness Stiffness Compliance of SSASSA Components Parallel mm mm GPa N/mm N/mm nm/N Compliance

Mirror Rod Flexure 27 2.10 143 193 4.7 126 7.9 10%

Small WT Triangle 9 69 13.5 122 8.2 10%

Triangle-Triangle Flexure 9 1.50 20 193 17.1 153 6.5 8%

Large WT Triangle 3 69 20.0 60 16.7 21%

MF to Large Triangle 3 3.00 45 193 30.3 91 11.0 14%

Moving Frame 1 69 62.5 63 16.0 20%

Actuator Flexure 3 5.50 115 193 39.9 120 8.4 11%

Fixed Frame+AAP 3 69 68.5 206 4.9 6%

Full SSA 12.57 79.6 100%


Flexure Design OverviewMaterial Selection:– No brittle materials– All flexures must be corrosion resistant

Plating not preferred– additional process– thickness of certain features critical

– Mirror rod flexures (27):Long and slender makes these difficult to heat-treatChoose Cold-drawn 304 stainless steel

Fty = 250 ksi (1724 MPa)

– Triangle Pivots (all 12):Too large in diameter for 304CD, must heat-treat theseChoose 17-4 PH H1025 (Lower cost precipitation hardened stainless steel)

Fty = 145 ksi (1000 MPa)

– Actuator rod flexureSubject to fatigue cycles and high stress levels (bending due to actuation)

– 10 cycles/night * 365 * 50 = 182,500 cycles

Choose Titanium 6Al-4V Annealed (no heat treat required – avoids distortion)

Fty = 125 ksi (862 MPa)


Sizing CalculationsFlexures are sized considering the effects of every load combination on each flexure separately.The controlling load cases are determined considering these loads in conjunction with the Factors Of Safety and Stiffness goals.We begin with Unit Cases:– FEA predicts loads from the following components:

Mirror Rod Flexures (27)Whiffletree Triangle-Triangle Pivots (9) Whiffletree Moving Frame-to-Large Triangle Pivots (3)WH Actuators (21)Actuator Rod Flexures (3)

– Unit Load Cases Analyzed by FEAOperational Configuration (Mirror supported by SSA)

– 1g-x,y,z– DT = +1C – 21 Warping Harness Actuators

Shipping Configuration (PMA inverted and supported by mirror)– Transportation g-x,y,z

Warping Harness Loads (derivation presented in WH presentation)– 100% Combined Case (Operational correction of Zernikes)– Hard-stop fault condition (Controller fault drives actuators to their limits)


Sizing CalculationsWe calculate a Component Load Matrix which contains the magnitudes of loads on each flexure subject to the unit loads– Absolute values taken (loads are +/- in sign)

– Worst of gx or gy load case used to envelope the lateral load cases

– Example:OPERATIONAL TRANSPORTATION WARPING HARNESS

Max Max CombinedLateral Lateral Zernike Hard Stop

Flexure # Node # 1g-x or y 1g-z 1Deg C 1g-x or y 1g-z Case Case

A19 299901 0.44 40.83 0.01 9.47 12.75 34.86 100.73A20 299902 0.62 76.73 0.01 17.80 22.95 39.58 130.83A21 299903 0.54 76.73 0.01 17.91 22.95 39.58 130.83A23 299904 0.61 51.33 0.01 11.98 15.76 50.28 163.22A25 299905 0.26 52.03 0.01 13.12 17.04 32.73 113.13A1 299906 0.50 40.83 0.01 10.97 12.80 29.36 100.73A3 299907 0.67 76.73 0.01 20.66 23.04 34.35 130.83A4 299908 0.33 52.03 0.01 14.99 16.74 33.07 113.13A7 299909 0.32 52.03 0.01 15.02 16.88 33.08 113.13A9 299910 0.09 52.54 0.01 15.21 16.73 39.48 139.78A8 299911 0.82 51.33 0.01 14.29 15.63 51.07 163.22

