Fast Calculation of Electromagnetic Forces in IPMSMs Under PWM VSI Supply Based on Small-Signal Time-Harmonic Finite Element Method

This paper introduces a novel method for fast calculating the electromagnetic forces in interior permanent magnet synchronous machines(IPMSMs)under pulse width modulation(PWM)voltage source inverter(VSI)supply based on the small-signal time-harmonic finite element analysis(THFEA),which has been successfully utilized for fast calculating the PWMinduced losses in silicon steel sheets and permanent magnets.Based on the small-signal THFEA,the functional relationships between high-frequency harmonic voltages(HFHVs)and corresponding airgap flux densities are established,which are used for calculating the flux density spectra caused by each HFHV in the PWM voltage spectra.Then,the superposition principle is applied for calculating the flux density spectra caused by fundamental currents and all HFHVs,which are converted to the electromagnetic force spectra at last.The relative errors between the force density spectra calculated with the proposed method and those obtained from traditional time-stepping finite element analysis(TSFEA)using PWM voltages as input are within 3.1%,while the proposed method is 24 times faster than the traditional TSFEA.

Phase-field modeling of dendritic growth under forced flow based on adaptive finite element method

A mathematical model combined projection algorithm with phase-field method was applied. The adaptive finite element method was adopted to solve the model based on the non-uniform grid, and the behavior of dendritic growth was simulated from undercooled nickel melt under the forced flow. The simulation results show that the asymmetry behavior of the dendritic growth is caused by the forced flow. When the flow velocity is less than the critical value, the asymmetry of dendrite is little influenced by the forced flow. Once the flow velocity reaches or exceeds the critical value, the controlling factor of dendrite growth gradually changes from thermal diffusion to convection. With the increase of the flow velocity, the deflection angle towards upstream direction of the primary dendrite stem becomes larger. The effect of the dendrite growth on the flow field of the melt is apparent. With the increase of the dendrite size, the vortex is present in the downstream regions, and the vortex region is gradually enlarged. Dendrite tips appear to remelt. In addition, the adaptive finite element method can reduce CPU running time by one order of magnitude compared with uniform grid method, and the speed-up ratio is proportional to the size of computational domain.

Mixed finite element and differential quadrature method for free and forced vibration and buckling analysis of rectangular plates

This paper presents a combined application of the finite element method （FEM） and the differential quadrature method （DQM） to vibration and buckling problems of rectangular plates. The proposed scheme combines the geometry flexibility of the FEM and the high accuracy and efficiency of the DQM. The accuracy of the present method is demonstrated by comparing the obtained results with those available in the literature. It is shown that highly accurate results can be obtained by using a small number of finite elements and DQM sample points. The proposed method is suitable for the problems considered due to its simplicity and potential for further development.

Circuit-field coupled finite element analysis method for an electromagnetic acoustic transducer under pulsed voltage excitation

This paper presents an analytical method for electromagnetic acoustic transducers （EMATs） under voltage excitation and considers the non-uniform distribution of the biased magnetic field. A complete model of EMATs including the non-uniform biased magnetic field, a pulsed eddy current field and the acoustic field is built up. The pulsed voltage excitation is transformed to the frequency domain by fast Fourier transformation （FFT）. In terms of the time harmonic field equations of the EMAT system, the impedances of the coils under different frequencies are calculated according to the circuit-field coupling method and Poynting＇s theorem. Then the currents under different frequencies are calculated according to Ohm＇s law and the pulsed current excitation is obtained by inverse fast Fourier transformation （IFFT）. Lastly, the sequentially coupled finite element method （FEM） is used to calculate the Lorentz force in the EMATs under the current excitation. An actual EMAT with a two-layer two-bundle printed circuit board （PCB） coil, a rectangular permanent magnet and an aluminium specimen is analysed. The coil impedances and the pulsed current are calculated and compared with the experimental results. Their agreement verified the validity of the proposed method. Furthermore, the influences of lift-off distances and the non-uniform static magnetic field on the Lorentz force under pulsed voltage excitation are studied.

