Optimizing an Interior-Permanent-Magnet Tooth-Coil-Winding Traction Motor for its Entire Operating range

This is the accepted version of a paper published in International Conference on Electrical Machines (ICEM), IEEE, 2024. The final version is available at IEEE Xplore: https://doi.org/10.1109/ICEM60801.2024.10700222. This research received funding from the EU Horizon Europe MSCA Doctoral Network [HIPO], Grant Agreement No. [101072580]. Optimizing an Interior-Permanent-Magnet ToothCoil-Winding Traction Motor for its Entire Operating range Arash Allahyari School of Energy Systems LUT University Lappeenranta, Finland [email protected] Pia Lind School of Energy Systems LUT University Lappeenranta, Finland [email protected] Emine Bostanci dept. of Electrical-Electronics Engineering Middle East Technical University Ankara, Turkey [email protected] Lassi Aarniovuori School of Energy Systems LUT University) Lappeenranta, Finland [email protected] Gamze Odabas Arcelik A.S Istanbul, Turkey [email protected] Juha Pyrhönen School of Energy Systems LUT University Lappeenranta, Finland [email protected] Abstract—Design and optimization of an interior-permanent magnet motor (IPM) with tooth-coil-windings (TCWs) for traction motors are studied. Main goals are to deliver high torque and low torque ripple in the entire range of operation with lowest possible magnet usage. Design of an IPM-TCW motor with acceptable torque ripple in its entire operation range is challenging due to several reasons such as variation of harmonics of stator and rotor current linkages with saturation, slotting effects, and unity winding factor for all harmonics (for 12 slot 8 pole). Moreover, torque ripple varies based on the requested current angle and current density. In this study, an effective optimization method is proposed to reach an acceptable average torque and torque ripple in the whole range of operation. To further decrease the torque ripple utilization of notches on the rotor surface and semi magnetic wedges in the stator are proposed and compared with rotor skewing as an alternative. A model of IPM traction motors, with single V positioned magnets for an electric motorcycle is implemented and investigated. The Optimized machine has a power rating of 6 kW with maximum speed of 10,000 r/min operating speed with a 48 V battery. Finite element method is utilized to optimize the geometry of the IPM motor. Keywords — tooth windings, interior permanent magnet motors, torque ripple reduction methods, variables speed drive, geometry optimization, semi magnetic wedges. I. INTRODUCTION Interior permanent magnet motors are widely adopted for propulsion of electric vehicles such as BMW, Nissan, Tesla, Toyota, Chevrolet etc. [1]. IPMs offer high torque density and high efficiency with the help of strong rare-earth magnets. These machines can operate in a wide speed range as placing the magnets inside the rotor increases the inductances necessary for good field-weakening performance. Embedding the magnets results in a fairly strong rotor structure capable of withstanding high centrifugal forces. Furthermore, by utilization of strong magnets, the total volume of the machine is decreased [1]. Thereby, use of IPMs are advantageous for lightweight EVs such as motorcycles to achieve a compact, lightweight, efficient, and possibly even cheap powertrain. Therefore, investigation of machine design requirements for such vehicles is valuable. Most important factors in the design of IPMs are, slot/pole combination, outer diameter of stator/rotor, stack length of the machine, winding configuration, topology of the magnets including number of layers and shape of the magnets. For a particular application, the torque-speed-curve requirements are different. Hence, selection of the parameters mentioned must be based on the operation points. Moreover, for light EVs such as motorcycles and electric bikes cost reduction is important. Utilization of motors with TCWs are attractive for these industries due to several advantages such as simplicity of mass production, reduced usage of copper which means lower cost in comparison with distributed windings due to shorter end windings and also higher effective length of the machine. However, resultant current linkages from TCWs are highly distorted and their back-EMFs have high harmonic content. Therefore, high torque ripple is possible in IPMs with TCWs. Therefore, the design of an IPM with TCWs is