The fused quartz hemispherical resonator is the core component of the hemispherical resonator gyroscope.It features a complex shape and is Made from a Material that is difficult to process.Scratches are easily introdu...The fused quartz hemispherical resonator is the core component of the hemispherical resonator gyroscope.It features a complex shape and is Made from a Material that is difficult to process.Scratches are easily introduced during grinding,potentially degrading the mass-stiffness-damping symmetry;however,the underlying mechanisms of this influence have not been fully understood.This paper aims to investigate the effects of scratch defects on the frequency splitting and quality factor of the hemispherical resonator.First,finite element models of the hemispherical resonator with scratches are established.Then,the effects of the mass-stiffness factor,as well as the latitude and length of the scratches,on frequency splitting are analyzed.Furthermore,the impacts of latitude,length,and the first four harmonics of the unbalanced mass caused by scratches on thermoelastic damping and anchor loss are examined.Simulation results indicate that scratches above 55°latitude cause frequency splitting solely due to stiffness changes.Frequency splitting caused by scratches of the same size on the inherent rigidity shaft at the rim is approximately 50%of that near the transition fillet.Frequency splitting varies linearly with the volume of material removed by scratches.Scratches have little effect on thermoelastic damping.The first three harmonics of the unbalanced mass due to scratches at the rim are the primary contributors to anchor loss.Finally,focused ion beam trimming experiments are conducted at different locations on the hemispherical resonator.The trends observed in the experimental results are consistent with the simulation results.This work provides guidance for evaluating the impact of scratches on the performance of hemispherical resonators and for developing appropriate trimming processes.展开更多
The mass non-uniformity of hemispherical resonator is one of reasons for frequency split,and frequency split can cause gyroscope to drift.Therefore,it is of great significance to analyze the relationship between mass ...The mass non-uniformity of hemispherical resonator is one of reasons for frequency split,and frequency split can cause gyroscope to drift.Therefore,it is of great significance to analyze the relationship between mass non-uniformity and frequency split,which can provide a theoretical basis for mass balance of imperfect resonator.The starting point of error mechanism analysis for gyroscope is the motion equations of resonator.Firstly,based on the Kirchhoff-Love hypothesis in the elastic thin shell theory,the geometric deformation equations of resonator are deduced.Secondly,the deformation energy equation of resonator is derived according to the vibration mode and relationship between the stress and strain of hemispherical thin shell.Thirdly,the kinetic energy equation of resonator is deduced by the Coriolis theorem.Finally,the motion equations of resonator are established by the Lagrange mechanics principle.The theoretical values of precession factor and natural frequency are calculated by the motion equations,which are substantially consistent with the ones by the finite element method and practical measurement,the errors are within a reasonable range.Simultaneously,the varying trend of natural frequency with respect to the geometrical and physical parameters of resonator by the motion equations is consistent with that by the finite element analysis.The above conclusions prove the correctness and rationality of motion equations.Similarly,the motion equations of resonator with mass non-uniformity are established by the same modeling method in case of ignoring the input angular rate and damping,and the state equations with respect to the velocity and displacement of vibration system are derived,then twonatural frequencies are solved by the characteristic equation.It is concluded that one of reasons for frequency split is the 4 th harmonic of mass non-uniformity,and thus much attention should be paid to minimizing the 4 th harmonic of mass non-uniformity in the course of mass balancing for imperfect resonator.展开更多
The mechanical balance process is the key process to eliminate the quadrature error and improve the performance of the cupped wave gyro. The conventional mechanical balance method for cupped wave gyro based on cup-wal...The mechanical balance process is the key process to eliminate the quadrature error and improve the performance of the cupped wave gyro. The conventional mechanical balance method for cupped wave gyro based on cup-wall trimming requires high control accuracy of trimming quantity, which increases the production cost and decreases the fabrication efficiency in large extent. However, it is hard to reach the high balance accuracy with the natural frequency split of mHz grade by using the conventional method. In this paper, the lumped mass dynamic model of the cupped wave gyro is built by discretization method, and the effects of different position trimming on the natural frequency are analyzed. It is pointed out that trimming off a tiny quantity of material from cup-wall causes large variation of the natural frequency is the main reason for the low accuracy of the conventional mechanical balance method. Then, a precision balance method for cupped wave gyro based on cup-bottom trimming is presented and the entire procedures of this method are given. The static balance process and dynamic balance process of the precision balance method are simulated by the finite element software. The simulation result shows that the precision balance method based on cup-bottom trimming brings less additional natural frequency split in the static balance process, minimizes the natural frequency split to mHz grade and rectify the angle of mode offset to 0.1° grade in the dynamic balance process, furthermore, the method decreases the requirement for control accuracy of trimming quantity evidently. The research work provides references for structure optimization design and balance process plan of the cupped wave gyro.展开更多
