Pasadena, California October 24-25, 2007 Contributors to the development effort: from IMTEC

TMT.OPT.PRE.07.059.REL01 HPS-280001-0105 – Volume-4 – October 24-25 2007 – Slide 1

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

Volume-4: WARPING HARNESS

(See last slide for Revision History)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.


ContentsWarping Harness Design/Analysis– Fundamental Approach & Architecture– Warping Harness Requirements

Opto-mechanicalMechanical

– Design Concept– Performance Analysis

Actuator arrangementSurface correction

– Derived Requirements for Components– Mechanical & Electrical Design– Quantization Error Estimate


FUNDAMENTAL APPROACH & ARCHITECTURE

Warping Harness


Fundamental Approach & ArchitecturePurpose:– Allow automated periodic correction of low order surface distortions:

Residual errors from polishingCoating stress distortionSeasonal fraction of thermal distortionSegment positioning errors within the array (Focus and Astigmatism)etc.

Fundamental Approach:– Extension of the Keck design– Re-figure the mirror by bending it in a controlled manner using whiffletree– Bending moments introduced into whiffletree by a set of moment actuators– Actuators are motorized, instrumented and tied into the M1CS

Architecture:– 21 whiffletree joints are fitted with moment-actuators– Lead screw pushes against an instrumented leaf-spring to create a moment – Stepper motor drives lead screw to permit automation

Slide Repeated from PDR Vol-1


WARPING HARNESS REQUIREMENTS

Warping Harness


System RequirementsOpto-Mechanical Requirements – per DRD– Correction of Prescribed Surface Distortions

Seven Pure Zernike Aberrations - Second & Third order termsAmplitudes (imposed on a circumscribed circle 1.44m dia)

One additional combined case: – Max Combination of 7 pure Zernike cases x 100%– Structural load case only (flexure and joint loads). No optical performance requirement.

Aberration Amplitude, nm Correction Factor

Focus 2,0 600 15

Astigmatism 2+2 1200 15

Coma 3+1 120 5

Trefoil 3+3 240 5


System RequirementsOpto-Mechanical Requirements – per DRD: continued– Warping Harness Actuator:

Parameter Requirement

Open loop force accuracy < 2% [of full scale TBC]

Open loop force repeatability < 0.5% [of full scale TBC]

Force resolution <0.1% [of full scale TBC]

Force capability As derived

Power-off Hold setting, No Heat

Dead Band Shall be discernable


Component RequirementsMechanical Requirements

– LifetimeOperates up to 10 times per night [DRD]Assume the adjustment is 10% of 0-peak range (conservative) [TBC]365 nights per year for 50 years (conservative)Cycles = (10 ops/night) * (10% of 10)turns/op * (365 nights/yr) * (50 yrs) = 18,250

– a very small number for a lead screw/stepper motor combination– wear should not be an issue, aging may be more of an unknown over 50 yrs

motor insulation, strain gauge attachment & encapsulation

– Power Dissipation Requirement:<0.2 Watts during adjustment [per M. Sirota]Power dissipation is sum of strain gage power and motor power:

– Assume ~ 1 adjustment/hour [derived from 10/night, TBC]– All strain gages powered for duration of adjustment sequence based on wiring scheme, slide 45.

Assume 5 seconds adjustment time per axis * 21 motors = 105 secondsGage power =[ 21 * (V2/R) * t] = [21 * (102/350) * 105/3600] = 0.175 W time averaged

– Each motor powered only during adjustment:Assume 2 seconds ON time per motor, 21 motors, P < 15 W per motorMotor Power = [ (21 motors) * (15w/motor)(2 sec/3600 sec)] = 0.175W time averaged

– Total power dissipation = Pgage + Pmotor = 0.175 + 0.175 = 0.350W– Actuators to be vacuum compatible– Maintenance:

Motors replaceable in-situ in the event of failure. Preventive Maintenance (PM) during segment re-coating change-outs


DESIGN CONCEPT

Warping Harness


Design Concept Each whiffletree has 4 pivots with 2 bending DOF each:– Gives 24 (3*4*2) available DOF for this 27-point WT based warping harness

3 joints between small & large triangles, per whiffletree1 joint between moving frame and large triangle, per whiffletree

– Analysis determines which of these actuators are useful

Indicates Applied Moments(Equal and Opposite)


Design Concept Actuator Schematic– Stepper motor driven screw displaces end of leaf-spring– Strain gauge on leaf-spring provides feedback for motor control– Motors will be mounted on the large whiffletree triangles and to the

moving frame

Screw

Leaf-spring

Stepper Motor

Nut

Strain GaugeWT Joint Flexure

(sheet flexure not shown)

Axial Support Flexure

Large Triangle

Small Whiffletree TriangleSmall Whiffletree Triangle



PERFORMANCE ANALYSIS

Warping Harness


Optical Performance AnalysisOpto-Mechanical Analysis Approach:– Assume: 1.44m regular hexagonal meniscus, 45mm thick glass ceramic– Influence functions for each actuator calculated using NASTRAN FEA

27 point WT has 24 joints available for Warping Harness inputsPrevious work on 1.2m segment showed only 18 inputs were required to meet rqts.

– See backup slide summarizing actuator effectiveness study– Mr at inner triangles and Mr at large triangles not effective for Zernike corrections

Mr at inner triangles eliminated

But packaging constraints lead us to retain two actuators on the large trianglesOrthogonal pair have been rotated 45 degrees in-plane

Unit load cases are imposed motion between leaf-spring and actuator – via thermal strain (moment magnitude ~1Nm)

– Correction of Prescribed Surface DistortionsSigfit Software – Adaptive Control Routine Used

– Solves for linear combination of inputs to minimize RMS for each case (7) evaluated

Results Include– Characterization of optical surface before and after actuation– Actuator load requirements– Rod Flexure & Pivot loads


Optical Performance Analysis

Mx’’ & My’’ Large Triangles, 3ea(Only M required) Mx’ & My’ Outer Triangles,

6ea

MInner Triangles, 3ea(Mr not required)

Performance Analysis Results– 21 Actuator arrangement adopted

Indicates Applied Moments(Equal and Opposite)



Influence Functions

WT-1

WT-2

WT-3

Mx’Outer Pivot

My’

Outer PivotMx’’

Large TriangleMy’’

Large TriangleM

Inner Triangle


Optical Performance Analysis ResultsFocus Correction

Input = 600 nm PV = 1200 nm surface, RMS = 310 nmCorrected: PV = 84.1 nm surface, RMS = 16.5 nm

