Comparison of multi-physics optimization methods for high speed synchronous reluctance machines

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Comparison of multi-physics optimization methods for high speed synchronous reluctance machines


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Comparison of multi-physics optimization methods for high speed synchronous reluctance machines


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Comparison of multi-physics optimization methods for high speed synchronous reluctance machines Mauro Di Nardo (1), Marco Palmieri (2), Michael Galea (1), Francesco Cupertino (2), Chris Gerada (1) 1: University of Nottingham - Nottingham, UK – 2: Politecnico di Bari – DEI, Bari, Italy Abstract This paper is focused on the electromagnetic and structural design of high-speed electrical machines for aerospace applications. Two multi-physics techniques, both based on Genetic Algorithm optimization (GA) and Finite Element Analysis (FEA), are investigated and compared in terms of computational time and quality of the final result. The first procedure combines an electromagnetic FE evaluation with an analytical estimation of the structural behaviour of the rotor laminations. The selected machine is then analysed more accurately by a more demanding electromagnetic and structural FEA. The second method includes both electromagnetic and structural FE into the optimization algorithm, thus avoiding the final re-evaluation. As a vessel to investigate these two methods, a Synchronous Reluctance (SyR) machine with strict requirements in terms of rotational speed has been chosen with main focus on the rotor design, due to it being the most critical aspect for high speed applications. Introduction In recent years there has been a growing interest towards high speed (HS) electrical machines for a wide range of applications [1]. This kind of machines allow direct-drive solutions, simplify the overall system and guarantee several improvements in terms of weight, maintenance and efficiency which are crucial for aero-space applications [1]. In fact, such benefits fall directly in the scope of the More Electric Aircraft (MEA) and More Electric Engine (MEE) concepts [2]. However, as rotational speed increases, mechanical issues become even more relevant and a multi-physics design approach, based on both electromagnetic and structural analysis is required. Several HS machines topologies (permanent magnet / reluctance / induction motors) with laminated or solid rotors have been presented in literature and the main advantages and challenges of each solution have been highlighted [1-7]. In this paper, a transversally laminated SyR machine, with strict requirements in terms of rotational speed, has been chosen as a vessel to compare two different design strategies both based on a Genetic Algorithm (GA) optimization and a finite element analysis (FEA). System specifications and design procedures are detailed in the next sections. The main attention has been focused on the rotor lamination design because it is considered the most critical design aspect for HS applications. In particular, the iron bridges dimensions are the design parameters that affect both the rotor structural integrity and the electromagnetic performances. The two design strategies presented in this work differ from each other in a number of ways, including the sizing method of the aforementioned iron bridges and the accuracy of the electromagnetic and mechanical performances evaluation. These two strategies are compared in terms of computational time, final rotor geometries, and mechanical and electromagnetic performances. Specification and preliminary design choices The stator axial length and external diameter of the machine are imposed by the maximum allowed space envelope. A distributed winding configuration has been chosen in order to reduce the rotor iron losses due to the harmonic content of the stator m.m.f. The number of poles has been fixed to 4 in order to limit the fundamental frequency. The shaft diameter and the airgap length have been chosen according to a preliminary mechanical analysis. The numbers of stator slots (i.e. 24) and rotor flux barriers (i.e. 3) of the SyR machine have to be suitably chosen in order to achieve a good trade-off between electromagnetic performances and simple construction [8]. In order to keep the iron losses to an acceptable value, silicon steel with a lamination thickness of 0.178 mm has been considered for the stator core. Considering the HS nature of the application, the two main criteria guiding the choice of the rotor material are its mechanical properties and its iron losses. A high strength lamination material was chosen (i.e. 35HXT) having a yield strength of 822 MPa at the cost of increased iron losses (50 W/Kg at 1T/400Hz). Table 1: Main machine parameters specifications Quantity Value Stator