This paper demonstrates the intensity modulation characters of orthogonally polarized HeNe lasers with different optical feedback level generated by the variable reflectivity of external reflector. The modulation dept...This paper demonstrates the intensity modulation characters of orthogonally polarized HeNe lasers with different optical feedback level generated by the variable reflectivity of external reflector. The modulation depths of the orthogonally polarized frequencies are increased when the optical feedback level becomes strong. It also observes that the modulation amplitudes are different for different external cavity length. Based on the vectorial extension of Lamb＇s semi-classical theory, it finds that the calculations are consistent with the experimental results.展开更多
In this paper,we discuss the coefficients of Gravitational waveform due to eccentric binaries periastron advance with evolved eccentricity.For the basic harmonic modes(n ≤ 5),the frequency split and corresponding rel...In this paper,we discuss the coefficients of Gravitational waveform due to eccentric binaries periastron advance with evolved eccentricity.For the basic harmonic modes(n ≤ 5),the frequency split and corresponding relative strengths in the spectrum are figured out.Taking the well known binary systems PSRB 1913+16 and PSRB 1534+12 as examples,we study the dominant harmonic and its frequency split caused by periastron advance in the spectra,and give an estimation of detectability for PSRB 1913+16 and PSRB 1534+12,which are the promising targets for space observatories of gravitational wave.展开更多
Butterworth band-pass filter has been applied to S-wave data recorded at 8 stations in China mainland, and S-wave splitting at different frequency bands is analyzed. The results show that the delay time and the fast p...Butterworth band-pass filter has been applied to S-wave data recorded at 8 stations in China mainland, and S-wave splitting at different frequency bands is analyzed. The results show that the delay time and the fast polarization directions of S-wave splitting depend upon the frequency bands. There is an absence of S-wave splitting at the station of Urumqi (WMQ) for the band of 0.1-0.2 Hz. With the frequency band broadening, the delay time of S-wave splitting decreases at the stations of Beijing (BJI), Enshi (ENH), Kunming (KMI) and Mudanjiang (MDJ); the fast polarization direction changes from westward to eastward at Enshi (ENH), and from eastward to westward at Hailaer (HIA). The variations of delay time with bands at Lanzhou (LZH) and Qiongzhong (QIZ) are similar, and there is a coherent trend of fast polarization directions at BJI, KMI and MDJ, respectively. Initial interpretations to the results of frequency band-dependence of S-wave splitting are also presented.展开更多
This paper analyzes the dynamic behavior of a two-degree-of-freedom system subjected to electromagnetic interaction modelled through a skew-symmetric coupling matrix.The system comprises two mechanically independent o...This paper analyzes the dynamic behavior of a two-degree-of-freedom system subjected to electromagnetic interaction modelled through a skew-symmetric coupling matrix.The system comprises two mechanically independent oscillators coupled by velocity-dependent electromagnetic forces.The equations of motion are formulated and analyzed in the modal domain,highlighting the effects of the antisymmetric interaction on natural frequencies and mode shapes.The classical orthogonality is broken,resulting in complex eigenvectors;nevertheless,the system remains conservative,as the interaction forces perform no work.The analysis is carried out using both configuration-space and state-space formulations,revealing modal frequency splitting and phase shifts induced by the skew-symmetric term.These modal features are further examined through time-domain simulations and frequency response functions.The main contribution of this study is the development and analysis of a deliberately simple yet general model that isolates the essential dynamic effects of skew-symmetric electromagnetic coupling.This minimal formulation,often hidden in more complex systems,reveals key phenomena such as modal frequency splitting,non-normal modes,and energy-conserving cross-effects.The model serves not only as a conceptual reference but also as a methodological framework applicable to a broad class of coupled electromechanical systems.展开更多
