Instrument & Mission Performance

Ratana Chhun

MICROSCOPE Colloquium II

Summary

• Centring and alignment budgets• Moments of inertia of test-masses• Instrument error budget• Mission error budget

3

QM radial centring budget

RQ-TS-PR-200 Parameter name construction (CONS)

Detector+ADC bias YZ TMA 1.11E-07

Surface diff. between electrodes + & - cylinder 1A 7.79E-07

25 Free course diameter centring hat/cylinder 1A 5.00E-07

28 Concentricity centring cylinder 1A/hat wrt cylinder 2B/hat 1.00E-06

40 Concentricity cylinder 1A 2.50E-0742 Cylindricity cylinder 1A 1.00E-06

07 Concentricity surface internal vs external TMA 3.36E-06

57 External vs internal surface coaxiality TMA included in 07

Detector+ADC bias YZ TMB 8.06E-08

Surface diff. between electrodes + & - cylinder 1B 3.80E-07

31 Free course diameter centring hat/cylinder 1B 3.47E-18

27 Concentricity centring cylinder 1B/hat wrt cylinder 2B/hat 1.00E-06

41 Concentricity cylinder 1B 5.00E-0743 Cylindricity cylinder 1B 1.00E-06

08 Concentricity surface internal vs external TMB 2.30E-06

60 External vs internal surface coaxiality TMB included in 08

Total direct 1.23E-05Total 1 4.68E-06

Contributors:• Capacitive detector• Electrode geometry• Free course between cylinder and hat• Cylinder geometry• Proof-mass geometry

Internal mass

External mass

Total < 20µm, direct or quadratic sum

4

QM axial centring budget

• Assessment requires more specific information• Profiles of masses and cylinders:

• Evaluation of des axial capacitive dissymmetries induced by mutual facing active surfaces

• Constraints one orientation for the mass during assembling

Cylindre 0250A-04

Masse 271E-01

5

QM axial centring budget

• Double budget:• Absolute excentring of each mass functional requirement

= to ensure a maximal free course at both ends• Relative excentring of 2 masses of 1 accelerometer (SU) performance

requirement= to minimise the effects of gravity gradient and of tensor of inertia in the differential measurement

Cylinder TM Delta (µm) Electrode symmetry (µm) Hat (µm) Total (µm)0350A-03 371B-01 2.44 -1.5 0 0.940350A-03 371B-01 INV -7.47 -1.5 0 -8.970250A-04 271E-01 -4.11 -1.7 0 -5.810250A-04 271E-01 INV 24.91 -1.7 0 23.210250A-04 272A-01 -10.82 -1.7 0 -12.520250A-04 272A-01 INV 31.57 -1.7 0 29.87

Delta (µm)0350A-03 371B-01 0250A-04 272A-01 13.460350A-03 371B-01 0250A-04 272A-01 INV -28.930350A-03 371B-01 INV 0250A-04 272A-01 3.550350A-03 371B-01 INV 0250A-04 272A-01 INV -38.84

Delta (µm)0350A-03 371B-01 0250A-04 271E-01 6.750350A-03 371B-01 0250A-04 271E-01 INV -22.270350A-03 371B-01 INV 0250A-04 271E-01 -3.160350A-03 371B-01 INV 0250A-04 271E-01 INV -32.18

SU-REF

SU-EP

Internal mass

External mass

Combination of the 2 masses

With the presented masses:• Internal mass orientation, upside down, straight up OK but upside down more interesting performance-wise• External mass orientation straight up

Absolute excentring

Relative excentring

6

QM alignment budgets

Parameter name construction (CONS) Knowledge (KNOW)Around YZ

RQ-TS-PR-60 Total = SUMI+COM SU+MAX(IS1,IS2) 4.91E-04Total quad = SUMI+COM SU+MAX(IS1,IS2) 2.07E-04

Around XRQ-TS-PR-60 Total = SUMI+COM SU+MAX(IS1,IS2) 5.18E-03 1.45E-03

Total quad = SUMI+COM SU+MAX(IS1,IS2) 3.75E-03 5.56E-04Around YZ

RQ-TS-PR-65 Total 1.81E-04Total quad 8.35E-05

Around XRQ-TS-PR-65 Total 8.69E-04

Total quad 4.76E-04Around XYZ

RQ-TS-PR-70 External vs internal surface coaxiality TMA 6.23E-05 1.00E-04 radExternal vs internal surface coaxiality TMB 1.00E-05 1.00E-04 rad

