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This paper presents an analysis of a permanent magnet synchronous machine (PMSM) with an unequal teeth width. The use of the concentrated nonoverlapping winding, also known as tooth-coil winding, has certain advantages. In addition, asymmetric features can be exploited by adopting this winding configuration to improve the machine performance. The procedure involves increasing the stator tooth width and, to the same extent, reducing the adjacent stator tooth width. In this paper, an analytical method was employed to predict and understand the back-EMF behavior, and a finite element analysis (FEA) was performed to verify the analytical method. Furthermore, a detailed study of the machine performance (electromagnetic torque, flux density, and losses) was carried out by the FEA. The machine was built and tested to validate the performance of the machine.

This paper addresses a new technique based on machine learning which reduces the number of evaluations required to perform robustness analysis of permanent magnet synchronous machines. This methodology is based on the logical behavior of possible faulty magnet combinations produced by manufacturing tolerances. Groups of faulty combinations with a similar structure and cogging output are identified by means of a fuzzy-logic algorithm. Subsequently, only a single faulty combination of each group needs to be evaluated through the finite element method, which severely decreases the computational burden of the tolerance analysis. A 6-slot 4-pole and a 9-slot 6-pole machine were subject to tolerance analysis considering the displacement of the magnets. Both machines were evaluated through the proposed method and the results were validated by means of the finite element method (FEM).

This work aims to identify and analyze the impact of static and dynamic eccentric tolerances on relevant performance measures of permanent-magnet synchronous-machines with modular stator core (MPMSMs). A 24-slot 28-pole machine with U-shape stator modules is evaluated by means of the finite element method. Also, a non-modular 24-slot 28-pole machine is assessed to compare the sensitiveness of modular vs non-modular PMSMs. Electromagnetic torque, cogging torque, back-emf, and the radial forces acting on the rotor were analyzed. It was found that most of the evaluated performance indices are not influenced by eccentric tolerances. However, a few relevant variables are severely affected, which could potentially endanger the mechanical integrity of the machine.

This paper presents a comparison of optimized tooth-coil-winding modular permanent-magnet synchronous machines (TCW-MPMSMs) with H-shape and U-shape stator segments for fault-tolerance applications. Four optimization objectives are studied by means of a Particle-Swarm-Optimization (PSO) based routine: maximum rated torque, minimum torque ripple, maximum efficiency, and minimum mutual inductance. Two 22-pole and 24-slot TCW-MPMSMs with H-shape and U-shape stator cores were evaluated and optimized aiming to optimize each objective. From the results, it was found that U-shape machines are suitable for high-torque and low-mutual-inductance requirements, crucial in fault-tolerant applications, whilst H-shape machines offer low ripple torque and slightly lower performance indices for fault-tolerance applications.

This paper reviews the recent developments of design optimization methods for electromagnetic devices, with a focus on machine learning methods. First, the recent advances in multi-objective, multidisciplinary, multilevel, topology, fuzzy, and robust design optimization of electromagnetic devices are overviewed. Second, a review is presented to the performance prediction and design optimization of electromagnetic devices based on the machine learning algorithms, including artificial neural network, support vector machine, extreme learning machine, random forest, and deep learning. Last, to meet modern requirements of high manufacturing/production quality and lifetime reliability, several promising topics, including the application of cloud services and digital twin, are discussed as future directions for design optimization of electromagnetic devices.

This work is about the analysis and optimization of radial flux modular stator synchronous machines. An outer rotor topology with surface-mounted permanent magnets is focused. The stator holds concentrated coils fixed to U-shaped segments made of laminated steel. An automated procedure for evaluating the characteristics of any design variant of this topology is presented. This includes a nonlinear finite element analysis conducted by taking advantage of a computer cluster and a consequently applied surrogate modeling technique for detailed performance evaluation. The approach is applied for solving an optimization problem with multiple objectives and several design parameters. The overall Pareto optimal results are illustrated. Selected Pareto-optimal designs are presented and compared in detail. Consequently, design guidelines can be derived that give valuable insights for future design tasks that were not yet presented in the past.