slots 24 Pole pairs 2 Rotor diameter 32.4 [mm] Stator diameter 60 [mm] Stack length 30 [mm] Airgap 0.3 [mm] Rated current (pk) 10 [A] Maximum speed 80000 rpm Type of cooling Water cooled With a preliminary analytical design, the stator geometry was chosen and the following design will focus on rotor geometry selection. It was also calculated that a current density about 6 A/mm² would produce a torque around 0.25 Nm that is the target torque of the considered design. A thermal analysis of the stator was used to verify that the winding temperature lies within a safe range. The main parameters and specifications of the SyR machine are reported in Table 1. Regarding the rotor geometry, a topology described by a reduced number of parameters was selected [9]. A simplified rotor geometry is better suited for design assisted by optimization algorithm because it reduces the number of parameters to be selected and does not compromise electromagnetic performances. In particular a rotor configuration with one external straight flux barrier and two internal U-shaped segmented barriers [10] has been considered (see Figure 1). Each barrier is described by two parameters, namely the angular position at the air- gap and the radial thickness (i and hi in Figure 1). Figure 1: Rotor geometry Design procedures After the preliminary sizing considerations, two different automated design procedures based on multi-objective GA optimization coupled to FEA have been compared. The optimized performance indexes are the average torque and torque ripple. Maximizing the torque for a given current and stator structure correspond to the maximization of the torque per joule losses ratio which has a strong impact on the overall efficiency. SyR machines can exhibit a considerably high torque ripple if the rotor structure is not properly designed therefore it has to be considered as a primary objective of the optimization problem. Electromagnetic FEA is mandatory to evaluate the performances of SyR machine, especially in the final design stages. This is mainly due to the impact of magnetic saturation on the performance of such machines. FE based design assisted by optimization algorithms is however not so common, due to the long computational time required to obtain the figures of merit to be optimized. However, in [9-10] it was shown how it is possible to reduce the dimension of the research space of the optimization problem, reduce the computational time of each candidate solution, and obtain a good trade-off between accuracy and computational time. Both electromagnetic and mechanical performances of a SyR machine strongly depend on the rotor geometry. In particular it is clear that from the electromagnetic point of view the bridge dimensions have to be as low as possible while from the mechanical perspective they need to guarantee the structural integrity at the maximum speed. The total length of the iron bridge of each flux barrier (2TBi+2LBi+CBi) depends on the mass of the flux guide (iron part between the flux barriers), therefore they depend on the angular position at the airgap and on the radial thickness of the barriers [11]. Since such parameters also influence electromagnetic performance, it is mandatory to design the rotor structure taking into account mechanic and electromagnetic design aspects, which are strongly coupled. The two design strategies compared in this work differ from each other according to the sizing method of the aforementioned iron bridges and to the accuracy with which the electromagnetic and mechanical performances are evaluated. In the following section, the design procedures are described in details. 1. Fast design procedure (FP) performs the evaluation of the average torque and torque ripple via magneto-static FE simulations with a reduced number of steps (5/6) over one stator tooth pitch. The mechanical analytical design of the iron bridges (required to guarantee the structural integrity) is carried out, for each rotor candidate, considering just one bridge per flux barrier (i.e. CBi) and imposing the tangential bridges (TBi) as to the fabrication tolerances (0.2 mm) and the lateral bridges (LBi) equal to zero [12]. After the optimization, one machine is selected from the Pareto front and is accurately re-evaluated by means of structural FEA. A spatial redistribution of the bridge position is carried out keeping the same total bridge dimension. The computational time needed for the evaluation of a single rotor candidate is about 6 seconds, while the total computational time of the optimization is 20 hours (with 100 elements per population for 80 generations). 