challenging. This situation gets worse when a machine is supposed to operate at various operating points like in EV applications in which the whole range of operation must be considered to keep torque ripple in an acceptable range. In literature the design of IPM motors with TCWs is presented. However, only the rated point operation is typically considered in minimizing the torque ripple. As it is known, torque ripple changes with current density and current angle. However, this is inappropriate for an EV application where the torque ripple is a function of speed and torque [4,5]. Hence, torque ripple matter should be considered more carefully. The first parameter to decide in IPMs with TCWs is slot/pole combination which highly affects torque ripple. [2,3] provided a comprehensive study on slot/pole combination of fractional slot TCW IPM motors. In reducing torque ripple an important task is to optimize the rotor geometry. Hence, based on the considered magnet layers and structures, rotor geometry variables are decided and optimized [6-9]. Naturally, most important rotor geometry variables are the ones that influence the directand quadrature-axis inductances (Ld and Lq). Moreover, introduction of geometric changes on the surface of the rotor will affect torque ripple. Such methods have been utilized in several studies [10]. Another means of reducing torque ripple is to optimize the stator teeth geometry. This is, however, not as effective as manipulating the rotor geometry [11]. Moreover, harmonic current injection is one of the methods suggested to reduce torque ripple. It can also increase the average torque as reported in [12]. This paper focuses on the optimization of IPM-TCW motors considering the whole range of operation taking all geometry variables in the rotor and stator into account to maximize the average torque, minimize torque ripple and magnet mass. Furthermore, utilizing notches in the rotor surface to reduce torque ripple is also studied and results compared with skewing of the rotor. This paper is organized as follows. Firstly, available slot pole combinations for TCW machines are presented in section II. Section |III introduces the IPM motor model and its variables plus initial design variables to perform the optimization. Section III explains the adopted method to optimize the machine and ensure that its performance is close to 6 kW up to maximum speed. In section IV, to further reduce the torque ripple, utilization of notches, semi magnetic wedges and rotor skewing are investigated and compared. Section V is dedicated to studying the performance of the machine in the whole torque-speed range of operation up to 10,000 r/min. II. MODEL OF INTERIOR PERMANENT MAGNET MACHINE WITH CONCENTRATED WINDINGS Utilizing concentrated non-overlapping i.e. tooth-coil windings in IPMs is beneficial because TCWs are easier to manufacture in comparison with distributed windings, TCWs can reach higher slot copper space factor (fill factor) (>50 %), higher stack to active length and better heat dissipation in end windings due to shorter end windings. These advantages make TCWs attractive also for automotive industry. However, there are disadvantages such as high harmonic content in the airgap which can create torque ripple or noise and vibration. Therefore, careful design measures must be adopted in the design of such machines. The number of available slot/pole combinations are limited for TCWs. In this regard, Table I shows several slotpole combinations and operating harmonic winding factors. Due to unbalance forces, slot-pole combinations with odd number of slots are not included in Table I. The main goal of this study is to design a naturally cooled 6 kW, 10,000 r/min motor for an electric motorcycle. High pole and slot numbers cannot be selected because the size of the machine is small, and it will not yield to an acceptable geometry for the magnets or teeth. It should be mentioned that noise and vibration are also important issues that should be considered in automotive industry, and according to literature 12s/8p is a good combination to have a low noise and vibration while 12s/10s can create higher noise and vibrations [13]. 