Calculation Of Magnetic Force Research Articles

Kinetic study of dry magnetic separation based on Gauss-Maxwell magnetic stress tensor: A 3D finite element method (FEM)

In this paper, two artificial magnetic particles (1#, 2#) with known magnetic parameters were taken as the objects, a finite element model based on Gauss’s law was established for the calculation of the transient Maxwell magnetic stress tensor on the surfaces of particles and kinetic study, a high-speed camera was used to obtain the motion behaviors of magnetic particles in comparison with the simulation. According to the results of multiple simulation-experiment comparisons, the motion behaviors of magnetic particles in the finite element simulation were consistent with experimental phenomena under the identical conditions, indicated that the accuracy of the model is reliable. In the comparison of two kinds of magnetic force calculations, the magnetic force FM based on the Gaussian formula had a similar tendency to FD based on the kinetic calculations, and since the FM was obtained by converting the surface tension of particles, it more accurately reflected the overall magnetic force and magnetic torque acting on the particles. Kinetic analysis showed that the magnetic force acting on a particle was strictly dependent on its magnetization, dynamic and non-uniform magnetization caused the magnetic particle to be subjected to magnetic force and magnetic torque in the non-uniform magnetic field, resulting in displacements and flips. In addition, compared to the particle release attitude, the influence of the distribution of magnetic substance and the particle’s release position on the displacement was particularly significant. The 3D finite element model established for dry magnetic separation can be further used for the study of dynamic, non-uniform magnetization and the force of magnetic particle or grain groups, which is of certain significance for the kinetic study of magnetic separation and improving research of magnetic separation equipment.

Magnetic Field and Force Calculation of Transverse Flux Linear Synchronous Motor With Improved Analysis Model

Magnetic Field and Force Calculation of Transverse Flux Linear Synchronous Motor With Improved Analysis Model

Magnetic Safety Equipment Development for Ship Cleaning Robot

This paper presents a comprehensive development process of magnetic adhesion modules designed for mobile robots working in shipyards, performing hull-cleaning duties. The main aim is to prepare a secure system that will allow robots to safely navigate on ferromagnetic hulls. Typical process involves sandblasting performed by human personnel, which creates highly dangerous working conditions and requires numerous safety precautions to prevent both human accidents and environmental contamination related to cleaning medium spreading. Delegating this task to robot allows the deployment of specially designed cleaning equipment, reducing accidents’ chance, medium spreading and its usage thanks to dedicated salvage system. Existing literature lacks precise information on magnetic force calculations due to the high complexity of the problem that can be accounted to magnet shape or used materials. This study could be used as a guideline for development of similar equipment. The Finite Element Method Magnetics (FEMM) software is utilized for modelling and simulating numerous solutions that align with the working conditions of the robot. To generate a high-density, low-range magnetic field, which would be highly compatible for working conditions, Halbach array was used and comparison with single magnet of equivalent size was provided. The paper also discusses material choice and geometric considerations for the chassis. Experimental measurements of physical system involved multiple magnets’ configurations. This study provides a thorough comparison of numerical predictions and an actual performance of developed magnetic adhesion modules, establishing a field-tested design that can serve as a valuable reference for future work.

Analytical Cogging Torque and Unbalanced Magnetic Force Calculations in Slotted Surface-PM Machines Assuming Finite Iron Permeability

Analytical Cogging Torque and Unbalanced Magnetic Force Calculations in Slotted Surface-PM Machines Assuming Finite Iron Permeability

Permanent magnet systems to study the interaction between magnetic nanoparticles and cells in microslide channels

We optimized designs of permanent magnet systems to study the effect of magnetic nanoparticles on cell cultures in microslide channels. This produced two designs, one of which is based on a large cylindrical magnet that applies a uniform force density of 6MN/m3 on soft magnetic iron-oxide spherical nanoparticles at a field strength of over 300mT. We achieved a force uniformity of better than 14% over the channel area, leading to a concentration variation that was below our measurement resolution. The second design was aimed at maximizing the force by using a Halbach array. We indeed increased the force by more than one order of magnitude at force density values over 400MN/m3, but at the cost of uniformity. However, the latter system can be used to trap magnetic nanoparticles efficiently and to create concentration gradients. We demonstrated both designs by analyzing the effect of magnetic forces on the cell viability of human hepatoma HepG2 cells in the presence of bare Fe2O3 and cross-linked dextran iron-oxide cluster-type particles (MicroMod). Python scripts for magnetic force calculations and particle trajectory modeling as well as source files for 3D prints have been made available so these designs can be easily adapted and optimized for other geometries.