Reduction Factor = 18.8

Input Corrected

Aberration Mag. Phi Residual Residualnm (Deg) RMS P-V

Input(wrt zero) 309.89 1200.00Input - BestPlane 309.89 1200.00Corrected Surface 16.52 84.11Bias 14.151 0.0 21.75 84.11Tilt 0.005 -71.0 21.75 84.11Power (Defocus) 35.728 0.0 24.75 87.33Pri Astigmatism 0.010 87.5 24.75 87.34Pri Coma 0.006 -108.9 24.75 87.34Pri Trefoil 2.110 30.0 24.76 87.34Pri Spherical 46.867 0.0 18.47 72.94Sec Astigmatism 0.008 37.7 18.47 72.94Pri Tetrafoil 0.010 4.0 18.47 72.94Sec Coma 0.010 -153.2 18.47 72.94Sec Trefoil 1.816 30.0 18.48 72.87Pri Pentafoil 0.007 -17.4 18.48 72.87Sec Spherical 23.479 0.0 14.78 104.81Ter Astigmatism 0.015 28.1 14.78 104.82Sec Tetrafoil 0.016 31.0 14.78 104.81Pri Hexafoil 70.290 30.0 8.13 43.49Ter Coma 0.007 -173.0 8.13 43.49Ter Trefoil 4.657 30.0 8.06 43.34Sec Pentafoil 0.007 0.9 8.06 43.34Ter Spherical -23.629 0.0 3.53 35.86Qua Astigmatism 0.010 24.4 3.53 35.87Ter Tetrafoil 0.004 27.6 3.53 35.87Sec Hexafoil 7.537 0.0 3.14 28.33

EXAMPLE: See Back-up slides for other aberrations


Zernike to be Corrected Corrected Reduction RequiredAberration P-V RMS RMS1 Factor CorrectionFocus Z20 1200 309.9 16.5 18.8 15.0

Astigmatism Z22 2100 409.9 10.1 40.5 15.0Astigmatism Z2-2 2078 410.0 10.1 40.5 15.0

Coma Z31 240 38.0 7.0 5.5 5.0Coma Z3-1 208 38.0 7.0 5.5 5.0Trefoil Z33 480 72.8 2.5 29.1 5.0Trefoil Z3-3 312 56.9 7.2 8.0 5.0

1) Units are nm surface distortion

Optical Performance Analysis ResultsPerformance meets requirements– Corrected amplitudes and reduction factors Meets Requirements


DERIVED REQUIREMENTS FOR COMPONENTS

Warping Harness

Warping Harness ActuatorsWarping Harness ActuatorsLeaf-SpringsLeaf-SpringsMirror Support Rod Flexures LoadsMirror Support Rod Flexures LoadsPivot LoadsPivot Loads


Component RequirementsDerived Opto-Mechanical Requirements– Resolution:

Requirement of 0.1% (Implies +/-1000 steps full scale, min.) We choose 2X this minimum value

– Motors are 200 steps per revolution with 10 turns gives 2000 steps full scale

– Lead Screw:We choose 5mm travel and screw with 0.5mm lead. (2.5 microns/step)

– Loads: MINIMUM required moment output (Mmin) sufficient to perform required corrections

REQUIRED OUTPUT (Mreq = 1.05* Mmin)

– Hard-Stops: Hard-stops set outside operational range We choose an additional +/-1.5mm of travel: Hard Stop = +/-6.5mm nominally

– 0.5mm for Assembly and mfg. tolerances in whiffletrees (triangle tip/tilt & piston misalignment)

– 0.5mm for WH components mfg, assembly and initial positioning error– 0.5 mm for Compliance of other parts in the system consume stroke– 0.125mm dead-band (lead-screw backlash)

Note that actuator may become temporarily jammed if it hits hard stop– hence, we want them out of the operational range


Design Load Calculation Methodology– 21 WH actuator unit cases in FE model

T on actuator screw element produces a known WH moment Calculate 1. Surface deformation, 2. Loads at actuators, rod flexures, and pivots

– Perform Zernike Correction SimulationStart with specified Zernike errorsCorrect using linear comb. of 21 actuators (minimize surface RMS)

– Back-Calculate Actuator, Rod Flexure, and Pivot Loads from actuation

– 8th load case calculated:Simultaneous correction of seven Zernike cases (absolute summation)

Interested in WH Actuator Loads (will discuss rod and pivot loads elsewhere)

Component Requirements

Unit Load Matrix60 x 21

Actuator Matrix21 x 7

Component Loads60 x 7

= Unit Load Matrix60 x 21

Actuator Matrix21 x 7

x

(60 FEA results by 21 load cases)

(Act. Correction Matrix: 21 Actuators Factors by 7 Load Cases)

Expanded Component Loads60 x 8 (60 results {actuator, rod, pivot} by 8 load cases)


Actuator RequirementsDesign Load Calculation Methodology, cont.– Expanded Component Loads Matrix gives Actuator Load requirements

Mmin (from Simultaneous Zernike Correction Case) Min MomentsWARPING HARNESS MOMENTS TO CORRECT SPECIFIED ZERNIKES (N-m)

Leaf Spring Focus Astig Coma Trefoil 100% Comb.Actuator Location Length, mm Z20 Z2+2 Z2-2 Z31 Z3-1 Z33 Z3-3 Load Case1

WT-1 M_Inner Triangle-a P1A M_ 0.190 -2.855 0.524 0.000 0.000 -2.020 0.000 -0.038 5.44WT-2 M_Inner Triangle-a P2A M_ 0.190 -2.853 -0.263 -0.455 1.749 1.009 0.000 -0.037 6.37 Max InnerWT-3 M_Inner Triangle-a P3A M_ 0.190 -2.855 -0.263 0.456 -1.749 1.010 0.000 -0.038 6.37 6.37WT-1 Mx'_Outer Triangle-b P1B M_X' 0.120 0.328 1.930 2.918 1.699 -0.033 -0.428 0.972 8.31 WT-1 Mx'_Outer Triangle-c P1C M_X' 0.120 0.328 1.930 -2.918 -1.699 -0.034 0.428 0.973 8.31WT-2 Mx'_Outer Triangle-b P2B M_X' 0.120 0.329 1.562 -3.130 -0.820 1.488 -0.428 0.972 8.73 WT-2 Mx'_Outer Triangle-c P2C M_X' 0.120 0.327 -3.493 -0.213 0.879 -1.454 0.428 0.973 7.77 WT-3 Mx'_Outer triangle-b P3B M_X' 0.120 0.328 -3.491 0.212 -0.878 -1.454 -0.427 0.972 7.76 WT-3 Mx'_Outer Triangle-c P3C M_X' 0.120 0.327 1.560 3.130 0.819 1.487 0.427 0.973 8.72 WT-1 My'_Outer Triangle-b P1B M_Y' 0.120 0.494 -2.363 1.011 0.001 0.526 -0.817 -0.569 5.78 WT-1 My'_Outer Triangle-c P1C M_Y' 0.120 0.493 -2.364 -1.013 -0.002 0.526 0.817 -0.569 5.78 WT-2 My'_Outer Triangle-b P2B M_Y' 0.120 0.493 2.057 1.541 -0.456 -0.262 -0.816 -0.569 6.19 WT-2 My'_Outer Triangle-c P2C M_Y' 0.120 0.493 0.305 2.552 -0.454 -0.264 0.817 -0.569 5.45 WT-3 My'_Outer Triangle-b P3B M_Y' 0.120 0.493 0.306 -2.551 0.454 -0.264 -0.817 -0.569 5.45 WT-3 My'_Outer Triangle-c P3C M_Y' 0.120 0.493 2.057 -1.540 0.456 -0.262 0.816 -0.568 6.19 WT-1 Mx''_Large_Triangle-d P1D M_X'' 0.120 -2.841 2.642 0.346 0.446 -0.872 -0.181 0.785 8.11 WT-2 Mx''_Large_Triangle-d P2D M_X'' 0.120 -2.842 -1.022 -2.463 0.533 0.823 -0.181 0.784 8.65 WT-3 Mx''_Large_Triangle-d P3D M_X'' 0.120 -2.841 -1.621 2.113 -0.978 0.049 -0.181 0.784 8.57 WT-1 My''_Large_Triangle-d P1D M_Y'' 0.120 -2.840 2.642 -0.345 -0.445 -0.873 0.180 0.784 8.11 WT-2 My''_Large_Triangle-d P2D M_Y'' 0.120 -2.841 -1.620 -2.112 0.978 0.050 0.181 0.783 8.57 Max Other WT-3 My''_Large_Triangle-d P3D M_Y'' 0.120 -2.840 -1.020 2.460 -0.533 0.822 0.181 0.783 8.64 8.73