12s/8p is one of most common slot/pole combinations among TCW machines. Hence, 12s/8p is selected for further study and optimization. This machine, in principle, contains four 3s/2p machines and therefore operates with the fundamental while e.g. the 12s/10p machine operates with the fifth harmonic. TABLEI SLOT/POLE COMBINATIONS WITH TCWS Slot/Pole Operating harmonic w inding factor 6s/4p, 6s/8p, 12s/8p, 18s/ 12p, 1 6s/ 6p, 0.866 12s/16p, 24s/16p, 6s/ 20p, 30s/ 20p 12s/10p 0.933 18s/10p 0.735 12s/14p 0.933 18/s14p 0.901 24s/20p 0.933 Fig. 1 Model of an IPM motor with TCWs and considered variables for optimization. TABLEII IPM MODEL VARIABLES FOR OPTIMIZATION Variables Explanation Range of value x1 Magnet height [mm] 3 - 6 x2 Magnet width [mm] 12 - 18 x3 Rotor radius [mm] 40 - 50 x4 V angle [deg.] 60 – 120 x5 Web length [mm] 1 - 5 x6 Slot opening length [mm] 4 (fixed) x7 Tooth width [mm] 9 – 13 x8 Slot height [mm] 19 - 26 TABLEIII IPM MODEL INITIAL DESIGN SPECIFICATIONS Active volume [litre] 0.9 Air gap length [mm] 0.8 Maximum current density [A/mm 2 ] 8 Slots/poles 12s/8p Number of phases 3 Slot copper space factor (fill factor) 0.48 DC link voltage (V) 48 Core material M250-35A Magnet type N42UH@65 ℃ Slot/pole/phase [ 𝑞 ] 0.5 Turns/phase 28 The design procedure is commenced with implementation of an IPM motor model for Finite Element Analysis (FEA). The model is shown in Fig. 1, where the rotor, stator, magnets, and windings of a 12s/8p machine plus geometry variables to perform optimization are depicted. Geometry variables are defined in Table II with their ranges considered for the optimization process. Initial design specifications are given in Table III. The machine is designed for maximum current density of 8 A/mm2 to reach its maximum torque. This value of current density is only supposed to be applied when the motorcycle is accelerating for a short time (<10 seconds). Furthermore, in this study the stator external diameter and stack length are fixed while other variables are optimized based on the required performance. III. OPTIMIZATION METHODOLOGY OF IPM MOTOR WITH CWS The adopted optimization algorithm is based on the multi objective genetic algorithm. The suggested methodology gathers required performance of the machine at two operating points of current density and current angle at 1500 r/min and 6000 r/min as listed in Table IV (point 1 is utilized to maximized the initial torque and pint 2 is utilized to make sure machine can generate sufficient power at high speeds). The current angle is defined by taking q-axis as reference and dand q-axes are defined in Fig. 3. and creates a cost function based on summation of average torque, torque ripple and magnet mass for every design. Optimization objectives are: Maximizing the summation of average torque at two points. Minimizing the summation of torque ripple percentage at two points. Minimizing the magnet mass. It should be noted that the design of the machine that can hold the maximum power up to maximum speed is a challenge. Hence, to make sure that the machine can deliver the requested power while operating at its maximum speed, terminal voltage and power are calculated at point 2 to make sure that machine stays in the voltage limit and can generate sufficient power at high speeds. So, a penalty is considered for objective function of the machines that do not stay in the voltage limit of 48 Volts and cannot operate at 6000 r/min. Implementing such a method makes sure that the machine can hold the power from the base speed to the maximum speed. It should be mentioned that in most of the studies on design of an IPM with TCWs, the methodology only optimizes the motor at a single speed (base speed) while in automotive applications, the motor must operate in a wide speed range and different torque-power points. Hence, this research fills the gap that exists in the design of IPM-TCW motors for automotive applications and presents an effective optimizing method. The optimization method is implemented to reach at least 22 Nm at point 1 with less than 10% and 30 % torque ripple at point 2, while minimizing the required magnet mass. The designs of all the generations created by the optimization algorithm are shown in Fig. 2. The selected design is marked among all the generated designs. The design is selected (Fig.2a) to have a maximum torque with sum of torque ripples less than 40%. Fig. 2b also shows the compromise between average torque and magnet mass. Fig. 3 shows the geometry variables of the selected design. Selected design delivers 23.7 Nm at current density of 8 A/mm2 and current angle of 20 degree (angle from q axis). with torque ripple of 11.7 % and magnet mass of 0.345 kg. To further