Study on Electromagnetic Force and Vibration of Turbogenerator End Windings under Impact Load(Ⅰ): Analysis of Electromagnetic Force of End Windings under Impact Load

In this paper, the boundary value problem (BVP) of 3 D transient eddy current field in the end region in the case that the generator is affected by impact load is specified. Besides, ways to implement discrete methods in both time domain and space domain during the solution of the problem are investigated. The Crank Nicolson scheme is utilized to attain the iterative format of time differential, after taking factors that can ensure both computation precision and stability into consideration. In this paper, the magnetic distribution in the end region of a turbogenerator in the case that the generator is affected by impact load is specified. As a result, it provides foundation for further study of electromagnetic force and electromagnetic vibration in the end region of the turbogenerator.

Effect of electromagnetic force on melt induced by traveling magnetic field

A new apparatus was designed to measure the electromagnetic force and a computational study of the traveling magnetic field(TMF)and its application to the Ga-In-Sn melt(with low melting point),then the forces on Al,Mg,and Li melt,were simulated. The result show that the electromagnetic force on the melt increases linearly with the increasing length of the melt in the TMF.The TMF-induced Lorentz force increases with increasing frequency,and then decreases.The maximum value is obtained when the current frequency is 160 Hz,over that frequency the force decreases rapidly.When the iron-core is activated,the force increases when the melt closes to the iron-core.The Lorentz forces have inversely-proportional relationships with the electrical resistivity,the dfx/dρdecreases and the dfy/dρincreases with the increasing electrical resistivity(df/dρis the slope of the Lorentz force profile).

AN IN SITU SURFACE COMPOSITE AND GRADIENT MATERIAL OF Al-Si ALLOY PRODUCED BY ELECTROMAGNETIC FORCE

Because of the different conductivities between the primary phase (low electric conduc tivity) and the metal melt, electromagnetic force scarcely acts on the primary phase. Thus, an electromagnetic repulsive force applied by the metal melt exerts on the pri mary phase when the movement of the melt in the direction of electromagnetic force is limited. As a result, the repulsive force exerts on the primary phase to push them to move in the direction opposite to that of the electromagnetic force when the metal melt with primary phase solidifies under an electromagnetic force field. Based on this, a new method for production of in situ surface composite and gradient material by electromagnetic force is proposed. An in situ primary Si reinforced surface composite of Al-15wt%Si alloy and gradient material of Al-l9wt%Si alloy were produced by this method. The microhardness of the primary Si is HV1320. The reinforced phase size is in the range from 40μm to 100μm. The wear resistance of Al-Si alloy gradient material can be more greatly increased than that of their matrix material.

Effect of electromagnetic force on turbulent flow of molten metal in aluminum electrolysis cells

The standard k-ε model was adopted to simulate the flow field of molten metal in three aluminum electrolysis cells with different anode risers. The Hartman number, Reynolds number and the turbulent Reynolds number of molten metal were calculated quantitatively. The turbulent Reynolds number is in the order of 103 , and Reynolds number is in the order of 104 if taking the depth of molten metal as the characteristic length. The results show that the molten metal flow is the turbulence of high Reynolds number, the turbulent Reynolds number is more appropriate than Reynolds number to be used to describe the turbulent characteristic of molten metal, and Hartman number displays very well that electromagnetic force inhibits turbulent motion of molten metal.

Effect of electromagnetic force and anode gas on electrolyte flow in aluminum electrolysis cell

Based on the commercial computational fluid dynamics software CFX-4.3, electrolyte flow fields in a 156 kA pre-baked anode aluminum electrolysis cell were investigated in three different cases where the electrolyte melt was driven by different kinds of force, i.e. electromagnetic force only, the anode gas drag force only and both of the former two forces. The results show that when electromagnetic force was introduced only, most of the electrolyte moves horizontally; when anode gas drag force was introduced only, the electrolyte flows mainly around each anode with small circulation; when electromagnetic force and anode gas drag force were both introduced together, the structure of the electrolyte flow fields and the velocity of electrolyte are similar to that of the case where only anode gas drag force is used. The electrolyte flow fields are mainly determined by the anode gas drag force.