Optical-phase-retardation elements are widely used in many fields.Accurate measurement of their phase retardation is crucial to the practical effect of the element's processing and application.The development and ...Optical-phase-retardation elements are widely used in many fields.Accurate measurement of their phase retardation is crucial to the practical effect of the element's processing and application.The development and present situation of the methods for optical phase retardation measurement are reviewed,with the wave plate,the most typical phase-retardation element,as an example.The latest research progress in this field is introduced;the principles and characteristics of individual measurement method are summarized and discussed.Three new methods based on laser frequency splitting or laser feedback are presented in detail,in which the laser is not only regarded as a light source but also plays a role of sensor.Moreover,no standard wave plates are needed and arbitrary phase retardation can be measured.Traceability,high precision and high repeatability are achieved as well.展开更多
The magnetically coupled resonant wireless power transfer(MCR-WPT)system for implantable medical devices has gradually become one of the research hotspots.The transmission characteristics of the system in weak-couplin...The magnetically coupled resonant wireless power transfer(MCR-WPT)system for implantable medical devices has gradually become one of the research hotspots.The transmission characteristics of the system in weak-coupling regions are of research significance.The mathematical model of the system's transmission characteristics is established by equivalent circuit theory.Several key factors that affect the transmission characteristics of the system are obtained,to include the self-inductance of the coil,the mutual inductance between the coils,and the load resistance.A magnetically coupled resonant wireless power transfer system is designed.A method of coil design is proposed.The transmission efficiency of the system in the weak-coupling region is improved by optimizing the design of the coil.Simulation and experimental results exhibited good consistency.The results show that the transmission performance of the system in the weak-coupling area is improved.This work provides guidance and practical significance for the research of the MCR-WPT system with implantable medical equipment.展开更多
Accuracy improvement of MEMS gyros requires not only microelectronic development but also the investigations of th mathematical model of sensitive element dynamics. In the present paper, we study the errors of the vib...Accuracy improvement of MEMS gyros requires not only microelectronic development but also the investigations of th mathematical model of sensitive element dynamics. In the present paper, we study the errors of the vibrating microgyroscop which arise because of nonlinear dynamics of a sensitive element. A MEMS tuning fork gyroscope with elastic rods is consid ered. Nonlinear differential equations of bending vibrations of sensitive element on the moving basis are derived. Free nonlin ear vibrations of gyroscopes as the flexible rod are studied. Nonlinear dynamics of gyroscope on the moving basis are investi gated by asymptotic two scales method. Sensitive element frequencies split on two frequencies resulted from slowly changin angular velocity are taken into account in the equations of zero approximation. The differential equations for slowly changin amplitudes and phases of two normal waves of the oscillations measured by capacitor gauges and an electronic contour of th device are obtained from the equations of the first approximation.展开更多
基金Supported by National Key Research and Development Program of China(Grant No.2022YFB3403600)the National Natural Science Foundation of China(Grant No.52305461)。
文摘The fused quartz hemispherical resonator is the core component of the hemispherical resonator gyroscope.It features a complex shape and is Made from a Material that is difficult to process.Scratches are easily introduced during grinding,potentially degrading the mass-stiffness-damping symmetry;however,the underlying mechanisms of this influence have not been fully understood.This paper aims to investigate the effects of scratch defects on the frequency splitting and quality factor of the hemispherical resonator.First,finite element models of the hemispherical resonator with scratches are established.Then,the effects of the mass-stiffness factor,as well as the latitude and length of the scratches,on frequency splitting are analyzed.Furthermore,the impacts of latitude,length,and the first four harmonics of the unbalanced mass caused by scratches on thermoelastic damping and anchor loss are examined.Simulation results indicate that scratches above 55°latitude cause frequency splitting solely due to stiffness changes.Frequency splitting caused by scratches of the same size on the inherent rigidity shaft at the rim is approximately 50%of that near the transition fillet.Frequency splitting varies linearly with the volume of material removed by scratches.Scratches have little effect on thermoelastic damping.The first three harmonics of the unbalanced mass due to scratches at the rim are the primary contributors to anchor loss.Finally,focused ion beam trimming experiments are conducted at different locations on the hemispherical resonator.The trends observed in the experimental results are consistent with the simulation results.This work provides guidance for evaluating the impact of scratches on the performance of hemispherical resonators and for developing appropriate trimming processes.
