Design and Fabrication of a Differential Electrostatic Accelerometer for Space-Station Testing of the Equivalence Principle.

sensors Article

Design and Fabrication of a Differential Electrostatic Accelerometer for Space-Station Testing of the Equivalence Principle Fengtian Han *, Tianyi Liu, Linlin Li and Qiuping Wu Department of Precision Instrument, Tsinghua University, Beijing 100084, China; [email protected] (T.L.); [email protected] (L.L.); [email protected] (Q.W.) * Correspondence: [email protected]; Tel.: +86-10-6279-8645 Academic Editor: Vittorio M. N. Passaro Received: 27 June 2016; Accepted: 1 August 2016; Published: 10 August 2016

Abstract: The differential electrostatic space accelerometer is an equivalence principle (EP) experiment instrument proposed to operate onboard China’s space station in the 2020s. It is designed to compare the spin-spin interaction between two rotating extended bodies and the Earth to a precision of 10´12 , which is five orders of magnitude better than terrestrial experiment results to date. To achieve the targeted test accuracy, the sensitive space accelerometer will use the very soft space environment provided by a quasi-drag-free floating capsule and long-time observation of the free-fall mass motion for integration of the measurements over 20 orbits. In this work, we describe the design and capability of the differential accelerometer to test weak space acceleration. Modeling and simulation results of the electrostatic suspension and electrostatic motor are presented based on attainable space microgravity condition. Noise evaluation shows that the electrostatic actuation and residual non-gravitational acceleration are two major noise sources. The evaluated differential acceleration noise is 1.01 ˆ 10´9 m/s2 /Hz1/2 at the NEP signal frequency of 0.182 mHz, by neglecting small acceleration disturbances. The preliminary work on development of the first instrument prototype is introduced for on-ground technological assessments. This development has already confirmed several crucial fabrication processes and measurement techniques and it will open the way to the construction of the final differential space accelerometer. Keywords: equivalence principle; differential accelerometer; electrostatic suspension; variable-capacitance motor; space station experiment; fundamental physics experiment

1. Introduction The equivalence principle (EP) is one of fundamental hypotheses of Einstein’s general relativity. The EP experiment is significant to verify the general relativity and search for new interactions or for new gravitational potential. The EP has been intensively tested by many experiments in a stated relative precision of several parts per 1013 [1,2], limited mainly by terrestrial environmental noises. Currently, several satellite- or balloon-based space experiment missions, such as the MicroSCOPE [3], STEP [4], GG [5], GreAT [6] and TEPO [7], are underway or proposed to test the equivalence to a precision better than 10´15 –10´18 . However, all of the above EP experiments tested the equivalence between non-spinning test masses. On the other hand, the gauge theory of gravitation with torsion predicts that a spin particle or a rotating extended body would deviate geodesic motion. In 2001, Zhang et al. developed a phenomenological model for the spin-spin interaction between rotating rigid spheres and suggested the idea for a space test of the new equivalence principle (NEP) [8]. A design case in which uses two concentric spherical shells with different rotations predicts a possible NEP

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violation on the order of 10´14 . Based on the model in [8], a dimensionless parameter ηs , which would imply existence of spin-spin force between rotating masses and the Earth can be defined as: ¨ Ñ Ñ ˛ Ñ Ñ ∆g SA ¨ Se SB ¨ Se ‚ ηs “ “ κ˝ ´ g GmA Me RA GmB Me RB

(1)

where G is the Newtonian gravitational constant, mA , mB , and Me are the masses of two rotating Ñ

Ñ

Ñ

bodies and the Earth, and S A , S B and S e are their spin angular momenta, RA and RB are the distances between the centers of the two masses and the Earth, respectively. The parameter κ represents the universal coupling factor for the spin-spin interaction with an upper limit of 3.4 ˆ 10´34 kg´1 [8]. A series of double free-fall based terrestrial experiments using a rotating gyroscope and a non-rotating one showed that the spin-gravity interaction between the extended bodies was not observed at a relative accuracy of 1.6 ˆ 10´7 [9,10]. The ground experiment is mainly limited by the friction of the mechanical gyroscopes, short duration of free fall and large seismic noises [11]. The experiment limits on the Earth have motivated a move to space. An indirect test for the NEP in space was from the data of GP-B space experiments, which gives indirectly the parameter ηs ď 10´11 [12]. A concept design of a double free-fall space NEP experiment onboard a drag-free satellite, in which two TMs made of the same material but rotated with much different angular velocity drop freely, was proposed to achieve an accuracy better than 10´15 [13]. However, this requires many challenging techniques to develop the NEP instrument, drag-free satellite, and extensive preflight testing to verify that the instrument performance can be reached once in space. Recently, China has revealed that it will start building its first permanent space station which will be a T-shaped station consisting of a core capsule and two experimental capsules [14]. China’s space station will be fully operational around 2022 and then run on the orbit for more than 10 years. The NEP experiment is one of candidate space-station experiment missions in the fields of fundamental physics. For the first such experiment, it is designed to reach a measurement precision of 10´12 with an observation period of 20 orbits, which is five orders of magnitude better than the results obtained on the Earth. In this work, we present the design and preliminary development of a NEP experiment instrument, i.e., differential electrostatic accelerometer. The design of the sensor unit, modeling and simulation of electrostatic suspension in five degrees of freedom (DoFs) and spin control along the sensitive axis are described to evaluate the instrument performance. Considering the attainable micro-gravity condition provided by a quasi-drag-free capsule inside the space station, acceleration noise analysis of the NEP instrument is discussed to verify the NEP test goal. The development status of the first NEP instrument is presented for preliminary ground testing and proof of concept design. This paper is organized as follows: in Section 2 we briefly introduce the concept design of the NEP experiment in the space station. The detailed design and noise evaluation of the NEP instrument are presented in Section 3. The preliminary work on developing an instrument prototype for ground testing is described in Section 4. Finally, Section 5 concludes this paper. 2. Concept of the Space Station-Based NEP Experiment The concept of the NEP experiment is basically a free fall test which will use the low-noise space environment, long measurement duration, and a very precise experimental instrument to achieve the target precision of 10´12 . The space station will provide a perfect comparison of the free falling of two rotating masses in the same significant gravity field over a long time span. Then, an observed nonzero value of ηs would imply violation of the NEP or existence of spin-spin force between the rotating extended mass and the Earth. In the modified double free-fall space test, the two test masses (TMs) are maintained on the same trajectory and rotating with much different spin angular momenta, as shown schematically in Figure 1. A difference in the forces necessary to maintain the common trajectory will indicate the existence of the spin-spin force between the rotating mass and the Earth. The measurements will be made by placing the two masses inside a differential electrostatic accelerometers (used as the

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toNEP maintain the mass position fixed relative to the will instrument frame. TwotoTMs have athe common center instrument), where surrounding electrodes apply weak forces maintain mass position offixed massrelative to be exposed to the sameframe. gravitational field, anda have a carefully formto to the instrument Two TMs have common center defined of mass cylindrical to be exposed tothe provide the desired measurement accuracy. The sensitive axis of the NEP instrument which lies in same gravitational field, and have a carefully defined cylindrical form to provide the desired the orbital plane is stabilized in a quasi-inertial pointing mode. The Earth gravity attraction measurement accuracy. The sensitive axis of the NEP instrument which lies in the orbital planeisis projected wave leading to themode. NEP violation signal detection at aisknown orbital stabilizedinina asine quasi-inertial pointing The Earth gravity attraction projected in afrequency sine wave fNEP and phase. leading to the NEP violation signal detection at a known orbital frequency f NEP and phase. The effects of of thethe space station will be be isolated by by a Theattitude, attitude,thermal thermaland andatmospheric atmosphericdrag drag effects space station will isolated low-pressure (~100 Pa)Pa) micro-gravity science experiment capsule inside a low-pressure (~100 micro-gravity science experiment capsule insidewhich whichthe theNEP NEPinstrument instrument will be accommodated. Similar to a drag-free spacecraft [15], the dedicated experiment capsulewill will will be accommodated. Similar to a drag-free spacecraft [15], the dedicated experiment capsule be be drag-compensated actuation of thrusters virtually floating inside the spacious drag-compensated byby thethe actuation of thrusters andand virtually free free floating inside the spacious space space the space station during tests. is expected to provide a microgravity level the orderof of theofspace station during NEPNEP tests. It isItexpected to provide a microgravity level onon the order ´6−6m/s of1010 m/s22 and and aa test testduration durationup uptoto4848h.h.InInthis this way, the experiment capsule will follow the way, the experiment capsule will follow the two two TMs TMs in their almost purely gravitational motion andin-orbit the in-orbit motions theTMs, two TMs, maintained in their almost purely gravitational motion and the motions of theof two maintained as free asasfree as possible, could be compared finely compared to estimate anyviolation NEP violation The experiment possible, could be finely to estimate any NEP signal. signal. The experiment capsule capsule will carry one differential accelerometer compatible with a room temperature experiment. will carry one differential accelerometer compatible with a room temperature experiment. The entire The entire space experiment mission willsix lastmonths over six months initial including initial verification of the space experiment mission will last over including verification of the instrument, instrument, in-orbit calibration and final NEP tests. in-orbit calibration and final NEP tests. Inner mass Outer mass

S1, S2

SE

One orbit

time

Figure Figure1.1.Concept Conceptofofthe thespace-station space-stationtest testofofgravitational gravitationaleffects effectsofoftwo twoconcentric concentricrotating rotatingmasses masses made of the same material. The cylindrical inner/outer test masses are suspended electrostatically made of the same material. The cylindrical inner/outer test masses are suspended electrostaticallyinin aadifferential differentialaccelerometer accelerometerand andspinning spinningwith withmuch muchdifferent differentangular angularmomenta. momenta.