In mass production, interlocks are an affordable staking solution for magnetic cores of electrical machines. However, the interlock dowels introduce an increase of core losses, not only for the appearance of conductive paths in the interlock regions, but also for a non-negligible worsening of the magnetic material properties (including the hysteresis losses), both inside the interlocks and in the surrounding areas. This study aims at developing a reliable and accurate three-dimensional FEM model that takes into account the contact resistance between interlocks and laminations, as well as layered regions constituted by damaged materials. The paper includes modelling hints and the fine-tuning of the 3D FEM that includes a detailed modeling of the interlock section. Examples of flux and eddy current density distributions are provided, together with the computation of the total iron losses for a variable number of rectangular dowels in the yoke of stator core samples. The numerical results are validated by experimental measurements conducted on multiple samples having different number of interlocks.

This paper investigates the impact of tolerances related to permanent magnets on the cogging torque performance of Permanent magnet synchronous machines (PMSMs). These machines usually show a considerable sensitivity regarding tolerances for geometric dimensions and material characteristics. A consistent approach is presented in order to minimize the computational effort for evaluating the sensitivity, robustness, or reliability. Thereby, design of experiments is used to minimize the required number of finite element simulations. In this work, a Box–Behnken-based approach is considered. Subsequently, a surrogate modeling technique based on a second-order equation is applied. As a consequence, a reduction of the computational cost by 96% is achieved. The obtained results are compared with outcomes solely derived by means of finite element computations and very good agreement is observed. This is illustrated by providing the probability distribution of the cogging torque for the considered machine design. In addition, the cumulative distribution is presented, which usually is applied for analyzing the reliability. Considering the analysis of the impact of tolerances as part of optimization scenarios increases the number of designs to be analyzed by at least one degree of magnitude. The obtained results look promising for achieving this at feasible computational cost.

Iron loss modeling is crucial for electric machine design. However, current models feature severe drawbacks. They are 1) very complex, and thus, can hardly be applied, 2) require very high effort for measuring and computation, and/or 3) are not very accurate. In this paper, a new modeling technique is introduced for calculating the instantaneous power loss in ferromagnetic materials without taking the magnetization history into account. A standard measurement setup and specimen shape is used. The considered approach comprises the required measurements, the nonlinear loss modeling by itself, and an extensive verification for different flux density waveforms and frequencies. In addition, a detailed qualitative comparison to well-known iron loss models is given. The presented technique gives very accurate results, while obtaining the model is comparably easy. Moreover, as the calculation of the instantaneous losses is not based on the previous magnetization state of the material, a modeling error for a particular instant of time has no impact on the subsequently calculated characteristics. In the future, this model should ensure a more accurate iron loss calculation for electric machine designs.

This paper presents an analytical model of U-shape tooth-coil-winding modular permanent magnet synchronous machines (TCW-MPMSMs) in terms of main design parameters. Analytical expressions for the flux density distribution, back EMF, and electromagnetic torque were derived. 2-D finite element (FE) simulations for a 24-slot 28-pole machine for several tooth tip widths were compared to validate the proposed equations. Comparison of analytical solutions and FE results showed good agreement for a range of feasible slot openings. Also, a sensitivity analysis through the analytical expressions was developed. By using proposed analytical models, the performance of the modular machine can be significantly improved by selecting optimum values of key parameters including the dimensions of tooth tips and PMs.

This paper compares different surface-mounted and flux-switching PM machine structures for automotive applications. At first, both structures are designed considering as relevant the final total cost of the used materials. Axial and radial flux magnetic structures have been taken into consideration for both machines. The performance of the four machines are evaluated using 2D- and 3D-FEA. The materials costs and volumes, output torque, back-EMF are investigated in detail, and the obtained results are compared with those of axial flux PM prototype. Then, an axial-field flux-switching PM machine is built in order to experimentally investigate its performance and validate its numerical FEM analyses.

