Error Analysis And Experimental Research On Frequency Measurement Based On Five-wire Pendulum

Space Gravitational Wave Detection belongs to the frontier scientific research.Its basic principle is to infer the existence of gravitational waves by measuring the distance between two free-floating test masses in space with a laser interferometer.As the key component of the space inertial sensor,the test mass provides the inertial reference for the Laser Interferometer.The“Taiji”requires residual acceleration noise in the sensitive axis of the inertial sensor test mass to be less than 3×10^-15ms^-2/Hz^1/2 in the 0.1m Hz to 1 Hz band.The space inertial sensor consists of test mass,electrode cage,front-end electronics system and auxiliary system.The test mass is a cuboid of au-pt alloy with a length of 46mm on one side.The electrode cage is the carrier of the electrode.In order to ensure that the test mass is at the center of the electrode cage,the front-end electronics reads the relation between the test quality and the relative position of the electrode cage by capacitive sensing,and carries on the electrostatic feedback control to the test mass.Because capacitive sensing detects the position of the center of the test mass’s shape relative to the center of the electrode cage,and the electrostatic feedback force acts on the mass center of the test mass,the misalignment of the mass center and the center of shape of test mass will cause the test mass to generate additional acceleration noise.Based on the principle of electrostatic drive,a mathematical model of the noise caused by the non-coincidence of the centroid of the test mass is established in this paper.The noise index is 3×10^-16ms^-2/Hz^1/2,then the offset of the center of mass relative to the center of shape should be controlled within3.75μm.At present,the methods of measuring mass center at home and abroad are mainly divided into static measurement and dynamic measurement,however,it is very complicated to get the mass center of the measured object by eliminating the position parameter of the mass center of the auxiliary structure.The mass center measurement method based on five-wire pendulum used in this paper belongs to dynamic measurement method,which places the measured object on the platform of pendulum which can produce single-degree-of-freedom rotation,the vibration natural frequency of the pendulum can indirectly reflect the moment of inertia of the measured object around the axis of rotation of the pendulum,which can be expressed as a function of the position parameter of the measured object’s mass center relative to its Parallel axis theorem.In this paper,through the dynamic analysis of a five-wire pendulum,the functional relationship between the offset of the mass center and the natural frequency of the pentagonal pendulum is given.According to this,the precision requirement of the natural frequency measurement is analyzed.If the measurement error of the mass center offset does not exceed 2.4μm,the precision of the natural frequency measurement of a five-wire pendulum needs to reach at least 2.9×10^-5Hz.Then,a device for measuring the natural frequency of a five-wire pendulum is designed.Firstly,an electromagnetic actuator based on electromagnetic solenoid and permanent magnet is designed by modeling and electromagnetic simulation to provide repetitive vibration excitation for five-wire pendulum.Then the principle of measuring torsional angular displacement of five-wire pendulum by using diffraction grating and four-quadrant detector is introduced.Finally,an experiment platform is built to measure the torsional vibration angular displacement of the five-wire pendulum,and the torsional vibration natural frequency of the five-wire pendulum is fitted by the recorded angular displacement data.The experimental results show that the measurement accuracy of the five-wire pendulum is 2.66×10^-5Hz under the torsional vibration with an initial amplitude of 3×10^-4Hz rad.It can meet the requirement of measuring mass center deviation by five-wire pendulum.