Quantitative power density limits of aerospace permanent magnet synchronous machines

03/02/2015
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Quantitative power density limits of aerospace permanent magnet synchronous machines

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application/pdf Quantitative power density limits of aerospace permanent magnet synchronous machines M. van der Geest, H. Polinder, J. A. Ferreira, M. Christmann
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Quantitative power density limits of aerospace permanent magnet synchronous machines

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Quantitative power density limits of aerospace permanent magnet synchronous machines M. van der Geest 1 , H. Polinder 1 , J. A. Ferreira 1 , M. Christmann 2 1 : Delft University of Technology, Delft, Netherlands - m.vandergeest@tudelft.nl 2 : Airbus Group Innovations - markus.christmann@airbus.com Abstract Electrical machines are inherently part of larger systems and the design optimization of the machine should not be approached separately from the system optimization and vice versa. Exemplary important interface parameters are the machine speed and applied cooling method. To determine the feasibility of an electrical drive for new applica- tions, detailed knowledge on the dependency of machine performance on these parameters is necessary. This paper quantifies the relation between performance and rotor surface speed, cooling scenario and power level, for surface mounted permanent magnet machines. Full FEM-based multi-objective optimization is used to obtain a realistic set of candidate machine designs, providing accurate quantitative trends for maximum achievable power density, as well as corresponding underlying properties such as dimensions, efficiency, shear force densities, flux densities, machine inductance or loss distribution. I. Introduction Electrical machines are inherently part of a larger system and should be designed together with the other parts of the system to approach a global optimum. This is particularly important for aerospace systems, where a low system weight and volume are essential to obtain a competitive system. In the early design phase of new systems, many different concepts and configurations may be considered which requires fast yet accurate models of all major subcomponents in the system. This paper proposes a method to accurately determine power density limits by filling a database with systemat- ically chosen and individually FE-based optimized machine designs. Advantages of this approach include that all machine properties –like dimensions, losses or electrical parameters– are known and that each resulting machine is optimized with identical targets, constraints and materials. This allows both global trends such as power density, and underlying trends including machine dimensions and performance, to be deter- mined and quantified. The results can provide a direct starting point for new designs or reference for compari- son with existing designs. II. Optimization approach A. Choice of main target and independent variables The main goal of this work is to determine the depend- ency of specific power density on rotor surface speed, power level and cooling effort. This is motivated by the following arguments:  Specific power density is chosen because in aircraft low weight is essential to obtain a high range and reduce operating costs.  Rotor surface speeds of 25, 50, 100 and 200 m/s are considered. A constant surface speed is chosen over a constant rotational speed, because the former represents a roughly constant mechanical design effort.  Power levels of 50, 100, 200, 500 and 1000 kW are considered.  Achievable machine performance strongly depends on cooling intensity and a wide range of cooling options exist, Therefore, four cooling scenarios are defined, as will be described below. B. Execution To ensure that each design in the database is indeed optimal, an individual multi-objective optimization is executed for each design point. The result of each optimization is a pareto optimal front (POF). In this case, each of the 80 resulting three dimensional POFs shows the trade-off between weight, efficiency and winding temperature for a given design point, but to determine high level trade-offs, the results from all POFs have to be compared. Each front contains hundreds of individual designs, making a direct comparison of the POFs infeasible. Therefore, the lightest designs meeting certain temperature constraints are selected from each POF and the performance and properties are averaged and plotted. III. Modeling, assumptions & material properties A. Electrical 1) Assumptions: With the emphasis on higher speed machines and high performance, SPM machines are considered. At high speeds SPM machines are more attractive than interior PM machines, because the latter require thicker magnetic bridges at higher speeds, which in turn requires more magnet material to maintain the airgap field strength [1]. In addition, a longer mechanical airgap reduces the saliency ratio, which further reduces the benefits of interior PM machines. Only concentrated tooth coil windings are considered, because this offers the benefits of short end-windings and simple manufacturing. Asynchronous space- harmonics can induce problematic rotor