A novel winding configuration for an open-slot permanent magnet synchronous machines with modular stator (MPMSM) that improves the electromagnetic performance is proposed in this paper. Core-coil-winding (CCW) in combination with tooth tips between the stator modules are used to increase the induced voltage and electromagnetic torque. Furthermore, the proposed topology helps to reduce the eddy current losses in the permanent magnets. A 24 slot and 20 poles CCW-MPMSM is analyzed by means of finite element method and compared with a machine with the same rotor structure and continuous stator core (classical topology). The preliminary results show that the CCWMPMSM achieves similar performance compared to the classical topology when a suitable value of tooth tips width is selected.

Optimizing mechatronic components is of increasing importance, e.g. for minimizing energy consumption and the use of rare materials. MagOpt is a modular software tool for the simulation and optimization of mechatronic components. Parametric design optimization can be carried out with various different optimization strategies like gradient-based methods or multi-objective evolutionary or genetic algorithms. MagOpt features a flexible structure for the storage of complex data and an open and modular interface to existing third-party programs. One such third-party program which can be used by MagOpt for the optimization of mechanic components is the multi-body software HOTINT. This article describes MagOpt and how it was coupled with HOTINT to optimize a rotor geometry.

This paper investigates the modeling of brushless permanent-magnet synchronous machines (PMSMs). The focus is on deriving an automatable process for obtaining dynamic motor models that take nonlinear effects, such as saturation, into account. The modeling is based on finite element (FE) simulations for different current vectors in the $dq$ plane over a full electrical period. The parameters obtained are the stator flux in terms of the direct and quadrature components and the air-gap torque, both modeled as functions of the rotor angle and the current vector. The data are preprocessed according to theoretical results on potential harmonics in the targets as functions of the rotor angle. A variety of modeling strategies were explored: linear regression, support vector machines, symbolic regression using genetic programming, random forests, and artificial neural networks. The motor models were optimized for each training technique, and their accuracy was then compared based on the initially available FE data and further FE simulations for additional current vectors. Artificial neural networks and symbolic regression using genetic programming achieved the highest accuracy, particularly with additional test data.

This paper is about the impact of modeling the temperature distribution of machine designs on the results for respective optimization scenarios. In the past, a lot of machine design optimizations were presented, but just a small share considers modeling of the temperature characteristics. In order to study the impact of including a temperature model, a test scenario was investigated that features the optimization of an induction machine with regard to material cost and efficiency. The analysis of the machine designs comprises the computation of electromagnetic and thermal characteristics. As there is a mutual coupling of the results of those two analyses, an iterative approach featuring sequential updates of the electromagnetic and thermal calculations based on the results obtained for the respective other computation is considered. Typical large scale optimization scenarios require the investigation of a very huge number of machine designs. Due to this circumstance and, in addition, the need for iteratively updating the thermal and electromagnetic computations when analyzing any particular design variant, analytic techniques are preferred for these investigations. This follows a lower computation time compared to complex finite element based analyses. To compare the obtained results with typically conducted analyses featuring a constant temperature, two more test scenarios are investigated with a fixed temperature of 40°C and 120°C, respectively, for the machine components regardless its size and losses. The Pareto fronts regarding the objectives material cost and efficiency for all scenarios are presented. Moreover, a detailed investigation of further characteristic data, e.g., the temperature of the stator windings and the rotor bars, is depicted. The derived results allow for a conclusion regarding the importance of incorporating a temperature model into the machine design optimization.

This article presents a study about cost-optimal machine designs fulfilling mandatory efficiency requirements. A case study for a rated power of 3kW and speed of 1500rpm is considered and the tradeoff material costs vs. efficiency are optimized. A comparison is made for induction machines and permanent magnet synchronous machines. As in the past the price for Neodymium-Iron-Boron magnets was volatile, two different scenarios regarding the material costs of the permanent magnets are evaluated. The cost-optimal machine designs for both topologies are further analyzed regarding thermal indices, power density, and optimal ratios of geometric dimensions. The results shall provide valuable insights and serve as a guidance for both people from academia and industry involved in the process of future machine design.

