Design And Noise Analysis Of Electrostatic Space Gyroscope/Accelerometers

The Equivalence Principle is one of fundamental hypotheses of Einstein’sgeneral relativity. Though the equivalence principle (EP) has been tested on theground with different materials as far back as Galileo, null result for violation of theequivalence principle has been found by all this experiments. Recently, gravitionaleffects of rotating bodies might violated the EP was proposed. In order to achieve atargeted precision of10-15, satellite-based gyroscope/accelerometers are utilized to doa long-duration free-fall test. According to the requirement of the novel equivalenceprinciple test in space, this thesis presents preliminary results regarding design andprecision evaluation of the high-precision differential electrostaticgyroscope/accelerometers. The main contents of this research are as following:The sensing structure of the differential accelerometer is designed to meet theexperiment requirements in space. The mathematical model of the motion of theproof mass is developed, which describes the differential capacitances and associatedelectrostatic forces/torques. Modal analysis using ANSYS finite element softwareshowed the lowest modal of the inner/outer proof masses is2.03kHz and1.56kHzrespectively, much higher than the rated speed of167Hz. The electrostatic levitationcontrol system in five degrees of freedom has been designed. The closed-loopbandwidths are0.34Hz and0.64Hz for aixial and radial levitation loops while themeasurement range of the inner and outer accelerometers is2.07×10-7m/s2and1.32×10-7m/s2, respectively.A variable-capacitance based spin-up scheme is proposed to spin the proof masselectrostatically. The analytical model of electrostatic torque, residual air dampingand magnetic damping were derived. Stimulation results of the start-up responseindicates that the accelerometer will experience a time duration of9.8days to spin upthe speed from0to104rpm.A prototype gyroscope/accelerometer structure for the ground test is designedwith a capacitive gap of50μm and a outline dimension of Ф62mm×70mm. It wasfound that the axial and radial measurement range of the accelerometer is10-4g and 2g, the lowest modal freqency of the proof mass is4.50kHz, and the spin-up time is1.30hours from0to104rpm, respectively. The proof mass and surrounded electrodecylinders are fabricated using crystallitic glass. The process flow design is presentedto achieve expected machining accuracy. The preliminary measurements of themachining prototype are introduced together with some discussions.The noise model of the differential electrostatic accelerometer is presented byanalyzing the various interference sources. Various accelerometer noises in spaceenvironment are evaluated and allocated according to the requirement of the targetednoise level below2.0×10-12ms-2/Hz1/2. Analytical results showed that the noise of theinternal/external accelerometer is1.01×10-12ms-2/Hz1/2and9.50×10-13ms-2/Hz1/2respectively，which is able to meet the requirement of testing of the equivalenceprinciple in space.