2. Accurate design procedure (AP) performs a three-objective optimization of the rotor structure having as an additional objective the maximum von Mises stress induced in the rotor laminations. This is evaluated by means of a structural FEA for each rotor candidate. In this method all the bridge dimensions (TBi, LBi, CBi) are included in the parameters to be optimized by the algorithm. Thus a structural FE re-design of the spatial distribution of the bridges is not required. The average torque and the torque ripple are obtained via transient with motion simulations with a significant number of steps (i.e. 16) over one stator tooth pitch. The computational time needed for the evaluation of a single rotor candidate is about 25 s, while the total computation time of the optimization is 96 hours (with 100 elements per population for 120 generations). The parameters of the optimization algorithm are increased for the AP because the number of variables to be optimized increases from 6 (in case of FP) to 14. Figure 2: Designed rotor geometries Results In this section, the results of the two design procedures are presented, and the differences between the obtained geometries and their electromagnetic performances are highlighted. The mechanical performances of the selected rotors will be included in the full paper, along with the mechanical analytical design and the structural FE re- evaluation carried out in the FP. Figure 2 shows the final rotor design obtained with the FP (a) and the results of the structural FE re-evaluation (b) carried out in post-processing. Figure 2c illustrates the obtained rotor structure by the AP. By comparing the obtained geometries it can be observed that the angular positions at the airgap of the barriers are quite similar but the thickness of the barriers are considerably different. As shown in Figure 3, this geometric difference has a considerable impact on the machine performances. It can be observed that the average torque produced by the machine designed with the AP is higher by 29% than the one obtained with the FP. This is mainly due to the approximation of the analytical model on which the design of the bridges in the FP is based. The bridge dimensions are overestimated with the FP. On the other hand, the machine designed with the AP shows a torque ripple which is higher by 117%. Figure 3: Torque waveforms at rated current and MTPA condition Conclusions This paper presents a comparative study between two design procedures for high speed electrical machines for aerospace applications. Both of them are based on GA optimization and multi-physical FE approach. The FP is a fast design tool, but it needs an accurate re-evaluation of the selected machine and eventually a “manual” re-distribution of the radial iron bridges. The AP method is more time consuming but results in a more optimized, rotor lamination design. More design aspects, mechanical results and details will be presented in the final paper. References 1 Tenconi A. et al, “Electrical machines for high speed applications: design considerations and tradeoffs”, IEEE Transaction on Industrial Electronics, 2014, Vol. 61, pp. 3022-3029. 2 Borg Bartolo J. et al, “High speed electrical generators, application, materials and design”, Electrical Machines Design Control and Diagnosis (WEMDCD), 2013 IEEE Workshop on. 3 Hofmann H. et al, “High-speed synchronous reluctance machine with minimized rotor losses”, IEEE Transactions on Industry Applications, Vol. 36, n. 2, 2000, pp. 531-539. 4 Gerada D. et al, “Electrical machines for high speed applications with a wide constant-power region requirement”, International Conference on Electrical Machines and Systems, ICEMS 2011. 5 Krahenbuhl D. et al, “A Miniature 500 000-r/min Electrically Driven Turbocompressor”, IEEE Transactions on Industry Applications, Vol. 46, n. 6, 2010, pp. 2459-2466. 6 Sung-Il Kim et al, “A Novel Rotor Configuration and Experimental Verification of Interior PM Synchronous Motor for High-Speed Applications”, IEEE Transactions on Magnetics, Vol. 48, n. 2, 2012, pp. 843-846. 7 Ikaheimo J. et al, “Synchronous High-Speed Reluctance Machine With Novel Rotor Construction”, IEEE Transactions on Industrial Electronics, Vol. 61, n. 6, 2014, pp. 2969-2975. 8 Vagati A et al, "Design of low-torque-ripple synchronous reluctance motors," IEEE Transactions on Industry Applications, 1998, vol. 34, pp. 758-765. 9 Pellegrino G. et al, “Barriers shapes and minimum set of rotor parameters in the automated design of Synchronous Reluctance machines” IEEE International Electric Machines & Drives Conference (IEMDC), pp. 1204-1210, 2013. 10 Cupertino F et al, “Design of Synchronous Reluctance Machines with Multi-Objective Optimization Algorithms”, IEEE Transactions on Industry Applications, DOI: 10.1109/ TIA.2014.2312540, in press. 11 Bianchi N et al, “Structural Analysis of the Interior PM Rotor Considering Both Static and Fatigue Loading” IEEE Energy Conversion Conference and Exposition, 2013. 12 Palmieri M. et al, ”High speed scalability of synchronous reluctance machines considering different lamination materials”, annual conference of IEEE industrial electronic society, IECON 2014.