Technologies Of Low Frequency Primary Vibration Calibration Based On Two-ends Excitation And Rectangular Closed Double Magnetic Circuit

Low frequency primary vibration calibration in a range of 0.1 Hz ~ 20 Hz is an important component of vibration metrology.Steady-state sinusoidal vibration is used to excite the low-frequency vibration transducers,the laser interferometic vibrometer is used to measure the low frequency vibration,and thus the sensitivities of the transducers in the range of 0.1 Hz~20 Hz are obtained.Thus,the vibration measurement result is traced to laser wavelength standard.The low-frequency vibration transducers represented by quartz flexible accelerometers and seismometers are widely used in the fields of aviation and aerospace equipment vibration monitoring,precision micro-vibration isolation,earthquake prediction and warning.The precisely calibration of the sensitivity of these transducers is of great significance to keep spacecraft attitude steady,ensure the imaging accuracy of the space camera,reduce the natural frequency of the vibration isolator,and warn earthquake intensity rapidly and early.Current techniques on low frequency primary vibration calibration have the following major problems: 1)When the frequency is reduced to approximately 0.1 Hz,the displacement amplitude of standard vibration signal is required to be more than one meter.However,in the prior art,as the stroke of the electromagnetic vibration exciter increases,the problem of uneven distribution of the magnetic field in the air gap becomes serious.As a result,harmonic distortion of steady-state sinusoidal vibration becomes more and more serious,which leads to serious harmonic distortion of vibration displacement and acceleration response signals.It is a key factor affecting the calibration results.2)When the frequency increases to close to 20 Hz,the displacement amplitude of the standard vibration signal falls to the micron level.For homodyne quadrature laser interferometric vibrometer,the beam splitting characteristics of the splitters are not ideal,resulting in a large quadrature error sensitivity to the optical axis angle error of the wave plates.The introduced nonlinear error is serious,which affects the measurement accuracy of vibration displacement and is another key factor affecting the calibration results.The purpose of this paper is to solve the above problems,explore a steady-state sinusoidal vibration generation method with ultra-large displacement amplitude and low acceleration waveform distortion,and a laser interferometic vibrometer with high precision,aim to make breakthroughs in key technical indices such as displacement amplitude,acceleration waveform distortion,nonlinear error,and measurement uncertainty,and achieve the goal of improving calibration accuracy.The following are the major issues addressed by this study:Firstly,for existing steady-state sinusoidal vibration generation methods,the non-uniformity of the magnetic field distribution in the air gap becomes more and more serious as the length of the air gap increases,which leads to serious harmonic distortion of steady-state sinusoidal vibration with ultra-large displacement amplitude.A steady-state sinusoidal vibration generation method based on two-ends excitation and rectangular closed double magnetic circuit is proposed.The main factors causing the harmonic distortion of steady-state sinusoidal and low-frequency vibration are analyzed: the non-uniformity of the magnetic field distribution in the air gap and the stiffness nonlinearity of elastic supportion structure.Rectangular and high-performance NdFeB permanent magnets and rectangular yokes are used to construct a closed double magnetic circuit with magnets at both ends of the center yoke.Vacuum annealing and grinding are used to make the rectangular yokes have high magnetic permeability and high machining accuracy,thus a uniform magnetic field distribution is obtained in the long air gap.A lumped parameter magnetic equivalent circuit model is established and iterative method is used to solve the magnetic field distribution in the air gap.An active positive stiffness elastic supportion structure based on displacement feedback is constructed,and a linear stiffness characteristic is realized in a range of large stroke.The method achieves ultra-large amplitude steady-state sinusoidal low frequency vibration while reducing the distortion of acceleration waveform.Secondly,for existing homodyne quadrature laser interferometric vibrometers,the angular error of wave plate optical axis introduces serious nonlinear errors,which affects the measurement accuracy of vibration displacement and the calibration accuracy.A homodyne quadrature laser interferometric vibrometer based on non-polarization beam splitting and wave plate yawing is proposed.The beam splitting characteristics of the splitters are experimentally tested and analyzed.Based on these,the quadrature phase error sensitivites of the wave plate in the existing homodyne quadrature laser interferometric vibrometers are theoretically analyzed.The reference and measurement beams are produced by non-polarization beam splitting,which suppresses the polarization aliasing.The influence of the wave plate yaw angle on the phase delay is theoretically analyzed.The phase shift errors of the non-polarization beam splitters are compensated by performing wave plate yawing in the measurement and reference arms.The method can make the quadrature phase error and the sensitivites of quadrature phase error to the optical axis rotation of the wave plates both zero,effectively suppresses nonlinear errors introduced by the angular error of wave plate optical axis which are caused by mechanical drift,adjusting errors,etc.,and thus increases the displacement measurement accuracy,and solve the problem that the nanometer level nonlinear error seriously affects calibration accuracy in the case of small amplitude vibration.Thirdly,in order to recover the vibration displacement through successive fringe phase unwrapping algorithm,it is necessary to oversample the high-frequency carrier signals modulated by homodyne quadrature laser interferometric vibrometer.However,it can result in a problem of large data amount and long data-processing time.A phase unwrapping algorithm based on motion parameter estimation is proposed.The principle of successive fringe phase unwrapping algorithm is analyzed in depth,and the feasibility of recovering vibration displacement based on undersampling is verified in theory.A mathematical model of phase unwrapping algorithm based on motion parameter estimation is established.The phase unwrapping is realized by estimating the displacement of the current sampling time according to the preamble motion parameters and correcting the estimating value according to current phase.On this basis,the processes of phase unwrapping algorithms based on velocity estimation and composite estimation by velocity and acceleration are elaborated.The algorithm is independent of the modulated high-frequency carrier signal,and can directly recover vibration displacement,markedly reducing the data sampling rate,and thus reducing the amount of data and data processing time.Finally,a low frequency primary vibration calibration prototype is successfully developed,experiments on key technical indices are conducted and analyzed,and uncertainty of meausrement results is evaluated.Experimental results show that nonlinear error of homodyne quadrature laser interferometer is 0.1 nm;the non-uniformity of magnetic field distribution is less than 0.12% in 1.4m long air gap;the distortion of displacement waveform of 1.2m full stroke vibration is 0.05%;the distortion of acceleration waveform is better than 1.2% in the frequency range of 0.1Hz to 20 Hz,and the relative expanded uncertainties of amplitude measurement of transducer sensitivity are 0.12% and 0.04%(k=2)at the reference frequencies of 0.1 Hz and 20 Hz.