In recent time, flux switching type of brushless permanent magnet machines has been receiving significant interest, especially for high-speed operation. Primary reason is the simple and robust structure of the rotor due to the fact that the permanent magnets are placed in the stator. In order to achieve best possible performance for particular applications, optimization on electric machines is increasingly considered with multiple design parameters and objectives. Such analysis is usually carried out by means of finite element simulations and thus can take considerable time. In order to speed up this process, this paper highlights recent advances for machine optimization and gives practical suggestions to reduce the time for optimization significantly. Presented measures are further discussed with regard to computational accuracy by focusing on specific aspects of flux switching permanent magnet machines. Such improvements will be useful for both people from academia and practicing engineers who design flux switching permanent magnet machines.

The experience recently gained by the authors in the field of production and testing of new magnetic materials, especially developed for small electric machines, has been applied to the production of an axial flux permanent magnet motor prototype. In particular, different materials have been used for the stator and the rotor core, together with low-cost bonded permanent magnets; the machine under investigation is equipped with fractional slot windings and foils conductors insulated by a dedicated electro-deposition process. The design and the production of all the machine parts, as well as the experimental activities, have been performed and carried out by the research team at their Universities, without outsourcing needs. The design and FEM simulation results have been validated by means of comparison with experiments, obtaining good agreements.

This paper presents a sizing procedure for the preliminary electromagnetic design of three-phase surface mounted permanent magnet machines having either inner or outer rotor structure. Starting from the requested rated data and few design specifications, the proposed approach consists on an iterative sizing procedure based on self-consistent equations. This sizing procedure is intended for those designers that, starting from scratch, have to define the main features of new machines for technical discussions and initial cost analysis for quotations. This analytical tool can also be easily integrated into sophisticated optimizers to manage the electromagnetic design and speed up the solution of high time-consuming multi-objective scenarios. To validate the proposed sizing approach, the paper reports as case studies the electromagnetic design of an inner rotor and an outer rotor surface mounted PM machine. The obtained results are validated both with an analytically-based commercial software dedicated to electrical machine analyses and with 2D FEM simulations.

We describe a hybrid and adaptive coevolutionary optimization method that can efficiently solve a wide range of multi-objective optimization problems (MOOPs) as it successfully combines positive traits from three main classes of multi-objective evolutionary algorithms (MOEAs): classical approaches that use Pareto-based selection for survival criteria, approaches that rely on differential evolution, and decomposition-based strategies. A key part of our hybrid evolutionary approach lies in the proposed fitness sharing mechanism that is able to smoothly transfer information between the coevolved subpopulations without negatively impacting the specific evolutionary process behavior that characterizes each subpopulation. The proposed MOEA also features an adaptive allocation of fitness evaluations between the coevolved populations to increase robustness and favor the evolutionary search strategy that proves more successful for solving the MOOP at hand. Apart from the new evolutionary algorithm, this paper also contains the description of a new hypervolume and racing-based methodology aimed at providing practitioners from the field of multi-objective optimization with a simple means of analyzing/reporting the general comparative run-time performance of multi-objective optimization algorithms over large problem sets.

