This chapter introduces the finite element method (FEM) as a tool for solution of classical electromagnetic problems. Although we discuss the main points in the application of the finite element method to electromagnetic design, including formulation and implementation, those who seek deeper understanding of the finite element method should consult some of the works listed in the bibliography section.

Introduction to the Finite Element Method

High-speed permanent-magnet synchronous machines (HS PMSMs) are a popular topology among modern electrical machines. Suitable applications for such machines are low-power vacuum pumps, compressors, and chillers. This paper describes a systematic design methodology for an HS PMSM using two case studies. The design process for such high-speed (HS) machines is multidisciplinary and highly iterative due to the complex interaction of the many design variables involved. Consequently, no single optimum solution exists, and multiple possible solutions can meet the customer requirements. Practical solutions should be within acceptable thermal limits, should be energy-efficient, and should be rigid enough to withstand the forces exerted during operation. The proposed design flow is divided into steps that are presented in this paper in the form of a flowchart with emphasis on mechanical aspects. Each step represents a task for a thermal, mechanical, or electrical engineer. The features of each step and the prerequisites for moving to the next step are discussed. The described methodology was implemented in the design of two HS PMSMs. The output performance results of the design flow are compared with measured results of the prototypes. The design process described in this paper provides a straightforward procedure for the multidisciplinary design of HS permanent magnet electrical machines.

Multidisciplinary Design Process of a 6-Slot 2-Pole High-Speed Permanent-Magnet Synchronous Machine

Recently, ferromagnetic soft continuum robots – a type of slender, thread-like robots that can be steered magnetically – have demonstrated the capability to navigate through the brain's narrow and winding vasculature, offering a range of captivating applications such as robotic endovascular neurosurgery. Composed of soft polymers with embedded hard-magnetic particles as distributed actuation sources, ferromagnetic soft continuum robots produce large-scale elastic deflections through magnetic torques and/or forces generated from the intrinsic magnetic dipoles under the influence of external magnetic fields. This unique actuation mechanism based on distributed intrinsic dipoles yields better steering and navigational capabilities at much smaller scales, which differentiate them from previously developed continuum robots. To account for the presence of intrinsic magnetic polarities, this emerging class of magnetic continuum robots provides a new type of active structure – hard-magnetic elastica – which means a thin, elastic strip or rod with hard-magnetic properties. In this work, we present a nonlinear theory for hard-magnetic elastica, which allows accurate prediction of large deflections induced by the magnetic body torque and force in the presence of an external magnetic field. From our model, explicit analytical solutions can be readily obtained when the applied magnetic field is spatially uniform. Our model is validated by comparing the obtained solutions with both experimental results and finite element simulations. The validated model is then used to calculate required magnetic fields for the robot's end tip to reach a target point in space, which essentially is an inverse problem challenging to solve with a linear theory or finite-element simulation. Providing facile routes to analyze nonlinear behavior of hard-magnetic elastica, the presented theory can be used to guide the design and control of the emerging class of magnetically steerable soft continuum robots.

Hard-magnetic elastica

High-speed permanent magnet synchronous machines (PMSMs) have attracted much attention due to their high power density, high efficiency, and compact size for direct-drive applications However, the consequent power loss density is high, and hence heat dissipation is a major technical challenge This is particularly the case for high-speed operation In this paper, a MW level high-speed PMSM is designed and its electromagnetic and mechanical power losses comprehensively investigated using finite element analysis The transient machine demagnetization performance is studied, and a composite rotor structure is proposed to improve machine antidemagnetization capability The temperature distribution of the proposed high-speed PMSM is also analyzed using a fluid-thermal coupling method with calculated power loss Experiments conducted on a prototype of the high-speed PMSM demonstrate the effectiveness of the numerical models developed and validate the results obtained

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Power Loss and Thermal Analysis of a MW High-Speed Permanent Magnet Synchronous Machine

Permanent-magnet synchronous machines (PMSMs) are considered a very promising machine type for high-speed (HS) applications. As permanent-magnet (PM) materials are generally fragile, a high-strength sleeve is required to protect the PMs from damage due to the extreme centrifugal forces. The rotor sleeve occupies space of the effective airgap of the PMSMs; therefore, it is difficult to perform the electromagnetic (EM) design without an accurate estimation of the sleeve thickness, which is determined by mechanical issues. In this paper, an integrated mechanical- EM design method is proposed for the rotor design of HS PMSMs. A 200-kW 40 000 r/min surface mounted PM machine is taken to illustrate the design procedure of the proposed method. Three commonly used sleeve materials are investigated and their mechanical performances are analyzed. The optimal dimensions for the rotors with different sleeves are obtained by considering the strength and EM limits. The EM, thermal, and rotor dynamic performances of the designed rotors are analyzed and compared. In the end, a new rotor sleeve topology is proposed to reduce the rotor eddy current losses.

