The modal vibration of the rotor is the main cause of excessive vibration of the aeroengine overall structure.To attenuate the vibration of the rotor under different modal shapes from the perspective of energy control...The modal vibration of the rotor is the main cause of excessive vibration of the aeroengine overall structure.To attenuate the vibration of the rotor under different modal shapes from the perspective of energy control,the intrinsic physical relationships between rotor modal shapes and instantaneous vibrational energy flow transmission characteristics is derived from the general equation of motion base on the structural intensity method.A dual-rotor-support-casing coupling model subjected to the rotor unbalanced forces is established by the finite element method in this paper.The transmission,conversion and balance relationships of the vibrational energy flow for the rotors in the first-order bending modal shape,the conical whirling modal shape and the translational modal shape are analyzed,respectively.The results show that the vibrational energy flow transmitted to the structure can be converted into the strain energy,the kinetic energy and the energy dissipated by the damping of the structure.The vibrational energy flow transmission characteristics of rotors with different modal shapes are quite different.Especially for the first-order bending modal shape,the vibrational energy flow and the strain energy are transmitted and converted to each other in the middle part of the rotor shaft,resulting in large deformation at this part.To attenuate this harmful vibration,the influences of grooving on the shaft on the first-order bending vibration are studied from the perspective of transmission control of vibrational energy flow.This study can provide theoretical references and guidance for the vibration attenuation of the rotors in different modal shapes from a more essential perspective.展开更多
The characteristics of vibrational power flow in an infinite elastic cylindrical shell filled with fluid are investigated. The simple harmonic motion of the shell and the pressure field in the contained fluid are desc...The characteristics of vibrational power flow in an infinite elastic cylindrical shell filled with fluid are investigated. The simple harmonic motion of the shell and the pressure field in the contained fluid are described by the Fltigge shell equations and Helmholtz equation respectively. The vibrational equation of this system is obtained by using the coupling of shell and fluid. The dispersion curves are discussed for different circumferential orders. By using Fourier transform and its inverse transform, the input power into this coupled system excited by a simple harmonic linearly distributed driving force is studied. Along the shell, the transmission of the power flow carried by different shell internal forces and by the contained fluid are discussed展开更多
The paper proposes an analytical approach to investigate the synchronization of the two coupled exciters in a vibrating system of spatial motion. Introducing the distur- bance parameters for average angular velocity o...The paper proposes an analytical approach to investigate the synchronization of the two coupled exciters in a vibrating system of spatial motion. Introducing the distur- bance parameters for average angular velocity of two excit- ers, we deduce the non-dimensional coupling equations of angular velocities of two exciters, in which the inertia cou- pling matrix is symmetric and the stiffness coupling matrix is antisymmetric in a non-resonant vibrating system. The analysis of the coupling dynamic characteristic shows that the coupled cosine effect of the phase angles will cause the torque acting on two motors to limit the increase of phase difference between two exciters as well as sustain its sym- metry of two exciters during the running process. It physi- cally explains the peculiarity of self-synchronization of two exciters. The cosine effect of phase angles of the vibrations excited by each exciter will decrease its moment of inertia. The residual moment of inertia of each exciter represents its relative moment of inertia. The stability condition of synchro- nization of two exciters is that the relative non-dimensional moments of inertia of two exciters are all greater than zero and four times their product is greater than the square of their coefficient of coupled cosine effect of phase angles, which is equivalent to that the inertia coupling matrix is positive definite and all its elements are positive. The numeric results show that the structure of the vibrating system can ensure the stability condition of synchronous operation.展开更多