The Theultra-sensitive ultra-sensitivedifferential differentialaccelerometer accelerometerisiscrucial crucialto tothe theNEP NEPtest testprecision. precision.The Theelectrostatic electrostatic suspension provides the capability to generate very weak but accurate force, suspension provides the capability to generate very weak but accurate force, allowing allowing the the accelerometers to achieve extremely high resolution by largely decreasing their measurement accelerometers to achieve extremely high resolution by largely decreasing their measurement ranges thethe instrument operation, bothboth masses are controlled with respect to the to same ranges[16]. [16].During During instrument operation, masses are controlled with respect the instrument frame: the sum of these forces is maintained virtually null benefiting from good same instrument frame: the sum of these forces is maintained virtually null benefiting from good microgravity microgravitylevel levelprovided providedby bythe thefloating floatingexperiment experimentcapsule. capsule.The TheNEP NEPinstrument instrumentprovides providesaa precise, low noise measurement of the difference in acceleration of the two masses to search precise, low noise measurement of the difference in acceleration of the two masses to searchfor forthe the NEP violating signal. For example, by considering the Earth gravity acceleration at an orbit altitude NEP violating signal. For example, by considering the Earth gravity acceleration at an orbit altitude of −12 by attaining of400 400km, km,i.e., i.e., 8.69 m/s theNEP NEPtest testcan canbebeperformed performedatatananaccuracy accuracybetter betterthan than 2 ,2,the ´12 8.69 m/s 1010 by attaining a 2 adifferential differentialacceleration accelerationresolution resolutionofof8 8ˆ×10 10´−12 12 m/s m/s.2 .Considering Consideringa ameasurement measurementintegrated integratedover over 5 s, the required measurement noise along the sensitive axis is 20 orbits, corresponding to 1.1 × 10 5 20 orbits, corresponding to 1.1 ˆ 10 s, the required measurement noise along the sensitive axis −9 m/s2/Hz1/2 in the vicinity of the frequency fNEP = 0.182 mHz. In our design goal, the allowed 2.65 × 10ˆ is 2.65 10´9 m/s2 /Hz1/2 in the vicinity of the frequency f NEP = 0.182 mHz. In our design goal, total noise fortotal the noise NEP instrument in space station environment is limited toisalimited spectralto the allowed for the NEPoperated instrument operated in space station environment −9 2 1/2 density lessdensity than 2.0less × 10 m/s fNEP. 2 /Hz1/2 at f 9 m/s a spectral than 2.0/Hz ˆ 10át . NEP

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The NEP instrument configuration is similar to the space accelerometer for gravitation experimentation developed for the on-orbit MicroSCOPE mission [17]. In this weak equivalent 3. Design and(SAGE) Simulation of the NEP Instrument principle (WEP) test, free fall motion of two non-spinning test masses which are composed of The NEP instrument configuration is similar to the space accelerometer for gravitation different materials is(SAGE) observed when both masses are MicroSCOPE subjected exactly to the gravitational experimentation developed for the on-orbit mission [17].same In this weak field.equivalent In comparison to the MicroSCOPE mission [3], the proposed NEP experiment aims to verify principle (WEP) test, free fall motion of two non-spinning test masses which are composed the spin-spin extended bodies and exactly the Earth. two TMs of the of differentinteraction materials isbetween observed rotating when both masses are subjected to theHence, same gravitational field. InNEP comparison to the MicroSCOPE mission [3], the proposed experiment aimsdifferent to verify the differential accelerometer are made of the same material butNEP rotated with much angular spin-spin interaction between rotating extended Earth. Hence, twothe TMs of TMs the are momenta. The most challenging aspect in designbodies of theand NEPtheinstrument is that two differential accelerometer are made the for same but and rotated different spinning duringNEP on-orbit tests, such as 104ofrpm thematerial inner TM 100with rpmmuch for the outer TM. angular momenta. The most challenging aspect in design of the NEP instrument is that the two TMsof the During operation there is no any physical contact on the TMs to enable continuous rotation are spinning during on-orbit tests, such as 104 rpm for the inner TM and 100 rpm for the outer TM. inner and outer masses. In this case, the thin gold wire scheme commonly used in traditional space During operation there is no any physical contact on the TMs to enable continuous rotation of the accelerometers, which enables the position detection and permits the control of the electric charge of inner and outer masses. In this case, the thin gold wire scheme commonly used in traditional space the mass [18], is notwhich applicable NEP detection accelerometer. Therefore, the NEP design is accelerometers, enablesto thethe position and permits the control of the instrument electric charge of significantly previous EPNEP instruments, suchTherefore, as SAGE.the A NEP comparison among the the mass different [18], is notfrom applicable to the accelerometer. instrument design is NEP instrument and two similar sensors are listedsuch in Table 1. The continuousamong rotation the two significantly different frominertial previous EP instruments, as SAGE. A comparison theof NEP two similar inertial sensors listed in Table 1. The continuous rotation of and the two TMs instrument makes theand NEP instrument design moreare complicated, especially in the sensor unit rotation TMs makes the NEP instrument design more complicated, especially in the sensor unit and rotation control electronics. control electronics. Table 1. Comparison of three inertial sensors for space-based fundamental physics experiments 1. Comparison of three inertial sensors for space-based fundamental physics experiments (NA:Table not applicable). (NA: not applicable). Description Description Inertialsensor sensor Inertial Measuredsignal signal Measured Accelerationnoise noise Acceleration signalfrequency frequency EPEPsignal Test Testmass mass Suspension Suspension Spinning Spinningup up Spin Spinrate rate(rpm) (rpm) Sinusoidal Sinusoidalexcitation excitation Charge Chargecontrol control

MicroSCOPE [3,19] MicroSCOPE [3,19] Differential Differentialaccelerometer accelerometer Differential Differentialacceleration acceleration −12 2 2 1/2 m/s /Hz/Hz1/2 ≤2.0ˆ× 10´12 ď2.0 m/s 0.17 0.17mHz mHzoror1 mHz 1 mHz Twoconcentric concentriccylinders cylinders Two EachTM TMininsixsix DoFs Each DoFs NA NA 00 Thingold gold wire Thin wire Thingold gold wire Thin wire

GP-B GP-B [20][20] Dual-axis gyroscope Dual-axis gyroscope Spin axis drift Spin axis drift NANA NANA One solid sphere One solid sphere three DoFs In In three DoFs helium flow helium gasgas flow 3738–4962 (Measured) 3738–4962 (Measured) Three phase excitation Three phase excitation Ultraviolet discharge Ultraviolet discharge

Space Spaceplatform platform

Drag-freesatellite satellite Drag-free

Drag-free satellite Drag-free satellite

(a)

NEPNEP Differential accelerometer Differential accelerometer Differential acceleration Differential acceleration ´9 2m/s 2 /Hz1/2 ≤2.0 10−9 /Hz1/2 ď2.0× ˆ 10m/s 0.182 mHzmHz 0.182 concentric cylinders TwoTwo concentric cylinders Each in five Each TM TM in five DoFsDoFs Electrostatic motor Electrostatic motor 10,000 design) 10,000 (By (By design) By injection electrode By injection electrode Ultraviolet discharge Ultraviolet discharge quasi-drag-free capsule quasi-drag-free capsule floating inside space station floating inside space station

(b)

Figure 2. NEP instrument: (a) Mechanical sensor core mounted in a tight housing with above the

Figure 2. NEP instrument: (a) Mechanical sensor core mounted in a tight housing with above the vacuum system and surrounding the suspension and rotation control units; (b) Cross-sectional view vacuum system and surrounding the suspension and rotation control units; (b) Cross-sectional view of of the differential accelerometer including two concentric test masses. the differential accelerometer including two concentric test masses.

Unlike those WEP space experiments using two or more onboard differential accelerometers for comparison [3,4], the space NEP experiment willusing need only differential accelerometers foraccelerometers the space Unlike those WEP experiments two one or more onboard differential

for comparison [3,4], the NEP experiment will need only one differential accelerometers for the

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space station-based EP mission. The design parameters should be compatible with the microgravity Sensors 2016, 16, 1262 5 of 18 environment provided by the floating experiment capsule. A conceptual design of the NEP instrument shown in Figure 2 has a profile dimension Φ280 mm ˆ 240 mm. The sensor unit is composed of station-based EP mission. The design parameters should be compatible with the microgravity two concentric electrostatic accelerometers in which each TM is suspended and centered by five-axis environment provided by the floating experiment capsule. A conceptual design of the NEP electrostatic suspension. The initial of the mass themm. sensitive axis is based instrument shown in Figure 2 hasspinning-up a profile dimension Ф280 around mm × 240 The sensor unit is on the principle variable capacitance motor [21]. Theinsensor consisting of two and four composedof ofatwo concentric electrostatic accelerometers which core each TM is suspended andTMs centered electrode cylinders will be fixed in a tight vacuum housing to reduce the radiometer effect by five-axis electrostatic suspension. The initial spinning-up of the mass around the sensitive axisand is gas fluctuation dissipation. based on the principle of a variable capacitance motor [21]. The sensor core consisting of two TMs and four electrode cylinders will be fixed in a tight vacuum housing to reduce the radiometer effect