Piston Correction (nm) 804.7 -0.1 0.0 0.0 0.0 0.0 -649.6 1454.5Tip Correction (nm) 0.0 0.1 -4266.4 1932.4 0.6 0.1 0.2 6199.7Tilt Correction (nm) -0.2 -4267.9 -2.2 -0.5 1933.6 0.0 -0.5 6204.9

Max WH Moment (N-m) 0.494 2.642 3.130 1.749 1.488 0.817 0.973 -Min WH Moment (N-m) -2.855 -3.493 -3.130 -1.749 -2.020 -0.817 -0.569 -

Max Abs WH Moment (N-m) 2.855 3.493 3.130 1.749 2.020 0.817 0.973 8.73Note: A positive moment on the actuator is consistent with a compressive force in the WH lead screw (WH knob turned CCW).

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Actuator RequirementsDesign Load Calculation Methodology, cont.– Add 5% margin then round up to nearest 0.5 Nm gives Mreq

– Packaging constraints produce two actuator geometries:Type-1: At 3-Inner Triangles: 190 mm long leaf spring

– Mreq = 7.00 Nm, Force = 37N

Type-2: At 18-Other locations: 120 mm long leaf spring– Mreq = 9.50 Nm, Force = 79N

– Required actuator force output: 79N (Operating)

Required WH Moments Leaf Required Actuator ForceActuator Operating - Load at 5mm stroke Hard Stop Spring Axial Load, NLocation Mmin 1.05Mmin Mreq

1 6.5mm Length, mm at 5mm Hard Stop

Inner Triangle 6.37 6.69 7.00 9.10 0.190 36.8 47.9Other Locations 8.73 9.17 9.50 12.35 0.120 79.2 102.9

Stroke = 5.00 mm Hard Stop= 6.50 mmNote: 1) Rounded up to next 0.5Nm value


Component RequirementsRod Flexure and Pivot Loads– Two design cases for Warping Harness

Simultaneous Zernike Correction Case– Extracted from the Expanded Component Loads Matrix (Slide 21)

Simultaneous actuator runaway against hard-stop (controller malfunction)– Unit Load Matrix scaled to Hard-Stop actuator load levels (absolute summation)

COMPONENT DESIGN LOADS, NSIMULTANEOUS MAX 1-g AXIAL

COMPONENT ZERNIKE CASE HARD-STOP CASE LOAD (for ref.)27 Mirror Support Flexures 51.1 163.2 76.79 Tri-Tri Pivots 78.4 274.2 200.83 Moving Frame to Lg Tri Pivots 122.3 229.8 568.9


MECHANICAL & ELECTRICAL DESIGN

Warping Harness

Moment Actuator SystemMoment Actuator SystemLinear ActuatorLinear ActuatorInstrumented Leaf SpringInstrumented Leaf SpringWiring & ConnectorsWiring & Connectors


Moment Actuator SystemWhiffletree Moment Actuator:– Linear Actuator pushing on Leaf Spring:

Linear actuator:– Stepper motor driven lead screw (0.5mm pitch)– NEMA-17 Stepper Motor, 30 oz-in holding torque [TBC by Dev. testing]– Stall-Torque Margin > 100% [TBC Derived Requirement)

Flexible leaf spring– Instrumented with strain gauge

– Low cost components (>12,000 assemblies required):Testing required to verify performance & reliability

– Two moment actuator types:Inner Triangle: 190mm Spring, M = 7.0 Nm (3 per segment)Other Locations: 120mm Spring, M = 9.5 Nm (18 per Segment)

– Same Linear Actuator used in each location, two leaf spring types:Capable of producing 79 N force


Moment Actuator System

Leaf Spring

Typical Warping Harness Moment Actuator:

Large TriangleInner Triangle

Actuator

Whiffletree Joint, typical


Linear ActuatorLinear Actuator Design:– Produces >79N force– Resolution better than 0.1%

5mm * (1 rev/0.5mm) * (200 steps/rev) = 2000 steps 0-peak (0.05% nominally)– Modular design

Built and tested as sub-assemblyMotors replaceable in-situ

– Internal hard-stops to prevent over-driving– +/- 6.5 mm Stroke (Between hard-stops)– Dead-band

0.125mm thrust clearance built into screw/nut combination– Low cost components– Vacuum compatible [Specific requirement TBD ]

Vacuum grease in motor bearingsLow out-gassing materialsClean

– Lead screw enclosed to keep mechanism cleanvented for vacuum


Linear ActuatorLinear Actuator Design:

Leaf Spring

Actuator Baseplate

StepperMotor

NEMA-1730 oz-in

Motor Mount(Extrusion)

Hand-knob

Dust cap

Bellows – Dust Seal

Whiffletree Triangles


Linear ActuatorLinear Actuator Design:

Stepper Motor

Extruded Alum.

Motor Mount

FlexibleShaftCoupling

Drive Screw (Stainless Steel)Lubricated with Krytox GPL 216 MoS2 filled vacuum grease

Drive Nut360 Brass

Shaft Bearing Set:Bushings (Rulon LR)Thrust Washers SST

Snap rings

Leaf Spring Capture Nut

Outer Hard StopSnap-ring + Washer


Retracted Against Hard StopExtended Against Hard Stop

Linear ActuatorLinear Actuator Design: Neutral Position


Linear ActuatorLinear Actuator Design:– Motor Removed

6 ea Access holes for coupling clamp Screws


Stepper Motor SpecificationStepper Motor Specs– Vendor: TBD; Model: HT17-30– NEMA 17 standard mount– 30 oz-in (212 N-mm) of holding torque– 1.8° step angle (200 per rev)– Coil current: 1.3 A– Detent torque: 5 Nmm – Dimensions:

Height: 33 mmWidth: 42 mmShaft: 5 mm Mass: 194 g

– Vacuum grease, low out-gassing materials and bake-out required– Considerations:

low inductance will reduce transients during multiplexing


Linear ActuatorLinear Actuator Design:– Actuator Design Calculations – Type-1: Inner Triangle Locations