Guided and Direct Wave Evaluation of Controlled Source Electromagnetic Survey Using Finite Element Method

Deep target hydrocarbon detection is still challenging and expensive. Direct hydrocarbon indicators (DHIs) in seismic data do not correspond to economical hydrocarbon exploration. Due to unreliability in seismic data for the detection of DHIs, new methods have been investigated. Marine controlled source electromagnet (MCSEM) or Sea bed logging (SBL) is new method for the detection of deep target hydrocarbon reservoir. Sea bed logging has also the potential to reduce the risks of DHIs in deep sea environment. Modelling of real sea environment helps to reduce the further risks before drilling the oil wells. 3D electromagnetic (EM) modelling of seabed logging requires more accurate methods for the detection of hydrocarbon reservoir. Finite element method (FEM) is chosen for the modelling of seabed logging to get more precise EM response from hydrocarbon reservoir below 4000 m from seabed. FEM allows to investigate the total electric and magnetic fields instead of scattered electric and magnetic fields, which shows accurate and precise resistivity contrast below the seabed. From the modelling results, It was investigated that Hz field shows higher magni- tude with 342% than the Ex field. It was observed that 0.125 Hz frequency can be able to show better resistivity contrast of Hz field (31.30%) and Ex field (16.49%) at target depth of 1000 m below seafloor for our proposed model. Hz and Ex field delineation was found to decrease as target depth increased from 1000 m to 4000 m. At the target depth of 4000 m, no field delineation response was seen from the current electromagnetic (EM) antenna used by the industry. New EM antenna has been used to see the EM response for deep target hydrocarbon detection. It was investigated that novel EM antenna shows better delineation at 4000 m target depth for Ex and Hz field up to 10.3% and 15.1% respectively. Novel EM antenna also shows better Hz phase response (128.4%) than the Ex phase response (38.3%) at the target depth of 4000 m below the seafloor.

Combined method for fast 3-D finite element modeling of nondestructive testing signal

A combined method for the fast 3-D finite element modeling of defect responses in nondestructive testing of electromagnetics is presented. The method consists of three numerical techniques: zoom-in technique, difference field technique and iterative solution technique. Utilizing the zoom-in technique, the computational zone focuses on a relatively small domain around the defect. Employing the difference field technique, the axisymmetrical field solution corresponding to the case with no defect can be used to simplify the mesh generation and obtain the modeling results quickly. Using the iterative solution technique, the matrix equation system in the 3-D finite element modeling of nondestructive probe signals can easily be solved. The sample calculation shows that the presented method is highly effective and can consequently save significant computer resources.

Finite element solution based on fast numerical technique for large-scale electromagnetic computation

A numerical technique of the target-region locating （TRL） solver in conjunction with the wave-front method is presented for the application of the finite element method （FEM） for 3-D electromagnetic computation. First, the principle of TRL technique is described. Then, the availability of TRL solver for nonlinear application is particularly discussed demonstrating that this solver can be easily used while still remaining great efficiency. The implementation on how to apply this technique in FEM based on magnetic vector potential （MVP） is also introduced. Finally, a numerical example of 3-D magnetostatic modeling using the TRL solver and FEMLAB is given. It shows that a huge computer resource can be saved by employing the new solver.

Modeling and finite element analysis of transduction process of electromagnetic acoustic transducers for nonferromagnetic metal material testing

Facing the problems lack of considering the non-uniform distribution of the static bias magnetic field and computing the panicle displacements in the simulation model of electromagnetic acoustic transducer （EMAT）, a multi-field coupled model was established and the finite element method （FEM） was presented to calculate the entire transduction process. The multi-field coupled model included the static magnetic field, pulsed eddy current field and mechanical field. The FEM equations of the three fields were derived by Garlerkin FEM method. Thus, the entire transduction process of the EMAT was calculated through sequentially coupling the three fields. The transduction process of a Lamb wave EMAT was calculated according to the present model and method. The results show that, by the present method, it is valid to calculate the particle displacement under the given excitation signal and non-uniformly distributed static magnetic field. Calculation error will be brought about if the non-uniform distribution of the static bias magnetic field is neglected.

A Finite Element Solution of Wave Forces on Submerged Horizontal Circular Cylinders

In this paper, a numerical model is established for estimating the wave forces on a submerged horizontal circular cylinder. For predicting the wave motion, a set of two dimensional Navier Stokes equations is solved numerically with a finite element method. In order to track the moving non linear wave surface boundary, the Navier Stokes equations are discretized in a moving mesh system. After each computational time step, the mesh is modified according to the changed wave surface boundary. In order to stabilize the numerical procedure, a three step finite element method is applied in the time integration. The water sloshing in a tank and wave propagation over a submerged bar are simulated for the first time to validate the present model. The computational results agree well with the analytical solution and the experimental data. Finally, the model is applied to the simulation of interaction between waves and a submerged horizontal circular cylinder. The effects of the KC number and the cylinder depth on the wave forces are studied.