3.1. Sensor and gasUnit fluctuation dissipation. This differential accelerometer is specifically optimized for the space test of the NEP. The mechanical core of the NEP instrument contains two concentric inertial sensors, each composed This differential accelerometer is specifically optimized for the space test of the NEP. The of one hollow quasi-cylindrical TM and two concentric electrode cylinders which are positioned mechanical core of the NEP instrument contains two concentric inertial sensors, each composed of within and without the mass, as shown in Figure 3. The material of the two masses has been selected one hollow quasi-cylindrical TM and two concentric electrode cylinders which are positioned within to titanium alloy by taking into account of the purity, specific gravity, homogeneity, machining and without the mass, as shown in Figure 3. The material of the two masses has been selected to ability, thermal conductivity magnetic Given that the two titanium alloystability, by takingelectrical into account of the purity,and specific gravity,susceptibility. homogeneity, machining ability, TMs thermal are notstability, idealized point conductivity masses, a common center of mass isGiven not sufficient to TMs guarantee electrical and magnetic susceptibility. that the two are not both bodies will bepoint subjected samecenter force.ofTherefore, cylinder dimensions idealized masses,toa the common mass is notthe sufficient to guarantee bothshould bodies be willcarefully be subjected to the same the force. Therefore, the cylinder dimensions be carefully designedgradient to designed to approximate monopole property and thus reduce should the effects of local gravity approximate the monopole property and thus reduce the effects of local gravity gradient fluctuations fluctuations [17,22]. This effect can be minimized by design of the TM dimensions with equal moments [17,22]. be minimized by designconsidered of the TM dimensions withbyequal moments of inertia [3,4]. of inertia onThis eacheffect axis,can which has been carefully and adopted several WEP missions on each axis, which has been carefully considered and adopted by several WEP missions [3,4]. Moreover, to further minimize the gravity gradient effects on the NEP signal, the off-centering between Moreover, to further minimize the gravity gradient effects on the NEP signal, the off-centering the two TMs is expected to be less than 20 µm after the instrument fabrication and integration [3]. between the two TMs is expected to be less than 20 μm after the instrument fabrication and The two TMs are[3]. initially designed by initially modeling and optimization of and overall suspension rotation integration The two TMs are designed by modeling optimization of and overall performances, listed in Table 2. suspensionas and rotation performances, as listed in Table 2. 3.1. Sensor Unit

Test masses Y/Z-axis electrodes X-axis electrodes Injection electrodes Rotation electrodes

Figure 3. Exploded view thedifferential differential accelerometer accelerometer core. inner andand outer test test masses are are Figure 3. Exploded view of of the core.The The inner outer masses aligned concentrically and coaxially. The sensitive axis of the NEP test is along the x direction. aligned concentrically and coaxially. The sensitive axis of the NEP test is along the x direction. Table 2. Physical properties of the two test masses.

Table 2. Physical properties of the two test masses. Description Symbol Inner TM Outer TM Material -Titanium alloy Description Symbol Inner TM Outer TM Mass (g) m 43.92 110.10 Material alloy −5 J 1.105 × 10Titanium 6.890 × 10−5 Moment of inertia (kg∙m2) – Mass (g)Inner radius (mm) m 43.92 r 15 25 110.10 2) J Moment of inertia (kg¨m 1.105 ˆ 10´5 6.890 ˆ 10´5 Outer radius (mm) R 17.5 27.5 Inner radius (mm) r 15 25 Length (mm) l 39.92 64.37 Outer radius (mm) 17.5 27.5 60 60 Radial nominal gap (μm) R d0 Length Rated (mm) spin speed (rpm) l 39.92 n0 10,000 100 64.37

Radial nominal gap (µm) Rated spin speed (rpm)

d0 n0

60 10,000

60 100

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Each test mass is surrounded by two gold coated cylinders made of ultra-low expansion (ULE) Sensors 2016, 16, 1262 6 of 18 glass ceramic, exhibiting a 1.6 ˆ 10´7 /˝ C coefficient of thermal expansion at 25 ˝ C. Associated with Eachstability test massofisthe surrounded by two gold coated cylinders made of ultra-low expansionconductors (ULE) high thermal instrument interfaces, it ensures a very steady set of electrical glass exhibiting a 1.6 × electrodes 10−7/°C coefficient thermal expansion at by 25 gold °C. Associated around theceramic, mass [3]. The necessary on twoofcylinders are defined coating towith function high thermal stability of the instrument interfaces, it ensures very steady set ofof electrical conductors as capacitive position sensing, electrostatic suspension andarotation control the mass, as depicted around the mass [3]. The necessary electrodes on two cylinders are defined by gold coating to in Figure 4. As the electrostatic force is always attractive, the actuation electrodes act in pairs to function as capacitive position sensing, electrostatic suspension and rotation control of the mass, as provide both a positive and a negative force for any degree of freedom. On the inner cylinder, there are depicted in Figure 4. As the electrostatic force is always attractive, the actuation electrodes act in pairs four quadrant electrodes (Z and , Za1´ , Z2+ , Zforce the radial z- and φ-axes suspension and other four 2´ ) for to provide both a positive1+ negative for any degree of freedom. On the inner cylinder, there quadrant electrodes (Y , Y , Y , Y ) for the radial y- and θ-axes, respectively. Moreover, enable 1+ 1 ´ 2+ 2 ´  -axes are four quadrant electrodes (Z1+, Z1−, Z2+, Z2−) for the radial z- and suspension and other to four the capacitive position detection, a sinusoidal excitation voltage is applied to the TM via one common quadrant electrodes (Y1+, Y1−, Y2+, Y2−) for the radial y- and θ-axes, respectively. Moreover, to enable injection electrodeposition (INJ). detection, On the outer cylinder, there are fouris axial electrodes (X1+one , Xcommon 1´ , X2+ , X2´ ) the capacitive a sinusoidal excitation voltage applied to the TM via around the entire circumference, wellcylinder, as a ringthere of six electrodes for (X rotation control around the injection electrode (INJ). On theasouter arestator four axial electrodes 1+, X1−, X 2+, X2−) around the entire circumference, as wellaround as a ringthe of x-axis six stator electrodes forprinciple rotation control around the x x direction. The rotation operation is based on the of variable-capacitance direction. The rotation operation around theaccelerometer x-axis is basedprovides on the principle of sensitive variable-capacitance electrostatic motors [21]. Note that the x-axis the most measurements, electrostatic motors [21]. Note that the x-axis accelerometer provides the most sensitive which are utilized to test gravitational effects of the spinning mass. Therefore, along the axial sensitive measurements, which are utilized to test gravitational effects of the spinning mass. Therefore, along direction, the configuration is such that the gradients of capacitances between the electrodes and the the axial sensitive direction, the configuration is such that the gradients of capacitances between the mass are quite independent of the position of the TM, which doesn’t induce the first-order electrostatic electrodes and the mass are quite independent of the position of the TM, which doesn’t induce the negative stiffness [22]. Likewise, the corresponding geometry parameters of the four electrode cylinders first-order electrostatic negative stiffness [22]. Likewise, the corresponding geometry parameters of are listed in Table 3. The four cylinders ofTable the two inertial sensors will integrated on a unique the four electrode cylinders are listed in 3. The four cylinders of thebetwo inertial sensors will be ULE centering part, serving as a reference frame for the NEP instrument. integrated on a unique ULE centering part, serving as a reference frame for the NEP instrument.

(a) Inner cylinder electrodes

(b) Outer cylinder electrodes

Figure 4. Electrode configuration of the NEP instrument with a cylindrical test mass (in orange):

Figure 4. Electrode configuration of the NEP instrument with a cylindrical test mass (in orange): (a) On the inner cylinder are four quadrant electrodes on the vertical axis for z and θ, four electrodes (a) Ononthe inner cylinder are four quadrant electrodes on the vertical axis for z and θ, four electrodes on the horizontal axis for y and ϕ, and one injection electrode for capacitive position sensing; (b) On the horizontal axis forare y and and one around injection for capacitive position sensing; On the the outer cylinder the xφ,electrodes theelectrode entire circumference, as well as a ring of six (b) stator outerelectrodes cylinder for arerotation the x electrodes around the entire circumference, as well as a ring of six stator control around the x axis. electrodes for rotation control around the x axis. Table 3. Parameters of the electrode cylinders.

Table 3. Parameters of the electrode cylinders. Outer Accelerometer Inner Accelerometer

Description Inner Electrodes Outer Electrodes Inner Accelerometer Cylinder radius (mm) 14.94 17.56 Description Electrode separation (mm) 1.5 1.5 Inner Electrodes Outer Electrodes y/z electrode length (mm) 8 -Cylinder radiuslength (mm)(mm) 14.94 17.56 x electrode -10 Electrode separation (mm) (mm) 1.5 1.5 Injection electrode length 15.92 -y/zRotation electrode length length (mm) (mm) 8 -– electrode 26.92

x electrode length (mm) Injection electrode length (mm) 3.2. Electrostatic Suspension Rotation electrode length (mm)

– 15.92 –

10 – 26.92

Inner Electrodes Outer Electrodes 24.94 Outer Accelerometer 27.56 1.5 1.5 Inner Electrodes Outer Electrodes 12 -24.94 -10 27.56 1.5 32.37 -- 1.5 -- 12 51.4 –

– 32.37 –

10 – 51.4

This electrostatic accelerometer is based on the force-balance technology which measures the electrostatic Suspension force necessary to maintain the TM motionless with respect to the sensor cage [22]. The 3.2. Electrostatic motion of each TM with respect to highly stable instrument frame is actively servo-controlled by

This electrostatic accelerometer based on the force-balance technology which measures electrostatic suspension in five DoFs:istranslations along the x, y and z axes, and rotations around two the electrostatic force necessary to maintain the TM motionless with respect to the sensor cage [22]. The motion of each TM with respect to highly stable instrument frame is actively servo-controlled