基金the Pre-Research Fund during the“13th Five-Year Plan” (No. 41417060101)。
文摘The mass non-uniformity of hemispherical resonator is one of reasons for frequency split,and frequency split can cause gyroscope to drift.Therefore,it is of great significance to analyze the relationship between mass non-uniformity and frequency split,which can provide a theoretical basis for mass balance of imperfect resonator.The starting point of error mechanism analysis for gyroscope is the motion equations of resonator.Firstly,based on the Kirchhoff-Love hypothesis in the elastic thin shell theory,the geometric deformation equations of resonator are deduced.Secondly,the deformation energy equation of resonator is derived according to the vibration mode and relationship between the stress and strain of hemispherical thin shell.Thirdly,the kinetic energy equation of resonator is deduced by the Coriolis theorem.Finally,the motion equations of resonator are established by the Lagrange mechanics principle.The theoretical values of precession factor and natural frequency are calculated by the motion equations,which are substantially consistent with the ones by the finite element method and practical measurement,the errors are within a reasonable range.Simultaneously,the varying trend of natural frequency with respect to the geometrical and physical parameters of resonator by the motion equations is consistent with that by the finite element analysis.The above conclusions prove the correctness and rationality of motion equations.Similarly,the motion equations of resonator with mass non-uniformity are established by the same modeling method in case of ignoring the input angular rate and damping,and the state equations with respect to the velocity and displacement of vibration system are derived,then twonatural frequencies are solved by the characteristic equation.It is concluded that one of reasons for frequency split is the 4 th harmonic of mass non-uniformity,and thus much attention should be paid to minimizing the 4 th harmonic of mass non-uniformity in the course of mass balancing for imperfect resonator.
基金supported by National Natural Science Foundation of China (Grant No. 51005239)
文摘The mechanical balance process is the key process to eliminate the quadrature error and improve the performance of the cupped wave gyro. The conventional mechanical balance method for cupped wave gyro based on cup-wall trimming requires high control accuracy of trimming quantity, which increases the production cost and decreases the fabrication efficiency in large extent. However, it is hard to reach the high balance accuracy with the natural frequency split of mHz grade by using the conventional method. In this paper, the lumped mass dynamic model of the cupped wave gyro is built by discretization method, and the effects of different position trimming on the natural frequency are analyzed. It is pointed out that trimming off a tiny quantity of material from cup-wall causes large variation of the natural frequency is the main reason for the low accuracy of the conventional mechanical balance method. Then, a precision balance method for cupped wave gyro based on cup-bottom trimming is presented and the entire procedures of this method are given. The static balance process and dynamic balance process of the precision balance method are simulated by the finite element software. The simulation result shows that the precision balance method based on cup-bottom trimming brings less additional natural frequency split in the static balance process, minimizes the natural frequency split to mHz grade and rectify the angle of mode offset to 0.1° grade in the dynamic balance process, furthermore, the method decreases the requirement for control accuracy of trimming quantity evidently. The research work provides references for structure optimization design and balance process plan of the cupped wave gyro.
基金Project supported by the State Key Program of National Natural Science of China (Grant No 60438010)
文摘This paper demonstrates the intensity modulation characters of orthogonally polarized HeNe lasers with different optical feedback level generated by the variable reflectivity of external reflector. The modulation depths of the orthogonally polarized frequencies are increased when the optical feedback level becomes strong. It also observes that the modulation amplitudes are different for different external cavity length. Based on the vectorial extension of Lamb＇s semi-classical theory, it finds that the calculations are consistent with the experimental results.
基金Supported by the Fundamental Research Funds for the Central Universities under Grant No. CDJZR11300005
文摘In this paper,we discuss the coefficients of Gravitational waveform due to eccentric binaries periastron advance with evolved eccentricity.For the basic harmonic modes(n ≤ 5),the frequency split and corresponding relative strengths in the spectrum are figured out.Taking the well known binary systems PSRB 1913+16 and PSRB 1534+12 as examples,we study the dominant harmonic and its frequency split caused by periastron advance in the spectra,and give an estimation of detectability for PSRB 1913+16 and PSRB 1534+12,which are the promising targets for space observatories of gravitational wave.
基金the National Natural Science Foundation of China (NSFC) (Grant No. 49774225), and the Outstanding Youth Scientist Project from NSFC (Grant No. 49825108).