FINITE ELEMENT DISPLACEMENT PERTURBATION METHOD FOR GEOMETRIC NONLINEAR BEHAVIORS OF SHELLS OF REVOLUTION OVERALL BEDING IN A MERIDIONAL PLANE AND APPLICATION TO BELLOW (Ⅱ)

The finite_element_displacement_perturbation method (FEDPM)for the geometric nonlinear behaviors of shells of revolution subjected to pure bending moments or lateral forces in one of their meridional planes (Ⅰ) was employed to calculate the stress distributions and the stiffness of the bellows. Firstly, by applying the first_order perturbation solution (the linear solution)of the FEDPM to the bellows, the obtained results were compared with those of the general solution and the initial parameter integration solution proposed by the present authors earlier, as well as of the experiments and the FEA by others.It is shown that the FEDPM is with good precision and reliability, and as it was pointed out in (Ⅰ) the abrupt changes of the meridian curvature of bellows would not affect the use of the usual straight element. Then the nonlinear behaviors of the bellows were discussed. As expected, the nonlinear effects mainly come from the bellows ring plate,and the wider the ring plate is, the stronger the nonlinear effects are. Contrarily, the vanishing of the ring plate, like the C_shaped bellows, the nonlinear effects almost vanish. In addition, when the pure bending moments act on the bellows, each convolution has the same stress distributions calculated by the linear solution and other linear theories, but by the present nonlinear solution they vary with respect to the convolutions of the bellows. Yet for most bellows, the linear solutions are valid in practice.

Introduction to Mesh Based Generated Lumped Parameter Models for Electromagnetic Problems using Triangular Elements

This paper is an introduction to mesh based generated reluctance network modeling using triangular elements.Many contributions on mesh based generated reluctance networks using rectangular shaped elements have been published,but very few on those generated from a mesh using triangular elements.The use of triangular elements is aimed at extending the application of the approach to any shape of modeled devices.Basic concepts of the approach are presented in the case of electromagnetic devices.The procedure for coding the approach in the case of a flat linear permanent magnet machine is presented.Codes developed under MATLAB environment are also included.

Simulated Experiments for Teaching CAD Techniques Using Analytic and Finite Element Solutions of Electromagnetic Two-Dimensional Problems with Longitudinal Symmetry

The paper describes an approach to teaching low-frequency electromagnetic CAD techniques to undergraduate students pursuing a degree course in electrical engineering. The simulated experiments make use of a two-dimensional open-access software based on the finite-element method. At the laboratory meetings, the problems are initially solved analytically. Upon this, students learn how to create the numeric model and how to define the sequence of field problems that lead to the required solution. Simulation tasks based on a force-producing electromagnet are used to introduce numeric techniques to determine magnetic field distribution, evaluation of energy storage and generation of magnetic forces. The nature of the magnetic force generated in the air gaps of the C-core electromagnet is explained in detail. Magnetic forces are calculated by the classical and weighted versions of the method of Maxwell stress tensor. The paper provides all the basic elements required for further exploration of devices with longitudinal symmetry.

FINITE ELEMENT DISPLACEMENT PERTURBATION METHOD FOR GEOMETRIC NONLINEAR BEHAVIORS OF SHELLS OF REVOLUTION OVERALL BENDING IN A MERIDIONAL PLANE AND APPLICATION TO BELLOWS (Ⅰ)

In order to analyze bellows effectively and practically, the finite_element_displacement_perturbation method (FEDPM) is proposed for the geometric nonlinear behaviors of shells of revolution subjected to pure bending moments or lateral forces in one of their meridional planes. The formulations are mainly based upon the idea of perturba_ tion that the nodal displacement vector and the nodal force vector of each finite element are expanded by taking root_mean_square value of circumferential strains of the shells as a perturbation parameter. The load steps and the iteration times are not as arbitrary and unpredictable as in usual nonlinear analysis. Instead, there are certain relations between the load steps and the displacement increments, and no need of iteration for each load step. Besides, in the formulations, the shell is idealized into a series of conical frusta for the convenience of practice, Sander's nonlinear geometric equations of moderate small rotation are used, and the shell made of more than one material ply is also considered.

Experiment and finite element analysis of micromilling force

For predicting the milling force in process of micromilling aluminum alloy, the law for micromilling force changing under different milling parameters was studied. The elastic-plastic finite elelent model of micromilling was found using general commercial software. During modeling, the Johnson-Cook＇ s coupled thermal- mechanical model was used as workpieee material model, the Johnson-Cook＇ s shear failure principle was adopted as workpiece failure principle, and the coupled thermal-mechanical hexahedron strain hybrid modules and serf-adaptive grid technology based on the updated Lagrange formulation were used to mesh the workpiece＇ s elements, while the friction between tool and workpiece obeys the modified Coulomb＇ s law that combines with the sliding friction and the adhesive friction. By means of finite element analysis, the law for micromilling force changing under different milling parameters was obtained, and the results were analyzed and compared. Finally micromilling experiments were carried out to validate the results of simulation.