WARPING HARNESS MOTOR TORQUE CALCULATIONQuantity Units Source/Basis Equation

LOAD REQUIREMENTSRqd. WH Torque T_WH = 7000 N-mm WH Analysis Rqd Torque

WH Beam Length L_WH = 190.00 mm CAD ModelWH Actuator Force F_WH = 36.84 N =T_WH/L_WH

F_WH = 8.28 lbSCREW GEOMETRY

Lead lead = 0.500 mmFriction Coefficient mu = 0.2 Per Shigley: Machine Design

Screw mean diameter dm = 4 mmThread angle alpha = 30 deg UNF

Secant (thread angle) sec = 1.155 =1/COS(alpha*PI()/180)Torque-Force Relationship K = 0.546 Nmm/N Shigley: T=KF =dm/2*((PI()*mu*dm*sec+lead)/(PI()*dm-mu*lead*sec))

BUSHING GEOMETRYThrust Bushing OD db = 11.11 mm 7/16" ODThrust Bushind ID dbo = 4.76 mm

Bushing friction mub = 0.15Bushing Thrust Pressure P_Bush = 0.465 N/mm2 =F_WH/(PI()*(db^2-dbo^2)/4)

P_Bush = 67 psi =145*P_BushFRICTION TORQUE

Rqd. Screw Torque T_screw 20.1 N-mm =F_WH*KRqd. Bushing Torque T_bush 21.9 N-mm acts at mean rad. =mub*F_WH*(db+dbo)/4

REQUIRED TORQUE T_rqd = 42.1 N-mm =T_bush+T_screwT_rqd = 6.0 in-oz =T_rqd/7.0616

MOTOR OUTPUT Rated Motor Torque T_Motor = 30.00 in-oz Holding Torque for HT17-30

T_Motor_Nmm = 211.8 N-mm =T_MOTOR*7.0616Driver De-rating Factor Derating = 0.70 Applied Motion - Motor/Driver factor for slow speedDerated Motor Torque Available Torque = 148.3 N-mm =T_Motor_Nmm*Derating

TORQUE MARGIN Margin = 3.53 =T_Motor_Nmm*G34/T_rqd


Linear ActuatorLinear Actuator Design:– Actuator Design Calculations – Type-2: Other Locations

WARPING HARNESS MOTOR TORQUE CALCULATIONQuantity Units Source/Basis Equation

LOAD REQUIREMENTSRqd. WH Torque T_WH = 9500 N-mm WH Analysis Rqd Torque

WH Beam Length L_WH = 120.00 mm CAD ModelWH Actuator Force F_WH = 79.17 N =T_WH/L_WH

F_WH = 17.80 lbSCREW GEOMETRY

Lead lead = 0.500 mmFriction Coefficient mu = 0.2 Per Shigley: Machine Design

Screw mean diameter dm = 4 mmThread angle alpha = 30 deg UNF

Secant (thread angle) sec = 1.155 =1/COS(alpha*PI()/180)Torque-Force Relationship K = 0.546 Nmm/N Shigley: T=KF =dm/2*((PI()*mu*dm*sec+lead)/(PI()*dm-mu*lead*sec))

BUSHING GEOMETRYThrust Bushing OD db = 11.11 mm 7/16" ODThrust Bushind ID dbo = 4.76 mm

Bushing friction mub = 0.15Bushing Thrust Pressure P_Bush = 1.000 N/mm2 =F_WH/(PI()*(db^2-dbo^2)/4)

P_Bush = 145 psi =145*P_BushCOMPONENTS OF TORQUE

Rqd. Screw Torque T_screw 43.3 N-mm =F_WH*KRqd. Bushing Torque T_bush 47.1 N-mm acts at mean rad. =mub*F_WH*(db+dbo)/4

REQUIRED TORQUE T_rqd = 90.4 N-mm =T_bush+T_screwT_rqd = 12.8 in-oz =T_rqd/7.0616

MOTOR OUTPUT Rated Motor Torque T_Motor = 30.00 in-oz Holding Torque for HT17-30

T_Motor_Nmm = 211.8 N-mm =T_MOTOR*7.0616Driver De-rating Factor Derating = 0.70 Applied Motion - Motor/Driver factor for slow speedDerated Motor Torque Available Torque = 148.3 N-mm =T_Motor_Nmm*Derating

TORQUE MARGIN Margin = 1.64 =T_Motor_Nmm*G34/T_rqd


Linear ActuatorLinear Actuator Design:– Hard-stop design loads (a function of friction)

Worst Case Analyzed: Low friction results in large hard-stop loads:

– Screw Friction 0.1 Thrust Washer Friction 0.05– Max Hard-stop load on Type-1 actuator: 243N– Shaft Stop (E-ring) reacts actuator force

E-ring strength = 289NFactor of Safety = 1.2 Outer Hard-stop

HARD-STOP REACTION LOADS FOR A RANGE OF FRICTION COEFFICIENTSLeaf Required Load Leaf Spring Motor Torque m_Screw = 0.3 0.2 0.15 0.1

Spring Moment Force Stiffness Hard Stop N-mm m_Thrust = 0.25 0.15 0.1 0.05Length, m N-m N N/mm Force, N Rated Derated Actuator Output, N = 84 130 180 290

Type-1 Force on Hardstop, N = 36 82 132 243Inner 0.190 7.0 36.8 7.37 47.9 212 148 Hard Stop FOS = 8.1 3.5 2.2 1.2

TriangleType-2 Force on Hardstop, N = Stalled 27 77 188Other 0.120 9.5 79.2 15.83 102.9 212 148 Hard Stop FOS = - 10.7 3.8 1.5

LocationsMotor Holding Torque = 30 in-oz = 212 N-mm HARD STOP STRENGTH: Controlled by snap-ring at end of screw.

Motor-driver Derating Factor = 0.7 E-Ring: 5133-12 (Truarc) Allowable load F_ring = 65 lbHard-stop travel = 6.5 mm F_ring = 289 N


Instrumented Leaf SpringsLeaf Spring Design Requirements– Two types: 190 mm and 120 mm long– Strokes:

5mm operational6.5mm at hard-stop

– Strain gauge for feedback:resolution 0.1% of full scalecalibrated

– Material: Aluminum 7075-T651 per AMS QQ-A-250/12Match CTE of whiffletreesYield Strength = 69 ksi (476 MPa), Ultimate Strength = 80 ksi (552 MPa)

– Considerations:Stress:

– Desire a high, uniform strain field at gauge location– Minimize stress elsewhere

Beam and gauge fatigue life (>100,000 cycles)gauge thermal compensationCost


Instrumented Leaf SpringsLeaf Spring Concept:– Re-entrant tab tuned to produce zero slope at drive screw

Prevents binding at drive screwNo additional spherical bearing required - low cost, simple

Note: Deflection Exaggerated 10X


120 mm

Instrumented Leaf SpringsBending-beam transducers

gauge locations as shown (one side only)