analyse the selected machine, a parametric analysis is conducted with current density range between 4-8 A/mm2 and current angles between 20-70 deg. Average torque and torque ripple percentage values are shown in the contour maps of Fig. 4. TABLEIV CURRENT DENSITY AND ANGLE POINTS USED TO CREATE THE COST FUNCTION Point Number Current Density [A/mm2]Current Angle [deg.] Speed [r/min] 1 8 20 1500 2 6 75 6000 The torque ripple values are in the range of 9-30% in most of the points in Fig.4b which is promising for the IPM-TCW motors. However, expectation for the torque ripple is to be less than 10%. The effects of notches to further reduce torque ripple is studied in section IV and compared with results from rotor skewing. (a) Sum of average torque vs. sum of torque ripple (b) Sum of average torque vs. magnet mass Fig. 2 Results of optimization, All the generated designs by optimization algorithm x1 = 3.8 mm x2 = 16.7 mm x3 = 47.8 mm x4 = 81 deg x5 = 1.6 mm x7 = 11.6 (top) , 12.5 mm (bottom) x8 = 20.7 mm x9 = 7.8 mm Fig. 3 Geometry of the selected IPM motor from the optimization results. (a) Average torque vs. current density and angle (b) Torque ripple percentage vs. current density and angle Fig. 4 Average torque and torque ripple percentage values versus current density and angle (angle from q axis) for the selected motor. Technically, this study suggests that the optimization is separated into two parts, the first optimization is performed with the introduced variables in Table II at two operating points and then the second optimization is performed with notches on the rotor surface to decrease the torque ripple at three different operating points. This is done to reduce the duration of optimizations and increase the chance of reaching an acceptable point. IV. METHODS TO REDUCE TORQUE RIPPLE IN THE WHOLE RANGE OF OPERATION Two methods are proposed, namely, notches on the rotor surface and using semi magnetic wedges in the stator slot openings to further reduce the torque ripple. The results are compared with the conventional rotor skewing method. A. Optimization of notch 1 and 2 to reduce torque ripple This chapter proposes utilization of notches on the rotor surface to reduce torque ripple and presents the optimization results. Since the torque ripple changes with saturation, current density and current angle, the provided results are beneficial to understand the effect of utilizing notches on the entire range of operation in variable speed motors. The proposed notches are shown in Fig. 5. Similar to section III, optimization is conducted to minimize the torque ripple and maximize the average torque on the selected design in section III by gathering sum of torque ripple and average torque values from three different point as shown in Table V. It is important that using notches does not cause the average torque to decrease. Hence, maximizing the average torque is also considered in the cost function. Optimization variables for the notches are shown in Fig. 5, every notch has two geometry variables (x8 and x9) plus notch 2 has an additional rotation angle variable which is considered as rotation from d-axis. Hence, in total, 5 variables are considered for optimization. All the designs generated by the optimization algorithm are shown in Fig. 6a and Fig. 6b shows the geometry of the selected notches. Moreover, Fig. 6c shows the torque ripple vs. current density and current angle. Results of Fig. 6c present that effective usage of two notches reduces torque ripple in the whole range of operation. Fig. 6c shows that the torque ripple is less than 9% for current densities higher than 6.5 A/mm2. It should be mentioned that using two notches reduces the average torque by roughly 0.2 Nm at current density 8 A/mm2 and current angle of 20 degrees. TABLEV CURRENT DENSITY AND ANGLE POINTS USED FOR OPTIMIZATION WITH NOTCHES Point Number Current Density [A/mm2]Current Angle [deg] Speed [r/min] 1 8 20 1500 2 8 70 1500 3 6 70 1500 Fig. 5 Utilization of notches in the rotor of an IPM model, introduction of variables for notch 1 and notch 2 (a) All generations of optimization algorithm when both notch1 and notch2 are considered (b) Selected geometry of notch 1 and notch 2 from optimization results (c) Torque ripple percentage vs. current density and current angle Fig. 6, Results of torque ripple minimization with notch1 and notch2. B. Utilization of semi magnetic wedges to reduce torque ripple Utilization