Finite Element Based Analysis of Magnetic Forces between Planar Spiral Coils

This paper elaborates on the magnetic forces between current carrying planar spiral coils. Direct and concentric rings methods are employed in order to calculate the magnetic force between these coils. The results obtained by two calculation methods show the efficiency of the replaced rings method in both simplicity and calculation time. Simula-tions using the Finite Element Method (FEM) are carried out to analyze the distribution of the magnetic flux density around the coils. Also, coils with precise size have been constructed and tested. The experimental results as well as the results obtained by FEM are used to validate the accuracy of the calculations.

Cup-drawing formation of steel sheet with nickel coating by finite element method

The finite element method(FEM) simulation of deep-drawing of steel sheet with nickel coating based on the solid element and dynamic explicit method was reported. Penalty function method was used to treat the contact algorithm. The friction between the punch and coating sheet was based on a Coulomb formulation. The combination of coating and substrate was defined as tied with failure contact. The results of the simulation illustrate that the steel sheet and the nickel coating do not delaminate at the interface. The stress field of the nickel coating is more complicated than that of the steel substrate. Furthermore,it is found that the punch-nose radius is the most unsubstantial part for the intensity of the entire deep-drawing part and the thinnest part,it is a dangerous zone for the break. At this zone,the thickness thinning of the steel sheet and the nickel coating are up to 4.8% and 6.7%,respectively. Meanwhile,it is found that the curve of the variable blankholder force(VBHF) designed can improve the formability of sheet.

Parameter Identification Based on Force-Displacement Curves for a Bolted Joint Finite Element Model

In order to identify the uncertain parameters of a bolted joint finite element model,a simple and applicable way of parameter identification is introduced.By utilizing numerical simulation with the Abaqus software and experimental investigation with the MTS material testing system,the tangential force-displacement curves that reflect the characteristics of the bolted joint were acquired.On the basis of this,by employing the response surface methodology（RSM）and genetic algorithms（GAs）,parameters in the FEM model were identified.The force-displacement curves by both virtual and experimental approaches are well correlated at the end.This phenomenon-based parameter identification method may help facilitate precise prediction of complex jointed connection structures.

Calculation method of ship collision force on bridge using artificial neural network

Ship collision on bridge is a dynamic process featured by high nonlinearity and instantaneity. Calculating ship-bridge collision force typically involves either the use of design-specification-stipulated equivalent static load, or the use of finite element method (FEM) which is more time-consuming and requires supercomputing resources. In this paper, we proposed an alternative approach that combines FEM with artificial neural network (ANN). The radial basis function neural network (RBFNN) employed for calculating the impact force in consideration of ship-bridge collision mechanics. With ship velocity and mass as the input vectors and ship collision force as the output vector, the neural networks for different network parameters are trained by the learning samples obtained from finite element simulation results. The error analyses of the learning and testing samples show that the proposed RBFNN is accurate enough to calculate ship-bridge collision force. The input-output relationship obtained by the RBFNN is essentially consistent with the typical empirical formulae. Finally, a special toolbox is developed for calculation efficiency in application using MATLAB software.

The finite element modeling of spiral ropes

Accurate understanding the behavior of spiral rope is complicated due to their complex geometry and complex contact conditions between the wires.This study proposed the finite element models of spiral ropes subjected to tensile loads.The parametric equations developed in this paper were implemented for geometric modeling of ropes.The 3D geometric models with different twisting manner,equal diameters of wires were generated in details by using Pro/ENGINEER software.The results of the present finite element analysis were on an acceptable level of accuracy as compared with those of theoretical and experimental data.Further development is ongoing to analysis the equivalent stresses induced by twisting manner of cables.The twisting manner of wires was important to spiral ropes in the three wire layers and the outer twisting manner of wires should be contrary to that of the second layer,no matter what is the first twisting manner of wires.

Detection technology and application of electromagnetic method for hidden danger of water gushing at coal face

The principles, methods, technologies and application effects of several electromagnetic methods for the detection of the hidden danger of water gushing at the coal face were introduced. Also, emphasis was laid on expounding the methods, principles and effects of down-hole detections by electric transmission tomography and transient electromagnetic method. The potential of point power supplied in the underground homogeneous semi-space, as well as the response to a low-resistivity abnormal body in the homogeneous semi-space, was simulated by adopting 3-D finite element method to interpret the basic theory of the electric transmission tomography. The results of actual measurement show that the mine electromagnetic method is sensitive to water-bearing low-resistivity bodies and can play a unique role in detecting the hidden danger of water gushing at the coal face.