Method Of Spatial Integral Equations Research Articles

To Calculation of Dynamic Characteristics of High-Speed Electromagnets of Traction Automatic Switches

The problems of numerical simulation of electromagnetic processes in high-speed electromagnetic drives of traction circuit breakers based on the method of spatial integral equations are considered. It is established that the proposed numerical model and algorithm for calculating the three-dimensional magnetic field by the method of spatial integral equations with subsequent determination of the integral characteristics and parameters of the electromagnetic drive allow to obtain sufficiently complete and reliable information about the static and dynamic modes of operation of the device. The possibility of regulation of static and dynamic setpoints on the current of the circuit breaker by changing the parameters of the armature start-up and actuation of the drive electromagnet by using the effects of saturation of steel, eddy currents in the solid elements of magnetic systems and short-circuited sleeves is shown. Currents and time of moving the armature of the electromagnet in static and dynamic modes are determined by the geometric dimensions of the magnetic system, the presence of solid elements of the magnetic circuit, short-circuited sleeves, their location on the elements of the magnetic system. The adequacy.

Force Interaction in Magnetic Systems with a Volumetric High-Temperature Superconductor

The paper presents the results of the theoretical and experimental studies of force interactions between permanent magnets and volumetric high-temperature superconductors (HTCs). The obtained data are of interest for the design of various devices with HTC elements: magnetic bearings, transport systems with magnetic levitation, electric machines, etc. Numerical analysis of the electromagnetic field was performed by the method of spatial integral equations for the field sources. The properties of the HTC materials and YBaCuO ceramics are represented by a traditional model for transport currents and a combined model that considers the types of field sources inside the superconductor—the transport current density and the related currents (magnetization). For the transport current density, a modification of the critical state model is applied. In this model, the specific electric resistance of the superconductor is presented by a hyperbolic function of the following three parameters: absolute temperature, magnetic field strength, and current density. The model for magnetization is based on the definition of the related currents in the form of the density of the magnetic moments’ combination of the small superconducting cylinders throughout the sample of a high-temperature superconductor. Experimental studies were performed on a specially designed installations with the HТС cryostatting system in a liquid-nitrogen atmosphere and equipment for precision force sensing. Comparison of the experimental results and calculation data confirms the reliability of the developed modeling methods.

Comparative Analysis of the Specific Characteristics of the Magnetic Bearings With HTS Elements Transactions on Applied Superconductivity

Selection of the most suitable design of the HTS bearing is based on the information about specific characteristics of existing constructions. One of the main parameters for comparison is a value of the specific axial and radial stiffness. The paper presents the results of calculation of the stiffness for different constructions of HTS bearing. Calculations were performed using the method of spatial integral equations and the model of superconducting properties confirmed by the experiments with the prototype of HTS bearing. Results of the research can be used for an effective selection of the HTS bearing construction for any device with magnetic suspension.

To Calculate Characteristics of Electromagnetic Actuators Electrical Apparatus

The article presents a review and analysis of existing methods of calculation of magnetic systems of electric drives of machines with complex spatial configuration. The advantages and disadvantages of the most common and widely used methods of finite differences, finite elements, boundary elements, boundary integral equations and the spatial integrated equations. Presents an analysis of the software used for the calculation of electromagnetic fields. It is noted that the accuracy and performance of the software depend on the methods underlying them and the schemes of calculation. The analysis established that the existing freely available software systems do not have the capacity for efficient three dimensional modeling of eddy currents, hysteresis, displacement of individual elements of magnetic systems of electric devices. There was a need to create new specialized algorithms and software, allowing to solve problems of volumetric calculations of magnetic fields and determining the characteristics of electromechanical transducers based on the method of spatial integral equations.

Electromechanical energy conversion in a system with a bulk high-temperature superconductor. Part 1. Mathematical simulation of processes

Features of energy conversion in the linear electromechanical vibration device with an element made of high-temperature superconducting (HTS) material are considered. A disk-shaped permanent magnet with axial magnetization moves inside a fixed circular coil, and a ceramic HTS element, also disk-shaped, is fixed at a distance from the permanent magnet. All converter elements are arranged coaxially. The HTS element transitions into a superconducting state in the magnetic field of the permanent magnet. The purpose of the investigation is to find the effect of the HTS element effect on the static and dynamic parameters of the converter by comparing the operation of the device with the HTS element and without it. Mathematical models are developed for the calculation of dynamic characteristics of the device in the Matlab/Simulink software environment for electrical and mechanical subsystems. The connection between the subsystems is defined by functions of flux linkage of the coil and the electromagnetic force, which are obtained by the analysis of the electromagnetic field by the method of spatial integral equations taking into account HTS material properties. A combined model of HTS material properties is proposed with two sources of magnetic fields (magnetization and current density), which is more universal than current only models.

Analysis of a double-stage magnetic multiplicator

Static characteristics of a version of a two-stage magnetic multiplicator with a gear ratio of 120 are analyzed using a numerical simulation technique. The magnetic system of the multiplication is simulated in a 2D approximation using the EASYMAG 3D numerical simulation software based on the method of spatial integral equations.

Solution of the inverse problem of creating a uniform magnetic field in coercimeters with partially closed magnetic systems

The use of a hybrid optimization technology by a swarm of particles with the evolutionary formation of swarm composition is considered together with the method of spatial integral equations in the synthesis of axially symmetric magnetic systems of coercimeters that contain ferromagnetic elements. The required uniformity of the magnetic field in the working volume is ensured by the optimal selection of the shape of pole pieces of a magnetizing device. A number of measures are proposed that allow acceleration of the synthesis process owing to shortening of the time spent for solving the problem of analyzing the distribution of the magnetic field in the working volume of the coercimeter.

Computer analysis of the configurations of magnetic fields of subsurface discontinuities of finite dimensions and arbitrary shapes in tested objects of finite length by the method of spatial integral equations

Using software developed by the authors and based on the method of spatial integral equations, the spatial configurations of the magnetic fields of tested objects of finite length that contain subsurface discontinuity flaws of finite dimensions and arbitrary shapes are studied. It is possible to take into account the influence of both uniform and nonuniform magnetizing fields, including real sources; an arbitrary geometry of tested objects; and a nonlinear character of the magnetic properties of materials. It is shown that software can be used in studies of the influence of the geometrical parameters of a defect on the topography of the informative magnetic field in the testing zone.

Computer analysis of the configuration of the magnetic fields of surface discontinuity flaws of finite dimensions in a ferromagnetic plate of finite dimensions by the spatial integral equation method

The spatial integral equation method is used to perform a numerical analysis of the magnetic-field configuration for ferromagnetic objects of finite dimensions having surface discontinuity flaws of arbitrary shape and finite dimensions. The range of application of the software developed for the design of technical devices for inspecting objects of irregular geometry was determined.

Mathematical simulation of magnetization processes of arbitrarily shaped ferromagnetic test objects in fields of given spatial configurations

On the basis of the method of spatial integral equations and developed software, a technique for simulating magnetization processes of ferromagnetic objects of complex geometric shapes, which are monitored by a magnetic method, has been developed. This procedure takes into account the spatial character of the informative magnetic field and nonlinear magnetic properties of the object material. The probable simulation-error level is estimated.