Around YZRQ-TS-PR-80 Budget (=max of the 2 sub-totals) 4.84E-04

Budget (=max of the 2 quad sub-totals) 2.32E-04Between SU1 and SU2 9.13E-04

Quad between SU1 and SU2 2.97E-04Around X

RQ-TS-PR-80 Total SU =max(sub-total TMA,sub-total TMB) 1.86E-03Quad Total SU =max(sub-total TMA,sub-total

TMB) 6.67E-04

Total SU1/SU2 3.73E-03Quad Total SU1/SU2 9.43E-04

RQ-TS-PR-90 1.00E-04 5.00E-04 mRQ-TS-PR-100 <<Spec 1.00E-07 rad

Spec

1.50E-03 rad

1.50E-03 rad

1.50E-03 rad

1.50E-03 rad

5.00E-03 rad

5.00E-03 rad

Orthogonality

AlignmentAcc/Acc &Acc/Base

AlignmentSensor/sensor

AlignmentknowledgeAcc/Cube

Origin position knowledgeAlignment Therm. Stab.

7

Determination of moments of inertia

• Major terms = diagonal terms of the non sphericity matrix

• Deduced from density measurement of material rings from mass manufacturing procedure Relative inhomogeneity = first diagonal term

• Same value considered for radial axes

488

848

884

101010101010101010

IINS

R1 R2TM

1

21_

R

RRTMNS

II

8

Moments of inertia of FM masses

Number Material Int./Ext.Max.Inhomogeneity

272C-02 PtRh External < 7 10-4

271E-02 TA6V External < 2 10-4

371D-04 PtRh Internal < 11 10-4

371D-05 PtRh Internal < 15 10-4

Impact on angular accelerometric measurement performance

9

Instrument budget

• Inputs:• Measurement frequency• Altitude• Pressure, temperature• Thermal filterings• SU core geometry • Gold wire implantation• Electronics

characteristics:• Bias• Noise• Thermal sensitivities

• Outputs per inertial sensor, per degree of freedom:

• Bias• Noise:

• Bias fluctuation• Parasitic forces• Scale factor

• Thermal sensitivities :• TMEC/TELEC/TMEC

• Bias fluctuation• Parasitic forces• Scale factor

• Measurement/control range

• Quadratic factors

Main hypotheses

• Thermal stabilities:• 1mK MEC@fepi• 5mK ELEC@fepi• 1mK/m TMEC@fepi, 0.1K/m/Hz1/2 around fepi

• 7µm gold wire:• Stiffness and performance extrapolated from 5µm wire

stiffness

• Performance of electronics measured on FM models• Metrological measurements on QM parts

11

Contributors distribution

Noise/ Bias fluctuation

Radial electrode dissymmetries due to machiningFront wall along X: due to defect of symmetry of the axial electrodesFront wall along X: Conicité de la PM vis-à-vis des surfaces en boutCylindricity defect of the silica external cylinder wrt cylindrical PM /m\Cylindricity defect of the PM wrt silica external cylinder c/ \cCylindricity defect of the silica internal cylinder wrt cylindrical PM m/ \mCylindricity defect of the PM wrt silica internal cylinder /c\Lever arm error: Centring of X electrodes wrt YZ electrodes (for )Lever arm error: Axial capacitive sensor bias (for )Lever arm error: PM conicity (for )Lever arm error: Electrode cylinder conicity (for )YZ bias error: DAC+DVA distribution over 4 electrodes (for )YZ bias error: CPD (for )YZ bias error: Radial electrode dissymmetries (for ) all in 0Concentricity of the two cagesDetection: Capacitive sensor + ADC, electronic noiseDetection: Capacitive sensor + ADC, position noiseRead-OutActuation: DAC+DVACPDWire stiffness/torsion constantWire dampingGas dampingTOTAL (quadratic sum)

Bias

Bias electronics thermal sensitivity

e.g., Measurement axis, SU-EPI

Gold wire damping

Gold wire stiffness

Read-Out

Scale factor electronics thermal sensitivity

Read-Out

12

Main contributors along measurement axis

• 7µm gold wire:• Stiffness• Damping

• Read-Out thermal sensitivity • Impact on bias fluctuation• Impact on scale factor fluctuation

• Parasitic forces thermal gradient sensitivity• e.g., SU-EPE / @1.7 10-4Hz

Total bias= 5.16 10-8ms-2

Gold wire stiffness bias= 4.72 10-8ms-2

Total noise= 4.89 10-12ms-2/Hz1/2

Gold wire damping noise= 4.85 10-12ms-2/Hz1/2

Total bias electronics thermal sensitivity= 9.47 10-14ms-2/K

RO bias electronics thermal sensitivity= 6.31 10-14ms-2/K

Total scale factor electronics thermal sensitivity= 5.68 10-6/K

RO scale factor electronics thermal sensitivity= 4.29 10-6/K

Total mechanics thermal gradient sensitivity= 4.92 10-12ms-2/(K/m)

