Blj Bart Gysen

General Formulation of the Electromagnetic Field Distribution in Machines and Devices Using Fourier Analysis

We present a general mesh-free description of the magnetic field distribution in various electromagnetic machines, actuators, and devices. Our method is based on transfer relations and Fourier theory, which gives the magnetic field solution for a wide class of two-dimensional (2-D) boundary value problems. This technique can be applied to rotary, linear, and tubular permanent-magnet actuators, either with a slotless or slotted armature. In addition to permanent-magnet machines, this technique can be applied to any 2-D geometry with the restriction that the geometry should consist of rectangular regions. The method obtains the electromagnetic field distribution by solving the Laplace and Poisson equations for every region, together with a set of boundary conditions. Here, we compare the method with finite-element analyses for various examples and show its applicability to a wide class of geometries.

Analytical Hybrid Model for Flux Switching Permanent Magnet Machines

With the emergence of energy related issues in the automotive sector, there is a tendency to find new efficient solutions to replace existing electrical machinery. One promising candidate is the flux switching permanent magnet machine (FSPMM). Due to its challenging structure and nonlinear characteristic, in the investigation of the machine, generally finite element method (FEM), and rarely the magnetic equivalent circuit (MEC), are implemented. The following paper introduces an alternative analytical modeling technique by means of a hybrid model, which combines the advantages of the MEC and the Fourier analysis.

Modeling of Flux Switching Permanent Magnet Machines With Fourier Analysis

For applications demanding a high torque density and high speed capability, the flux switching permanent magnet machine is an excellent candidate. However, the double salient structure and nonlinear behavior increases the challenge to model the magnetic field distribution and torque output. To date, only the magnetic equivalent circuit (MEC) is employed to model the magnetic field in an analytical manner. However, the MEC method suffers from a coarse discretization and the need for a relative complex adjustment when rotor movement or a parametric sweep is considered. Therefore this paper discusses an alternative technique based on the harmonic or Fourier model which solves these difficulties.

Design Aspects of an Active Electromagnetic Suspension System for Automotive Applications

This paper is concerned with the design aspects of an active electromagnet suspension system for automotive applications which combines a brushless tubular permanent-magnet actuator with a passive spring. This system provides for additional stability and safety by performing active roll and pitch control during cornering and braking. Furthermore, elimination of the road irregularities is possible, hence, passenger drive comfort is increased. Based upon measurements, static and dynamic specifications of the actuator are derived. The electromagnetic suspension is installed on a quarter-car test setup, and the improved performance using roll control is measured and compared with a commercial passive system. An alternative design using a slotless external-magnet tubular actuator is proposed which fulfills the thermal and volume specifications.

Halbach Permanent Magnet Shape Selection for Slotless Tubular Actuators

This paper describes the effects of changing the magnet shape of permanent magnets (PMs) in a Halbach array applied in a slotless tubular actuator. More specifically, the square shaped magnets are replaced by trapezoidal shaped magnets. A semi-analytical magnetic field solution of regular square shaped magnets is presented and used to approximate the airgap field produced by the trapezoidal shaped PMs. The method is based on dividing the magnets into several radial layers and superposition of the fields to calculate the total magnetic field. The results are compared to finite element analysis (FEA) and show excellent agreement. Using this magnetic field solution, the effect of the shape of the magnets on the magnetic field waveform is analyzed by means of a parametric search.

Analytical and Numerical Techniques for Solving Laplace and Poisson Equations in a Tubular Permanent-Magnet Actuator: Part I. Semi-Analytical Framework

We present analytical and numerical methods for determining the magnetic field distribution in a tubular permanent-magnet actuator (TPMA). In Part I, we present the semianalytical method. This method has the advantage of a relatively short computation time and it gives physical insight. We make an extension for skewed topologies, which offer the benefit of reducing the large force ripples of the TPMA. However, a lot of assumptions and simplifications with respect to the slotted structure have to be made in order to come to a relatively simple semianalytical description. To model the slotting effect and the related cogging force, we apply a Schwarz-Christoffel (SC) mapping for magnetic field and force calculations in Part II of the paper. Validation of the models is done with finite-element analysis.

Active electromagnetic suspension system for improved vehicle dynamics

This paper offers motivations for an electromagnetic active suspension system that provides both additional stability and maneuverability by performing active roll and pitch control during cornering and braking, as well as eliminating road irregularities, hence increasing both vehicle and passenger safety and drive comfort. Various technologies are compared with the proposed electromagnetic suspension system that uses a tubular permanent-magnet actuator (TPMA) with a passive spring. Based on on-road measurements and results from the literature, several specifications for the design of an electromagnetic suspension system are derived. The measured on-road movement of the passive suspension system is reproduced by electromagnetic actuation on a quarter car setup, proving the dynamic capabilities of an electromagnetic suspension system.

Analytical and Numerical Techniques for Solving Laplace and Poisson Equations in a Tubular Permanent Magnet Actuator: Part II. Schwarz–Christoffel Mapping

In Part I of the paper, we derive a semianalytical framework for the magnetic field calculation in the air gap of a tubular permanent-magnet (PM) actuator. We also make an extension for skewed topologies. However, the slotting effect and its related cogging force cannot be determined in a straightforward way. Therefore, in Part II, we apply the Schwarz-Christoffel (SC) conformal mapping method to one pole-pair of the tubular PM actuator. This mapping allows for field calculation in a domain where standard field solutions can be used. In this way, slotting effects can be taken into account; however, skewing cannot be implemented directly. The SC-conformal mapping method is valid only for two-dimensional Cartesian domains. We therefore apply a special transformation from the cylindrical to the Cartesian coordinate system to describe the tubular actuator as a linear actuator.

3-D Analytical and Numerical Modeling of Tubular Actuators With Skewed Permanent Magnets

This paper considers analytical and numerical techniques to model the magnetic field distribution in a tubular actuator with skewed permanent magnets (PMs). A fast 3-D analytical model based on Fourier analysis is developed for calculation of the various field components resulting from the skewed PMs for various skewing topologies. This techniques provides means for validating the assumptions of 2.5-D multilayer methods. Furthermore, a 2.5-D analytical multilayer model is derived for calculation of the cogging force due to the slot openings including skewed PMs. The analytical methods are validated by means of 3-D finite element analysis.

Three-Dimensional Magnetic Field Modeling of a Cylindrical Halbach Array

A semi-analytical description of the 3-D magnetic field distribution of a cylindrical quasi-Halbach permanent magnet array is derived. This model avoids the necessity of time-consuming finite element analyses and allows for fast parameterization to investigate the influence of the number of segments on the magnetic flux density distribution. The segmented magnet is used to approximate an ideal radial magnetized ring in a cylindrical quasi-Halbach array. The model is obtained by solving the Maxwell equations using the magnetic scalar potential and describes the magnetic fields by a Fourier series.