A12 299912 0.62 76.74 0.01 17.84 22.98 39.57 130.83A13 299913 0.27 52.04 0.01 13.06 16.86 32.74 113.13A2 299914 0.67 76.73 0.01 20.66 23.04 34.35 130.83A6 299915 0.09 52.54 0.01 15.17 16.61 39.46 139.78A5 299916 0.81 51.33 0.01 14.37 15.88 51.07 163.22

A10 299917 0.44 40.83 0.01 9.52 12.76 34.84 100.73A11 299918 0.54 76.74 0.01 17.96 22.98 39.57 130.83A15 299919 0.08 52.55 0.01 13.22 16.66 48.31 139.78A14 299920 0.82 51.34 0.01 12.83 15.77 45.09 163.22A16 299921 0.30 52.04 0.01 12.97 17.04 27.68 113.13A18 299922 0.10 52.55 0.01 13.18 16.80 46.75 139.78A17 299923 0.61 51.34 0.01 11.89 15.45 50.29 163.22A22 299924 0.30 52.03 0.01 12.97 16.87 27.67 113.13A24 299925 0.10 52.54 0.01 13.15 16.67 46.71 139.78A27 299926 0.09 52.54 0.01 13.25 16.80 48.31 139.78A26 299927 0.82 51.33 0.01 12.74 15.45 45.07 163.22

Fo

rce

at 2

7 M

irro

r R

od

Fel

xure

s, N


Sizing CalculationsWe then multiply the Load Combination Matrix by the Component Load Matrix to determine loads on each flexure for every load case.

We then extract the max value acting on each flexure-type for every load combination and use these to size the components

Imposed displacements are added to the component loads to determine max stress conditions– Actuator rod subject to tip deflection and rotation due to full tip/tilt

Deflection = 1.0mm, Rotation = 0.5 deg (from 1.2m design – conservative)

– Other flexures subject to 0.1mm offsets (deflections)

After tuning the sizes, the flexures meet requirements:– see next page

Combined Load Max Values, NewtonsWH Non-Observing Survival Handling4 Transportation3

Observing Fault Vertical Lateral Vertical Lateral Vertical Lateral Vertical Lateral Coating

27 Mirror Rods 117 216 147 117 270 119 270 119 234 233 78

9 Tri-Tri Pivots 243 439 307 243 616 245 616 245 527 577 203

3 Large Tri Pivots 695 804 921 697 1831 701 1831 701 962 1524 574

21 WH Actuators 73 105 73 73 73 73 73 73 12 11 13 Actuator Rods 625 625 862 628 1848 643 0 0 0 0 0


Handling Transportation3 Coating Minimum FOS

Flexure LocationLoad,

N FSbu

s,

MPa FSy

Load, N FSbu

s,

MPa FSy

Load, N FSbu

s,

MPa FSy Buckling Yield

Mirror Support Rods 270.1 1.32 83.9 20.5 234.2 1.52 73.6 23.4 78 4.58 28.4 60.8 1.32 20.5

Triangle-Triangle Pivot 616.1 7.7 353.9 2.8 576.6 8.2 331.6 3.0 203 23.3 120.0 8.3 7.68 2.15

M.F.-Triangle Pivots 1831 8.2 263.4 3.8 1524 9.8 220.0 4.5 574 26.1 85.5 11.7 8.17 3.80

Actuator Flexure - - - - - - - - - - - - 24.3 2.45

Minimum FOS 1.32 2.83 1.52 3.0 4.6 8.3 1.32 2.15

Required FOS 1.1 1.1 1.1 1.1 1.5 1.5

Design Load Case Material D L A I AE/L EI/L2 Buckling

Flexure Location

Load, P (N)

Offset1, mm

Tip Rot.