Mechanics thermal gradient sensitivity radiometer effect and radiation pressure= 4.70 10-12ms-2/(K/m)

13

Mission budget

• Inputs:• Instrument budget• Mass centring budget• Satellite drag-free and attitude control budget• Calibration parameters• Temperature stabilities:

• 1mK MEC@fepi• 5mK ELEC@fepi• 1mK/m TMEC@fepi, 0.1K/m/Hz1/2 around fepi

• Self-gravity• Magnetic field• Integration time wrt inertial or spin test

• Outputs:• Total noise• Total harmonic noise or tone error• Test accuracy EP

14

Main contributorsError general form (in mesd)

0 Md x T x OdfpO in DF res.acc. 0.00E+00 0.0% 0.00E+00 0.0%1 1/2 x (I+Mc) x (T x res + Tres x ) 7.27E-16 0.0% 8.79E-16 15.7%2 1/2 x ( TTres+resTres

T) 2.05E-18 0.0% 1.86E-15 33.3%3 Instrument self gravity (wrt thermal stability) from finite elements model 6.00E-14 1.3% 2.00E-16 3.6%4 Satellite Gravity in DF residual acceleration 0.00E+00 0.0% 0.00E+00 0.0%5 Md x Tsc x OdfpO in DF res.acc. 0.00E+00 0.0% 0.00E+00 0.0%6 1/2 x (I+Mc) x Tsc x 1.21E-13 2.6% 3.04E-16 5.4%7 Md x 2 x OdfpO in DF res.acc. 0.00E+00 0.0% 0.00E+00 0.0%8 1/2 x (I+Mc) x 2 x 1.72E-18 0.0% 3.54E-18 0.1%9 Md x d/dt x OdfpO in DF res.acc. 0.00E+00 0.0% 0.00E+00 0.0%

10 1/2 x (I+Mc) x d/dt x 1.28E-14 0.3% 6.96E-16 12.4%11 in DF residual acceleration 0.00E+00 0.0% 0.00E+00 0.0%12 1/2 x (I+Mc) x x d/dt 1.70E-19 0.0% 3.99E-21 0.0%13 in DF residual acceleration 0.00E+00 0.0% 0.00E+00 0.0%14 1/2 x (I+Mc) x d2/dt2 3.13E-16 0.0% 1.05E-18 0.0%15 in DF residual acceleration 0.00E+00 0.0% 0.00E+00 0.0%16 1/2 x (I+Mc) x (T+Tsc+2+d/dt) x 4.25E-16 0.0% 3.03E-18 0.1%17 d x c 3.32E-14 0.7% 0.00E+00 0.0%18 c x d 2.16E-14 0.5% 1.38E-15 24.6%19 d x (c + Binst) 2.04E-13 4.3% 0.00E+00 0.0%20 c x (d + Binst) 3.04E-13 6.4% 0.00E+00 0.0%21 d x (c + Binst) 1.24E-13 2.6% 0.00E+00 0.0%22 c x (d + Binst) 8.79E-14 1.9% 0.00E+00 0.0%23 Accelerometer measurement noise Instrument error budget 6.20E-12 131.2% 0.00E+00 0.0%24 Bias sensitivity to SU temperature variation dBinst/dTmec x Tmec 1.89E-12 39.9% 6.29E-15 112.4%25 Bias sensitivity to FEEU temperature variation dBinst/dTelec x Telec 3.69E-14 0.8% 3.69E-16 6.6%26 dd/dTmec x Tmec x (c) 4.98E-14 1.1% 1.72E-16 3.1%27 dc/dTmec x Tmec x (d) 6.09E-18 0.0% 3.74E-20 0.0%28 dd/dTelec x Telec x (c) 8.30E-15 0.2% 8.60E-17 1.5%29 dc/dTelec x Telec x (d) 1.01E-18 0.0% 1.87E-20 0.0%30 dKd/dTmec x Tmec x (c+Binst_c) 4.23E-14 0.9% 4.28E-19 0.0%31 dKc/dTmec x Tmec x (d+Binst_d) 6.31E-14 1.3% 2.10E-16 3.8%32 dKd/dTelec x Telec x (c+Binst_c) 2.16E-14 0.5% 6.56E-19 0.0%33 dKc/dTelec x Telec x (d+Binst_d) 2.22E-13 4.7% 2.22E-15 39.6%34 dd/dTmec x Tmec x (c+Binst_c) 7.41E-14 1.6% 3.44E-16 6.1%35 dc/dTmec x Tmec x (d+Binst_d) 5.28E-14 1.1% 2.49E-16 4.4%36 dd/dTelec x Telec x (c+Binst_c) 1.24E-14 0.3% 1.72E-16 3.1%37 dc/dTelec x Telec x (d+Binst_d) 8.79E-15 0.2% 1.24E-16 2.2%38 Bias sensitivity to SU thermal gradient variation dBinst/dgradT x gradT 3.82E-13 8.1% 3.82E-15 68.3%39 Satellite positioning 1/2 x dT x 5.27E-17 0.0% 3.26E-16 5.8%40 Timing error 1/2 x T x 3.54E-17 0.0% 4.63E-17 0.8%41 Synchronisation error ep x t x c + ep x t x c 1.49E-19 0.0% 3.67E-19 0.0%42 DF residual acceleration Md x Resdrag 5.69E-18 0.0% 1.98E-18 0.0%43 Magnetic field (Earth+local) effect Analysis 8.00E-14 1.7% 4.00E-16 7.1%44 Radial measurement noise introduced by data processing (d+d)est x ninst_c 1.98E-13 4.2% 0.00E+00 0.0%