Type-2 Leaf Springs5.80 mm thick – made in orthogonal pairs

Type-1 Leaf Springs6.70 mm thick190 mm


Instrumented Leaf SpringsLeaf Spring Concept: Type-2 (Other locations)– Deflection, Slope, and Stress Results:

Deflection Exaggerated 5x

Deflection: 6.5mm at drive screw Hard stop displacement

Deflection, mm

Slope, rad.

von Mises Stress, MPa

Stress: 261 MPa (38 ksi)at Hard-stop FSy = 69/38 = 1.81

Slope: 0.33 mradAt drive Screw

F=102.9N


Instrumented Leaf SpringsStrain Gauge Location– Beam root necked-down and tapered to shape stress field:

High, uniform stress field preferred for gauge resolution and lifetimeVishay recommends <1700 micro-strain for 1E6 fully reversed cycles (100me shift)We relax by 1.5x to <2550 micro-strain for our design (<1E6, and rarely reversed)

Type-1 (Inner Triangle)Longitudinal Strain at Gauge Location

x = 1513 me at 6.5mm deflection

Type-2 (Other Locations)Longitudinal Strain at Gauge Location

x = 2276 me at 6.5mm deflection

GaugeLocation Gauge

Location

Axial Strain m/m Axial Strain m/m


Instrumented Leaf SpringsLeaf Spring Stress, Strain, FOS Summary

Leaf Spring Results for 5.0 mm deflection Results for 6.5 mm deflectionDimensions, mm Max Stress Yield Axial Strain Max Stress Yield Axial Strain

Location Length Thk. MPa (ksi) FOS at gage me MPa (ksi) FOS at gage me

Type-1, Inner Tri 190 6.70 123.8 3.84 1164 161.0 2.96 1513(18.0) (23.3)

Type-2, Other 120 5.80 200.8 2.37 1982 261.0 1.82 2576(29.1) (37.8)

Material: 7075-T651 Yield Strength 69 ksi476 MPa


Instrumented Leaf SpringsStrain Gauge– Bending-beam transducer: Full Poisson Bridge

Vishay JA2-13-S1425-35B 5.64mm x 6.66mmBending strain amplified by Poisson effectInherently temperature compensatingGauge CTE matched to leaf spring material

– Gauge installation by transducer manufacturer:Gauge bonding, lead attachment, encapsulation, strain relief & connectorizationCalibration

– each beam has engraved S/N and barcode sticker– calibration results entered into database

– Strain Gauge heat dissipationP = V2 / R = (10V)2 / 350 = 286 mW/bridgeNeed to investigate on/off transient of gauges

– what is time constant for stable reading– 12,000 gauges x may be significant if serial op.– 12,000 * 286 mW also significant (3.4KW)

Heating and timeline must be balanced– Will investigate (literature, experts, prototypes)

+VIN Sign

al

-VIN

4

312

Sign

al

BC A D


Strain GaugesSummary of Predicted Strain Gauge Performance:– See backup slides for supporting calculations

– Required resolution (0.1%) corresponds to 2 steps:Type 1 Leaf Spring output is 16.26 mV (for 10 V excitation) Type 2 Leaf Spring output is 27.68 mV (for 10 V excitation)

Strain at Gauge Location, micro strain Micro Strain Micro volts/stepLocation 5mm nom. Stroke 6.5mm hard stop per step 10V Excitation

Type-1, Inner Triangle 1164 1513 0.582 8.13

Type-2, Outer Triangle 1982 2576 0.991 13.84


Wiring & ConnectorsWarping Harness Wiring and Connectors– Stepper motor windings connected in series (max low speed torque)

Winding splice and connectorizing performed by stepper motor supplier4 wires per motor

– 2 of which are common to all 21 motors say -A and -B

– 2 of which are unique (switched to driver)say +A and +B

– Strain Gauges have 4 leads each2 leads are common to all gauges (A & C)2 output signals are unique for each gauge (B & D)

+VIN Sign

al

-VIN

4

312

Sign

al

BC A D


Strain Gauge WiringWarping Harness Wiring and Connectors– 44 pins/segment

– Type-1 Leaf Spring requires one 4 pin connector: 1 strain gauge bridge per assembly

– Type-2 Leaf Spring requires 6 pin connector 2 bridges/assembly ( 2 common, 4 gauge signal)

+Vin

-Vin

WH-1 WH-2 WH-3 WH-4 WH-5

Signal-1 Signal-1 Signal-2 Signal-2 Signal-3 Signal-3 Signal-4 Signal-4 Signal-5 Signal-5

2 x 21 Outputs = 42 channels

21 Warping Harness Gauges per Segment

2 Common Inputs

44 pins required for strain gauges


Stepper Motor Wiring and Connectors– 44 pins/segment

Stepper Motor WiringPh

ase-

A

Phase-B

Phas

e-A

Phase-B

Phas

e-A

Phase-B

Phas

e-A

Phase-B

Common A

Common B

2 x 21 Inputs = 42 channels from relay panel

44 pins required for stepper motors

WH-1 WH-2 WH-3 WH-4


Warping Harness Wiring and Connectors– Layout:

44 pins for strain gauges44 pins for stepper motors2 pins for segment serial number communication I/O1 ground pin89 TOTAL PINS

– Connector types and models TBD

Stepper Motor Wiring

89 pins required


Warping Harness Control Layout – 3 of N Segments Shown

Stepper Motor Wiring

21 Strain gauges21 Strain gauges21 Stepper motors21 Stepper motors

Stepper DriverStepper Driver(Single Axis)(Single Axis)



Stepper RelayStepper Relay BoxBox

M1CS

Power

Coolant

44 wires44 wires 44 wires44 wires 44 wires44 wires

Segment-i Segment-j Segment-k

DAQDAQ

Strain Gauge Strain Gauge Relay BoxRelay Box

44 wires44 wires44 wires44 wires 44 wires44 wires

WH Control Node (Supports N segments) Cell Mounted

Processor/Communication/Power supplyProcessor/Communication/Power supply


Connector Bulkhead Panel

SSA Wiring



SSA Wiring



SSA Wiring

Cable passage around base of tower


QUANTIZATION ERROR ESTIMATE

Warping Harness


Quantization Error EstimateQuantization Error– Actuators adjustments are in discrete steps– Error is an even distribution between -1/2 and +1/2 from desired setting

RMS of this distribution is 1/(120.5) for each term– System quantization error calculated as:

RSS of [(RMS/stepi)/(120.5)]i=1:21

Result: Quantization Error = 0.182 nm RMS– See BACK-UP charts for calculation details


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

Warping Harness


Actuator Effectiveness Warping Harness Actuator Effectiveness:– Maximum # actuators on 27-point whiffletree is 24: [N-3 = 27-3 = 24]– Actuator effectiveness studied by systematically eliminating sets of actuators

and recalculating performance (these are 1.2m results, valid for 1.44m)Case # Full Set 2 3 4 5 6 7 8 9 10 (3+7) 11 (3+9)