deg.1 E, GPa Fty, MPa mm mm m2 m4 N/m x106

NStrength Pcr, N

Mirror Support Rods 297.1 0.1 193 1724 2.10 143.0 3.46E-06 9.55E-13 5 9 356

Triangle-Triangle Pivot 677.7 0.1 193 1000 1.50 20 1.77E-06 2.49E-13 17 120 4734

M.F.-Triangle Pivots 2014.1 0.1 193 1000 3.00 45 7.07E-06 3.98E-12 30 379 14961

Actuator Flexure 2032.4 1.0 0.5 112 862 7.23 115 4.11E-05 1.34E-10 40 1137 44880

Sizing CalculationsCalculation of Rod Flexure Stress, Bucking and Factors of Safety

Observing WH Fault Non-Observing Survival Handling

Flexure LocationLoad,

N FSbu

s,

MPa FSy

Load, N FSbu

s,

MPa FSy

Load, N FSbu

s,

MPa FSy

Load, N FSbu

s,

MPa FSy

Mirror Support Rods 117.2 3.0 39.8 43.3 215.7 1.6 68.2 25.3 147.3 2.4 48.5 35.6 270.1 1.3 83.9 20.5

Triangle-Triangle Pivot 242.8 19.5 142.7 7.0 438.8 10.8 465.4 2.1 307.1 15.4 179.0 5.6 616.1 7.7 353.9 2.8

M.F.-Triangle Pivots 695.3 21.5 102.7 9.7 803.6 18.6 199.5 5.0 920.6 16.3 134.6 7.4 1831 8.2 263.4 3.8

Actuator Flexure 624.8 71.8 321.9 2.7 624.8 71.8 198.9 4.3 862.2 52.0 327.6 2.6 1848 24.3 351.6 2.45

Minimum FOS 3.0 2.7 1.6 2.1 2.4 2.6 1.3 2.45

Required FOS 1.5 1.5 1.1 1.1 1.5 1.5 1.1 1.1


Results SummaryFlexure Design Summary

Flexure designs meet requirements

Risks:– Distortion (bending) of flexure during machining or heat treating

– Tolerances on tapered pin/holes may cause misalignment

Factors of Safety

Material Controlling Controlling Buckling, FSbu Yield, FSy

Flexure Location Type Parameter Load Case Min. Reqd. Min. Reqd.

Mirror Support Rods 304V 92% CW Buckling, FSbu > 1.1 Handling 1.32 1.1 20.5 1.1

Triangle-Triangle Pivot 17-4PH H1025 Length Envelope < 20mm Handling 7.7 1.1 2.1 1.1

Fty = 145 ksi and Stiffness>15N/micron WH Fault

M.F.-Triangle Pivots 17-4PH H1025 Length Envelope < 45mm Handling 8.2 1.1 3.8 1.1

Fty = 145 ksi Axial Stiffness, Ka >30E6 N/m

Actuator Flexure Ti 6Al-4V Cond A Yield, FSy>2.0 Survival 24.3 1.1 2.5 1.1

Fty = 125 ksi Ka > 40E6 N/m and Stress


LATERAL GUIDE FLEXURE

Flexures

Design approachDesign approach


Design descriptionDesign description




Design ApproachDesign Approach:– Lateral Guide Flexure:

Supports Moving Frame (hence segment), reacting lateral gravity load

Accommodates piston/tip/tilt actuation

Provides center-of-rotation close to the mirror– minimizes segment de-center due to tip/tilt motion

– Several design options explored:Flat diaphragm – too stiff in piston

Stacked Diaphragms - too soft in lateral

C-Flexures – too soft in lateral

Three blades oriented at 120 degrees – too stiff in piston

Circular diaphragm with OD convolution - Suitable


Requirements & GoalsDesign Requirements & Goals– Accommodate piston compliance:

Elastic response at 3.0mm piston

– Lateral (In-plane) Stiffness: 50 N/µm (Derived)Lateral vibration mode: ~85 Hz SDOF fits with system requirement of 35 Hz

– Piston Force: <150 N at 3.0 mm (Derived/Chosen)Limit the nonlinear load each actuator must apply to piston 3.0mm to 50N ea.