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by electrostatic suspension in five DoFs: translations along the x, y and z axes, and rotations around two in-plane axe, θθ and and ϕ, φ, respectively. respectively.Figure Figure 5 shows a schematic diagram of the electrostatic in-plane axe, 5 shows a schematic diagram of the electrostatic suspension looploop forfor thethe x axis. carriersignal signalVV (~100 kHz) is applied to the injection suspension x axis.AAsinusoidal sinusoidal carrier S S(~100 kHz) is applied to the injection electrode which is utilized to capacitively couple the excitation signal to the for capacitive position electrode which is utilized to capacitively couple the excitation signal to TM the TM for capacitive sensing [23]. In the presence of external force, the TM displaces away from its nominal position, position sensing [23]. In the presence of external force, the TM displaces away from its nominal position, in the a change in the differential capacitance, and aofpair resulting in a resulting change in differential capacitance, Cx1 ´ Cx2 ,Cbetween the TMthe andTM a pair top and x1  C x 2 , between bottom suspension electrodes. position sensor senses this capacitance changechange and then feeds the of top and bottom suspensionThe electrodes. The position sensor senses this capacitance and then xs into feeds the position a feedbacktocontroller stabilize the suspension servo position signal xs intosignal a feedback controller stabilizeto the suspension servo loop. Inloop. orderIntoorder linearize to linearize feedback the electrostatic feedback force,system the suspension system is normally operated fashion in a so the electrostatic force, the suspension is normally operated in a differential differential so that the voltage on the positive is theV sum of a bias voltage Vb and that the voltage fashion on the positive electrode is the sum of aelectrode bias voltage Vx while b and a control voltage V a control voltage while the voltage on the negative electrode is produced by subtracting the bias the voltage on the negative electrode is produced by subtracting the bias voltage from the control x voltage from the the feedback control voltage. Finally, feedback fromare twoapplied voltage on amplifiers are voltage. Finally, voltages fromthe two voltagevoltages amplifiers the suspension applied the suspension electrodes by which the the electrostatic generated to balance electrodes byon which the the electrostatic force is generated to balanceforce the is external force, pullingthe the TM external force, pulling the TM back to its nominal position. The resultant feedback forces are derived back to its nominal position. The resultant feedback forces are derived from the accurate measurement from the accurate measurement of the applied voltages on the pairs of electrodes. Note that these of the applied voltages on the pairs of electrodes. Note that these suspension electrodes function suspension electrodes function in pairs to simultaneously measure and control the TM position, with in pairs to simultaneously measure and control the TM position, with the complete set providing the complete set providing contactless electrostatic suspension in five DoFs. The RC networks shown contactless electrostatic in five DoFs. The RC networks shownfrom in Figure 5 are used to in Figure 5 are used suspension to separate relatively low frequency forcing voltages high frequency separate relatively low frequency forcing voltages from high frequency position sensing signals. position sensing signals. fe, x  f x +  f x fx+ Cx +

R

Vb  Vx

C

VS

Vx

xs

Cin

Vb

Cx f x-

C

Vb  Vx

R

Figure 5. Schematic sketch of the x-axis electrostaticsuspension suspensionloop. loop. Five Five loops Figure 5. Schematic sketch of the x-axis electrostatic loopssimilar similartotothis thisone one are are required to suspend each test mass electrostatically. required to suspend each test mass electrostatically.

Adequate suspension stiffness and precise centering control of the TM are important to ensure

Adequate suspensionofstiffness and precise centeringaccelerometer. control of theToTM are important to ensure desirable performance the force-balanced electrostatic stabilize the movement of each TM, we need control its motion electrostatic in five DoFs. If all the cross-coupling effects the desirable performance ofto the force-balanced accelerometer. To stabilize theamong movement of axes to arecontrol ignoreditsby assuming small position the dynamics of among the TMthe candifferent be each different TM, we need motion in five DoFs. If all deviation, the cross-coupling effects by five axes modeled are ignored by uncoupled assuming 1-DoF small systems: position deviation, the dynamics of the TM can be modeled by five uncoupled 1-DoF systems: mei  f e,i  f in,i (2a) .. mei “ f e,i ` f in,i (2a) J j j  M e,i  M in ,i ..

(2b)

Jj α j “ Me,i ` Min,i

(2b)

where m and J are the mass and moment of inertia of the TM, e and  the linear and angular and eMand displacements of the away from its equilibrium position, where m and J are theTM mass and moment of inertia of thef e TM, αelectrostatic the linear feedback and angular e the

f in away force and torque, and M the applied inputf eforce torque, the subscript displacements of the TM from its externally equilibrium position, and and Me the electrostatic feedback in  x, ytorque, , z denotes j  torque, ,  denotes the axis which the force is produced and and axis around force iand f in and Minalong the externally applied input force the the subscript i “ x, y, z which torque produced, respectively. The residual air-film damping effect neglected in the denotes thethe axis alongiswhich the force is produced and j “ θ, φ denotes the axisisaround which Equation (2) by considering that the TM is suspended in high vacuum. torque is produced, respectively. The residual air-film damping effect is neglected in Equation (2) by Forthat instance, the is electric force produced by the charged set of the feedback electrodes on the considering the TM suspended in high vacuum. mass along the considered x-axis can be linearized as [24]: For instance, the electric force produced by the charged set of the feedback electrodes on the mass f e, x as  k[24]: along the considered x-axis can be linearized (3) vVx  k x x where kv is the actuator gain and k x thef position “ k Vstiffness ` k xor negative spring constant, respectively. e,x

v x

x

The maximum electric force applied on the centered TM is kvVb by considering the condition

(3)

where k v is the actuator gain and k x the position stiffness or negative spring constant, respectively. The maximum electric force applied on the centered TM is kv Vb by considering the condition |Vx | ď Vb

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Sensors 2016, 16, 1262 18 holds. Note that the x-axis suspension design is optimized to generate weak electrostatic8 offorce by using an area variation scheme [18]. In principle, it is free of the negative position stiffness, i.e., k x “ 0. Vx  Vb holds. Note that the x-axis suspension design is optimized to generate weak electrostatic On the other hand, the position stiffness has a significant effect on other four suspension axes in which force by using an areaisvariation [18]. Inrelatively principle, large it is free of the negative position stiffness, a gap variation scheme utilizedscheme to generate electrostatic force in order to balance i.e., k x  0 . On the other hand, the position stiffness has a significant effect on other four suspension possible disturbance resulted from the TM spinning. axes in whichmodel a gap variation scheme is utilized generate relatively electrostatic force in order This linear is valid by assuming thattothe motion of the large PM is very small, e.g., in a range to balance possible disturbance resulted from the TM spinning. less than 10% of the nominal gap. This assumption can be ensured by adequate suspension stiffness This linear model is valid by assuming that the motion of the PM is very small, e.g., in a range provided through design of the suspension control loop. Substituting Equation (3) into Equation (2a) less than 10% of the nominal gap. This assumption can be ensured by adequate suspension stiffness and then taking the Laplace transform yield control the dynamics of the TM: provided through design of the suspension loop. Substituting Equation (3) into Equation (2a)

and then taking the Laplace transform yield the dynamics of the TM:

Xpsq 1 “ 12 Fin,x psq `X k( sv)Vx psq  ms ´ kx

(4) (4)

ms 2  k x

Fin, x ( s )  kvVx ( s )

where Fin,x psq ` k v Vx psq represents the total forces applied on the TM along the x-direction. where Fin , x ( s )  k vVx ( s ) represents the total forces applied on the TM along the x-direction. The The dynamics of the TM in four other DoFs can be found by substituting appropriate variables dynamics of the TM in four other DoFs can be found by substituting appropriate variables in in Equation (4). Equation (4). Open loop instability due to the negative position stiffness can be found by inspecting the Open loop instability due to the negative position stiffness can be found by inspecting the characteristic equation of the transfer function in Equation (4) given the presence of a pole on the characteristic equation of the transfer function in Equation (4) given the presence of a pole on the right-hand sideside of the s-plane. feedbackcontrol control must be used to stabilize right-hand of the s-plane.Consequently, Consequently, active active feedback must be used to stabilize the the suspension servo loop. A simplified ofthe theclosed-loop closed-loop suspension control is shown in suspension servo loop. A simplifiedblock blockdiagram diagram of suspension control is shown in Figure 6, where k , k and G psq are the sensitivity of the position sensor, gain of the voltage amplifier Figure 6, where s aks , k a cand Gc ( s ) are the sensitivity of the position sensor, gain of the voltage and transfer of the feedback to be designed, respectively. It is It assumed that no amplifierfunction and transfer function of thecontroller feedback controller to be designed, respectively. is assumed that notime significant time delay occurs in thesensor, positiondigital sensor,controller digital controller andamplifier drive significant delay (phase lag)(phase occurslag) in the position and drive in amplifier in the frequency range of the instrument operation. the frequency range of the instrument operation. TM dynamics ain

m

fin

1 ms 2  k x

 

fe, x

x

ks

kv

 xs 

xr Gc ( s )

Vx

ka

Figure 6. Block diagram controlsystem system used a force-balanced Figure 6. Block diagramofofthe theclosed-loop closed-loop suspension suspension control used as aasforce-balanced electrostatic accelerometer: xr xand xsxsare referenceinput input and position sensor output r and arethe the position position reference and position sensor output used used electrostatic accelerometer: to evaluate the loop frequency responseasasdefined defined in Equation to evaluate the loop frequency response Equation(6). (6).

For the NEP instrument operating in high vacuum, a typical lag-lead compensator is utilized to

For the NEP instrument operating in high vacuum, a typical lag-lead compensator is utilized to illustrate the design procedure: illustrate the design procedure: (1  T1 s ) (1  T2 s ) , a  1, b  1, T1  T2 ) (1` T22ssq/ b) p1 ` (1 T1sqaT1 sp1

Gc ( s )  kc

Gc psq “ kc

,

(5)

a ą 1, b ą 1, T1 ąą T2

p1 ` aT1 sq p1 ` T2 s{bq according to the stiffness requirements, T1 and T2 where kc is the compensator gain selected

(5)

the compensator time constants gain of theselected lag and according lead compensators, respectively. wheredenote kc is the to the stiffness requirements, T1 and T2 denote the The closed-loop transfer function from the position reference input xr to the position sensor time constants of the lag and lead compensators, respectively. xs is used as a measure of the loop performance and is givenxby:to the position sensor output The closed-loop transfer function fromdynamic the position reference input r output xs is used as a measure of the loopXdynamic performance and is given by: ( s ) k k k G ( s ) s s a v c Gcl ( s ) 

X (s)



ms 2  k  k k k G ( s )

(6)

r c Xs psq kxs ka ks vaGvc psq Gcl psq “ “ Equation (6) describes the frequency response suspension Xr psq ms2of´the kx ` ks ka kv Gcservo psq to the position input. On

(6)

other hand, the feedback control voltage is a measure of the acceleration input ain applied to the