# Actuators Eliminated 0 6 3 3 6 6 3 3 6 6 9Number of Actuators Active 24 18 21 21 18 18 21 21 18 18 15

Best fit Correction Eliminated Actuator Locations - M_act Mr_act M_act Mr_o M_o Mr_i M_i Mr_i, M_i Mr_i, Mr_act Mr_i, M_i, Mr_act RequiredLoad Initial Reduction Reduction Reduction Reduction Reduction Reduction Reduction Reduction Reduction Reduction Reduction ReductionCase Aberration Phi P-V RMS Factor Factor Factor Factor Factor Factor Factor Factor Factor Factor Factor Fctor

1 Focus 0 1000 258.2 18.5 4.7 18.5 4.7 18.4 16.2 18.5 12.4 12.4 18.5 12.4 15.02 Astigamtism-1 0 1750 341.6 54.1 36.2 49.9 43.3 31.5 40.4 43.1 53.9 53.9 42.5 42.4 15.03 Astigamtism-2 45 1732 341.6 54.1 36.2 49.9 43.3 31.5 40.4 43.1 53.9 53.9 42.5 42.4 15.04 Coma-1 0 200 31.7 6.0 5.8 5.8 6.0 5.3 4.8 5.5 5.1 5.1 5.4 4.6 5.05 Coma-2 90 173 31.7 6.0 5.8 5.8 6.0 5.3 4.8 5.5 5.1 5.1 5.4 4.6 5.06 Trefoil-1 0 400 60.7 31.0 29.4 29.4 31.0 31.0 15.4 28.9 31.0 31.0 28.4 28.4 5.07 Trefoil-2 30 260 47.5 8.0 3.1 8.0 3.1 1.0 8.0 8.0 8.0 8.0 8.0 8.0 5.0

Max Actuator Moment, N-m 3.1 7.6 3.9 7.6 4.3 3.1 2.9 3.6 3.6 2.9 3.6

Case # Full Set 2 3 4 5 6 7 8 9 10 (3+7) 11 (3+9)# Actuators Eliminated 0 6 3 3 6 6 3 3 6 6 9

Number of Actuators Active 24 18 21 21 18 18 21 21 18 18 15















Optical Performance Analysis ResultsFocus Correction



Input Corrected


Input(wrt zero) 309.89 1200.00Input - BestPlane 309.89 1200.00Corrected Surface 16.52 84.11Bias 14.151 0.0 21.75 84.11Tilt 0.005 -71.0 21.75 84.11Power (Defocus) 35.728 0.0 24.75 87.33Pri Astigmatism 0.010 87.5 24.75 87.34Pri Coma 0.006 -108.9 24.75 87.34Pri Trefoil 2.110 30.0 24.76 87.34Pri Spherical 46.867 0.0 18.47 72.94Sec Astigmatism 0.008 37.7 18.47 72.94Pri Tetrafoil 0.010 4.0 18.47 72.94Sec Coma 0.010 -153.2 18.47 72.94Sec Trefoil 1.816 30.0 18.48 72.87Pri Pentafoil 0.007 -17.4 18.48 72.87Sec Spherical 23.479 0.0 14.78 104.81Ter Astigmatism 0.015 28.1 14.78 104.82Sec Tetrafoil 0.016 31.0 14.78 104.81Pri Hexafoil 70.290 30.0 8.13 43.49Ter Coma 0.007 -173.0 8.13 43.49Ter Trefoil 4.657 30.0 8.06 43.34Sec Pentafoil 0.007 0.9 8.06 43.34Ter Spherical -23.629 0.0 3.53 35.86Qua Astigmatism 0.010 24.4 3.53 35.87Ter Tetrafoil 0.004 27.6 3.53 35.87Sec Hexafoil 7.537 0.0 3.14 28.33


Optical Performance Analysis ResultsAstigmatism Correction



Input Corrected


Input(wrt zero) 409.91 2100.00Input - BestPlane 409.91 2100.00Corrected Surface 10.12 77.05Bias 0.007 0.0 10.12 77.05Tilt 1.929 -90.1 10.16 78.92Power (Defocus) 0.020 0.0 10.16 78.92Pri Astigmatism 20.722 0.0 12.24 59.78Pri Coma 2.210 -90.2 12.26 58.63Pri Trefoil 0.019 31.6 12.26 58.63Pri Spherical 0.027 0.0 12.26 58.64Sec Astigmatism 30.498 0.0 9.78 67.69Pri Tetrafoil 32.140 45.0 9.49 52.92Sec Coma 6.494 -90.1 9.36 51.73Sec Trefoil 0.021 34.4 9.36 51.73Pri Pentafoil 0.726 -17.9 9.36 51.51Sec Spherical 0.025 0.0 9.36 51.51Ter Astigmatism 0.175 1.0 9.37 51.54Sec Tetrafoil 23.858 45.0 6.75 44.44Pri Hexafoil 0.048 27.5 6.75 44.41Ter Coma 2.901 -90.2 6.72 44.55Ter Trefoil 0.011 35.1 6.72 44.55Sec Pentafoil 1.750 -18.0 6.71 45.12Ter Spherical 0.009 0.0 6.71 45.12Qua Astigmatism 3.022 0.0 6.66 45.43Ter Tetrafoil 10.004 0.0 6.29 43.06Sec Hexafoil 0.027 27.0 6.29 43.08


Optical Performance Analysis ResultsAstigmatism Correction



Input Corrected


Input(wrt zero) 409.95 2078.46Input - BestPlane 409.95 2078.46Corrected Surface 10.12 85.63Bias -0.002 0.0 10.12 85.63Tilt 1.928 180.0 10.16 88.35Power (Defocus) -0.004 0.0 10.16 88.35Pri Astigmatism 20.730 45.0 12.24 61.98Pri Coma 2.208 180.0 12.27 61.74Pri Trefoil 0.016 30.1 12.27 61.74Pri Spherical -0.003 0.0 12.27 61.74Sec Astigmatism 30.515 45.0 9.79 74.55Pri Tetrafoil 32.166 22.5 9.49 60.63Sec Coma 6.492 -180.0 9.37 59.62Sec Trefoil 0.010 27.6 9.37 59.62Pri Pentafoil 0.725 0.0 9.37 59.36Sec Spherical -0.001 0.0 9.37 59.36Ter Astigmatism 0.188 44.2 9.37 59.40Sec Tetrafoil 23.896 22.5 6.75 45.95Pri Hexafoil 0.019 -13.5 6.75 45.95Ter Coma 2.897 180.0 6.72 46.96Ter Trefoil 0.006 27.9 6.72 46.96Sec Pentafoil 1.751 0.0 6.71 46.24Ter Spherical -0.002 0.0 6.71 46.24Qua Astigmatism 3.029 45.0 6.66 45.27Ter Tetrafoil 9.989 -22.5 6.29 48.78Sec Hexafoil 0.009 -14.5 6.29 48.77


Optical Performance Analysis ResultsComa Correction

Input = 120 nm PV = 240 nm surface, RMS = 38.0 nmCorrected: PV = 61.8 nm surface, RMS = 6.96 nm