Experimental Validation of a Mesh-to-Mesh Magnetic Force Projection for e-NVH Simulation

This article discusses the use of simulation for analyzing the vibro-acoustic behavior of radial flux electrical machines under magnetic forces. Numerical simulation enables a systematic investigation of electromagnetic Noise, Vibration and Harshness (e-NVH) issues, but requires accurate modeling and this despite manufacturing uncertainties. Experimental validation is a necessary step to setup a multiphysic virtual prototyping e-NVH workflow. In particular, a key point is the magneto-mechanical coupling. In this study, the Virtual Work Principle (VWP) is used for magnetic force calculation. The goal is to propose an accurate e-NVH model applied to a 12s10p radial flux electrical machine using a mesh-to-mesh projection. This e-NVH model enables to understand the origin of the noisiest orders along the whole speed range of the machine. Differences between simulation and experiments are discussed thanks to the modal participation factor of specific harmonics. Mesh-to-mesh projection results are compared to those obtained by using lumped tooth force, highlighting the contribution of the tooth tip moment to the vibration. Finally, the tooth modulation effect is discussed in the light of these results.

MagTetris: A simulator for fast magnetic field and force calculation for permanent magnet array designs

In this paper, a simulator named “MagTetris” is proposed for fast magnetic field (B-field) and force calculation for permanent magnet arrays (PMAs) designs consisting of cuboid and arc-shaped magnets (approximated by cuboids) with arbitrary configurations. The proposed simulator can compute the B-field of a PMA on arbitrary observation planes and the magnetic force acting on any magnet/group of magnets. An accelerated calculation method for B-fields of PMAs is developed based on the current model of permanent magnet, which is further extended to magnetic force calculation. The proposed method and the associated codes were validated with numerical simulation and experimental results. The calculation speed of “MagTetris” is at least 500 times higher than that using finite-element method (FEM)-based software with uncompromised accuracy. Compared with a freeware in Python, Magpylib, “MagTetris” has a calculation acceleration of greater than 50% using the same language. “MagTetris” has a simple data structure, which can be easily migrated to other programming languages maintaining similar performances. This proposed simulator can accelerate a PMA design and/or allow designs with high flexibility considering the B-field and force simultaneously. It can facilitate and accelerate innovations of magnet designs to advance dedicated portable MRI in terms of compactness, weight, and performance.

Applicability of magnetic force models for multi-stable energy harvesters

Multi-stable piezoelectric energy harvesters have been exploited to enhance performance for extracting ambient vibrational energy from a broadband energy source. Since magnetic force plays a significant role in enhancing the dynamic behavior of harvesters, it is necessary to model and understand the significant influencing of structural parameters on magnetic force. Recently, several theoretical modeling methods, including magnetic dipole, improved dipole, magnetic current, and magnetic charge models, have been developed to calculate the magnetic force in multi-stable energy harvesters. However, the influence of structural parameters and magnet dimensions on the accuracy of magnetic force calculation for these methods has not been analyzed. Therefore, it is necessary to investigate the applicability of these methods under a range of operating conditions. New insights into the accuracy and application constraints of these methods are presented in this paper to calculate the impact of magnetic force on multi-stable energy harvesters. From the theoretical derivation of models and numerical results obtained, a quantitative assessment of errors under different structural parameters and magnet sizes is presented and compared to evaluate the application constraints. Moreover, experimental measurements are performed to verify the applicability of these modeling methods for bi-stable and tri-stable energy harvesters with different structural parameters.