Equation describes the frequency response theaccelerometer suspension input-output servo to the response positionisinput. instrument(6) case. The transfer function that describesofthe defined as: the feedback control voltage is a measure of the acceleration input ain applied to On other hand, the instrument case. The transfer function that describes the accelerometer input-output response is defined as:

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Ga psq “

m Vx psq “ G psq Ain psq kv cl

(7)

Equation (7) shows that the static and dynamic performance is closely related to design of the suspension control loop. At frequencies much lower than the suspension loop bandwidth, the TM is kept motionless in the electrode cavity due to high loop gain. In this case, Equation (7) can be simplified to a scale factor Ga psq « Ka “ m{kv by considering that Gcl psq « 1. The electrostatic suspension loop is basically a regulator that keeps the TM centered at its equilibrium position. One of the most important characteristics of the accelerometer is the electrostatic stiffness provided by feedback control. The stiffness transfer function of the closed-loop system that relates the equivalent acceleration input force main to the position change x is derived from Figure 6 and given by: mAin psq Kpsq “ “ ms2 ´ k x ` ks ka kv Gc psq (8) X psq A fundamental controller design criteria for the suspension loop is to provide adequate stiffness and damping for stable suspension of the TM. The suspension stiffness is largely determined by the feedback controller within the loop bandwidth [24]. Closed-loop suspension control must provide adequate positive stiffness, which is greater than the inherent negative position stiffness k x to ensure loop stability. Hence, the suspension design must satisfy the following condition: kc ą n ¨ ak x {ka kv ks ,

ną1

(9)

where n is the ratio of the lowest overall stiffness to the negative stiffness of the TM and is usually n ě 5 by design. Given that the residual air-film effect in high vacuum can be neglected in design of the suspension loop, the lead compensation is utilized to provide adequate damping force and ensure desirable stability. The compensated open-loop transfer function in Figure 6 can be given by: Gol psq “

ks ka kv Gc psq ms2 ´ k x

(10)

It will be helpful to relate the lead compensator ? parameters in Equation (5) to the cross-over frequency of the open-loop system, e.g., let ωc “ b{T2 . Substituting s = jω into Equation (10), the cross-over frequency can be obtained by definition, i.e., |Gol psq|s“ jωc “ 1: d ωc “

? pn b ´ 1qk x m

(11)

where n can be set by stiffness requirement and ? b for desirable phase margin. The time constant of the lead compensator can be derived as T2 “ b{ωc while the lag compensator usually has a time constant setting that satisfies T1 ě 3T2 and a ě 10. The design parameters of the x, y, z-axis suspension are listed in Table 4, where the y/z position stiffness also contains the contributions from the x, y, z-axis suspension electrodes and the injection electrode. The closed-loop frequency responses of the differential accelerometer operated in vacuum are simulated based on Equation (6). The simulation results of totally six closed-loop suspension loops, three for the inner TM and three for the outer TM, are shown in Figure 7. It is clear that much different closed-loop bandwidths between the x-axis and the y/z-axis suspension loops are shown in Figure 7a,b. This result is attributed to the measuring range in the y and z axes of the inner/outer accelerometers being over 50 times larger than that in the sensitive x axis.

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Table 4. Parameters of the electrostatic suspension loops.

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Inner TM Outer TM Table 4. Parameters of the electrostatic suspension loops. Symbol y/z x y/z x Inner TM Outer TM Parameter (unit) V b Symbol 20 Bias voltage (V) 20 20 20 y/z x y/z x Ain,max Full-scale range (m/s2 ) 1.48 ˆ 10´2 2.96 ˆ 10´4 1.48 ˆ 10´2 1.85 ˆ 10´4 Bias voltage (V) Vb3.26 ˆ 10´520 20 ˆ 10´5 201.02 ˆ 10´6 Actuator gain (N/V) kv 6.50 ˆ20 10´7 8.16 −4 Full-scale range (m/s2) kx Ain,max 24.14 1.48 × 10−2 2.96 1.48 ×54.71 10−2 1.85 × 10−4 0 Position stiffness (N/m) 0 × 10 −5 −7 6.50 8.16 × 10 106−5 1.02 × 105−6ˆ 105 Actuator gain (N/V) ks kv Position sensor gain (V/m) 1063.26 × 10 5ˆ10×510 Position stiffness (N/m) ka kx 54.714 0 Voltage driver gain (V/V) 4 24.14 40 4 106 5×10 106 15 5 × 105 – Position design sensor gain (V/m)n ks Ratio in stiffness 15 – 5 Controller gain 83.61 4 475.41 4 120.62 Voltage driver gain (V/V)kc ka 83.34 4 Cross-over Ratio frequency (Hz) designω c 2.48 2.35 in stiffness n 24.75 15 -1523.53 -Parameter (unit)

Controller gain Cross-over frequency (Hz)

kc ωc

83.34 24.75

83.61 2.48

75.41 23.53

120.62 2.35

Frequency responses of the suspension stiffness based on Equation (8) are shown in Figure 7c,d. The simulated curves clearlyof indicate that these suspension loops have(8) similar stiffness characteristics, Frequency responses the suspension stiffness based on Equation are shown in Figure 7c,d. except that the two radial (y/z) suspension loops have much higher stiffness than the axial (x) loop in The simulated curves clearly indicate that these suspension loops have similar stiffness characteristics, the low-frequency andradial medium-frequency ranges. the higher other hand, these closely except that the two (y/z) suspension loops haveOn much stiffness than curves the axialcoincide (x) loop in the low-frequency and medium-frequency On the hand,by these curves coincide closely in the high-frequency range (>200 Hz). Thisranges. result can be other explained considering Equation (8) that the high-frequency (>200 inertial Hz). Thisstiffness, result can be2explained considering Equation that eachin accelerometer has anrange identical mω . A designbyconsideration in these(8) suspension 2. A design consideration in these suspension each accelerometer has an identical inertial stiffness, mω loops is that the stiffness characteristics must match the full-scale range of the accelerometer input. loops is that the stiffness characteristics must match the full-scale range of the accelerometer input. As an example, since the allowable input range in the radial direction is over 50 times larger than that As an example, since the allowable input range in the radial direction is over 50 times larger than that in the sensitive x direction, it can be observed that the radial suspension has extremely high stiffness in the sensitive x direction, it can be observed that the radial suspension has extremely high stiffness 3 Hz, Figure 7 indicates that the compared with that ofofthe a frequency 10´Figure −3 Hz, compared with that theaxial axial suspension. suspension. AtAt a frequency of 10of 7 indicates that the y/zy/z-axis stiffnessis is 100 times higher of thesuspension x-axis suspension in our design. results axis stiffness 100 times higher than than that ofthat the x-axis in our design. These resultsThese confirm confirm the optimization of the instrument configuration foras the axis as the measurement axis for the optimization of the instrument configuration for the x axis thex measurement axis for the NEP the NEP test.small The full-scale small full-scale range low stiffness make it the most axis sensitive for the test. The range and lowand stiffness make it the most sensitive for theaxis NEP measurements. NEP measurements.

Figure 7. Simulationresults resultsof of the the active control loops for the inner (leftTM side) andside) the and Figure 7. Simulation activesuspension suspension control loops for the TM inner (left outer TM (right side): (a,b) Closed-loop frequency responses; (c,d) Suspension stiffness of the closedthe outer TM (right side): (a,b) Closed-loop frequency responses; (c,d) Suspension stiffness of the loop control system. closed-loop control system.

It seems that the closed-loop system exhibits relatively high suspension stiffness by setting a larger n (nthat = 15). instance, the allowable displacement the inner TM is less than 1.72 μm, only It seems theFor closed-loop system exhibits relativelyofhigh suspension stiffness by setting a larger

n (n = 15). For instance, the allowable displacement of the inner TM is less than 1.72 µm, only 2.87% of

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the nominal gap. However, the spin drive voltage during the electrostatic motor operation will Sensors 2016, 16, 1262 11 of 18 also generate large unstable position stiffness [25], e.g., 135.0 N/m by the inner motor and 404.5 N/m by 2.87%motor of the nominal gap. However, the V. spin voltage the electrostatic motor the outer at a drive voltage of 100 In drive this case, theduring allowable motion range ofoperation the inner TM will also generate large unstable position stiffness [25], e.g., 135.0 N/m by the inner motor is increased to 2.67 µm but also well below the design goal of 10 µm. Considering that the and unstable 404.5 N/m by the outer motor at a drive voltage of 100 V. In this case, the allowable motion range of motor stiffness is over five times larger than the negative position stiffness kx , its effect on the loop the inner TM is increased to 2.67 μm but also well below the design goal of 10 μm. Considering that stability should be taken into account in design of the controller gain, as in Equation (9). In our design the unstable motor stiffness is over five times larger than the negative position stiffness kx, its effect by setting = 15, the lowest stiffnessinisdesign over of two higher total negative on the n loop stability should closed-loop be taken into account thetimes controller gain,than as inthe Equation (9). spring constant, ensures stability evenstiffness duringisthe initial spin-up process. In our designwhich by setting n = 15,the theloop lowest closed-loop over two times higher than the total negative spring constant, which ensures the loop stability even during the initial spin-up process.

3.3. Electrostatic Motor

3.3. Electrostatic Motor

One important feature of the NEP instrument is that the two test masses are spinning with One important feature the space NEP instrument is that the two testalso masses are spinning withareas muchon its much different rotations. Forofthis accelerometer, each TM features eight flat different rotations. For this space accelerometer, each TM also features eight flat areas on its external external surface as depicted in Figure 8a, allowing the measurement and control of the axial mass spin. surface asofdepicted in Figure 8a,the allowing the measurement and control of the the axial mass spin. The The rotation the mass around sensitive axis is measured though differential capacitance rotation of the mass around the sensitive axis is measured though the differential capacitance change change between the dedicated flat areas on the mass and associated rotation electrodes on the outer between the dedicated flat areas on the mass and associated rotation electrodes on the outer cylinder [21]. The spinning-up of the mass is based on principle of the variable capacitance motor cylinder [21]. The spinning-up of the mass is based on principle of the variable capacitance motor (VCM) consisting of aof6-pole stator electrodes)and andanan 8-pole rotor mass). This VCM (VCM) consisting a 6-pole stator(six (sixrotation rotation electrodes) 8-pole rotor (test(test mass). This VCM ˝ , as shown in Figure 8. operates in a three-phase drive mode and produces a step angle of 15 operates in a three-phase drive mode and produces a step angle of 15°, as shown in Figure 8.