45 Radial bias sensitivity to SU temperature variation introduced by data processing (d+d)est x dBinst_c/dTmec x Tmec 8.76E-15 0.2% 4.13E-17 0.7%

46 Radial bias sensitivity to FEEU temperature variation introduced by data processing (d+d)est x dBinst_c/dTmec x Telec 1.48E-14 0.3% 2.09E-16 3.7%

47 Radial bias sensitivity to SU thermal gradient variation introduced by data processing (d+d)est x dBinst_c/dgradT x gradT 4.57E-13 9.7% 3.23E-16 5.8%

48 Accelerometer angular noise x acc_ang 3.94E-17 0.0% 0.00E+00 0.0%49 Angular attitude control variations x d/dt 1.25E-17 0.0% 5.14E-18 0.1%50 Angular bias sensitivity to SU temperature variation x dacc_ang/dTmec x Tmec 3.45E-18 0.0% 1.63E-20 0.0%51 Angular bias sensitivity to FEEU temperature variation x dacc_ang/dTmec x Telec 7.63E-19 0.0% 1.07E-20 0.0%52 Angular/linear coupling noise x angular accelerometer bias x acc_ang 1.78E-13 3.8% 0.00E+00 0.0%53 Angular/linear coupling noise x attitude control bias x d/dt 7.13E-18 0.0% 0.00E+00 0.0%54 Ang/Lin coupling sensitivity to SU temperature variation d/dTmec x acc_ang x Tmec 1.07E-13 2.3% 5.03E-16 9.0%55 Ang/Lin coupling sensitivity to SU temperature variation d/dTmec x d/dt x Tmec 4.28E-18 0.0% 2.02E-20 0.0%56 Ang/Lin coupling sensitivity to FEEU temperature variation d/dTelec x acc_ang x Telec 0.00E+00 0.0% 0.00E+00 0.0%57 Ang/Lin coupling sensitivity to FEEU temperature variation d/dTelec x d/dt x Telec 0.00E+00 0.0% 0.00E+00 0.0%58 K2c x appc x appd 4.77E-16 0.0% 3.14E-16 5.6%59 K2d x (appc

2 + appd2) 3.20E-16 0.0% 6.38E-19 0.0%

Coupling (not thermal stability)

Coupling sensitivity to SU temperature variation

Earth Gravity Gradient

PM average and relative accelerations (wrt thermal stability)

Satellite Gravity Gradient

Centrifugal acceleration

Angular acceleration

Scale Factor (not thermal stability)

Quadratic factor

tone @fep (m/s²) in 2mesd

Coupling sensitivity to FEEU temperature variation

Alignment sensitivity to SU temperature variation

Alignment sensitivity to FEEU temperature variation

Scale Factor sensitivity to SU temperature variation

Scale Factor sensitivity to FEEU temperature variation

Alignment (not thermal stability)

Coriolis (wrt thermal stability)

PM average and relative positions (wrt thermal stability)

noise (m/s²/Hz^1/2) in 2mesd

Stochastic budget

SU-EP, inertial

Harmonic budget

Accelerometer measurement noise

Thermal gradient variation

Mechanics temperature variation

Thermal gradient variation

Electronics temperature variation

15

Resolution EP

TOTAL (direct sum)/3 7.19E-15 128.3%TOTAL (quadratic sum) 6.54E-12 138.2%

SPECEP 1.33E-15

4.73E-12 5.60E-15

SU-EP, inertial

TOTAL (direct sum)/3 3.34E-15 59.6%TOTAL (quadratic sum) 2.68E-12 138.7%

SPECEP 1.07E-15

1.93E-12 5.60E-15

SU-EP, spin