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The purpose of this paper is to minimize the torque pulsation in Halbach array permanent magnet synchronous machines (PMSMs).

Because of its specific structure, the cogging torque influences the main part of the torque pulsation in a Halbach array PMSM. In this paper, first it is shown that the conventional magnet skewing method does not have a significant effect on the torque pulsation in this motor, and then an improved skewing method with fewer skewing steps is proposed. In this method permanent magnet segments are placed sinusoidally, with two‐step skewing along the rotor. Generalization with different combinations of slots and poles is considered for a Halbach array PMSM.

Using a detailed finite element method (FEM) it was found that with the proposed technique the cogging torque factor is reduced to as low as 8 percent, while the average value of the torque is maintained near the machine nominal average torque.

Halbach array PMSMs are very good candidates for high dynamic performance applications such as aerospace applications due to their high acceleration and deceleration features. This technique also resolves the mechanical vibration and acoustic noise issues, which are caused by torque pulsation and significantly affect machine performance.

The originality of this paper lies in the FEM results. Since Halbach array PMSMs have a special structure it was shown that the conventional skewing method does not work well for this machine. The new proposed technique has a significant effect on the torque pulsation.

In the present paper the influence of the magnetization patterns of rotor magnets on the performance characteristics of a surface permanent magnet (SPM) motor has been investigated. The purpose of this paper is to show how the electromagnetic and electromechanical characteristics of this type of motor can be significantly changed by applying various magnetization patterns of permanent magnets (PM) on the rotor surface.

First, a survey of possible and most frequently used magnetization patterns for PM motors is presented. The research is focussed on the comparison of performance characteristics and is developed at three levels. The study starts with investigation of a conventional SPM motor having segmented PM, and two magnetization patterns are considered: parallel and radial. As there was no significant difference in motor performance at parallel and radial magnetization, for further investigation only radial magnetization, being more conventional, was considered. In the second step, the counterparts of SPM with two Halbach array configurations, under the constraint of fixed magnet volume, are studied. Finally, detailed comparative analyses of SPM at radial, Halbach 1, and Halbach 2 magnetic patterns are presented. The advantages and drawbacks of the suggested magnetic configurations are then discussed.

The authors have shown how the magnetization pattern of rotor PM can have a substantial impact on the SPM motor performance characteristics. From the analysis of magnetic field properties at various types of magnetization, it is observed that both the shape and the rates of the characteristics, for radial magnetization and Halbach 2 configuration, exhibit similar features. This is because the Halbach 2 array cancels the magnetic flux above the PM – that is, it strengthens the magnetic field in the rotor, and enhances the coupling between the rotor and stator magnetic field. It is worth emphasizing that, because of less saturation of the magnetic core and lower iron loss at Halbach 1 and Halbach 2 magnetization, it is possible to increase the armature current and consequently increase the electromagnetic torque. This finding could be an interesting for further research.

The paper presents an original comparative analysis of the performance characteristics of a surface permanent motor at various magnetization patterns. The novelty of the paper is seen in the introduction of two Halbach magnetization arrays for PM and improvement of the performance characteristics of the analysed motor.

The purpose of this paper is to present a double‐sided tubular linear machine layout direct‐drive applications, with particular focus on wave‐energy conversion. The paper documents both the computational and mathematical analysis of this novel machine layout.

The selection and finite‐element optimisation of the permanent‐magnet array is presented. The machine is then modelled using magnetic circuit theory. By simultaneously solving the system of equations, a demonstrative design is developed and simulated so as to validate the mathematical model and compare the performance of the new layout with a traditional layout.

A surface‐mounted magnetic array, with unshaped‐poles, is most suitable for the proposed layout. The mathematical model exhibits a suitable level of accuracy for design and analysis purposes. The calculated resultant force differs from the FEA calculation by 1.85 per cent. A higher force‐density is exhibited by the proposed layout, when compared with flat layouts, with a reduction of 36.5 per cent in the spatial footprint and magnetic material of the machine.

Although the research is focused on the application of wave‐energy conversion, the techniques are application‐independent. However, certain design decisions should be reviewed for other applications.

The practical implementation of such a machine poses many mechanical obstacles. These have been solved in theory, and are being implemented at the time of writing.