Input Corrected


Input(wrt zero) 38.01 240.00Input - BestPlane 38.01 240.00Corrected Surface 6.96 61.77Bias -0.006 0.0 6.96 61.77Tilt 12.806 0.0 9.09 55.27Power (Defocus) -0.015 0.0 9.09 55.27Pri Astigmatism 0.313 -45.3 9.09 55.26Pri Coma 22.234 0.0 8.74 55.11Pri Trefoil 0.010 20.4 8.74 55.11Pri Spherical -0.020 0.0 8.74 55.11Sec Astigmatism 0.962 45.2 8.72 55.11Pri Tetrafoil 2.912 22.5 8.73 55.21Sec Coma 22.702 0.0 6.51 53.73Sec Trefoil 0.014 20.1 6.51 53.74Pri Pentafoil 22.344 36.0 5.78 43.98Sec Spherical -0.016 0.0 5.78 43.98Ter Astigmatism 6.564 -45.0 5.46 42.05Sec Tetrafoil 2.477 22.5 5.45 41.38Pri Hexafoil 0.033 -1.9 5.45 41.39Ter Coma 2.820 0.0 5.42 41.90Ter Trefoil 0.009 15.8 5.42 41.90Sec Pentafoil 7.606 36.0 5.14 38.24Ter Spherical -0.006 0.0 5.14 38.24Qua Astigmatism 2.846 45.0 5.10 39.24Ter Tetrafoil 2.869 22.5 5.07 37.27Sec Hexafoil 0.019 -1.1 5.07 37.27


Optical Performance Analysis ResultsComa Correction



Input Corrected


Input(wrt zero) 38.01 207.85Input - BestPlane 38.01 207.85Corrected Surface 6.96 64.58Bias 0.001 0.0 6.96 64.58Tilt 12.798 90.0 9.09 48.99Power (Defocus) 0.002 0.0 9.09 48.99Pri Astigmatism 0.319 87.7 9.09 49.13Pri Coma 22.219 90.0 8.73 47.85Pri Trefoil 0.006 -44.0 8.73 47.85Pri Spherical 0.003 0.0 8.73 47.85Sec Astigmatism 0.955 0.9 8.72 47.86Pri Tetrafoil 2.901 44.8 8.73 47.89Sec Coma 22.682 90.0 6.51 50.00Sec Trefoil 0.006 51.4 6.51 49.99Pri Pentafoil 22.310 18.0 5.78 38.46Sec Spherical 0.003 0.0 5.78 38.46Ter Astigmatism 6.567 89.9 5.46 36.92Sec Tetrafoil 2.465 44.8 5.45 36.29Pri Hexafoil 0.025 18.1 5.45 36.29Ter Coma 2.810 90.1 5.42 36.75Ter Trefoil 0.004 -51.4 5.42 36.75Sec Pentafoil 7.578 18.0 5.14 34.11Ter Spherical 0.001 0.0 5.14 34.11Qua Astigmatism 2.844 0.2 5.10 34.98Ter Tetrafoil 2.864 44.9 5.07 33.16Sec Hexafoil 0.014 17.5 5.07 33.15


Optical Performance Analysis ResultsTrefoil Correction



Input Corrected


Input(wrt zero) 72.79 480.00Input - BestPlane 72.79 480.00Corrected Surface 2.50 30.09Bias -0.001 0.0 2.50 30.09Tilt 0.000 89.2 2.50 30.09Power (Defocus) -0.003 0.0 2.50 30.09Pri Astigmatism 0.004 66.2 2.50 30.09Pri Coma 0.001 71.4 2.50 30.09Pri Trefoil 3.461 0.0 2.68 23.17Pri Spherical -0.004 0.0 2.68 23.17Sec Astigmatism 0.005 67.1 2.68 23.18Pri Tetrafoil 0.006 16.0 2.68 23.17Sec Coma 0.001 51.1 2.68 23.17Sec Trefoil 6.290 0.0 2.23 14.43Pri Pentafoil 0.002 4.1 2.23 14.42Sec Spherical -0.004 0.0 2.23 14.42Ter Astigmatism 0.004 68.3 2.23 14.42Sec Tetrafoil 0.005 17.2 2.23 14.43Pri Hexafoil 0.290 -14.8 2.23 14.42Ter Coma 0.001 33.4 2.23 14.42Ter Trefoil 2.793 0.0 2.13 12.15Sec Pentafoil 0.003 5.4 2.13 12.15Ter Spherical -0.002 0.0 2.13 12.15Qua Astigmatism 0.001 65.1 2.13 12.15Ter Tetrafoil 0.002 19.2 2.13 12.15Sec Hexafoil 0.185 -14.9 2.13 12.15


Optical Performance Analysis ResultsTrefoil Correction



Input Corrected


Input(wrt zero) 56.94 311.77Input - BestPlane 56.94 311.77Corrected Surface 7.16 42.02Bias -0.058 0.0 7.16 42.02Tilt 0.009 -119.4 7.16 42.02Power (Defocus) -0.161 0.0 7.16 42.02Pri Astigmatism 0.008 51.2 7.16 42.02Pri Coma 0.011 -119.1 7.16 42.03Pri Trefoil 40.420 30.0 11.22 46.34Pri Spherical -0.285 0.0 11.22 46.34Sec Astigmatism 0.007 50.9 11.22 46.35Pri Tetrafoil 0.011 22.6 11.22 46.34Sec Coma 0.003 -112.5 11.22 46.34Sec Trefoil 43.128 30.0 0.68 5.20Pri Pentafoil 0.011 -14.2 0.68 5.20Sec Spherical 0.224 0.0 0.67 5.20Ter Astigmatism 0.004 48.0 0.67 5.20Sec Tetrafoil 0.003 22.6 0.67 5.20Pri Hexafoil 0.304 0.1 0.67 5.20Ter Coma 0.001 -4.3 0.67 5.20Ter Trefoil 1.490 -30.0 0.58 6.53Sec Pentafoil 0.001 26.2 0.58 6.53Ter Spherical -0.287 0.0 0.57 6.53Qua Astigmatism 0.002 46.1 0.57 6.53Ter Tetrafoil 0.003 22.0 0.57 6.53Sec Hexafoil 0.090 -29.9 0.57 6.53


Strain GaugesPredicted Strain Gauge Performance: Type-1 (Inner Triangle )

WARPING HARNESS LEAF SPRING ANALYSISQuantity Units Source/Basis

Unit FEA ResultsLoad PFEA = 47.9 N

Deflection dFEA = 6.5 mm

X-Normal Strain FEA = 1513 me Axial Strain at Gage Location

Beam Modulus E_beam = 7.21E+10 MPa 7075-T651Beam Poisson's Ratio n_beam = 0.33

WH Beam Stiffness K_beam = 7.369 N/mmStroke Rqd D_max = 5.00 mm Stroke to produce F_WH

Stepper Motor N_steps = 200 steps/revPredicted Resolution: Res = 0.0500% Percent of max per stepRequired Resolution Res_Rqd = 0.1% Percent of full scaleSteps for 0.1% Load Steps_for_Res. = 2.00 Steps Steps to acheive 0.1% of max load

