Kj Koen Meessen

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.

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.

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.

Force Calculations in 3-D Cylindrical Structures Using Fourier Analysis and the Maxwell Stress Tensor

Analytical modeling is still a very effective manner to calculate the magnetic fields in permanent magnet devices. From these magnetic fields, device quantities, e.g., force, emf, or inductance, can be calculated. This paper presents a semianalytical technique, based on a 2-D Fourier series to represent the magnetic field, to describe the force components due to permanent magnets in 3-D cylindrical structures. The Maxwell stress tensor method is selected to calculate these force components in the cylindrical coordinate system. The method is analytically evaluated by inserting the analytical expressions describing the magnetic fields. The obtained force equations avoid the use of numerical integration of the magnetic fields resulting in a fast and accurate force calculation method. An example of a 3-D cylindrical structure is modeled and validated by means of a magnetostatic finite element analysis (FEA), and excellent agreement is found.

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.

Modeling and Experimental Verification of a Tubular Actuator for 20-g Acceleration in a Pick-and-Place Application

This paper presents the modeling and the experimental verification of a tubular actuator for a pick-and-place application. To increase the throughput of a placement robot for printed circuit boards, a very fast linear motion is required. A moving-magnet tubular actuator with axially magnetized magnets is selected. Using a semianalytical magnetic field model coupled to a thermal one, a design is created that achieves a translator acceleration of 20 g. A prototype of the designed actuator is built and coupled with a Simulink dSpace system to perform extensive measurements in order to validate the models and investigate the achievable acceleration within a predetermined motion profile. The electromotive force is measured, and the disturbance forces are identified. The position error is measured during the motion profile with an acceleration of 20 g and a stroke of 30 mm. Furthermore, thermal measurements are performed to check the achievable duty cycle. The built design shows good agreement with the models, and the specified acceleration of 20 g is achieved.

General Formulation of Fringing Fields in 3-D Cylindrical Structures Using Fourier Analysis

Soft and hard-magnetic material improvements give rise to ever more complex electromagnetic devices that require fast and accurate modeling in the three-dimensional domain. This paper is the first to present a semianalytical 3-D modeling technique based on Fourier analysis that is able to calculate the fringing fields in 3-D slotted cylindrical structures assuming linear material properties. The magnetic field distribution is obtained by subdividing such structures into concentric regions and by selecting the appropriate boundary conditions. The complete model is introduced and a generic magnetic field formulation in the cylindrical coordinate system is obtained. Furthermore, the boundary conditions are extensively discussed and the numerical implementation is presented. The method is described in a general manner to enable modeling of a wide range of electromagnetic devices. By means of an example, the modeling technique is validated with a finite element analysis.

Analysis of 3-D Effects in Segmented Cylindrical Quasi-Halbach Magnet Arrays

To improve the performance of permanent magnet (PM) machines, quasi-Halbach PM arrays are used to increase the magnetic loading in these machines. In tubular PM actuators, these arrays are often approximated using segmented magnets resulting in a 3-D magnetic field effect. This paper describes the results of this segmentation obtained from an analytical model. The influence of the number of segments on the magnetic flux density in the air gap is investigated for several actuator dimensions. Furthermore, the effect of this segmentation on the mean value of the radial component of the flux density over the circumference of the cylindrical air gap is analyzed and a 2-D definition of this effect is given. A general rule is presented as a table showing the decrease of the magnetic field as function of the design parameters.

Influence of Multiple Air Gaps on the Performance of Electrical Machines With (Semi) Halbach Magnetization

The ever increasing necessity to improve torque density while simultaneously maintaining high efficiency is a constant point of concern for electrical machine designers. This is mainly driven by the need for direct-drive solutions in evermore applications. This paper presents a general mesh-free description of the magnetic field distribution in multiple air-gap electromagnetic machines, although the tool is also useful for single air-gap machines, actuators, and other magnetic devices. The used method is based on transfer relations and Fourier theory, which can provide the magnetic field solution for a wide class of 2-D boundary value problems. This technique is in this paper applied to the rotary multiple air-gap machine with slotless (without slots but with and without rotor back-iron) armature. The presented analysis is compared to finite-element analysis for the multiple-layer winding, which shows the applicability of this method for future optimization. It is shown that multiple air-gap machines make better use of the volume and for short axial lengths where a single-side bearing configuration can be utilized provides a means to improve the achievable torque density.