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.

Numerical simulation of applied electromagnetic field and electromagnetic force in all-position welding

All-position welding is an important technology in energy sources, chemical, shipbuilding and other industries. When welding current is larger than 200 A, the molten metal tends to flow down due to the force of gravity. In order to ＂push＂ the molten metal into the weld, a new kind of U-frame excitation model, which could produce electromagnetic force to balance the gravity of the molten pool, was designed. The related parameters of the excitation model were simulated by Maxwell 3D, and the relationships between the parameters and the magnetic induction intensity were analyzed. Finally, the electromagnetic force in the molten pool was calculated, and the appropriate parameters of the U-frame excitation model were determined. The results of the simulation verify the feasibility of the all-position welding excitation model.

Simulation and Analysis of Electromagnetic Force in Laser Melting Deposition by Electromagnetic Impact

Magnetic field was introduced in laser melting deposition to reduce the pores in workpieces.Finite 3-D model of the coil-deposition layer-substrate was established.Simulation results show that the electromagnetic force in deposition layer mainly concentrates in the projection area of the coil.Axial electromagnetic force shows repulsion in one cycle.The experimental results indicate that the magnetic field is beneficial for grain refinement,microhardness increasement and decline of quantities and average sizes of pores.

Numerical analysis of electromagnetic force field through the use of two examples

In modern processing of conducting materials, such as steel,the time-varying electromagnetic field plays a key role in obtaining the desired microstructure or eliminating solidification defects such as porosity and segregation in cast billets. Up to now,few studies on the induced electromagnetic force （also called the Lorentz force） field in liquid metal have been reported. Compared with the magnetic field, the induced force field is the real and only direct cause for flow control. The electromagnetic force is comprised of two components. One is time-independent and the other is time- dependent. The time-dependent component varies with time in both amplitude and direction. When it reaches the extreme value,it can be one dozen times larger than the time-independent component. In this paper, a new method to quantitatively describe the induced electromagnetic force in liquid metal under a harmonic electromagnetic field,including both its time- independent and dependent components, was proposed based on the formula derivation from the data of amplitude and phase angle. Through this method ,the features of the time-dependent component were discussed, including the directions of rotation and the long axis. As a result, the force pattern was described. With two example calculations, the method was explained in detail. The results of both examples show that the force field in liquid metal can be divided into several regions with different force features. Example 1 shows the effect of coil position on the evolution of the force field pattern in liquid metal. Example 2 is a kind of stirring by the travelling magnetic field ,whose results present the sub-structures in metal and show that most of them have almost the same rotating direction.

Dynamic balancing with rotating radial electromagnetic force

A method of producing rotating radial electromagnetic force with a separable structure is proposed, and an experimental model was designed on which open loop vibration control experiments were carried out. Experimental results prove that the electromagnetic force designed has a constant magnitude and an uniform speed, and the idea of using an electromagnetic force as an active control in automatic balancing is correct in principle, and practicable in engineering.

Theoretical Model for Particle Behavio at Solidifying Front in Electromagnetic Force Field

The particle migrating behavior at solidifying front is discussed in theory with the application of electromagnetic force field(EMFF), on the basis of foregone analysis of force upon particle ahead of solidifying front without electromagnetic force field. The critical solidification velocities of particle pushing/engulfment transition ahead of horizontal and vertical interface are derived respectively when a certain EMFF is applied. And the critical electromagnetic forces of particle pushing/engulfment transition ahead of horizontal and vertical interface are also derived separately when a certain solidifying velocity is given.

A Tool for the Assessment of the Electromagnetic Forces in Power Distribution Transformers

This paper compares the estimated electromagnetic forces due to short circuits in power transformers using two computational models. The first model is based on approximate analytical expressions of the electromagnetic lbrces as they have been compiled in earlier versions of the IEC standard 60076-5. The second model is based on a finite element model of the transformer using the software FEMM （Finite Element Method Magnetics）. The paper shows how valid the analytical model is for design purposes. Results have been obtained and compared from both models in a number of actual power distribution transformers. It is possible to conclude that the analytical formulation provides satisfactory results for the design of power transformers compared to detailed finite element models. A tool has been designed for this purpose and the main features of it will be described in the paper.