In this paper, the synchronization problem of three homodromy coupled exciters in a non-resonant vibrating system of plane motion is studied. By introducing the average method of modified small parameters, we deduced ...In this paper, the synchronization problem of three homodromy coupled exciters in a non-resonant vibrating system of plane motion is studied. By introducing the average method of modified small parameters, we deduced dimensionless coupling equation of three exciters, which converted the problem of synchronization into that of the existence and stability of zero solutions for the average differential equations of the small parameters. Based on the dimensionless coupling torques and characteristics of the cor- responding limited functions, the synchronization criterion for three exciters was derived as the absolute value of dimensionless residual torque difference between arbitrary two motors being less than the maximum of their dimensionless coupling torques. The stability criterion of its synchronous state lies in the double-condition that the inertia coupling matrix is positive definite and all its elements are positive as well. The synchronization determinants are the coefficients of synchronization ability, also called as the general dynamical symmetry coefficients. The double-equilibrium state of the vibrating system is manifested by numeric method, and the numeric and simulation results derived thereof indicate the indispensable and crucial role the structural parameters of the vibrating system play in the stability criterion of synchronous operation. Besides, by adjusting its structural parameters, the elliptical motion of the vibrating system successfully met the requirements in engineering applications.展开更多
Ce^（3＋） substituted Cu-spinel nanoferrites CuCe_xFe_（2-x）O_4（x=0.00, 0.02, 0.04, 0.06, 0.08 and 0.10） were synthesized via sol-gel self-combustion hybrid route. Single phase spinel ferrite of Cu nanoferrites we...Ce^（3＋） substituted Cu-spinel nanoferrites CuCe_xFe_（2-x）O_4（x=0.00, 0.02, 0.04, 0.06, 0.08 and 0.10） were synthesized via sol-gel self-combustion hybrid route. Single phase spinel ferrite of Cu nanoferrites were examined using X-ray diffraction（XRD） analysis whereas the multiphase structure was observed as Ce contents increased from x=0.06. Field emission scanning electron microscopy（FESEM）, Thermogravimetric and differential thermal analysis（TGA and DTA） and Fourier transform infrared spectroscopy（FTIR） were used to find out the morphology phase and metal stretching vibrations of Ce^（3＋） substituted nanocrystalline ferrites. The crystallite size was increased and found in the range of 25-91 nm. The agglomerations in Cu ferrite samples increase as the Ce^（3＋） concentration increases. The magnetic properties such as remanence, saturation magnetization, coercivity, Bohr magneton and magnetocrystalline anisotropy constant（K） were determined using M-H loops recorded from a vibrating sample magnetometer（VSM）. Saturation magnetization, remanence and coercivity are increased as the Ce^（3＋）contents increase in Cu nanocrystalline samples. Moreover, law of approach to saturation（LoA） was used to calculate the maximum value of saturation for Ce-doped Cu nanoferrites. The soft magnetic behaviour of the Cu nanoferrite is observed as compared to the samples substituted with the increased Ce contents in Cu nanocrystalline ferrite. Bohr magneton and magnetocrystalline anisotropy are found to increase with the substitution of rare earth Ce^（3＋） contents in Cu spinel nanocrystalline ferrite. Cedoped Cu nanocrystalline ferrites with excellent properties may be suitable for potential applications in sensing, security, switching, core, multilayer chip inductor, biomedical and microwave absorption applications.展开更多
基金supported by the National Key Technology Research and Development Program of China(No.2016YFB0901402)the Major Program of National Natural Science Foundation of China(No.51790513)。
文摘The modal vibration of the rotor is the main cause of excessive vibration of the aeroengine overall structure.To attenuate the vibration of the rotor under different modal shapes from the perspective of energy control,the intrinsic physical relationships between rotor modal shapes and instantaneous vibrational energy flow transmission characteristics is derived from the general equation of motion base on the structural intensity method.A dual-rotor-support-casing coupling model subjected to the rotor unbalanced forces is established by the finite element method in this paper.The transmission,conversion and balance relationships of the vibrational energy flow for the rotors in the first-order bending modal shape,the conical whirling modal shape and the translational modal shape are analyzed,respectively.The results show that the vibrational energy flow transmitted to the structure can be converted into the strain energy,the kinetic energy and the energy dissipated by the damping of the structure.The vibrational energy flow transmission characteristics of rotors with different modal shapes are quite different.Especially for the first-order bending modal shape,the vibrational energy flow and the strain energy are transmitted and converted to each other in the middle part of the rotor shaft,resulting in large deformation at this part.To attenuate this harmful vibration,the influences of grooving on the shaft on the first-order bending vibration are studied from the perspective of transmission control of vibrational energy flow.This study can provide theoretical references and guidance for the vibration attenuation of the rotors in different modal shapes from a more essential perspective.