文摘Butterworth band-pass filter has been applied to S-wave data recorded at 8 stations in China mainland, and S-wave splitting at different frequency bands is analyzed. The results show that the delay time and the fast polarization directions of S-wave splitting depend upon the frequency bands. There is an absence of S-wave splitting at the station of Urumqi (WMQ) for the band of 0.1-0.2 Hz. With the frequency band broadening, the delay time of S-wave splitting decreases at the stations of Beijing (BJI), Enshi (ENH), Kunming (KMI) and Mudanjiang (MDJ); the fast polarization direction changes from westward to eastward at Enshi (ENH), and from eastward to westward at Hailaer (HIA). The variations of delay time with bands at Lanzhou (LZH) and Qiongzhong (QIZ) are similar, and there is a coherent trend of fast polarization directions at BJI, KMI and MDJ, respectively. Initial interpretations to the results of frequency band-dependence of S-wave splitting are also presented.
基金supported by the Department of Education of the Basque Government for the Research Group program IT1507–22.
文摘This paper analyzes the dynamic behavior of a two-degree-of-freedom system subjected to electromagnetic interaction modelled through a skew-symmetric coupling matrix.The system comprises two mechanically independent oscillators coupled by velocity-dependent electromagnetic forces.The equations of motion are formulated and analyzed in the modal domain,highlighting the effects of the antisymmetric interaction on natural frequencies and mode shapes.The classical orthogonality is broken,resulting in complex eigenvectors;nevertheless,the system remains conservative,as the interaction forces perform no work.The analysis is carried out using both configuration-space and state-space formulations,revealing modal frequency splitting and phase shifts induced by the skew-symmetric term.These modal features are further examined through time-domain simulations and frequency response functions.The main contribution of this study is the development and analysis of a deliberately simple yet general model that isolates the essential dynamic effects of skew-symmetric electromagnetic coupling.This minimal formulation,often hidden in more complex systems,reveals key phenomena such as modal frequency splitting,non-normal modes,and energy-conserving cross-effects.The model serves not only as a conceptual reference but also as a methodological framework applicable to a broad class of coupled electromechanical systems.
基金supported by the Key Program of National Natural Science Foundation of China(Grant No.61036016)
文摘Optical-phase-retardation elements are widely used in many fields.Accurate measurement of their phase retardation is crucial to the practical effect of the element's processing and application.The development and present situation of the methods for optical phase retardation measurement are reviewed,with the wave plate,the most typical phase-retardation element,as an example.The latest research progress in this field is introduced;the principles and characteristics of individual measurement method are summarized and discussed.Three new methods based on laser frequency splitting or laser feedback are presented in detail,in which the laser is not only regarded as a light source but also plays a role of sensor.Moreover,no standard wave plates are needed and arbitrary phase retardation can be measured.Traceability,high precision and high repeatability are achieved as well.
基金Supported by National Natural Science Foundation of China(51307120,51477117).
文摘The magnetically coupled resonant wireless power transfer(MCR-WPT)system for implantable medical devices has gradually become one of the research hotspots.The transmission characteristics of the system in weak-coupling regions are of research significance.The mathematical model of the system's transmission characteristics is established by equivalent circuit theory.Several key factors that affect the transmission characteristics of the system are obtained,to include the self-inductance of the coil,the mutual inductance between the coils,and the load resistance.A magnetically coupled resonant wireless power transfer system is designed.A method of coil design is proposed.The transmission efficiency of the system in the weak-coupling region is improved by optimizing the design of the coil.Simulation and experimental results exhibited good consistency.The results show that the transmission performance of the system in the weak-coupling area is improved.This work provides guidance and practical significance for the research of the MCR-WPT system with implantable medical equipment.
基金supported by the Russian Foundation for Basic Research (Grant Nos. 09-01-00756-a, 09-08-01184-a)
文摘Accuracy improvement of MEMS gyros requires not only microelectronic development but also the investigations of th mathematical model of sensitive element dynamics. In the present paper, we study the errors of the vibrating microgyroscop which arise because of nonlinear dynamics of a sensitive element. A MEMS tuning fork gyroscope with elastic rods is consid ered. Nonlinear differential equations of bending vibrations of sensitive element on the moving basis are derived. Free nonlin ear vibrations of gyroscopes as the flexible rod are studied. Nonlinear dynamics of gyroscope on the moving basis are investi gated by asymptotic two scales method. Sensitive element frequencies split on two frequencies resulted from slowly changin angular velocity are taken into account in the equations of zero approximation. The differential equations for slowly changin amplitudes and phases of two normal waves of the oscillations measured by capacitor gauges and an electronic contour of th device are obtained from the equations of the first approximation.