The combination of a double‐sided and a tubular layout has not previously been researched. This research fills that void and provides designers with the technical background and a mathematical model for development of such devices.

The purpose of this paper is to investigate Halbach array effects in surface mounted permanent magnet machine (SMPM) in terms of both self-sensing and torque capabilities. A comparison between a conventional SMPM, which has radially magnetized rotor, and a Halbach machine has been carried out.

The geometric parameters of the two machines have been optimized using genetic algorithm (GA) with looking Pareto. The performance of the machines’ geometry has been calculated by finite element analysis (FEA) software, and two parametric machine models have been realized in Matlab coupled with the FEA and GA toolboxes. Outer volume of the machine, thus copper loss per volume has been kept constant. The Pareto front approach, which simultaneously considers looks two aims, has been used to provide the trade-off between the torque and sensorless performances.

The two machines’ results have been compared separately for each loading condition. According to the results, the superiority of the Halbach machine has been shown in terms of sensorless capability compromising torque performance. Additionally, this paper shows that the self-sensing properties of a SMPM machine should be considered at the design stage of the machine.

A Halbach machine design optimization has been presented using Pareto optimal set which provides a trade-off comparison between two aims without using weightings. These are sensorless performance and torque capability. There is no such a work about sensorless capability of the Halbach type SMPM in the literature.

The waste recycling industry increasingly relies on magnetic density separators. These devices generate an upward magnetic force in ferro-fluids allowing to separate the immersed particles according to their mass density. Recently, a new separator design has been proposed that significantly reduces the required amount of permanent magnet material. The purpose of this paper is to alleviate the undesired end-effects in this design by altering the shape of the ferromagnetic covers of the individual poles.

The paper represents the shape of the ferromagnetic pole covers with B-splines and defines a cost functional that measures the non-uniformity of the magnetic field in an area above the poles. The authors apply an iso-geometric shape optimization procedure, which allows us to accurately represent, analyze and optimize the geometry using only a few design variables. The design problem is regularized by imposing constraints that enforce the convexity of the pole cover shapes and is solved by a non-linear optimization procedure. The paper validates the implementation of the algorithm using a simplified variant of the design problem with a known analytical solution. The algorithm is subsequently applied to the problem posed.

The shape optimization attains its target and yields pole cover shapes that give rise to a magnetic field that is uniform over a larger domain.

This increased magnetic field uniformity is obtained at the cost of a pole cover shape that differs per pole. This limitation has negligible impact on the manufacturing of the separator. The new pole cover shapes therefore lead to improved performance of the density separation.

Due to the larger uniformity the generated field, these shapes should enable larger amounts of waste to be processed than the previous design.

This paper treats the shapes optimization of magnetic density separators systematically and presents new shapes for the ferromagnetic poles covers.

This study aims to accurately calculate the magnetic field distribution, which is a prerequisite for pre-design and optimization of electromagnetic performance. Accurate calculation of magnetic field distribution is a prerequisite for pre-design and optimization.

This paper proposes an analytical model of permanent magnet machines with segmented Halbach array (SHA-PMMs) to predict the magnetic field distribution and electromagnetic performance. The field problem is divided into four subdomains, i.e. permanent magnet, air-gap, stator slot and slot opening. The Poisson’s equation or Laplace’s equation of magnetic vector potential for each subdomain is solved. The field’s solution is obtained by applying the boundary conditions. The electromagnetic performances, such as magnetic flux density, unbalanced magnetic force, cogging torque and electromagnetic torque, are analytically predicted. Then, the influence of design parameters on the torque is explored by using the analytical model.

The finite element analysis and prototype experiments verify the analytical model’s accuracy. Adjusting the design parameters, e.g. segments per pole and air-gap length, can effectively increase the electromagnetic torque and simultaneously reduce the torque ripple.

The main contribution of this paper is to develop an accurate magnetic field analytical model of the SHA-PMMs. It can precisely describe complex topology, e.g. arbitrary segmented Halbach array and semi-closed slots, etc., and can quickly predict the magnetic field distribution and electromagnetic performance simultaneously.

