In this paper,the simultaneous resonance of a ferromagnetic thin plate in a time-varying magnetic field,having axial speed and being subjected to a periodic line load,is studied.Based on the large deflection theory of...In this paper,the simultaneous resonance of a ferromagnetic thin plate in a time-varying magnetic field,having axial speed and being subjected to a periodic line load,is studied.Based on the large deflection theory of thin plates and electromagnetic field theory,the nonlinear vibration differential equation of the plate is obtained by using the Hamilton′s principle and the Galerkin method.Then the boundary condition in which the longer opposite sides are clamped and hinged is considered.The dimensionless nonlinear differential equations are solved by using the method of multiple scales,and the analytical solution is given.In addition,the stability analysis is also carried out by using Lyapunov stability theory.Through numerical analysis,the variation curves of system resonance amplitude with frequency tuning parameter,magnetic field strength and external excitation amplitude are obtained.Different parameters that have significant effects on the response of the system,such as the thickness,the axial velocity,the magnetic field intensity,the position,and the frequency of external excitation,are considered and analyzed.The results show that the system has multiple solution regions and obvious nonlinear coupled characteristics.展开更多
An energy theory is proposed on the buckling of a ferromagnetic thin plate in a transverse static magnetic field. The analytic solution of critical field for plates is obtained by using variational method. It is shown...An energy theory is proposed on the buckling of a ferromagnetic thin plate in a transverse static magnetic field. The analytic solution of critical field for plates is obtained by using variational method. It is shown that the critical magnetic field is not only influenced by the ratio of the thickness to the length, but also by the width, total length and the magnetic susceptibility of the specimen. Theoretical calculations agree with experiments reasonably.展开更多
To determine the wall thickness, conductivity and permeability of a ferromagnetic plate, an inverse problem is established with measured values and calculated values of time-domain induced voltage in pulsed eddy curre...To determine the wall thickness, conductivity and permeability of a ferromagnetic plate, an inverse problem is established with measured values and calculated values of time-domain induced voltage in pulsed eddy current testing on the plate. From time-domain analytical expressions of the partial derivatives of induced voltage with respect to parameters,it is deduced that the partial derivatives are approximately linearly dependent. Then the constraints of these parameters are obtained by solving a partial linear differential equation. It is indicated that only the product of conductivity and wall thickness, and the product of relative permeability and wall thickness can be determined accurately through the inverse problem with time-domain induced voltage. In the practical testing, supposing the conductivity of the ferromagnetic plate under test is a fixed value, and then the relative variation of wall thickness between two testing points can be calculated via the ratio of the corresponding inversion results of the product of conductivity and wall thickness. Finally, this method for wall thickness measurement is verified by the experiment results of a carbon steel plate.展开更多
Aiming at the air-gap magnetic field excited by wall armatures,Laplace’s partial differential equation of air-gap magnetic potential is achieved by means of the electromagnetic field theory.According to the magnetic ...Aiming at the air-gap magnetic field excited by wall armatures,Laplace’s partial differential equation of air-gap magnetic potential is achieved by means of the electromagnetic field theory.According to the magnetic boundary conditions and the method of separation of variables,the magnetic potential of the air-gap magnetic field is obtained.Based on the magnetization force model and Lorentz force of ferromagnetic thin-walled structures,and introducing the electromagnetic constitutive relations and boundary conditions,the calculation model of electromagnetic force of the soft ferromagnetic thin plate moving in air-gap magnetic field is established.Considering geometric nonlinearity,expressions of strain energy and kinetic energy of the elastic thin plate and the work of forces are given,respectively.The magnetic-structure coupling nonlinear vibration equations of ferromagnetic thin plate parallel moving in the air-gap magnetic field excited by armatures are obtained by using the Hamilton principle,which can be of the characterization of the system dynamics model with electro-magneto-velocity-mechanical interaction.Through numerical examples,primary resonance characteristics of the strip thin plate under the action of air-gap magnetic force are obtained.The results show that the two stable amplitude values will increase as amplitude of magnetic potential increases and thickness of air-gap decreases,and the amplitude’s multi-valued region will change due to the varieties of magnetic potential,air-gap and velocity.The model established in this paper is a theoretical reference for investigation on the multi-field coupling dynamic behaviors of structures moving in complex electromagnetic fields.展开更多
The electromagnetic balance head is used for balancing the electric spindle. This paper analyzes the internal structure of the electromagnetic balance head and introduces the structure of the counterweight plate and t...The electromagnetic balance head is used for balancing the electric spindle. This paper analyzes the internal structure of the electromagnetic balance head and introduces the structure of the counterweight plate and the range of the balance in the moving ring.The principle of how the electromagnetic field generated by the static coil acts on the moving ring is also investigated. The model is built in Ansoft Maxwell and the excitation parameters and boundary conditions are set up. Through the analysis of the magnetic field generated by the static coil in the position of the moving ring, it is verified that the static loop coil can drive the counterweight plate.展开更多
基金National Natural Science Foundation of China under Grant Nos.12172321 and 11472239Hebei Provincial Natural Science Foundation of China under Grant No.A2020203007Hebei Provincial Graduate Innovation Foundation of China under Grant No.CXZZBS2022146。
文摘In this paper,the simultaneous resonance of a ferromagnetic thin plate in a time-varying magnetic field,having axial speed and being subjected to a periodic line load,is studied.Based on the large deflection theory of thin plates and electromagnetic field theory,the nonlinear vibration differential equation of the plate is obtained by using the Hamilton′s principle and the Galerkin method.Then the boundary condition in which the longer opposite sides are clamped and hinged is considered.The dimensionless nonlinear differential equations are solved by using the method of multiple scales,and the analytical solution is given.In addition,the stability analysis is also carried out by using Lyapunov stability theory.Through numerical analysis,the variation curves of system resonance amplitude with frequency tuning parameter,magnetic field strength and external excitation amplitude are obtained.Different parameters that have significant effects on the response of the system,such as the thickness,the axial velocity,the magnetic field intensity,the position,and the frequency of external excitation,are considered and analyzed.The results show that the system has multiple solution regions and obvious nonlinear coupled characteristics.