Figure 8. Three-phase variable-capacitance motor: (a) Stator electrodes and test mass (rotor); Figure 8. Three-phase variable-capacitance motor: (a) Stator electrodes and test mass (rotor); (b) Layout (b) Layout of the 6-electrode stator and 8-pole rotor; (c) Three-phase excitation voltages and of the 6-electrode stator and 8-pole rotor; (c) Three-phase excitation voltages and (d) Three-phase (d) Three-phase stator-rotor capacitances as a function of the mechanical rotation angle. stator-rotor capacitances as a function of the mechanical rotation angle.

In order to simulate the steady-state speed and start-up time responses of the electrostatic motor, an model governing the rotation behavior necessary. For this three-phase operatedmotor, In analytical order to simulate the steady-state speed and is start-up time responses of the VCM electrostatic in high vacuum, the dynamic equation describing the TM rotation around the x-axis can be expressed an analytical model governing the rotation behavior is necessary. For this three-phase VCM operated in high as: vacuum, the dynamic equation describing the TM rotation around the x-axis can be expressed as: J.x  bx  Te Jx ω ` bx ω “ Te

(3)

where J x and bx are the axial moment of inertia of the mass and the damping coefficient generated

(12)

byJxthe residual vacuum cavity, and Te of the drive torque produced by three-phase rotation by where and bx are gas the in axial moment of inertia the mass and the damping coefficient generated electrodes. the residual gas in vacuum cavity, and Te the drive torque produced by three-phase rotation electrodes.

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Although the NEP instrument measurements are quite insensitive to the effects of electrostatic Sensors 2016, 16, 1262 12 of 18 drive by comparing with classical electromagnetic motors, the drive torque produced by the electrostatic motorthe is NEP extremely weak. Therefore,are thequite start-up duration a non-spinning Although instrument measurements insensitive to thefor effects of electrostaticmass 4 or 102 rpm in this work, will be quite long. Assuming the drive voltage is set to its drive rated by speeds, 10 comparing with classical electromagnetic motors, the drive torque produced by the at 100electrostatic V and themotor ultra-high vacuum reaches 10´5the Pa,start-up Figureduration 9 showsfor the start-up timemass responses is extremely weak. Therefore, a non-spinning to its of 4 2 rated with speeds, 10 or 10 rpm in this work, will long. Assuming the drive the voltage is setprocess at the motor different geometry parameters ofbe thequite spinning TM. For instance, start-up 4 rpm 4 s (4.603 4 s (9.588of the will ultra-high vacuum 10−5h)Pa, 9 shows theand start-up from 100 0 toV10and last 1.657 ˆ 10reaches forFigure the inner mass 3.452time ˆ 10responses h)the for the different geometry parameters of the For instance, thethe start-up process from outermotor mass,with respectively. Fortunately, once the TMspinning reachesTM. its desired speed, rotation drive will be 0 to 104 rpm will last 1.657 × 104 s (4.603 h) for the inner mass and 3.452 × 104 s (9.588 h) for the outer switched off to avoid any possible disturbing forces produced by the rotation electrodes. Then the mass, respectively. Fortunately, once the TM reaches its desired speed, the rotation drive will be two TMs will be keeping free rotation virtually at their rated speeds. The small speed decay during switched off to avoid any possible disturbing forces produced by the rotation electrodes. Then the each NEP experiment can befree measured a capacitive sensorThe andsmall thus speed used to assist the NEP two TMs will be keeping rotation by virtually at their speed rated speeds. decay during experiment data processing. Although longer time is needed to spin up the TM, the VCM drive is each NEP experiment can be measured by a capacitive speed sensor and thus used to assist the NEP compatible with electrostatic suspension design and well suited for long-term space test of the experiment data processing. Although longer time is needed to spin up the TM, the VCM drive isNEP. The NEP instrument can be set at several operation for space calibration or NEP. NEP test, compatible with electrostatic suspension design basic and well suited formodes long-term test of the The NEP can can be set at several basicspeed operation modes for calibration or NEP by at by considering thatinstrument the two TMs spin at various settings. When the two TMs are test, spinning considering that the two TMs can spin at various speed settings. When the two TMs are spinning at an equal speed, the instrument will be used as a reference to estimate various experimental limitations an equal speed, the instrument will be used as a reference to estimate various experimental or systematic errors. On the other hand, in the NEP tests the two masses will be spinning at much limitations or systematic errors. On the other hand, in the NEP tests the two masses will be spinning different speeds, e.g., 104 rpm for the4 inner mass and 100 rpm for the outer mass and vice versa. Hence, at much different speeds, e.g., 10 rpm for the inner mass and 100 rpm for the outer mass and vice unlike the STEP or MicroSCOPE mission enclosing two or more differential instruments made of versa. Hence, unlike the STEP or MicroSCOPE mission enclosing two or more differential different materials, theofNEP testsmaterials, can be performed using only one differential instruments made different the NEP tests can be performed using onlyaccelerometer one differential with multiple rotation modes. accelerometer with multiple rotation modes.

Figure 9. The start-up time of the motor required to spin up from 0 to its rate speed of 104 rpm vs. the

Figure 9. The start-up time of the motor required to spin up from 0 to its rate speed of 104 rpm vs. inner radius of the TM. The thickness of the cylindrical mass Th is set at 2.0, 2.5 and 3.0 mm for the inner radius of the TM. The thickness of the cylindrical mass Th is set at 2.0, 2.5 and 3.0 mm comparison. for comparison.

3.4. Noise Analysis

3.4. Noise Analysis

As stated in Section 2, the desired acceleration noise along the sensitive axis is less than

1/2 in order to test the NEP at a level of 10−12. The resolution of the NEP instrument 2.0 ×stated 10−9 m/s As in2/Hz Section 2, the desired acceleration noise along the sensitive axis is less than 12 . The resolution ´9 m/s 1/2 noise by2 /Hz various sources. The noise performance of the comprisingof of both 2.0 îs10limited in order to test the NEP at a level ofNEP 10ínstrument the NEP the inner and outer accelerometers will be evaluated considering the following four major noise sources. instrument is limited by various noise sources. The noise performance of the NEP instrument First, the differential acceleration between the TMs coupling from the residual non-gravitational comprising of both the inner and outer accelerometers will be evaluated considering the following acceleration aec acting on the NEP experiment capsule can be written as: four major noise sources. ad the  aecTMs / Rcmrcoupling from the residual non-gravitational (4) First, the differential acceleration between acceleration acting on the NEP capsule be written as: ec is the common modeexperiment rejection ratio of the can differential accelerometer along the sensitive where Racmr

axis. In the NEP space tests, a drag-free control system with micro-Newtonian thrusters will be used

ad “ aec {Rcmr

(13)

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where Rcmr is the common mode rejection ratio of the differential accelerometer along the sensitive 16, space 1262 13 ofbe 18 used axis. Sensors In the2016, NEP tests, a drag-free control system with micro-Newtonian thrusters will to compensate for the non-gravitational forces acting on the experiment capsule, such as atmospheric to compensate for the non-gravitational forces acting on the experiment capsule, such as atmospheric drag force. It is estimated that the residual non-gravitational acceleration could be reduced down drag´force. It is estimated that the residual non-gravitational acceleration could be reduced down to to 5 ˆ 10 6 ˆ (1 + f /0.1) m/s2 /Hz1/2 . According to the requirement of the MicroSCOPE mission, 5 × 10−6 × (1 + f/0.1) m/s2/Hz1/2. According to the requirement of the MicroSCOPE mission, the Rcmr 4 . Thus the acceleration disturbance a is estimated to be lower than the Rcould be realized be4. 10 cmr could d be realized to beto10 Thus the acceleration disturbance ad is estimated to be lower than ´ 10 2 1/2 −10 2 1/2 5 ˆ 10 m/s /Hz , as shown by line 1 in Figure 10. 5 × 10 m/s /Hz , as shown by line 1 in Figure 10.

Figure Accelerationnoise noise budget sensitive axis axis of theofNEP The lines 1, 2, 3,lines 4 Figure 10. 10. Acceleration budgetfor forthethe sensitive theinstrument. NEP instrument. The 1, and 5 represent the differential acceleration coupling from the residual non-gravitational acceleration, 2, 3, 4 and 5 represent the differential acceleration coupling from the residual non-gravitational temperature effect, position sensing induced noise, electrostatic actuation noise and total NEP acceleration, temperature effect, position sensing induced noise, electrostatic actuation noise and total instrument noise, respectively. NEP instrument noise, respectively.