Performance optimization of electrical drives implies a lot of degrees of freedom in the variation of design parameters, which in turn makes the process overly complex and sometimes impossible to handle for classical analytical optimization approaches. This, and the fact that multiple non-independent design parameter have to be optimized synchronously, makes a soft computing approach based on multi-objective evolutionary algorithms (MOEAs) a feasible alternative. In this paper, we describe the application of the well known Non-dominated Sorting Genetic Algorithm II (NSGA-II) in order to obtain high-quality Pareto-optimal solutions for three optimization scenarios. The nature of these scenarios requires the usage of fitness evaluation functions that rely on very time-intensive finite element (FE) simulations. The key and novel aspect of our optimization procedure is the on-the-fly automated creation of highly accurate and stable surrogate fitness functions based on artificial neural networks (ANNs). We employ these surrogate fitness functions in the middle and end parts of the NSGA-II run (->hybridization) in order to significantly reduce the very high computational effort required by the optimization process. The results show that by using this hybrid optimization procedure, the computation time of a single optimization run can be reduced by 46-72% while achieving Pareto-optimal solution sets with similar, or even slightly better, quality as those obtained when conducting NSGA-II runs that use FE simulations over the whole run-time of the optimization process.

This paper presents a study about cost-optimal induction machines fulfilling particular efficiency requirements. As an increase of efficiency inevitably causes higher material costs, the tradeoff for these two conflicting objectives is analyzed in particular. Optimization scenarios comprising crucial design parameters are investigated and evolutionary algorithms are employed to reduce the overall computational cost. To obtain results in satisfactory time, the performance of machine designs is determined by means of an analytic approach. A case study for rated power of 11kW is presented. All number of poles and efficiency classes considered in corresponding regulations are investigated. This allows a comparison of the relative cost increase with regard to mandatory efficiency requirements, starting from IE1 up to the IE4 class. The results further provide interesting insights into optimal length to diameter ratios, air gap flux densities, and stator current densities.

High-speed machines require structurally robust rotor to withstand high centrifugal forces. Flux switching permanent magnet (FSPM) machines are ideal for high speeds since they have a simple and robust rotor structure. They also utilize permanent magnet (PM) in the stator enabling them to achieve high power density. It is desirable to keep the operating frequency minimized to reduce core losses and cost of power electronics. A 6-stator slot, 4-rotor pole (6/4) FSPM machine has the lowest operating frequency for a three phase FSPM configuration but suffers from heavy harmonic distortion in flux linkage. This paper aims to identify structural modifications that can minimize the dominant 2nd order harmonic component to make the 6/4 configuration amiable for high-speed applications. The analysis and methods proposed in this paper will be useful in tackling harmonic content of FSPM machines in general.

Flux switching permanent magnet machines provide many advantages. Due to their superior behavior associated with sinusoidal Back-EMF and low torque ripple, topologies featuring 12 stator teeth and 10 rotor poles (12/10) are favored. However, this follows that for a given mechanical rotor speed, the required electric fundamental frequency is ten times to that of a conventional two pole PM machine imposing challenging requirements are set on the power electronics. In this paper, a 6/4 FSPM machine design is investigated since it has the lowest feasible slot-pole combination. The conventional 6/4 FSPM machine design is not a viable design due to the presence of dominant second order harmonic component of flux linkage and high torque ripple. Thus, a split magnet design is introduced which allows achieving better performance by significantly reducing the second harmonic component. A multi-objective optimization scenario is carried out utilizing an evolutionary algorithm and performing massively distributed finite element simulations on a computer cluster. The selected machine design and its particular torque characteristics are analyzed. The achieved results reveal that by considering split magnet topologies, the low slot-pole FSPM machine configurations can unlock their potential for high-speed operation.

This article is about measurement-based modeling of PMSMs. Typically, these machine designs feature nonlinear characteristics regarding the stator phase currents and show rotor angle dependent behavior. Thus, non-sinusoidal linked fluxes as well as higher torque harmonics occur. As this cannot be represented by classical dq0-based theory, a feasible modeling strategy had do be established and its suitability is illustrated by analyzing a prototype in detail. Measurements are conducted on a test rig and a nonlinear machine model is derived. The measurement setup and the automatized measurement process are described and the obtained machine characteristics are analyzed. When compared with results based upon finite element (FE-) simulations, this allows for identifying manufacturing tolerances and deviations of the material characteristics compared to presumed behavior. Moreover, tolerances among the rotor pole pairs can be identified if the measurements are conducted for an entire rotor revolution. The suitability of the derived model is verified by determining ideal stator phase currents for a particular optimization task.