文摘The characteristics of vibrational power flow in an infinite elastic cylindrical shell filled with fluid are investigated. The simple harmonic motion of the shell and the pressure field in the contained fluid are described by the Fltigge shell equations and Helmholtz equation respectively. The vibrational equation of this system is obtained by using the coupling of shell and fluid. The dispersion curves are discussed for different circumferential orders. By using Fourier transform and its inverse transform, the input power into this coupled system excited by a simple harmonic linearly distributed driving force is studied. Along the shell, the transmission of the power flow carried by different shell internal forces and by the contained fluid are discussed
基金supported by Liaoning Province College Science and Research(2008S095)the Key Project of the National Natural Science Foundation of China(50535010,50805020)High-tech Research and Development Program of China(2007AA04Z442)
文摘The paper proposes an analytical approach to investigate the synchronization of the two coupled exciters in a vibrating system of spatial motion. Introducing the distur- bance parameters for average angular velocity of two excit- ers, we deduce the non-dimensional coupling equations of angular velocities of two exciters, in which the inertia cou- pling matrix is symmetric and the stiffness coupling matrix is antisymmetric in a non-resonant vibrating system. The analysis of the coupling dynamic characteristic shows that the coupled cosine effect of the phase angles will cause the torque acting on two motors to limit the increase of phase difference between two exciters as well as sustain its sym- metry of two exciters during the running process. It physi- cally explains the peculiarity of self-synchronization of two exciters. The cosine effect of phase angles of the vibrations excited by each exciter will decrease its moment of inertia. The residual moment of inertia of each exciter represents its relative moment of inertia. The stability condition of synchro- nization of two exciters is that the relative non-dimensional moments of inertia of two exciters are all greater than zero and four times their product is greater than the square of their coefficient of coupled cosine effect of phase angles, which is equivalent to that the inertia coupling matrix is positive definite and all its elements are positive. The numeric results show that the structure of the vibrating system can ensure the stability condition of synchronous operation.
基金supported by the National Key Technology R&D Program (2009BAG12A01-F01-3)the National Natural Science Foundation of China (51075063)
文摘In this paper, the synchronization problem of three homodromy coupled exciters in a non-resonant vibrating system of plane motion is studied. By introducing the average method of modified small parameters, we deduced dimensionless coupling equation of three exciters, which converted the problem of synchronization into that of the existence and stability of zero solutions for the average differential equations of the small parameters. Based on the dimensionless coupling torques and characteristics of the cor- responding limited functions, the synchronization criterion for three exciters was derived as the absolute value of dimensionless residual torque difference between arbitrary two motors being less than the maximum of their dimensionless coupling torques. The stability criterion of its synchronous state lies in the double-condition that the inertia coupling matrix is positive definite and all its elements are positive as well. The synchronization determinants are the coefficients of synchronization ability, also called as the general dynamical symmetry coefficients. The double-equilibrium state of the vibrating system is manifested by numeric method, and the numeric and simulation results derived thereof indicate the indispensable and crucial role the structural parameters of the vibrating system play in the stability criterion of synchronous operation. Besides, by adjusting its structural parameters, the elliptical motion of the vibrating system successfully met the requirements in engineering applications.
文摘Ce^（3＋） substituted Cu-spinel nanoferrites CuCe_xFe_（2-x）O_4（x=0.00, 0.02, 0.04, 0.06, 0.08 and 0.10） were synthesized via sol-gel self-combustion hybrid route. Single phase spinel ferrite of Cu nanoferrites were examined using X-ray diffraction（XRD） analysis whereas the multiphase structure was observed as Ce contents increased from x=0.06. Field emission scanning electron microscopy（FESEM）, Thermogravimetric and differential thermal analysis（TGA and DTA） and Fourier transform infrared spectroscopy（FTIR） were used to find out the morphology phase and metal stretching vibrations of Ce^（3＋） substituted nanocrystalline ferrites. The crystallite size was increased and found in the range of 25-91 nm. The agglomerations in Cu ferrite samples increase as the Ce^（3＋） concentration increases. The magnetic properties such as remanence, saturation magnetization, coercivity, Bohr magneton and magnetocrystalline anisotropy constant（K） were determined using M-H loops recorded from a vibrating sample magnetometer（VSM）. Saturation magnetization, remanence and coercivity are increased as the Ce^（3＋）contents increase in Cu nanocrystalline samples. Moreover, law of approach to saturation（LoA） was used to calculate the maximum value of saturation for Ce-doped Cu nanoferrites. The soft magnetic behaviour of the Cu nanoferrite is observed as compared to the samples substituted with the increased Ce contents in Cu nanocrystalline ferrite. Bohr magneton and magnetocrystalline anisotropy are found to increase with the substitution of rare earth Ce^（3＋） contents in Cu spinel nanocrystalline ferrite. Cedoped Cu nanocrystalline ferrites with excellent properties may be suitable for potential applications in sensing, security, switching, core, multilayer chip inductor, biomedical and microwave absorption applications.