文摘An energy theory is proposed on the buckling of a ferromagnetic thin plate in a transverse static magnetic field. The analytic solution of critical field for plates is obtained by using variational method. It is shown that the critical magnetic field is not only influenced by the ratio of the thickness to the length, but also by the width, total length and the magnetic susceptibility of the specimen. Theoretical calculations agree with experiments reasonably.
基金supported by the National Defense Basic Technology Research Program of China(Grant No.Z132013T001)
文摘To determine the wall thickness, conductivity and permeability of a ferromagnetic plate, an inverse problem is established with measured values and calculated values of time-domain induced voltage in pulsed eddy current testing on the plate. From time-domain analytical expressions of the partial derivatives of induced voltage with respect to parameters,it is deduced that the partial derivatives are approximately linearly dependent. Then the constraints of these parameters are obtained by solving a partial linear differential equation. It is indicated that only the product of conductivity and wall thickness, and the product of relative permeability and wall thickness can be determined accurately through the inverse problem with time-domain induced voltage. In the practical testing, supposing the conductivity of the ferromagnetic plate under test is a fixed value, and then the relative variation of wall thickness between two testing points can be calculated via the ratio of the corresponding inversion results of the product of conductivity and wall thickness. Finally, this method for wall thickness measurement is verified by the experiment results of a carbon steel plate.
基金the National Natural Science Foundation of China(Grant Nos.12172321 and 11472239)the Hebei Provincial Natural Science Foundation of China(Grant No.A2020203007).
文摘Aiming at the air-gap magnetic field excited by wall armatures,Laplace’s partial differential equation of air-gap magnetic potential is achieved by means of the electromagnetic field theory.According to the magnetic boundary conditions and the method of separation of variables,the magnetic potential of the air-gap magnetic field is obtained.Based on the magnetization force model and Lorentz force of ferromagnetic thin-walled structures,and introducing the electromagnetic constitutive relations and boundary conditions,the calculation model of electromagnetic force of the soft ferromagnetic thin plate moving in air-gap magnetic field is established.Considering geometric nonlinearity,expressions of strain energy and kinetic energy of the elastic thin plate and the work of forces are given,respectively.The magnetic-structure coupling nonlinear vibration equations of ferromagnetic thin plate parallel moving in the air-gap magnetic field excited by armatures are obtained by using the Hamilton principle,which can be of the characterization of the system dynamics model with electro-magneto-velocity-mechanical interaction.Through numerical examples,primary resonance characteristics of the strip thin plate under the action of air-gap magnetic force are obtained.The results show that the two stable amplitude values will increase as amplitude of magnetic potential increases and thickness of air-gap decreases,and the amplitude’s multi-valued region will change due to the varieties of magnetic potential,air-gap and velocity.The model established in this paper is a theoretical reference for investigation on the multi-field coupling dynamic behaviors of structures moving in complex electromagnetic fields.
基金Supported by National Natural Science Foundation of China(61370088)National Special Project of International Cooperation in Science and Technology(2014DFB10060)
文摘The electromagnetic balance head is used for balancing the electric spindle. This paper analyzes the internal structure of the electromagnetic balance head and introduces the structure of the counterweight plate and the range of the balance in the moving ring.The principle of how the electromagnetic field generated by the static coil acts on the moving ring is also investigated. The model is built in Ansoft Maxwell and the excitation parameters and boundary conditions are set up. Through the analysis of the magnetic field generated by the static coil in the position of the moving ring, it is verified that the static loop coil can drive the counterweight plate.