This article deals with accelerating typical optimization scenarios for electrical machine designs. Besides the advantage of a reduced computation time, this leads to a reduction in computational power and thus to a lower power consumption when running the optimization. If high power density is required, usually highly-utilized electrical machines which feature nonlinear characteristics are applied. As a consequence, typically optimization scenarios are considered where the evaluation of a potential design requires computationally expensive nonlinear finite element (FE) simulations. It is obvious that improving the speed of optimization runs takes top priority and various measures can be considered. This article is about (i) basic easily achievable measures, (ii) techniques for an efficient exploration of the design space, and (iii) advanced strategies to reduce the simulation time, e.g., (a) sophisticated emerging techniques for modeling machine characteristics by paring the number of required FE simulations down to the minimum and (b) nonlinear modeling of the targets of the optimization scenario as functions of the design parameters to further reduce the number of FE evaluations. By way of illustration, the analysis of a typical optimization task is given and achievable speed improvements as well as still present bottlenecks are discussed.

This article presents the nonlinear modeling of the torque of brushless PMSMs by using symbolic regression. It is still popular to characterize the operational behavior of electrical machines by employing linear models. However, nowadays most PMSMs are highly utilized and thus a linear motor model does not give an adequate accuracy for subsequently derived analyses, e.g., for the calculation of the maximum torque per ampere (MTPA) trajectory. This article focuses on modeling PMSMs by nonlinear white-box models derived by symbolic regression methods. An optimized algebraic equation for modeling the machine behavior is derived using genetic programming. By using a Fourier series representation of the motor torque a simple to handle model with high accuracy can be derived. A case study is provided for a given motor design and the motor model obtained is used for deriving the MTPA-trajectory for sinusoidal phase currents. The model is further applied for determining optimized phase current waveforms ensuring zero torque ripple.

Brushless permanent magnet machines (BPMMs) gained more importance due to the high power density ensured by permanent magnets with high energy densities. Therefore, a more compact design can be achieved compared to other types of electrical machines. However, the ferromagnetic components are typically driven near or above the saturation flux density at least at nominal load operation. This leads to non-sinusoidal linked fluxes in the stator coils and, hence, creates disruptive torque ripple during operation when the motor is fed with sinusoidal currents. Additionally, BPMMs often show a considerable cogging torque and, hence, torque ripple can even be noticed at no-load operation. In this article, a motor design with a certain number of significant flux harmonics is presented. Non-sinusoidal current waveforms were optimized in order to fulfill the operating performance requirements of the electric drive regarding efficiency and torque ripple. For impressing the desired current waveforms including higher harmonics related to the electrical frequency of the motor, the specification of the used power electronics has to be taken into account. Furthermore, the structure and design of the current control has a big impact on the possibility to impress specific current waveforms even at higher rotor speeds. This article is about a current control structure using an iterative learning control algorithm (ilc). In the introduction, different current control strategies are given that were published in the past. This will be followed by the presentation of the considered motor design. The control structure and the hardware used for experimental results are subsequently described. This will be followed by measurement results of the achieved currents and load torques and finally a conclusion is derived.

The task of designing electrical drives is a multi-objective optimization problem (MOOP) that remains very slow even when using state-of-the-art approaches like particle swarm optimization and evolutionary algorithms because the fitness function used to assess the quality of a proposed design is based on time-intensive finite element (FE) simulations. One straightforward solution is to replace the original FE-based fitness function with a much faster-to-evaluate surrogate. In our particular case each optimization scenario poses rather unique challenges (i.e., goals and constraints) and the surrogate models need to be constructed on-the-fly, automatically, during the run of the evolutionary algorithm. In the present research, using three industrial MOOPs, we investigated several approaches for creating such surrogate models and discovered that a strategy that uses ensembles of multi-layer perceptron neural networks and Pareto-trimmed training sets is able to produce very high quality surrogate models in a relatively short time interval.

