IEEE TRANSACTIONS ON MAGNETICS, VOL. 51, NO. 3, MARCH 2015
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Optimal Design of the Synchronous Motor With the Permanent Magnets on the Rotor Surface Alexander Kalimov1 and Sergey Shimansky1,2 1 Institute
of Power Engineering and Transportation, Department of Theoretical Electrical Engineering, Saint Petersburg State Polytechnic University, Saint Petersburg 190251, Russia 2 CADFEM-CIS, Saint Petersburg 195197, Russia
This paper proposes a strategy for the optimal design of a synchronous motor with permanent magnets on the rotor surface. The proposed strategy includes several steps during which the general parameters of the rotor arrangements, currents in the stator windings, and the parameters of the slot tooth in the stator are consequently defined. The motor with the optimized cross section demonstrates significantly better performance than its initial prototype. All calculations are performed using industry-standard finite element method software. Index Terms— Magnetic field, optimization, permanent magnets (PMs), synchronous motor.
I. I NTRODUCTION
T
HE SYNCHRONOUS motors with permanent magnets (PMs) on the surface of the rotor and a high pole number are often used for low-speed direct-drive applications. The main advantages of such a motor structure are simplicity and relatively low manufacturing cost compared with other designs of motors with PMs. The motors of this type are especially advantageous in the application where low rotation speed is required, such as wind generators, ship propulsion engines, and so on [1], [2]. Relatively low centrifugal force in these cases reduces the danger of magnet detachment from the rotor, which cannot be neglected in high-speed electrical motors. Design principles of such electric machines are described in [3] and [4]. In this paper, we consider a methodology of the optimal design of surface-mounted PM (SMPM) based on the reduction of the high-order field harmonics in the main motor gap. All calculations including dynamic processes and parametric optimization were performed using ANSYS Maxwell software package. II. S YNCHRONOUS M OTOR W ITH THE S URFACE PMs In this paper, we consider performance of a low-speed PM motor with concentrated winding developed for a ship propulsion drive. Our goal was to design a motor with rated output power Pn , rated voltage Un , and rated speed n n matching predefined main dimensions (rotor inner diameter, stator outer diameter, air gap size, and length of the motor were strictly defined by the technical conditions) that has encouraged us to write this paper. The key requirement for this motor was to achieve the minimal torque pulsations. As a prototype of this motor, we took an existing design of SMPM with distributed winding developed before for the same purposes. However, the torque pulsations in this existing design did not meet the requirements, which was confirmed by the results of numerical simulation.
Manuscript received May 23, 2014; revised August 25, 2014; accepted October 3, 2014. Date of current version April 22, 2015. Corresponding author: S. Shimansky (e-mail:
[email protected]). Digital Object Identifier 10.1109/TMAG.2014.2362961
The torque is pulsating because of the following [6]. 1) The cogging torque—It is generated by the variation of the magnetic permeance seen by the PMs due to the slotting of the stator surface, even when there is no stator excitation. 2) The variation of permeance seen by the PMs due to magnetic saturation. 3) Space harmonics—The interaction between the spatial harmonics in the field produced by the PMs and the harmonics in the field produced by the windings. If the machine is supplied with a sinusoidal current, the torque ripple without cogging can then be calculated from the harmonics in the back electromotive force. 4) Time harmonics—The inverter induces time harmonics in the field produced by the windings, which generates a pulsating torque when interacting with the rotor field. 5) Undesirable imperfections in the motor such as the eventual eccentricity of the rotor or uneven magnetization of the magnets. A new motor design with concentrated winding was created according to the recommendations given by Prof. Florence Libert (Sweden) in his book, Design Optimization, and Comparison of PM Motors for a Low Speed Direct Driven Mixer. Prof. Libert names the following advantages that make the concentrated windings interesting. 1) Their end-windings are much shorter than those of distributed windings. As a consequence, the copper losses are lower. 2) They can be mounted very easily around the teeth since the end-windings are not overlapping. This simplifies the production and reduces the cost. 3) Some configurations enable a low torque ripple [4]. A conventional three-phase stator winding was replaced by a concentrated one. In addition to that, the form and the number of slots were changed, respectively, with the main dimensions (rotor inner diameter, stator outer diameter, air gap size, and length of the machine) being the same. The number of the poles chosen for this design is 64 and the number of the stator slots for the coils is 72. Such ratio was
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8101704
IEEE TRANSACTIONS ON MAGNETICS, VOL. 51, NO. 3, MARCH 2015
Fig. 3. B-field distribution in the gap for the different values of the PMs height.
Fig. 1.
Cross section of the motor with the PMs on the rotor surface.
Fig. 4. B-field distribution in the gap for the different values of the PMs width. Fig. 2. Optimized parameters for achieving maximum flux density in the gap between the rotor and the stator.
chosen based on [4]. The outer radius of the stator is 1.5 m. The general view of the motor cross section is shown in Fig. 1. The feature of this calculation was the optimization of the motor design by means of the finite element analysis (FEA). We have developed our own method of particular geometry modification, based on optimization using ANSYS Maxwell an interactive software package that utilizes FEA. The magnet shape and stator slots size optimization was aimed at reducing the manufacturing cost and decreasing the vibrations of the rotor caused by the high-order angular harmonics of electromagnetic torque in the main motor gap. III. A NALYSIS OF THE O PERATIONAL PARAMETERS OF THE M OTOR AND THE O PTIMIZATION S TRATEGY A general procedure of the motor shape optimization, which we consider in this paper, consists of several stages. At the first of them, an optimal configuration of the rotor arrangement was defined. For this purpose, the first optimization model was created (represented in Fig. 2). Four parameters change so as to keep the air gap constant. Optimization was conducted using four parameter values with following priorities: 1) maximal magnetic induction amplitude in the gap; 2) maximal slot depth; 3) minimal magnets mass; and 4) minimal distance between the magnets. At this stage, we have set zero current value in the stator windings and fixed mutual position between the motor parts. Performed numerical experiments have demonstrated that the key parameters, which define the amplitude and the quality
Fig. 5.