Strain Gage AnalysisAxial strain per mm stroke

x_per_mm 232.8 me/mm

Axial Strain per step x_per_step 0.582 me/step

Strain at operating deflection x_op 1164 me

Gage Factor GF 2.1Gage nominal resistance R0 350 Ohms

Input Voltage VIN = 10 VoltsStrain at Gages e_1 = 0.582 me/step Longitudinal

e_2 = -0.192 me/step Transversee_3 = 0.582 me/step Longitudinale_4 = -0.192 me/step Transverse

Gage Resistances R_1 = 350.0004 ohmsR_2 = 349.9999 ohmsR_3 = 350.0004 ohmsR_4 = 349.9999 ohms

Ouput per Step Vout/Vin = 8.127E-07 per step

Vout = 8.127 mV output/step for 10V ExcitationV_res_rqd 16.251 mV for 0.1% resolution (2 steps)


Strain GaugesPredicted Strain Gauge Performance: Type-2 (Other Locations)

WARPING HARNESS LEAF SPRING ANALYSISQuantity Units Source/Basis

Unit FEA ResultsLoad PFEA = 102.9 N

Deflection dFEA = 6.5 mm

X-Normal Strain FEA = 2576 me Axial Strain at Gage Location

Beam Modulus E_beam = 7.21E+10 MPa 7075-T651Beam Poisson's Ratio n_beam = 0.33

WH Beam Stiffness K_beam = 15.831 N/mmStroke Rqd D_max = 5.00 mm Stroke to produce F_WH

Stepper Motor N_steps = 200 steps/revPredicted Resolution: Res = 0.0500% Percent of max per stepRequired Resolution Res_Rqd = 0.1% Percent of full scaleSteps for 0.1% Load Steps_for_Res. = 2.00 Steps Steps to acheive 0.1% of max load

Strain Gage AnalysisAxial strain per mm stroke

x_per_mm 396.3 me/mm

Axial Strain per step x_per_step 0.991 me/step

Strain at operating deflection x_op 1982 me

Gage Factor GF 2.1Gage nominal resistance R0 350 Ohms

Input Voltage VIN = 10 VoltsStrain at Gages e_1 = 0.991 me/step Longitudinal

e_2 = -0.327 me/step Transversee_3 = 0.991 me/step Longitudinale_4 = -0.327 me/step Transverse

Gage Resistances R_1 = 350.0007 ohmsR_2 = 349.9998 ohmsR_3 = 350.0007 ohmsR_4 = 349.9998 ohms

Ouput per Step Vout/Vin = 1.384E-06 per step

Vout = 13.837 mV output/step for 10V ExcitationV_res_rqd 27.677 mV for 0.1% resolution (2 steps)


Quantization Error CalculationsQuantization Error - Actuators adjustments are in discrete steps– System quantization error calculated as: RSS of [(RMS/stepi)/(120.5)]i=1:21

Determine actuator step size:

Scale unit actuator cases to determine RMS error per stepCalculate segment-level system error (Next slide)

Leaf Required Actuator Force Leaf-spring Stiffness Minimum Step Size1

Actuator Spring Axial Load, N Axial Bending Axial MomentLocation Length, mm at 5mm Hard Stop N/mm Nm/mm N/step N-m/step

Inner Triangle 0.190 36.8 47.9 7.368 1.400 0.01842 0.00350Other Locations 0.120 79.2 102.9 15.833 1.900 0.03958 0.00475

Note: 1) Step_Size = 0.0025 mm (0.5mm per turn / 200 Steps per turn)


Quantization Error CalculationsQuantization Error – Cont.

Actuator Unit Cases Step Minimum Increment QuantizationActuator for 1 N-m moment Size nm/Step Error,

# Actuator Location RMS, m PV, m N-m/step RMS PV RMS per step/120.5

1 WT-1 M_Inner Triangle 1.01E-08 6.15E-08 0.00350 3.54E-02 2.15E-01 0.0102 WT-2 M_Inner Triangle 2.04E-08 1.15E-07 0.00350 7.15E-02 4.03E-01 0.0213 WT-3 M_Inner Triangle 2.04E-08 1.15E-07 0.00350 7.15E-02 4.03E-01 0.0214 WT-1 Mx'_Outer Triangle-a 2.04E-08 1.15E-07 0.00475 9.70E-02 5.47E-01 0.0285 WT-1 Mx'_Outer Triangle-b 2.04E-08 1.15E-07 0.00475 9.70E-02 5.47E-01 0.0286 WT-2 Mx'_Outer Triangle-a 2.04E-08 1.15E-07 0.00475 9.70E-02 5.47E-01 0.0287 WT-2 Mx'_Outer Triangle-b 2.04E-08 1.15E-07 0.00475 9.70E-02 5.47E-01 0.0288 WT-3 Mx'_Outer triangle-a 3.70E-08 2.53E-07 0.00475 1.76E-01 1.20E+00 0.0519 WT-3 Mx'_Outer Triangle-b 3.70E-08 2.53E-07 0.00475 1.76E-01 1.20E+00 0.051

10 WT-1 My'_Outer Triangle-a 3.70E-08 2.53E-07 0.00475 1.76E-01 1.20E+00 0.05111 WT-1 My'_Outer Triangle-b 3.70E-08 2.53E-07 0.00475 1.76E-01 1.20E+00 0.05112 WT-2 My'_Outer Triangle-a 3.70E-08 2.53E-07 0.00475 1.76E-01 1.20E+00 0.05113 WT-2 My'_Outer Triangle-b 3.70E-08 2.53E-07 0.00475 1.76E-01 1.20E+00 0.05114 WT-3 My'_Outer Triangle-a 3.37E-08 1.72E-07 0.00475 1.60E-01 8.17E-01 0.04615 WT-3 My'_Outer Triangle-b 3.37E-08 1.72E-07 0.00475 1.60E-01 8.17E-01 0.04616 WT-1 Mx''_Large_Triangle 3.37E-08 1.72E-07 0.00475 1.60E-01 8.17E-01 0.04617 WT-2 Mx''_Large_Triangle 3.37E-08 1.72E-07 0.00475 1.60E-01 8.17E-01 0.04618 WT-3 Mx''_Large_Triangle 3.37E-08 1.72E-07 0.00475 1.60E-01 8.17E-01 0.04619 WT-1 My''_Large_Triangle 3.37E-08 1.72E-07 0.00475 1.60E-01 8.17E-01 0.04620 WT-2 My''_Large_Triangle 1.56E-08 2.52E-07 0.00475 7.42E-02 1.20E+00 0.02121 WT-3 My''_Large_Triangle 1.56E-08 2.53E-07 0.00475 7.42E-02 1.20E+00 0.021

MAX Value 1.76E-01 1.20E+00Quantization Error (RSS of above column), nm RMS surface 0.182


Revision History11/13/07 Post PDR Corrections– Slide-8: Update power dissipation numbers– Slide 47: Added S/N ID circuit (2 pins)– Slide 53: Changed quantization calculation to cover range -1/2 to + 1/2

Documents

Pasadena, California October 24-25, 2007 Contributors to the development effort: from IMTEC