Rotor Design for High-Speed High-Power Permanent-Magnet Synchronous Machines

Two-stage oil-free centrifugal air compressors can bring significant advantages and open new market opportunities for compressor manufacturers. One of the core technologies behind this compressor type is the high-speed electrical machine supported by active magnetic bearings. In this paper, the requirements set by the compressor on the electrical machine design are presented. The design solutions aimed to satisfy these requirements are discussed. Two case studies illustrate possible design approaches for the target application with examples of a 120-kW, 60 000-r/min induction machine with a solid rotor and a 225-kW, 50 000-r/min permanent-magnet synchronous machine (PMSM) with a full cylindrical magnet. The system design and simulation results are confirmed by measurements of a PMSM prototype.

Design Aspects of High-Speed Electrical Machines With Active Magnetic Bearings for Compressor Applications

High-speed (HS) electrical machines provide high system efficiency, compact design, and low material consumption. Active magnetic bearings (AMBs) bring additional benefits to the HS system, such as elimination of the friction losses, reduced wear and maintenance, and a built-in monitoring system. HS drivetrains are usually designed for specific applications and require a high level of integration. This paper describes a design method of the HS electrical machine supported by AMBs, considering their mutual influence on the system performance. The optimization procedure, which takes into account both the electrical machine and bearing designs, is developed. The optimization is based on a multiobjective genetic algorithm. The selected optimization parameters include the AMB and machine dimensions. The optimization objectives cover the electrical machine performance and the rotordynamics. The results of the proposed optimization algorithm are implemented in the constructed 350-kW, 15 000-r/min induction machine with a solid rotor supported by AMBs. The prototype tests verify the design and optimization results.

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High-Speed Electrical Machine with Active Magnetic Bearing System Optimization

This paper presents a multidisciplinary design algorithm of the ultra-high-speed electrical machine (UHSEM). Presented algorithm enables UHSEM design with a rotational speed of 0.5–1.2 Mrpm, taking into account the mutual influence of thermal, mechanical, and electromagnetic processes. Based on the algorithm, the 138 W UHSEM with a 1.2 Mrpm rotational speed was calculated. Material selection for the active parts of the machine is described. Analysis of the suitable bearings for UHSEM application is presented. Mechanical, electromagnetic, and cooling design aspects are shown with example of the calculated machine. To evaluate the effectiveness of the developed computer models and the calculation method, the experimental model of the 100 W UHSEM was tested in the motor mode at the rotational speed of 500 000 rpm. The test results demonstrated that the multidisciplinary design algorithm has high accuracy and is suitable for UHSEMs. The discrepancy between developed models and experimental results does not exceed 7%.

Multidisciplinary Design of Ultra-High-Speed Electrical Machines

Permanent magnet (PM) materials are nowadays widely used in the electrical machine manufacturing industry. The eddy-current loss models of PMs used in electrical machines are frequently discussed in research papers. In magnetic steel materials we have, in addition to eddy-current losses, there are hysteresis losses when alternating current or a rotating flux travels through the material. Should a similar phenomenon be also taken into account in calculating the losses of PMs? Every now and then, authors seem to assume that some significant hysteresis losses are present in rotating machine PMs. This paper studies the mechanisms of possible hysteresis losses in PMs and their role in PMs when used in rotating electrical machines.

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Nikita Uzhegov

Papers

Multidisciplinary Design Process of a 6-Slot 2-Pole High-Speed Permanent-Magnet Synchronous Machine

Design Aspects of High-Speed Electrical Machines With Active Magnetic Bearings for Compressor Applications

High-Speed Electrical Machine with Active Magnetic Bearing System Optimization

Multidisciplinary Design of Ultra-High-Speed Electrical Machines

Hysteresis Losses in Sintered NdFeB Permanent Magnets in Rotating Electrical Machines