– Buckling and Stress Factors of SafetyFSy = 2.0

FSbu = 1.5

– Design Loads:3g Lateral: 5739N (Supported mass = 195 kg)

Required buckling strength: 8600 N Lateral

3g * 1.5 FOS

– Fatigue Cycles:assume 10 cycles/night * 365 * 50 years = 182,500 cycles


Design Details

Mirror Segment

MovingFrame

GuideFlexure

Clearance hole for Mirror Support Rod Flexure


ConstructionConstruction– Fabrication Method TBD

Formed or Machined – lowest cost part that meets requirements

– Baseline Material: Aluminum: 7075-T651 (assumes machined part)

Yield strength: 462 MPa (67 ksi)

Fatigue stress limit for 1E6 cycles ~172 mPa (25 ksi) • R = -1.0 (fully reversed bending)• Kt = 1.0 (no notches, peak stress not at stress concentration)

• 1E6 cycles is 5x on lifetime

Material CTE chosen to match Tower and Moving Frame

Avoid thermal buckling


FEAGeometry– Outer bolt radius = 161 mm

– Inner bolt radius = 39.5 mm

– Rim thickness = 10 mm

– Thickness = Design Parameter

Loads:– Radial: 1913N (1g)

– Piston: 3.0 mm


FEA ResultsThickness 0.7 mm 0.725 mm 0.75 mm

Buckling Limit 8175 N 9190 N 10295 N

Force for 3 mm Vertical Displacement

133.7 N 144.5 N 150.6 N

Torsional Stiffness 555 KN*m/rad 568 KN*m/rad 588 KN*m/rad

Lateral Stiffness 50.0 N/µm 52.6 N/µm 54.6 N/µm

Stress @ 3 G 62.5 MPa 59.8 MPa 57.3 MPa

Stress @ 3 mm Displacement

51.6.0 MPa 50.4 MPa 54.5 MPa

1st Buckling Mode

Baseline Design

F


Nonlinear Analysis

Initial Stiffness = 23 N/mm

Stiffness at 3 mm of piston = 92 N/mm

Load at 2.5 mm ≈ 100 N

Load at 3.0 mm <150 N

Displacement Loads For 0.725 mm Thickness

0

20

40

60

80

100

120

140

160

0 0.5 1 1.5 2 2.5 3

Displacement (mm)

Fo

rce

(N)


Guide Flexure SummaryFlexure provides adequate lateral and torsional stiffness– K_lateral = 52.6 N/mm (Exceeds 50N/mm goal)

Stress levels are acceptable– Yield Strength: FSy = 462 / 59.8 = 7.7 (2.0 required)

– Fatigue: Piston stress (50.4MPa) well below fatigue strength (172MPa)

Buckling load exceeds design goal– 3g Survival/Handling Load Case: FSbu = 9190 / 5739 = 1.60 (1.50 required)

Piston force acceptable:– F3.0mm = 144.5N (less than the 150N goal)


Acknowledgements

Acknowledgements:

The TMT Project gratefully acknowledges the support of the TMT partner institutions. They are the Association of Canadian Universities for Research in Astronomy (ACURA), the California Institute of Technology and the University of California. This work was supported as well by the Gordon and Betty Moore Foundation, the Canada Foundation for Innovation, the Ontario Ministry of Research and Innovation, the National Research Council of Canada, the Natural Sciences and Engineering Research Council of Canada, the British Columbia Knowledge Development Fund, the Association of Universities for Research in Astronomy (AURA) and the U.S. National Science Foundation.


BACKUP SLIDES

Flexures


Central Diaphragm SizingHub sizing study– Original work performed for 1.2m segment

– Showed that small hub diameters are weak and soft in torsion.

