Bert Hannon

2-D Analytical Subdomain Model of a Slotted PMSM With Shielding Cylinder

Due to their high efficiency and power density, permanent magnet synchronous machines (PMSMs) operating at high speed have recently gained a lot of attention. The development of high-speed PMSMs requires a good understanding of the physics related to the operation of such machines. Moreover, accurate modeling tools are needed when designing high-speed electrical machines. In this paper, the subdomain modeling technique is used to analytically compute the magnetic field of an electrical machine. The idea behind this technique is to divide the machine in a number of subdomains, in which the problem is simplified. The solutions in the different subdomains are then linked by imposing physical boundary conditions. The described model immediately considers the slotting effect and the eddy-current reaction field of a shielding cylinder (SC). The SC is a conductive sleeve, which is wrapped around the magnets. Its goal is to reduce the rotor losses at high-speed operation. This paper starts by introducing the applied modeling technique and the studied machine. Second, the basics of the model and its development are discussed. Finally, the results are compared with results of a finite-element (FE) model. A very good agreement between the proposed model and the FE model is observed. This implies that the developed model is indeed a powerful modeling tool for high-speed PMSMs. Moreover, it provides great insight in the machines physics as well.

Torque and torque components in high-speed permanent-magnet synchronous machines with a shielding cylinder

A demand for more efficient electrical machines with a high power density is driving the interest for high-speed permanent-magnet synchronous machines (PMSMs). However, the design of such machines is a challenging task. One of the problems is that the effect of the shielding cylinder, a conductive sleeve around the magnets, on the machines performance has not been studied extensively. To cope with that problem the authors of this work introduce an analytical method to study the torque in high-speed PMSMs. The presented method implies dividing the torque into two components, depending on how they are produced. The method is successfully validated and an illustration of its advantages is provided.

Comparison of Three Analytical Methods for the Precise Calculation of Cogging Torque and Torque Ripple in Axial Flux PM Machines

A comparison between different analytical and finite-element (FE) tools for the computation of cogging torque and torque ripple in axial flux permanent-magnet synchronous machines is made. 2D and 3D FE models are the most accurate for the computation of cogging torque and torque ripple. However, they are too time consuming to be used for optimization studies. Therefore, analytical tools are also used to obtain the cogging torque and torque ripple. In this paper, three types of analytical models are considered. They are all based on dividing the machine into many slices in the radial direction. One model computes the lateral force based on the magnetic field distribution in the air gap area. Another model is based on conformal mapping and uses complex Schwarz Christoffel (SC) transformations. The last model is based on the subdomain technique, which divides the studied geometry into a number of separate domains. The different types of models are compared for different slot openings and permanent-magnet widths. One of the main conclusions is that the subdomain model is best suited to compute the cogging torque and torque ripple with a much higher accuracy than the SC model.

Time- and Spatial-Harmonic Content in Synchronous Electrical Machines

The use of power electronics has led to a growing importance of higher time-harmonic content in electrical machines. To gain insight in phenomena related to these higher harmonics, such as noise and losses, a good understanding of the magnetic fields harmonic content is mandatory. Moreover, the development of highly-accurate analytical models requires a qualitative knowledge of the machines harmonic content. Therefore this work aims at studying the harmonic content of synchronous electrical machines. To do so the three aspects that determine the harmonic content of the machines magnetic field are discussed: the excitation source, the stator-current density and the geometry. Based on that discussion, general expressions for the time- and spatial-harmonic combinations are formulated. These expressions are proven to be valid for a very broad range of synchronous machines.

Study of the Effect of a Shielding Cylinder on the Torque in a Permanent-Magnet Synchronous Machine Considering Two Torque-Producing Mechanisms

Despite an ever-growing interest, a lot of questions related to the design and operation of high-speed permanent-magnet synchronous machines remain unanswered. One aspect of such high-speed machines that requires special attention is the effect of the shielding cylinder (SC), a conductive sleeve that is wrapped around the magnets and which’ goal is to reduce the rotor losses and/or retain the magnets. Therefore, this paper aims at theoretically studying the effect of the SC on the torque production. The study is performed using a 2-D analytical subdomain model that accounts for slotting and the eddy-current reaction field. The torque is divided in two components, the classical torque due to interaction between the magnets and the stator currents and the torque due to interaction with the eddy currents in the SC. This approach is unique and results in a better insight in the machine’s physics.

Voltage Sources in 2D Fourier-Based Analytical Models of Electric Machines

The importance of extensive optimizations during the design of electric machines entails a need for fast and accurate simulation tools. For that reason, Fourier-based analytical models have gained a lot of popularity. The problem, however, is that these models typically require a current density as input. This is in contrast with the fact that the great majority of modern drive trains are powered with the help of a pulse-width modulated voltage-source inverter. To overcome that mismatch, this paper presents a coupling of classical Fourier-based models with the equation for the terminal voltage of an electric machine, a technique that is well known in finite-element modeling but has not yet been translated to Fourier-based analytical models. Both a very general discussion of the technique and a specific example are discussed. The presented work is validated with the help of a finite-element model. A very good accuracy is obtained.

2D analytical torque study of slotted high-speed PMSMs considering pole pairs, slots per pole per phase and coil throw

Recently the interest in permanent-magnet synchronous machines (PMSMs) operating at high speed has grown. However, a lot of design and operation questions remain unanswered. This work aims at studying the effect of the number of pole pairs, the number of slots per pole per phase and the coil throw on the torque and the torque ripple in high-speed PMSMs. High-speed machines are often equipped with a shielding cylinder, i.e. a conductive sleeve wrapped around the magnets. The study is therefore performed using a 2D analytical subdomain model that accounts for slotting and the eddy-current reaction field. The classical torque component and the torque due to interaction with the eddy-currents in the shielding cylinder are regarded separately.

Effect of control strategies on the two torque-producing mechanisms in high-speed PMSMs

The interest for high-speed Permanent-Magnet Synchronous Machines (PMSMs) is high. Often such machines are equipped with a conductive sleeve that is wrapped around the magnets, i.e. the Shielding Cylinder (SC). Its goal is to reduce the overall rotor losses, thereby protecting the magnets from overheating. In such machines torque is produced in two ways [1]; due to interaction between the magnets and the stator currents and due to interaction between the SC and asynchronous components in the magnetic field. The resulting torque components are indicated as TPM and TSC.