Calculation of magnetic forces and torques on the Kibble coil

Analytically the force acting on a current-carrying coil in a magnetic field can be calculated in two ways. First, a line integral can be conducted along the coil’s wire, summing up the differential force contributions. Each contribution results from a cross-product of the corresponding differential line segment with the magnetic flux density at that location. Alternatively, the coil’s energy in the field is given as a product of three factors, the number of turns, the current, and the flux threading the coil. The energy can then be obtained by executing a surface integral over the coil’s open surface using the scalar product of the differential surface element with the magnetic flux density as its integrand. The force on the coil is the negative derivative of the energy with respect to the appropriate coordinate. For yoke-based Kibble balances, the latter method is much simpler since most of the flux is contained in the inner yoke of the magnet and can be written as a simple equation. Here, we use this method to provide simple equations and their results for finding the torques and forces that act on a coil in a yoke-based magnet system. We further introduce a straightforward method that allows the calculation of the position and orientation difference between the coil and the magnet from three measurements.

Magnetic Force Calculation in Reluctance Force Launcher

To study the clamping device in reluctance force launcher, the Maxwell stress tensor method is extended to contact force calculations. It is generally believed that the Maxwell stress tensor method is only suitable for objects surrounded by air or vacuum. However, in this article, the Maxwell stress tensor applicable to ferromagnetic materials is re-derived, and the classical Maxwell stress tensor is successfully reproduced. Its integral region is determined as the outer surface of the interface between the object and the outside world, which means that the Maxwell stress tensor method can be used for contact force calculations. Subsequently, the Maxwell stress tensor method was used for force studies in the clamping device. The needed clamping force of the clamping device is calculated. The reducing effect of ferromagnetic materials on the clamping force and the effect on the acceleration force of the projectile are analyzed. Finally, based on the determined integral region, the reason why the integral result of Maxwell stress tensor method is related to the integral path is successfully explained, which provides another theoretical basis for the contact force calculation method in this article.

Calculation of magnetic force and torque between two arbitrarily oriented circular filaments using Kalantarov–Zeitlin’s method

In this article, formulas for calculation of magnetic force and torque between two circular filaments arbitrarily oriented in space were derived by using Kalantarov–Zeitlin’s method. Formulas are presented in an analytical form through integral expressions, whose kernel function is expressed in terms of the elliptic integrals of the first and second kinds, and provide an alternative formulation to Babič’s expressions. The derived new formulas were validated via comparison with a series of reference examples. Also, we obtained additional expressions for calculation of force and torque between two circular filaments by means of differentiation of Grover’s formula for the mutual inductance between two circular filaments with respect to appropriate coordinates. These additional expressions allow to verifying comprehensively and independently derived new formulas.

The magnetic field force calculation in magnetic systems with stationary current

Three different approaches to calculating the forces acting on ferromagnets in a stationary magnetic field are considered. The results of calculating of the magnetic field forces by these methods on a test model are compared with the measurement data obtained using an experimental unit. Keywords: numerical simulation, magnetostatics, calculation of magnetic force, Maxwell tensor.

MagTetris: A Simulator for Fast Magnetic Field and Force Calculation for Permanent Magnet Array Designs

MagTetris: A Simulator for Fast Magnetic Field and Force Calculation for Permanent Magnet Array Designs

Vector Potential, Magnetic Field, Mutual Inductance, Magnetic Force, Torque and Stiffness Calculation between Current-Carrying Arc Segments with Inclined Axes in Air

In this paper, the improved and the new analytical and semi-analytical expressions for calculating the magnetic vector potential, magnetic field, magnetic force, mutual inductance, torque, and stiffness between two inclined current-carrying arc segments in air are given. The expressions are obtained either in the analytical form over the incomplete elliptic integrals of the first and the second kind or by the single numerical integration of some elliptical integrals of the first and the second kind. The validity of the presented formulas is proved from the particular cases when the inclined circular loops are addressed. We mention that all formulas are obtained by the integral approach, except the stiffness, which is found by the derivative of the magnetic force. The novelty of this paper is the treatment of the inclined circular carting-current arc segments for which the calculations of the previously mentioned electromagnetic quantities are given.