– 60mm hub diameter chosen as a good compromise

Mirror DIAPHRAGM Axial Buckling Capacity Torsional Torsional Yield Strength Yield StrengthPocket Dia. OD ID thickness Stiffness In-plane Torsional Stiffness Frequency Torque Force @ 0.6m Axial Defl. In-plane Shear

mm mm mm mm kN/m N N-m kN-m/rad hz N-m N lb. mm kN

120 100 15 0.44 33.7 3003 173.3 18.7 5.26 27.2 45 10 1.36 3.91

120 100 30 0.368 37.9 3007 249.4 67.3 9.98 83.3 139 31 1.39 6.15

150 130 60 0.323 36.6 3008 407 273.5 20.1 281.3 469 105 1.86 11.4

180 160 90 0.294 36.0 3003 561 645.2 30.9 570 950 214 2.25 16.7


Rod-Type FlexuresTMT Mirror Rod Flexure Design Options

Material: 304V Stainless Steel, Cold Drawn 250 ksi Modulus: E = 1.93E+11 Pa Yield: Fty = 1724 MPa

INPUT VARIABLES CALCULATED QUANTITIES

Design Load: HANDLING P = 270 NBuckling Safety Factor SFbuck = 1.10 Rqd. Buckling Capacity Pcr = 297 N

Buckling End Coefficient K = 4.0 Bending Stiffness EI/L2 = 7.523 NDist fm mirror CL to basse of rod dpuck 0.043 m Axial Stiffness Ka = 4.3E+06 N/m

Mirror Mass on Flexure (153 kg / 27) Mass = 5.667 kg Axial Frequency fn = 138.2 Hz

Lateral deflection - Estimate delta = 0.0001 m Flexure End Moment M0 = 0.00451 Nm

Moment on Mirror Flexure Stresses and Factor of Safety HandlingFLEXURE GEOMETRY Flexure at Mid Plane, Nm Axial Bending Comb. Yield

Shear, N Due to V Total Sa Sb Stot = Sa+Sb Load

Dia, m Dia, mm Dia, in. Lcr, m Lcr, mm L/rho V M' Mc MPa MPa MPa ksi FSy N

0.00050 0.50 0.020 0.00887 8.9 71 1.018 0.043 0.048 1375 368 1743 254 0.99 2.380.00075 0.75 0.030 0.020 20.0 106 0.452 0.019 0.024 611 109 720 105 2.39 3.580.00100 1.00 0.039 0.035 35.5 142 0.254 0.011 0.015 344 46 390 57 4.42 4.770.00125 1.25 0.049 0.055 55.4 177 0.163 0.007 0.011 220 24 244 36 7.08 5.960.00150 1.50 0.059 0.080 79.8 213 0.113 0.005 0.009 153 14 166 24 10.36 7.150.00175 1.75 0.069 0.109 108.7 248 0.083 0.004 0.008 112 9 121 18 14.27 8.350.00200 2.00 0.079 0.142 141.9 284 0.064 0.003 0.007 86 6 92 13 18.80 9.540.00225 2.25 0.0886 0.180 179.7 319 0.050 0.002 0.007 68 4 72 11 23.96 10.730.00225 2.25 0.089 0.180 179.7 319 0.050 0.002 0.007 68 4 72 11 23.96 10.730.00250 2.50 0.098 0.222 221.8 355 0.041 0.002 0.006 55 3 58 8 29.75 11.92

0

20

40

60

80

100

120

140

160

180

200

0.50 0.70 0.90 1.10 1.30 1.50 1.70 1.90 2.10 2.30 2.50

Flexure Diameter, mm

Fle

xu

re L

en

gth

, mm

0.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

0.040

0.045

0.050

Mir

ror

Mo

men

t, N

m

Buckling Critical Design

Mirror Moment


Rod-Type FlexuresTMT – Keck Rod Flexure Comparison

TMT KECK

Mirror Mass 153 398 kgNumber of WT Rods 27 36Average Weight/Rod 55.6 108.6 N

Rod Dia 2.100 1.980 mmRod Length 143.00 104.14 mm

Rod Buckling Capacity 272 534 N

1G Buckling FOS 4.89 4.92

tmt.opt.pre.07.060.rel01 hps-280001-0105 – volume-5 – october 24-25 2007 – slide 1 tmt m1...

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