Current density distribution in the concentrated winding.
of the field distribution in the gap are the dimensions of the PMs. With the magnet width increasing so does the magnetic leakage, at the same time, the induction amplitude
KALIMOV AND SHIMANSKY: OPTIMAL DESIGN OF THE SYNCHRONOUS MOTOR
Fig. 8.
Fig. 6.
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Optimization model and parameters of the stator slot tooth.
Flux lines of magnetic potential.
Fig. 9. Dependence of the torque applied to the rotor along the angular coordinate for the initial motor prototype.
Fig. 10. Dependence of the torque applied to the rotor along the angular coordinate for the optimized motor cross section. Fig. 7.
Optimization model and parameters of the stator slot tooth.
rises slightly. However, an excessive decrease in the magnet width can lead to the negative values of the torque pulsations. With an increase of the magnet height to a certain value, the amplitude of the magnetic induction in the gap increases significantly. The plots illustrating corresponding dependencies are shown in Figs. 3 and 4. At the second stage of the optimization procedure, a dynamic problem (constant power motor simulation) involving the rotor movement was solved. In the model, we have used geometry of the rotor obtained during the first stage and an approximate stator geometry. The rotation speed of the rotor was assumed to be constant. The tooth-concentrated double-layer windings were connected to a rated sinusoidal time-varying voltage source. This task was solved to make sure that the preliminary torque pulsations do not exceed permissible value and the choice of the excitation source of the motor was right. As a result, we can also define the values
of the phase currents for the steady operation type with rated power. These currents were used for the final optimization of the yoke configuration. This task was solved within a 2-D formulation. Since the geometry is symmetric and we expect end effects to be negligible. End-winding leakage is considered as phases’ inductive reactance value. Fig. 5 shows the change in the magnitude of the current versus time for the three phases and the distribution of current density for a certain moment of time (the moment of time chosen is when the rotor and the stator are located symmetrically to each other and the model is being located in the same position as in the static optimization task). The latter is marked with dotted line on the plot. This formulation allows determining the distribution of currents with torque angle being considered. Fig. 6 shows the flux lines of magnetic potential a few time steps before.
8101704
IEEE TRANSACTIONS ON MAGNETICS, VOL. 51, NO. 3, MARCH 2015
with the torque angle being considered. Having solved the task, we have determined the distribution of the equivalent mass, which is the area of the stator core segment and as well in the previous case, we have obtained a distribution B-field value along gap for a chosen sector of the motor and have integrated it. This dependence is shown in Fig. 8. The chosen optimum is marked with a dotted circle. The field quality was controlled by dynamic modeling of SMPM using ANSYS Maxwell software (transient problem type). Corresponding plots for the initial motor prototype and the optimized version are shown in Figs. 9 and 10. In these plots, one can observe a significant improvement of the field quality in the motor gap. IV. C ONCLUSION This paper proposes an optimization strategy for the cross section of a PM motor. The procedure allows to increase the maximum flux density in the motor gap and to improve the torque distribution along the angular coordinate. These improvements lead to the reduction of manufacturing costs for the motor of the same overall dimensions and a decrease of the torque ripple by 12 times. A new design with concentrated winding drastically reduces the end-winding length, as shown in Fig. 11. Fig. 11. End-winding length in concentrated and distributed winding designs.
R EFERENCES
At the third stage of the optimization procedure, the parameters of the slot tooth were varied to achieve the best field distribution along the gap. The best field distribution is considered the one that grants optimal high lengthwise magnetic field integral value with optimal low weight of the stator core. This goal was achieved by suppressing high-order field harmonics along the angular coordinate. The optimization model and parameters are shown in Fig. 7. This task was also performed using ANSYS Maxwell Optimetrics module. The task belongs to a parametric type task, with dimensions of the slot tooth being parameters and minimal stator core mass and peak value of magnetic induction in the gap being criteria. The task specifies the phases’ currents
[1] L. Soderlund, J.-T. Eriksson, J. Salonen, H. Vihriala, and R. Perala, “A permanent-magnet generator for wind power applications,” IEEE Trans. Magn., vol. 32, no. 4, pp. 2389–2392, Jul. 1996. [2] F. Caricchi, F. Crescimbini, and O. Honorati, “Modular axial-flux permanent-magnet motor for ship propulsion drives,” IEEE Trans. Energy Convers., vol. 14, no. 3, pp. 673–679, Sep. 1999. [3] T. Higuchi, J. Oyama, E. Yamada, E. Chiricozzi, F. Parasiliti, and M. Villani, “Optimization procedure of surface PM synchronous motors,” IEEE Trans. Magn., vol. 33, no. 2, pp. 1943–1946, Mar. 1997. [4] F. Libert, “Design, optimization and comparison of permanent magnet motors for a low-speed direct-driven mixer,” Ph.D. dissertation, Dept. Elect. Eng., Roy. Inst. Technol., Stockholm, Sweden, 2004, p. 132. [5] J. Cros and P. Viarouge, “Synthesis of high performance PM motors with concentrated windings,” IEEE Trans. Energy Convers., vol. 17, no. 2, pp. 248–253, Jun. 2002. [6] F. Meier, “Permanent-magnet synchronous machines with nonoverlapping concentrated windings for low-speed direct-drive applications,” Ph.D. dissertation, Dept. Elect. Eng., Roy. Inst. Technol., Stockholm, Sweden, 2008, p. 177.