Magnetic Force Calculation of Movable YBCO Superconducting Helical Coils Applicable to Electric Vehicles Wireless Power Transfer

Background and Objectives: Today, replacing gasoline-powered vehicles with electric vehicles (EVs) and connecting them to an electric power source have made the optimal usage of energy-saving resources. Therefore, wireless Power Transfer (WPT) outstands as an alternative technology to improve the user perception about the charging process of the EVs. Superconducting coils (SCs) with high-temperature have an applied feature in decreasing losses of wireless power transmission (WPT). The Magnetic force has effects of overall deformation modes between two current carrier superconducting coils, i.e. axial extension, torsion, and bending. Coil misalignment is a fundamental problem and its impact on wireless power transmission efficiency is very complex. The analysis of a magnetic force which is presented in this paper are beneficially for the design and application of the WPT systems. Here, a fast analytical solution is presented to obtain the magnetic force between the transmitter and receiver helical superconducting coils in different positions.Methods: In this paper, a new method applied to solve the numerically magnetic force solutions in different superconducting coils mismatch states for WPT. Finally, for improvement of efficiency, the WPT system has been designed on the basis of mutual inductance changes which receiving helical coil was moved inside the transmitting helical coil. Hence, the magnetic force calculation of movable YBCO superconducting helical coils inside each other is presented. These models have been compared with the FEM.Results: Results show that the presented equations are reliable as well. According to the comparing the analysis and FEM data, the obtained results indicated the errors with less than 0.0064%. Also, results show an excellent agreement with respect to the finite element method.Conclusion: In this paper, the numerical solutions of magnetic force in different superconducting coils mismatch states were solved by a new method. The magnetic force analysis basics introduced in this paper are useful to develop and apply for wireless power transmission system. The simulation results show that only by applying some constraints, the efficiency of the transmitted wireless power will be optimized. Then, analytical models have been presented which make it possible to calculate the axial force which was exerted between two axially Helical magnetized and two thin coils in air. Also, the analytical stiffness calculation applied between these distributions of magnetic source has been presented. These models have been compared with the FEM to show an appropriate consistency.

Torque Analysis for Rotational Devices with Nonmagnetic Rotor Driven by Magnetic Fluid Filled in Air Gap

In magnetomechanical applications, it is necessary to calculate the magnetic force or torque of specific objects. If the magnetic fluid is involved, the force and torque also include the effect of pressure caused by the fluid. The standard method is to solve the Navier–Stokes equation. However, obtaining magnetic body force density is still under controversy. To resolve this problem, this paper shows that the calculation of the torque of these applications should not only use the magnetic force calculation method, but also consider the mechanical pressure using an indirect approach, such as the virtual work principle. To illustrate this, we use an experimental motor made of a nonmagnetic rotor immersed in a magnetic fluid. Then, we show that the virtual work principle in appropriate approach can calculate the output torque of the nonmagnetic rotor due to pressure of the magnetic fluid. Numerical analysis and experimental results show the validity of this approach. In addition, we also explain how the magnetic fluid transmits its magnetic force to the stator and rotor, respectively.

Simulation of Magnetic Force between Two Coaxial Coils with Air Core and Uniform Flow in MATLAB

Magnetic field is one of the most used sciences in today's industry, which is applied in many cases such as electromagnets, electric motors, and generators, electric transformers, electromagnetic wave propagation in antennas, magnetic levitation, etc. that has led to many types of research in this field. Therefore, correct calculation of magnetic force is one of effective and important discussions in this field. One of the subsets of the force calculation is between two coils. The purpose of this research is to implement and simulate two cylindrical coaxial coils with uniform current. We calculate the axial magnetic force of the cylindrical coil by simulating and implementing two coils and applying numerical integration methods, parametric integration, and finite element method in MATLAB software. The results show that the implemented codes are able to calculate the force between two coils quickly, with small error, and with high accuracy. These results will help to implement a proper system with real term and very high accuracy by choosing the best method that fits your system's constraints, conditions, and type.