Next, the thermal instability δTd of the instrument core induces radiation pressure and radiometer effects due to the residual gasinstrument pressure P inside the tightradiation housing pressure [7]. The temperature Next, the thermal instability δTd of the core induces and radiometer effect the thermal radiationPpressure andtight radiometer acceleration can be expressed as:including effects dueincluding to the residual gas pressure inside the housing [7]. The temperature effect 3 the thermal radiation pressure and radiometer acceleration can as: PA 16 be AmTexpressed atem  aRadiometer  aRad-Pres  m  Td   Td

2Tm

PAm

3mc

16σAm

(5)

T3

` aRad-Pres « δT ` δTd area of the TM, (14) where σ, c and Amatem are “ theaRadiometer Stefan-Boltzmann constant, and section 2Tmlightd speed3mc −5 respectively. Given the residual gas pressure P = 10 Pa, temperature T = 300 K, δTd = 0.5 K/Hz1/2, the 2/Hz1/2 resulting acceleration disturbance for the inner and outer TMs are 1.27 10−10 m/s where σ, c and Am are the Stefan-Boltzmann constant, light speed and× section area of and the TM, −11 2 1/2 −10 2 1/2 ´ 5 8.22 × 10 Given m/s /Hz , respectively. The total temperature atem is 1.51T× 10 m/s , as shown respectively. the residual gas pressure P = 10 Pa,effect temperature = 300 K,/Hz δTd = 0.5 K/Hz1/2 , by line 2 in Figure 10. disturbance for the inner and outer TMs are 1.27 ˆ 10´10 m/s2 /Hz1/2 and the resulting acceleration At frequency higher than 0.076 thetemperature position sensing noise affects ´ 11 1/2 , respectively. 10 m/s2 /Hz1/2 , 8.22 ˆ 10 m/s2 /Hzrange TheHz, total effect atemxnoise is 1.51 ˆ the 10ácceleration resolution with a square frequency law, i.e., as shown by line 2 in Figure 10. 2 2 aPosition (4 position f  p2 ) xsensing At frequency range higher than 0.076 Hz,the noise xnoise affects the acceleration (6) noise resolution with a square frequency law, i.e., where p  k x / m is the frequency associated to the residual passive stiffness kx between the TM

2 2 and associated suspension electrodes, which is evaluated to be less than 0.1 N/m by considering (15) aPosition “ p4π f ` ωp2 qx noise electrostatic field boundary effects. If the capacitive position sensor noise can be expressed as xnoise = 4a× 10−11 × (1 + 10−3/f)1/2 m/Hz1/2 [26], the total acceleration noise aPosition is less than where ωp “ k x {m is the frequency associated to the residual passive stiffness kx between the TM 2.95 × 10−10 m/s2/Hz1/2 at fNEP, as shown in line 3 in Figure 10. and associated suspension electrodes, −3 which is evaluated to be less than 0.1 N/m by considering At frequency range lower than 10 Hz, the electrostatic actuation acceleration noise is the major electrostatic field boundary effects. If the capacitive position sensor noise can be expressed as source of noise and given by:

xnoise = 4 ˆ 10´11 ˆ (1 + 10´3 /f )1/2 m/Hz1/2 [26], the total acceleration noise aPosition is less than k 2.95 ˆ 10´10 m/s2 /Hz1/2 at f NEP , as shown inaealine Figure 10.  v3 vin (7) noise m ´ 3 At frequency range lower than 10 Hz, the electrostatic actuation acceleration noise is the major which depends mainlyby: on the noise of the voltage amplifier vnoise. In [27], the voltage noise is source of noise and given estimated as vnoise = 1.2 × 10−8 × Vb × (1 + 7/f)1/2 V/Hz1/2 kv. Considering the actuator gain kv and bias voltage aea “ vnoise (16) m

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which depends mainly on the noise of the voltage amplifier vnoise . In [27], the voltage noise is estimated as vnoise = 1.2 ˆ 10´8 ˆ V b ˆ (1 + 7/f )1/2 V/Hz1/2 . Considering the actuator gain kv and bias voltage V b in Table 4, the voltage amplifier will contribute a total acceleration noise of 8.18 ˆ 10´10 m/s2 /Hz1/2 at f epSensors , as shown in line 4 in Figure 10. 2016, 16, 1262 14 of 18 Other accelerometer noise sources [7], such as the thermal noise induced by the residual gas 2/Hz1/2 Vb in Table 4, thebetween voltage the amplifier will contribute a total noise of the 8.18two × 10−10 m/ssuspension damping, coupling capsule’s attitude and the acceleration relative position TMs, at fep,electrical as shown in line due 4 in Figure induced noise to the10. spinning TM, the Earth’s gravity gradient effect and magnetic Other accelerometer noise sources [7], such as the thermal induced therange residual gas two effect, have also been considered for the noise evaluation. Thesenoise effects are inbythe of over damping, coupling between the capsule’s attitude and the relative position of the two TMs, ´ 11 2 orders of magnitude less than the NEP instrument noise goal, i.e., below 2 ˆ 10 m/s /Hz1/2 at suspension induced electrical noise due to the spinning TM, the Earth’s gravity gradient effect and f NEP . Thus these noise sources are negligible in the noise evaluation. magnetic effect, have also been considered for the noise evaluation. These effects are in the range of Taking the square root of the quadratic sum of four considered acceleration noises, the total over two orders of magnitude less than the NEP instrument noise goal, i.e., below 2 × 10−11 m/s2/Hz1/2 differential acceleration byin line 5 in Figure 10. The evaluated noise is at fNEP. Thus these noise noise sourcesis areshown negligible the noise evaluation. 9 m/s2 /Hz1/2 at the NEP signal frequency, by neglecting other small acceleration 1.01 ˆ 10´ Taking the square root of the quadratic sum of four considered acceleration noises, the total disturbances. clear that the electrostatic differentialIt is acceleration noise is shownactuation by line and 5 inresidual Figure non-gravitational 10. The evaluatedacceleration noise is are −9 m/s 2/Hz1/2 atat 1.01 × 10 the NEP signal frequency, by neglecting other small acceleration disturbances. two major noise sources the NEP signal frequency. It is clear that the electrostatic actuation and residual non-gravitational acceleration are two major

4. Development Status of asignal NEPfrequency. Instrument Prototype noise sources at the NEP A Development single cylindrical accelerometer prototype is proposed to demonstrate its technological 4. Status of a NEP Instrument Prototype feasibility. This section presents the configuration and design performance of the first NEP instrument A single cylindrical accelerometer prototype is proposed to demonstrate its technological prototype, presently developed by the authors at Tsinghua University. feasibility. This section presents the configuration and design performance of the first NEP instrument prototype, presently developed by the authors at Tsinghua University. 4.1. The Sensor Unit

4.1. Sensor Unit ThisThe prototype has similar dimensions to the inner cylindrical accelerometer of the differential

NEP instrument. However, very dimensions high voltage needs tocylindrical be generated in order of to the counteract the 1 g This prototype has similar to the inner accelerometer differential Earth’s gravity along the y/z axes [28]. To lower the required suspension voltage, the injection electrode NEP instrument. However, very high voltage needs to be generated in order to counteract the 1 g is moved from the inner to the outer sothe as to provide larger radial suspension electrode Earth’s gravity along cylinder the y/z axes [28]. To one lower required suspension voltage, the injection is moved fromof thethe inner to the outer one provide larger radial suspension areas.electrode The full-scale range y/zcylinder acceleration inputs is so setasatto3.0 g by applying a high suspension electrode The full-scale of theconfiguration y/z accelerationofinputs is set atunit. 3.0 gThe by applying high for voltage of 786areas. V. Figure 11 showsrange the basic the sensor materialachosen suspension voltage of 786 V. Figure 11 shows the basic configuration of the sensor unit. The material the TM is an ultra-low thermal expansion glass ceramic, which is lighter than titanium alloy and thus chosen for the TM is an ultra-low thermal expansion glass ceramic, which is lighter than titanium easier to suspend under 1 g. The inner and outer cylinders are also made of the identical glass ceramic alloy and thus easier to suspend under 1 g. The inner and outer cylinders are also made of the for better temperature stability. The necessary electrodes for electrostatic suspension and electrostatic identical glass ceramic for better temperature stability. The necessary electrodes for electrostatic motor are defined gold coatings. noisecoatings. along the ground suspension andby electrostatic motorTo areachieve definedlow by gold Tooptimized achieve lowx axis noiseduring along the tests,optimized this sensitive axis is placed inside the horizontal plane and set at a much small input range of x axis during ground tests, this sensitive axis is placed inside the horizontal plane and set ´ 4 −4 only at 10a much g. small input range of only 10 g.

Figure 11. The sensor unit configuration:(a) (a) Test Test mass mass and cylinders; (b) Exploded view view Figure 11. The sensor unit configuration: andinner/outer inner/outer cylinders; (b) Exploded of various electrodes; (c) The assembled senor unit operated inside a vacuum chamber. of various electrodes; (c) The assembled senor unit operated inside a vacuum chamber.

From the present design of the sensor core, the production of the first laboratory model was From the present design of integration the sensoriscore, production of the the firstchallenging laboratory model completed and the instrument now the in progress. To achieve NEP test was accuracy, thethe geometry of the integration core parts of the accelerometer, i.e., To the achieve electrodethe cylinders and theNEP test test completed and instrument is now in progress. challenging mass, the must be machined with anparts accuracy of aaccelerometer, few micrometers order to guarantee the fine accuracy, geometry of the core of the i.e.,inthe electrode cylinders and the electrostatic actuation of the instrument. Thus, the performance of the NEP mission relies test mass, must be machined with an accuracy of a few micrometers in order to guarantee the fine dramatically on theofmachining and precise metrology of the partsofofthe theNEP sensor core and particularly electrostatic actuation the instrument. Thus, the performance mission relies dramatically on the test mass. Figure 12 shows three core parts and the fabricated sensor unit. These ULE parts are fabricated using a specific ultrasonic machining and precise grinding process. After fabrication, these core parts have undergone extensive measurements. The form and dimension measurements were

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on the machining and precise metrology of the parts of the sensor core and particularly on the test mass. Figure 12 shows three core parts and the fabricated sensor unit. These ULE parts are fabricated using a specific ultrasonic machining and precise grinding process. After fabrication, these core parts have undergone extensive measurements. The form and dimension measurements were performed Sensors 2016, 16, 1262 15 of 18 using a coordinate measuring machine. From these measurements, all necessary features (diameters, length, concentricity, cylindricity, parallelism andFrom perpendicularity) are determined. It is shown performed using a coordinate measuring machine. these measurements, all necessary features (diameters, concentricity, cylindricity, parallelism and perpendicularity) determined. It is mm, that the TM haslength, a mass of 25.898 g, inner diameter 29.9986 mm, and outer are diameter 35.0070 shown that the TM has a mass of 25.898 g, inner diameter 29.9986 mm, and outer diameter 35.0070 mm, where the dimensional tolerances are less than 7 µm while the geometrical tolerances are all less than where the dimensional tolerances arebetween less thanthe 7 μm while the tolerances are all less than 0.8 µm. Moreover, the capacitive gaps hollow TMgeometrical cylinder and two inner/outer electrode 0.8 μm. Moreover, the capacitive gaps between the hollow TM cylinder and two inner/outer cylinders are adjusted and calibrated by measuring the electrode capacitances using aelectrode precise LCR cylinders are adjusted and calibrated by measuring the electrode capacitances using a precise LCR meter. The measured result shows that the mean gap is 45.7 µm and the gap variation throughout meter. The measured result shows that the mean gap is 45.7 μm and the gap variation throughout the entire sensitive axis is less than 0.6 µm. In addition, the vacuum chamber can be maintained at the entire sensitive axis is less than 0.6 μm. In addition, the vacuum chamber can be maintained at ´5 2 ˆ 10 byby a miniaturized ionpump. pump. −5 Pa 2 × 10Pa a miniaturizedsputtering sputtering ion

Figure 12. The fabricated sensor unit:core coreparts parts before before (a) (b)(b) gold-coating; (c) Assembled Figure 12. The fabricated sensor unit: (a)and andafter after gold-coating; (c) Assembled sensor unit core; (d) Sensor unit mounted inside a vacuum chamber. sensor unit core; (d) Sensor unit mounted inside a vacuum chamber.