Design of bionic water jet thruster with double-chamber driven by electromagnetic force

In response to the limitations of the single-chamber water jet thruster used in underwater vehicles mimicked by natural cephalopods,a novel approach involving a double-chamber water jet thruster has been proposed.This thruster utilizes electromagnetic force to manipulate the diaphragm,thereby altering the volume of the upper and lower chambers to achieve water jet propulsion.Experimental investigations were conducted to determine the tensile length-force characteristics of the diaphragm made of Agileus30.Subsequently,key parameters of essential propulsion components,such as solenoid coils,electromagnets,and currents,were established based on the tensile length-force curve,and the propulsion capabilities of the system were evaluated through theoretical analysis.Theoretical assessments indicate that the system does not produce reverse thrust regardless of whether the coil moves up or down.Further experimental results demonstrate that the maximum peak propulsion force generated by the dual-chamber water jet thruster within a 3-s cycle is 0.253N.

Formation keeping control through inter-satellite electromagnetic force

Satellite formation keeping through inter-satellite electromagnetic force provides an attractive alternative for future space missions due to its distinct advantages of no propellant consumption or plume contamination as compared to conventional approaches.However,the internal force nature as well as the high nonlinearity and coupling of electromagnetic force brings new control challenges for this novel technique.In this paper,analysis on the dynamics characteristics and special control issues in the presence of electromagnetic force is carried out on the basis of the derived relatively translational dynamics.Considering the model uncertainties,external disturbances and sensor noise,a combined nonlinear control scheme involving feed-forward and feedback control components is proposed for electromagnetic-force-based formation keeping.The feed-forward component is directly obtained through desired configuration and dynamics under nominal conditions while the feedback component is realized utilizing active disturbance rejection control methodology with some reasonable improvement.Numerical simulation is presented to verify the feasibility and validity of the combined control scheme.

Mechanical Response of Conductor on Round Core(CORC)Cables Under Electromagnetic Force

The conductor on round core(CORC)cables are fabricated with multilayer high-temperature superconductor tapes,which are helically wound around a circular central former.The large Lorentz force will be generated by the transport current in CORC cables under high magnetic field,which will affect the stress and strain distributions of tapes in the cables and the performance of superconducting tape.This paper establishes a two-dimensional axisymmetric model to analyze the mechanical response of CORC cables subjected to the Lorentz force and analyzes the influence of air gaps on stress and strain distributions inside the cables.The T-A method is used to calculate the distributions of current density,magnetic field and the Lorentz force in CORC cables.The mechanical response of CORC cables is analyzed by applying the Lorentz force as an external load in the mechanical model.The direction of electromagnetic force is analyzed in CORC cables with and without shielding current,and the results show that the shielding current can lead to the concentration of electromagnetic force.The maximum stress and strain occur on both sides of the superconducting tapes in the cables with shielding current.Reducing the size of air gaps can reduce the stress and strain in the superconducting layers.The analysis of mechanical response of CORC cables can play an important role in optimizing the design of CORC cables and improving transmission performance.

Flow Field of Metallic Fluid Acted by Electromagnetic and Centrifugal Force

According to the principle of electromagnetism and hydrodynamics,a mathematical model of flow field for metallic fluid acted by electromagnetic and centrifugal forces was established.The calculation results showed that the relative velocity between metallic fluid layers rises and the absolute rotational velocity of metallic fluid falls with the increase of magnetic induction intensity.The increase of centrifugal revolution hardly affects the relative velocity between metallic fluid layers,but can enhance the absolute rotational velocity of metallic fluid.