eddy-current losses with such windings. To minimize these losses, only windings from the 3 slot, 2 pole family (q=0.5) are chosen, as these have a relatively clean space- harmonic spectrum; a carbon fiber retaining sleeve is assumed; and axial magnet segmentation in 8 pieces. Iron-cobalt laminations are assumed, as they allow high flux saturation levels (2.4 T) and are available in thin sheets to reduce losses. Further material properties, constants and variables are summarized in Table I. 2) Modeling: Each machine is completely analyzed with 2D FEA, allowing saturation, rotor eddy-current losses and all geometric details to be accounted for. B. Thermal A wide variety of cooling systems exist and quantifying a complete cooling system is difficult. Therefore, the following four cooling scenarios are defined: C1 – Pessimistic air cooling The machine is cooled only by a forced airflow through the airgap. The stator yoke outside surface is assumed to be insulated. C2 – Optimistic air cooling has increased flow rates compared to the previous case, as well as cooling on the stator yoke outside surface. C3 – Liquid jacket, totally enclosed The stator outside is cooled by a liquid jacket. The machine is closed, but air is circulated in the machine to transfer rotor heat to the stator. C4 – Liquid jacket & rotor air cooling Is similar to the previous case, but ambient air is forced through the airgap, although far less than in the pessimistic air cooling case. These scenarios are implemented as different surface heat transfer coefficients (HTC) to ambient air that are applied as boundary conditions on a model of the solid machine parts. The full paper will contain the values used. In the case of a liquid jacket, the weight of the jacket and liquid are added to the machine weight. C. Optimization Particle swarm optimization (PSO) is used to determine the POF for each design point. For each design point, 200 iterations with 20 particles are executed, so that ultimately 320,000 machines have been analyzed to arrive at the final data set. IV. Results Fig. 1 shows specific power density versus rotor surface speed and so fulfills the main goal of this paper. Discussing the dependency on the main variables individually:  Improving the cooling system is most beneficial for improving the power density. Compared to pessimis- tic air cooling, optimistic air cooling increases the power density by 1.5–2.5×, the totally enclosed system with liquid jacket by 1.2–1.6× and the mixed cooling system by 2–3×. The TE enclosed system performs worse than the optimistically air cooled system, mostly due to the limit on the rotor tempera- ture.  Increasing the rotor surface speed also increases the power density, but with diminishing returns. This is attributed to the iron and rotor losses, which increase with speed. This demonstrates that with increasing surface speed, the importance of a good cooling system increases.  The dependency of the power density on the power level is small, compared to the cooling system or speed, but higher power machines occupy the lower end of the spectrum for most cooling/speed design points. The difference in power density is typically 20% across the considered power range. This is believed to be correct, since the machine volume, where the losses originate, scales with n 3 , while the area, which dissipates the losses, scales with n 2 . The full paper will contain more results, including temperatures, efficiencies, flux densities, dimensions and scaling paramters. V. Conclusions This paper proposed and demonstrated a method to determine machine capabilities, bridging the gap between inaccurate but fast analytical design methods and literature based studies. By using FEA and accurate lumped element models, all relevant geomet- rical, magnetic and thermal effects are accounted for, providing more accurate results than analytical models. The dependency of specific power density on rotor surface speed, power level, efficiency and cooling effort was quantified, demonstrating that an increased cooling capacity can improve the power density more than rotor surface speed. Results indicate that well designed air cooled machines may outperform totally enclosed liquid jacket cooled designs. By further inspection of the results, it is shown amongst others that at high speeds the high flux density of FeCo laminations is not necessary. Also the optimal mechanical airgap length increases, allowing thicker sleeves to be used or reducing windage losses. It is validated that the shear force is a good machine dimensioning parameter, if quoted with cooling level and rotor surface speed. Using the final results, it is for instance possible to determine the machine losses as a function of machine weight for given power and surface speed levels. References [1] A. Binder, T. Schneider and M. Klohr, "Fixation of buried and surface-mounted magnets in high-speed permanent- magnet synchronous machines," IEEE Trans. Ind. Appl., vol. 42, no. 4, pp. 1031-1037, 2006. Table I: Relevant material properties Stat./Rot. Lam, Winding Magnets Retain. Sleeve μr FeCo 1 1.05 1 Losses 0.15 mm fill 50% ρ = 1μΩm ρ = 100μΩm Br - - 1.2 T - Density1 8120 5185 7500 1600 Therm. cond.2 29 / 0.7 1.2 / 195 7.5 / 2.5 0.77 1 In kg/m 3 ; 2 In W/(mK), in-plane / axial Fig. 1 Specific power density versus rotor surface speed.