The purpose of the paper is to study the stability control of permanent magnet (PM) and electromagnetic hybrid Halbach array electrodynamic suspension (EDS) system because of the poor suspension stability caused by the well-known under-damped nature of PM EDS system. The adjustment control is realized by PM and electromagnetic hybrid Halbach array, which is composed by winding active normal conductor coils on PM surface.

The three-dimensional (3-D) electromagnetic force analytical expression of PM and electromagnetic hybrid Halbach array EDS system for a nonmagnetic conductive plate is derived. And the accuracy of the derived equations is verified by a 3-D finite-element model (FEM). Basing on the 3-D levitation force expression, an acceleration feedback suspension controller is designed to suppress the vibration of PM EDS system, and the suspension stability of the system under the track and load disturbance was simulated and analyzed.

The 3-D electromagnetic force comparison of analytical model and FEM are in good agreement, which verifies the correctness of the analytical expression. The simulation results show that the acceleration feedback suspension controller can make the system have good suspension stability under the external disturbance. So it proved that the PM and electromagnetic hybrid Halbach array EDS system can overcome the poor suspension stability caused by the under-damped nature of PM EDS system through the designed acceleration feedback suspension controller.

This paper designed an acceleration feedback suspension controller to suppress the vibration of PM and electromagnetic hybrid Halbach array EDS system under external disturbance, basing on the derived levitation force analytical expression. And the simulation results show that the acceleration feedback suspension controller can make the system have good suspension stability under the external disturbance.

The purpose of this paper is to simulate a pseudo direct drive (PDD) by using permanent magnet arrays.

A 2D finite element model of the PDD was built. The static magnetic torque on air-gaps was obtained by Coulomb’s virtual work method using Ansys Maxwell software. To simulate the relative movement between input rotor and output rotor, two movement bands were applied.

The PDD’s torque relation was proved. The PDD simulated presents low cogging torque.

The manufacturing steps and materials applied in a construction of a coaxial magnetic gear, PDD’s main component, are presented.

The value of this paper is to present the numerical techniques applied to simulate a PDD and the manufacturing steps and materials applied in a construction of a coaxial magnetic gear.

Force output is extremely important for electromagnetic linear machines. The purpose of this study is to explore new permanent magnet (PM) array and winding patterns to increase the magnetic flux density and thus to improve the force output of electromagnetic tubular linear machines.

Based on investigations on various PM patterns, a novel dual Halbach PM array is proposed in this paper to increase the radial component of flux density in three-dimensional machine space, which in turn can increase the force output of tubular linear machine significantly. The force outputs and force ripples for different winding patterns are formulated and analyzed, to select optimized structure parameters.

The proposed dual Halbach array can increase the radial component of flux density and force output of tubular linear machines effectively. It also helps to decrease the axial component of flux density and thus to reduce the deformation and vibration of machines. By using analytical force models, the influence of winding patterns and structure parameters on the machine force output and force ripples can be analyzed. As a result, one set of optimized structure parameters are selected for the design of electromagnetic tubular linear machines.

The proposed dual Halbach array and winding patterns are effective ways to improve the linear machine performance. It can also be implemented into rotary machines. The analyzing and design methods could be extended into the development of other electromagnetic machines.

Semi-active suspension systems with electromagnetic dampers allow energy regeneration and the required control strategies are easier to implement than the active suspensions are. This paper aims to address the application of a tubular linear permanent magnet synchronous machine for a semi-active suspension system.

Classical rules of mechanics and electromagnetics were applied to describe a dynamic model combining vibration and electrical machines theories. A multifaceted MATLAB®/Simulink model was implemented to incorporate equations and simulate global performance. Experimental tests on an actual prototype were carried out to investigate displacement transmissibility of the passive case. In addition, simulation results were shown for the dissipative semi-active case.

The application of the developed model suggests convergent results. For the passive case, numerical and experimental outcomes validate the parameters and confirm system function and proposed methodology. MATLAB®/Simulink results for the semi-active case are consistent, showing an improvement on the displacement transmissibility. These agree with the initial conceptual thoughts.

The use of linear electromagnetic devices in suspension systems is not a novel idea. However, most published papers on this subject outline active solutions, neglect semi-active ones and focus on experimental studies. However, here a dynamic mechanical-electromagnetic coupled model for a semi-active suspension system is reported. This is in conjunction with a linear electromagnetic damper.