2-D and 3-D Analytical Calculation of the Magnetic Field and Levitation Force Between Two Halbach Permanent Magnet Arrays

As we know, the analytical calculation of magnetic field and magnetic force has important guiding significance for the optimal design of the size and structure of a magnet. At present, the magnetic field and magnetic force between two permanent magnet (PM) monomers have been described by effective analytical models. However, the magnetic field strength and magnetic force generated by two PM monomers are limited and cannot meet the requirements of a PM levitation system with high magnetic field strength and large levitation force. To this end, this article establishes analytical calculation models of magnetic field and levitation force between two Halbach PM arrays. First, on the basis of Ampere molecular circulation hypothesis, the 2-D analytical model of magnetic field was established based on the surface current method; on the basis of magnetic charge theory, the 3-D analytical model of magnetic field was established based on the magnetic charge method. Second, based on the analytical models of magnetic field, the 2-D and 3-D analytic models of levitation force were derived by virtual work method, respectively. Numerically, the results of two analytical models of magnetic field and two analytical models of levitation force have been compared to verify the accuracy of the models. At the same time, the 2-D and 3-D finite element simulation models of magnetic field and levitation force were established, respectively, and the accuracy of the analytical models were verified again. The results show that the analytical models established in this article is effective and can be used to guide the design and optimization of the magnet composed of two Halbach arrays.

Enhanced modeling of nonlinear restoring force in multi-stable energy harvesters

It is acknowledged that traditional linear piezoelectric cantilever energy harvesters are not effective to extract ambient energy due to the narrow resonant bandwidth and low efficiency. A popular strategy to overcome these disadvantages is applying external magnets to realize multi-stable energy harvesters. Under the external excitation, the inter-well motion occurs between different potential wells in multi-stable energy harvesters, so as to bring out larger displacement and higher voltage output than intra-well motion. The performance of multi-stable energy harvesters has a strong relationship with the nonlinear restoring force, but there is lack of models for accurately describing nonlinear restoring force. This paper proposes a new enhanced model of the nonlinear restoring force to improve the calculating accuracy by taking the influence of rotational angle and axial displacement into consideration. The rotational magnetic charge is presented to calculate the magnetic force exerted by the external magnets. Then, the trajectory method of cantilever beams is employed to reduce the calculation error caused by axial displacement during oscillation. The accuracy of the proposed model for magnetic force calculation along horizontal and vertical directions is verified by the results of numerical simulation. Additionally, experimental results of the nonlinear restoring force for multi-stable energy harvesters show a good agreement with theoretical results. The influence of system parameters on equilibrium points, nonlinear restoring force and dynamic responses of multi-stable energy harvesters has been investigated based on the proposed model.

Analysis of the component forces of the nonlinear magnetic force in energy harvester

In the piezoelectric vibration energy harvester, permanent magnets are often used to generate nonlinear applied magnetics force to improve the energy utilization rate of the system, the modeling analysis and accurate calculation of the force between magnets in the system is a difficult problem in the study of nonlinear bistable vibration energy harvesting. During the deformation of the cantilever beam, the direct force of the permanent magnet block can be divided into horizontal and vertical component forces. In most existing literatures analyzing such problems, the magnetizing current method magnetic force calculation model of double-stabilized electric beam mainly considers the influence of vertical magnetic force on the system of cantilever beam, and it is considered that the horizontal component of magnetic force has little influence on the vibration response of cantilever beam, but there is no detailed proof and elaboration of this problem. In this paper, the magnetic force, the effect of magnetic force on natural frequency and magnetic potential energy are calculated and simulated from three aspects. Through the comparison of results, it is proved that the effect of the horizontal magnetic force on the whole nonlinear piezoelectric beam vibration energy harvester can be ignored.