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The effects of patch-potentials on the gravity probe B gyroscopes
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Figures

Image of FIG. 1.

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FIG. 1.

The relativity mission, gravity probe B concept.

Image of FIG. 2.

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FIG. 2.

Schematic of gyroscope (left), and photo of disassembled gyroscope (right).

Image of FIG. 3.

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FIG. 3.

Coordinate systems for: (a) housing with C axis out of page rolling around the Z space vehicle axis and the spin to roll misalignment angle β, (b) space vehicle with housing axes for one gyro pair and misalignment phase α, and (c) rotor referenced to mass center (MC) with moments of inertia and Euler angles.

Image of FIG. 4.

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FIG. 4.

Electric field for ideal equipotential metal surface (left), and surface with patch-effect (right).

Image of FIG. 5.

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FIG. 5.

Axial thrust toward the guide star (Z sv axis) during the GP-B mission.

Image of FIG. 6.

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FIG. 6.

Power spectral density of drag-free control effort (acceleration) along the Z sv axis with gyro 3 acting as the drag-free reference.

Image of FIG. 7.

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FIG. 7.

Power spectral density of A axis control effort for gyro 1 for two periods during the science mission showing polhode harmonics at 10 083 s and 3121 s, respectively

Image of FIG. 8.

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FIG. 8.

Root mean square amplitude of A-axis control effort for gyro 1 at polhode harmonics for three different periods during the science mission.

Image of FIG. 9.

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FIG. 9.

Patch potential spectra found from Z sv-axis force at zero frequency and at harmonics of polhode. Spectrum amplitude V 0 as a function of the spectrum power r. The constant black line is V 0 for the zero-frequency Z sv-axis force on gyro 3, which involves only the rotor charge and the dipole spherical harmonics of the rotor and the housing. The other lines are for the Z sv-axis force on gyro 1 modulated by the first 5 harmonics of polhode when the polhode angle is 1.3 rad (1st to 5th harmonics {red, green, orange, blue, dashed-red}).

Image of FIG. 10.

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FIG. 10.

Control effort modulation at 1.23 Hz spin-speed.

Image of FIG. 11.

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FIG. 11.

Plot of spectrum amplitude V 0 as a function of spectrum power r derived from gyro control effort at the first three harmonics of spin speed; gyro 1 (red), gyro 3 (orange), gyro 4 (blue), and fundamental spin speed (solid lines), 2nd harmonic (dashed lines), 3rd harmonic (dotted-dashed lines).

Image of FIG. 12.

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FIG. 12.

Gyro 1 spin speed for 12 h period.

Image of FIG. 13.

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FIG. 13.

Spin-speed damping df S /dt of gyroscopes during the science mission.

Image of FIG. 14.

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FIG. 14.

Patch potential spectra found from gyro spindown data. Spectrum amplitude V 0 as a function of the spectrum power r for gyro 1 (red), gyro 2 (green), gyro 3 (orange), and gyro 4 (blue). The curves for gyro 2 and gyro 3 are nearly indistinguishable.

Image of FIG. 15.

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FIG. 15.

Relative position of gyro 3 (top) and charge measurement for A, B, and C axes (bottom).

Image of FIG. 16.

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FIG. 16.

Schematic view of the spin averaged patch voltages V 1,2,3 on the rotor, the V A 1/A2,B1/B2,C1/C2 voltages on the electrodes, and the grounding scheme for electrodes and the dashed ground plane.

Image of FIG. 17.

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FIG. 17.

Patch potential spectrum found from charge measurement data. Spectrum amplitude V 0 as a function of spectrum power r using the charge measurements.

Image of FIG. 18.

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FIG. 18.

Patch potential spectrum found from misalignment torque and roll-polhode resonance torque data. Spectrum amplitude V 0 as a function of spectrum power r using the measured misalignment torque coefficient for gyro 3 (solid curve) and using the measured roll-polhode resonance torque for gyro 2 with m = 143 (dashed curve).

Image of FIG. 19.

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FIG. 19.

Spectrum amplitude V 0 for all effects as a function of r (left) and a (right). The curves are zero-frequency Z sv-axis force (red), Z sv-axis force modulated at polhode harmonic (green), gyro control effort at fundamental spin speed (orange), gyro control effort at 2nd and 3rd harmonics of spin speed (blue), spin-speed damping (red-dashed), charge measurement (green-dashed), misalignment torque (orange-dashed), and roll-polhode resonance torque (blue-dashed).

Image of FIG. 20.

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FIG. 20.

Spectrum amplitude V 0 for all effects as a function of r for the type III spectrum described in the text. The curves are zero-frequency Z sv-axis force (red), Z sv-axis force modulated at polhode harmonic (green), gyro control effort at fundamental spin speed (orange), gyro control effort at 2nd and 3rd harmonics of spin speed (blue), spin-speed damping (red-dashed), charge measurement (green-dashed), misalignment torque (orange-dashed), and roll-polhode resonance torque (blue-dashed).

Tables

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Table I.

Principal properties of gyroscopes.

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Table II.

Spin properties of gyroscopes.

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Table III.

Asymptotic polhode period and damping time and differences in the principal moments of inertia.

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Table IV.

Polhode power dissipation P p when γ p = π/4 and the ratio P p /P S .

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Table V.

Dependence of patch-potential effects on spherical harmonic coefficients for the rotor potential R l,m , the housing potential H l,m, and the rotor voltage V Q , and spherical harmonic number l. The l dependence assumes a flat spectrum, namely, for r = 0.

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/content/aip/journal/rsi/82/7/10.1063/1.3608615
2011-07-21
2014-04-20

Abstract

Gravity probe B (GP-B) was designed to measure the geodetic and frame dragging precessions of gyroscopes in the near field of the Earth using a drag-free satellite in a 642 km polar orbit. Four electrostatically suspended cryogenic gyroscopes were designed to measure the precession of the local inertial frame of reference with a disturbance drift of about 0.1 marc sec/yr–0.2 marc sec/yr. A number of unexpected gyro disturbance effects were observed during the mission: spin-speed and polhode damping, misalignment and roll-polhode resonance torques, forces acting on the gyroscopes, and anomalies in the measurement of the gyro potentials. We show that all these effects except possibly polhode damping can be accounted for by electrostatic patch potentials on both the gyro rotors and the gyro housing suspension and ground-plane electrodes. We express the rotor and housing patch potentials as expansions in spherical harmonics Y l,m (θ,ϕ). Our analysis demonstrates that these disturbance effects are approximated by a power spectrum for the coefficients of the spherical harmonics of the form with V 0 ≈ 100 mV and r ≈ 1.7.

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Scitation: The effects of patch-potentials on the gravity probe B gyroscopes
http://aip.metastore.ingenta.com/content/aip/journal/rsi/82/7/10.1063/1.3608615
10.1063/1.3608615
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