4.2. The Sensing and Control Electronics

4.2. The Sensing and Control Electronics

Evaluating the performance of electrostatic accelerometers on the ground is inevitably limited

Evaluating performance of electrostatic accelerometers on the ground is inevitably limited by by Earth’s 1 gthe gravity. To meet the needs of the electrostatic levitation, a high voltage amplifier-based suspension scheme suitable to test the engineering and flight modelsa of accelerometers for space Earth’s 1 g gravity. To is meet the needs of the electrostatic levitation, high voltage amplifier-based missions, even though the resolution the accelerometers could not beofdirectly verified atfor thespace suspension scheme is suitable to test theofengineering and flight models accelerometers designed level due to the seismic noise and the high-voltage coupling limits [28]. Figure 13a illustrates missions, even though the resolution of the accelerometers could not be directly verified at the the block diagram of the accelerometer electronics mainly consist of six capacitive position sensors, designed level due to the seismic noise and the high-voltage coupling limits [28]. Figure 13a illustrates 16 high-voltage amplifiers and a 32-bit control-optimized digital signal processor (DSP), as well as the block diagram of the accelerometer electronics mainly consist of six capacitive position sensors, the necessary ADCs and DACs. Five capacitive position sensors and ten high-voltage suspension 16 high-voltage amplifiers and a 32-bit control-optimized digital signal processor (DSP), as well as amplifiers are used to maintain the TM at its equilibrium position by active electrostatic suspension the necessary ADCs position sensors and tensensor high-voltage suspension in five DoFs. Theand spinDACs. angle ofFive the capacitive TM is detected by a capacitive speed and continuous amplifiers areisused maintain the TMsix at high-voltage its equilibrium position by active electrostaticFigure suspension rotation then to realized by driving rotation amplifiers synchronously. 13b in five DoFs. spin angle and of the TM iscontrol detected by a capacitive speed sensor andground continuous showsThe the suspension rotation electronics developed for subsequent testingrotation of the NEP instrument. The measured results show that the capacitive sensor has a sensitivity of 0.45 V/pF is then realized by driving six high-voltage rotation amplifiers synchronously. Figure 13b shows and a bandwidth of 11.2 KHz. Theelectronics gain of the developed high-voltagefor dc subsequent amplifier circuit is about 46 V/V the suspension and rotation control ground testing of and the NEP the output voltage range results is from 0show to 920that V. The frequency showsof a large instrument. The measured theexperimental capacitive sensor hasresponse a sensitivity 0.45 signal V/pF and bandwidth of 8.5 kHz. Considering the simulated closed-loop bandwidth in the radial (y/z) a bandwidth of 11.2 KHz. The gain of the high-voltage dc amplifier circuit is about 46 V/V and the suspension loops is 1.11 kHz, the sampling frequency of the DSP-based digital controller output voltage range is from 0 to 920 V. The experimental frequency response shows a large signal (TMS320F28335) is set at 20 kHz. The simulation results shows the radial suspension loops exhibit bandwidth of 8.5 kHz. Considering the simulated closed-loop bandwidth in the radial (y/z) suspension much higher bandwidth and suspension stiffness than the sensitive axis owing to much different loopsfull-scale is 1.11 kHz, the sampling of the DSP-based digital measuring ranges. frequency Moreover, the simulated start-up timecontroller of the TM(TMS320F28335) from 0 to 104 rpmisisset at 20 kHz. The simulation results shows the radial suspension loops exhibit much higher bandwidth 36.9 minutes by applying a high drive voltage of 300 V. and suspension stiffness than the sensitive axis owing to much different full-scale measuring ranges. Moreover, the simulated start-up time of the TM from 0 to 104 rpm is 36.9 min by applying a high drive voltage of 300 V.

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Figure 13.Schematic (a) Schematic electrostaticsuspension suspension and electronics; (b) A photograph Figure 13. (a) of of electrostatic androtation rotationcontrol control electronics; (b) A photograph of the assembled control electronics unit. of the assembled control electronics unit.

In this ground-test mode, the instrument functionality and performance will be evaluated as

In thisasground-test mode, the functionality and performance evaluated as much possible. According to instrument current design and simulation results of the will NEP be instrument during 1 g operation, the main design are summarized in Table 5. muchprototype as possible. According to current design andspecifications simulation results of the NEP instrument prototype during 1 g operation, the main design specifications are summarized in Table 5. Table 5. Summary of main design specifications of the NEP instrument prototype.

Table 5. Summary of main design specifications of the NEP instrument prototype. Description (Unit) x-Axis y/z-Axis Acceleration measuring range (g) Scale factor (V/g) Description (Unit) Acceleration noise at 0.1 Hz (m/s2/Hz1/2) Acceleration measuring range (g) Suspension loop bandwidth (Hz) Scale factor (V/g) Suspension (N/m) Acceleration noisestiffness at 0.1 Hz (m/s2 /Hz1/2 ) Rated spin speed (rpm) Suspension loop bandwidth (Hz) Start-up time (min) (N/m) Suspension stiffness

10−4 105 x-Axis 10−7 10´4 10.7 5 10 >19.5 ´7 10 104 10.7 36.9 >19.5

Rated spin speed (rpm) Start-up time (min)

104 36.9

5. Conclusions

3.0 3.3 y/z-Axis --

3.0 1110.0 3.3 5 >1.58 – × 10 -1110.0 >1.58 ˆ--105 – –

A space station based free-fall test of the equivalence principle with two rotating test masses is proposed to test the spin-gravity interaction at a precision of 10−12. We present the design of the 5. Conclusions differential electrostatic accelerometer specially optimized for the in-orbit test of the NEP and the

A space stationtobased free-fall test of the equivalence principle with two rotatingcapsule. test masses noise evaluation perform such a sensitive experiment on board a microgravity experiment ´ 12 is proposed to test the spin-gravity interaction atthan a precision ofperformed 10 . Weonpresent This is more than five orders of magnitude better the results ground the withdesign free-fallof the differential specially optimized for theto in-orbit test the NEP and the rotatingelectrostatic gyroscopes. accelerometer This requires many challenging techniques develop theofNEP instrument, asnoise evaluation perform such a sensitive on board a microgravity This is well astoin-orbit calibration and fine experiment data processing. The configuration andexperiment fabrication capsule. of a single cylindrical accelerometer prototype are presented for ground testing and proof of concept. Extensive more than five orders of magnitude better than the results performed on ground with free-fall rotating effort hasThis beenrequires carried out to develop the means for accurate assembly and measurements gyroscopes. many challenging techniques tofabrication, develop the NEP instrument, as well as of the core components. development of the sensitive NEP instrument is extremely in-orbit calibration and fine The datacompleted processing. The configuration and fabrication of a single cylindrical challenging and time-consuming. Current work has already confirmed some technological accelerometer prototype are presented for ground testing and proof of concept. Extensive effort has assessments and it should continue to open the way to the final construction of a differential been carried out to develop the means for accurate fabrication, assembly and measurements of the core accelerometer. Future work will focus on electrostatic suspension, rotation control, calibration and components. The completed development of the sensitive NEPinnovative instrumenttechnologies is extremely challenging ground testing of the accelerometer prototype. Most of these will be tested and time-consuming. Current work has already confirmed some technological assessments and it should and verified in a series of ground-based pre-flight experiments. continue to open the way to the final construction of a differential accelerometer. Future work will The authors would like control, to acknowledge the support offered by the following programs: focusAcknowledgments: on electrostatic suspension, rotation calibration and ground testing of the accelerometer National Natural Science Foundation of China (61374207, 91436107) and Tsinghua University Initiative Scientific prototype. Most of these innovative technologies will be tested and verified in a series of ground-based Research Program (2014Z09106). pre-flight experiments. Author Contributions: Fengtian Han contributed to the design of the differential space accelerometer; Tianyi Liu developed sensing and control Linlinthe Li developed the single sensor programs: unit; Acknowledgments: The the authors would like toelectronics; acknowledge support offered bycylindrical the following Qiuping Wu contributed to the concept design of the NEP experiment; Fengtian Han contributed in writing National Natural Science Foundation of China (61374207, 91436107) and Tsinghua University Initiative Scientific this paper. Research Program (2014Z09106). Conflicts of Interest:Fengtian The authors no conflict of interest. Author Contributions: Handeclare contributed to the design of the differential space accelerometer; Tianyi Liu developed the sensing and control electronics; Linlin Li developed the single cylindrical sensor unit; Qiuping Wu contributed to the concept design of the NEP experiment; Fengtian Han contributed in writing this paper.

Conflicts of Interest: The authors declare no conflict of interest.

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