Extraction on the Contact Forces Among the Opaque and Non-photoelastic Particles Under Electromagnetic Force

Contact force is related to the mechanical response of superconducting strands under a large electromagnetic body force,which is important for the safety of the international t hermonuclear experimen tai reac tor(ITER)magne t struc ture.Due to the complex st rue ture of the cable-in-conduit conductor(CICC),the component unit of the ITER magnet,and the extreme operating environment,the research on the strand contact force caused by the electromagnetic force has been progressing slowly.In this study,a two-dimensional(2D)theoretical model based on the granular elemen t method is construe ted to compute the contac t forces among some opaque and non-photoelastic ferromagnetic particles which are placed in a non-uniform magnetic field.In the experiment,the contact deformations of these particles may be obtained by the digital image correlation method.We also propose a method,which is similar to the least-squares method,to calculate the electromagnetic body forces of different particles.Subsequently,the distributional and statistical characteristics of the contac t force chains and contact angles are presen ted.It is considered that the method proposed in this paper is suitable for the contact force analysis of the cross section of superconducting strands in the ITER CICC that is subjected to a transverse elec-tromagnetic force.In the end,this 2D theoretical model is generalized to the three-dimensional(3D)case,and the concise mathematical framework is presented.

COMPUTER SIMULATION OF CONTINUOUS ELECTROMAGNETIC STIRRING FOR MAKING RHEOLOGIC SEMI-SOLID SLURRY OF ZL112Y ALUMINUM ALLOY

To realize the technology of fabricating the rheologic semi-solid slurry of ZL112Y aluminum alloy via continues electromagnetic stirring process, ANSYS software was used to simulate electromagnetic force field and fluid velocity field in the alloy melt in a crucible tube in three coils. In the first section of the paper, eletromagnetic force field and fluid velocity field caused by single coil were simulated. The result of this simulation gives an average velocity of 3.2 cm/s and it is called critical velocity because a fluid velocity over it will cause a fine and spherical structure of solid primary a in a semi-solid melt. And, from this result, a reasonable temperature of semi-solid of the alloy and an electrical current intensity were established. The electrical current intensity of the result of this simulation corresponded to the current intensity used in a practice experiment, in which the primary α was obviously refined and sphericized. Based on this simulation of single coil electromagnetic stirring, in the second section of the paper, eletromagnetic force field and fluid velocity field caused by three coils were simulated. The result of the simulation shows that, 1） there is a semi-solid zone of 32 mm from bottom of the crucible tube to the upper; 2） the electrical current intensities of three coils of 400 A, 600 A, and 400 A, which were set to top range, middle range and bottom range of the tube, respectively, were the optimum parameters of electromagnetic current intensity under the condition of this investigation; and 3） under effect of these electromagnetic current intensity, the fluid velocities of the melt in the tube were 6.3 cm/s in top range, 3.75 cm/s in middle range, and 3.9 cm/s in bottom range of it, respectively.

Calculation and Optimization of ITER Upper VS Feeder Under an Electromagnetic Load

The upper vertical stability （VS） feeder is a part connected to the upper VS coil by a welding joint. The function of the feeder is to transfer current and coolant water to the VS coil. A giant electron^agnetic force will be generated during normal operation by the current flowing in the VS coils, interacting with the external background field. The Lorentz force will induce Tresca stress in the feeder. The amplitudes of the magnetic field and Lorentz force along the conductor running direction have been calculated based on Maxwell＇s equations. To extract the Tresca stress in the feeder, a finite element model was created using the software ANSYS and an electromagnetic load was applied on the model. According to the analytical design, the stresses were classified and evaluated based on ASME. In order to reduce the Tresca stress, some optimization works have been done and the Tresca stress has had a significant reduction in the optimized model. This analytical work figured out the stress distribution in the feeder and checked the feasibility of the prototype design model. The ANSYS analysis results will provide a guidance for later improvement and fabrication.

Electromagnetic Analyses of ITER Lower ELM Right Bottom Corner

ELM （edge localized mode） coils are key components of ITER that suppress the edge localized mode phenomenon. A giant electromagnetic force is generated during normal operations by the current flowing in the ELM coils interacting with the external background field. The Lorentz force will induce Tresca stress in the ELM coils. If the load goes beyond the allowable threshold, the coils can hardly satisfy the safety requirements. The right-hand bottom corner was chosen to perform our electromagnetic analyses. Based on the Maxwell equation, the detailed magnetic field and Lorentz force were calculated. By use of the finite element software ANSYS, the Tresca stress was extracted and evaluated based on our analytical design. The present analysis aims to verify the feasibility of the current design. It can also serve as guidance for fabrication and structural optimization.