ANALYSIS ON THE MAGNETO-ELASTIC-PLASTIC BUCKLING/SNAPPING OF CANTILEVER RECTANGULAR FERROMAGNETIC PLATES

An analysis of buckling/snapping and bending behaviors of magneto-elastic-plastic interaction and coupling for cantilever rectangular soft ferromagnetic plates is presented. Based on the expression of magnetic force from the variational principle of ferromagnetic plates, the buckling and bending theory of thin plates, the Mises yield criterion and the increment theory for plastic deformation, we establish a numerical code to quantitatively simulate the behaviors of the nonlinearly multi-fields coupling problems by the finite element method. Along with the phenomena of buckling/snapping and bending, or the characteristic curve of deflection versus magnitude of applied magnetic fields being numerically displayed, the critical loads of buckling/snapping, and the influences of plastic deformation and the width of plate on these critical loads, the plastic regions expanding with the magnitude of applied magnetic field, as well as the evolvement of deflection configuration of the plate are numerically obtained in a case study.

Inverse problem of pulsed eddy current field of ferromagnetic plates

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.

Simultaneous resonance of an axially moving ferromagnetic thin plate under a line load in a time-varying magnetic field

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.

MAGNETOELASTIC BENDING AND STABILITY OF SOFT FERROMAGNETIC RECTANGULAR PLATES

In this paper, the phenomenon of magnetoelastic bending is theoretically simulated for soft ferromagnetic rectangular thin plates in applied magnetic fields. A numerical program of 3d FEM is established to capture the nonlinear coupling interaction between magnetic fields and bending deflection. After the nonlinear characteristic of the bending deflection and the magnetic (field) force is quantitatively displayed, we discuss the critical magnetic field and the effect of the incident angle of obliquely applied magnetic field on the critical field to the phenomenon of magnetoelastic instability.

Study on magneto-elastic-plastic deformation characteristics of ferromagnetic rectangular plate with simple supports

In this paper, the magnetic-elastic-plastic deformation behavior is studied for a ferromagnetic plate with simple supports. The perturbation formula of magnetic force is first derived based on the perturbation technique, and is then applied to the analysis of deformation characteristics with emphasis laid on the analyses of modes, symmetry of deformation and influences of incident angle of applied magnetic field on the plate deformation. The theoretical analyses offer explanations why the configuration offer- romagnetic rectangular plate with simple supports under an oblique magnetic field is in-wavy type along the x-direction, and why the largest deformation of the ferromagnetic plate occurs at the incident angle of 45°for the magnetic field. A numerical code based on the finite element method is developed to simulate quantitatively behaviors of the nonlinearly coupled multi-field problem. Some characteristic curves are plotted to illustrate the magneto--elastic-plastic deflections, and to reveal how the deflections can be influenced by the incident angle of applied magnetic field. The deformation characteristics obtained from the numerical simulations are found in good agreement with the theoretical analyses.

Magnetic-structure coupling dynamic model of a ferromagnetic plate parallel moving in air-gap magnetic field

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.

ANALYSIS ON DYNAMIC CHARACTERISTICS FOR FERROMAGNETIC CONDUCTING PLATES IN A TRANSVERSE UNIFORM MAGNETIC FIELD

In this paper, a set of basic equations for free vibration of ferromagnetic conducting plates in a transverse magnetic field are presented, in which the coupled effects of magnetization and eddy current on the mechanical behavior of the plate are included. Based on the quantitative analyses on the vibration frequency and the values of the critical magnetic field for several supporting conditions of the plate, the effects of the conductivity, the magnetic permeability, the thickness of the plate and supporting conditions on the vibration frequency of the plate and the critical magnetic field are discussed.

A VARIATIONAL PRINCIPLE ON MAGNETOELASTIC INTERACTION OF FERROMAGNETIC THIN PLATES

The key to revealing the behaviors of magnetoelastic interaction is how to express the magnetic forces applying on a ferromagnetic elastic body. In this paper, a functional for a ferromagnetic thin plate in magnetic fields is proposed by taking the summation of the magnetic energy of the magnetic system and the strain energy of the elastic plates. We present a variational principle for the problem by choosing the variations of magnetic potential and deflection as independent variates each other. Based on the principle, not only are the simultaneous governing equations for magnetic fields and deformation of structures deduced, but also a general expression of magnetic force acting on the plates is gained, which makes it possible to commonly simulate the distinct two experiments of magnetoelastic interaction in a theoretical model. Thus, it can be used to theoretical prediction of the magnetoelastic interaction of ferromagnetic plates in a complex environment of applied magnetic fields.

Design and simulation of an electromagnetic balance head for electric spindle

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.