This paper describes an advanced method of modeling synchronous machines, in particular interior permanent magnet (IPM) motors. The dynamic motor model considers magnetic saturation and the dependence of electrical, magnetic and mechanical quantities on the rotation angle, and can be integrated into multidisciplinary system simulations. A set of magnetic finite element method (FEM) solutions is used to set up the model based on radial basis function (RBF) interpolation. The presented motor model can be used to simulate any time-stepping cases, such as studies of field weakening control, sensorless motor control algorithms or short circuit behavior. No magnetic FEM simulation is needed at runtime. We demonstrate the functionality of our method using the example of a BLDC motor simulation with voltage block commutation. The model derivated results are in good accordance with our measurements.

Due to the increasing significance of energy saving, multiple regulations have been introduced by countries or international organizations regarding the efficiency of electric drives, e.g. the IEC 60034-30 [1]. In the past, many companies replaced induction machines (IMs) by permanent magnet excited synchronous machines (PMSMs). This lead to a considerable increase of the efficiency, but due to the fluctuating price of the permanent magnets, especially of Neodymium-Iron-Boron(NdFeB)-magnets, the cost of PMSMs is hardly predictable. Therefore, many manufacturers are investigating in synchronous reluctance machines (SyncRM) now. In this article, the motor design for standardized rated power Prate = 3kW and nominal synchronous speed of nrate = 1500rpm is taken into consideration. Different motor topologies are analyzed regarding the trade-off between efficiency and material costs, including PMSMs and SyncRMs. This is done for two different cost scenarios. Finally, the cheapest designs that fulfill the IE-2 and IE-3 requirements, respectively, can be determined.

Bearingless motors and active magnetic bearings work completely contact- and wearless. With these properties, hermetically sealed and lubricant free rotating systems for various applications can be designed. It is possible to stabilize three degrees of freedom by reluctance forces, when a permanent magnet excited rotor disc is used. This constructional design is called bearingless slice motor. The bearingless segment motor is a subtype of the slice motor, featuring a segmented stator composition. This paper comprises the design process of a novel bearingless segment motor with axial magnetized rotor magnets, five stator elements and concentrated windings. Finite-element-simulations are applied to maximize the bearing forces and the motor torque per ampere and minimize the reluctance forces. However, the mathematical model of the system is nonlinear, so an appropriate nonlinear control scheme has to be applied to put the system into operation. The introduction of a prototype together with measurements completes the paper.

Today magnetically levitated rotors are mainly used in applications where wearless operation and high life cycle are of importance (e.g. in the pharmaceutical, biomedical, chemical and semiconductor industry). The bearingless slice motor features a very compact design because three degrees of freedom (one translational and two rotatory) are passively stabilized by reluctance forces. Therefore, only two translational degrees of freedom remain to be actively controlled. This paper introduces a new bearingless segment motor (a subtype of the bearingless slice motor) featuring a Halbach magnet ring mounted on the rotor. Thus, no back iron is needed on the rotor and therefore the overall weight of the permanent magnet excited disc-shaped rotor is reduced to a minimum. The bearing forces which can be created by one optimized stator segment are calculated analytically. These results allow conclusions for the total force locus. A prototype is built and measurements verify the results of the analytic considerations.

This article is about the cogging torque sensitivity of brushless permanent magnet machines. Thereby, the sensitivity calculation of the On-/Off-method is used for determining the change of the cogging torque due to varying material behavior of the ferromagnetic parts of the motor. The results are obtained by using finite element calculations and the sensitivity is separately derived for each finite element. A practical example is examined, where two different machine designs are compared with respect to their nominal cogging torque values and their cogging torque changes for varying material characteristics. From the insights gained by this analysis it can be followed that sensitivity analyses will get more and more important for future machine design optimization.