of semi magnetic wedges to reduce torque ripple is investigated in this section. The proposed semimagnetic wedges are shown in Fig.7a. Results in Fig. 7b show that utilizing semi-magnetic wedges with relative permeability of 3 can effectively reduce the torque ripple, thereby, based on the application requirement, it is possible that careful usage of semi magnetic wedges eliminates the need for other methods such as notches in the rotor surface or rotor skew to reduce torque ripple and thus highly beneficial for mass production. It should be mentioned that using semi magnetic wedges reduces the average torque by roughly 0.5 Nm at current density of 8 A/mm2 and current angle of 20 degree. (a) proposed semi magnetic wedges (b) Effect of semi magnetic wedges on the torque ripple percentage vs. current density and current angle (angle from q axis). Fig. 7, Results of study on the semi magnetic wedges in the stator C. Optimization of both notch 1 and 2 while using semi magnetic wedegs to reduce torque ripple Optimization of both notch 1 and 2 while semi magnetic wedges are used in the stator is investigated in this section. Optimization is performed to minimize torque ripple and maximize average torque at three different operating points as shown in Table V. In this optimization, five variables of notch1 and 2 are investigated. Pareto front of this optimization is presented in Fig. 8a along with selected design. The selection is based on reaching minimum torque ripple. Moreover, Fig. 8b shows the optimized geometry of notches 1 and 2. Fig. 8c shows the effectiveness of the torque ripple reduction method at various current densities and current angles. Results in Fig. 8 demonstrate that this method is an effective one to reduce torque ripple in the whole operating range as the torque ripple is less than 7% in most of operating points. Another important factor is the effect of torque ripple reduction methods on the average torque which will be investigated at the end of this section. (a) Optimization pareto front when using both notches 1 and 2 in the rotor and semi-magnetic wedges in the stator (b) Selected geometry of notch 1 and 2 while using semi magnetic wedges Fig. 8, Effect of using both notch 1 and 2 in rotor and semi magnetic wedges in the stator on the torque ripple percentage vs. current density and current angle (angle from q axis). D. Utilization of rotor skew to reduce torque ripple To complete the discussion about torque ripple reduction methods, the effect of skew is studied in this section. Skewing is one of the most effective methods to reduce torque ripple. However, skewing introduces manufacturing challenges, and it increases the cost of production. Moreover, skewing means that rotor laminations should be produced separately and assembled thereafter. The considered skew for this motor, is a step skew with 5 slices and total 10-degrees angle for the slices (-5 deg, -2.5 deg, 0, 2.5 deg, 5 deg). Such an arrangement can effectively reduce the 6th harmonic in the torque and, therefore, reduce the torque ripple. The results for torque ripple with skewed rotor are demonstrated in Fig. 9. It shows that skewing is effective. However, skewing reduces the average torque roughly by 1 Nm at current density of 8 A/mm2 and current angle of 20 degrees. This is an important disadvantage of skewing. Fig. 9 Results of torque ripple percentage with skewing (total 10 deg, 5 slices) vs. current density and current angle (angle from q axis). E. Effect of investigated torque ripple reduction methods on the average torque A deeper look into the effect of notches, semi-magnetic wedges and rotor skew on the average torque and torque ripple is presented in this section. The effect of these methods on the average torque and their effectiveness to reduce torque ripple is studied considering nine operating points in Fig. 10a-b respectively. Interestingly, among these methods, the highest torque ripple reduction is achieved by simultaneous use of the notches on the rotor surface with semi-magnetic wedges in the stator or using rotor skew. However, rotor skew reduces the average torque roughly by 1 Nm (4.2%) while using both notches and semi magnetic wedges does not reduce the average torque. (a) Effect of investigated torque ripple reduction methods on the average torque at various operating points (b) Comparison on the effectiveness of investigated torque ripple reduction methods at various operating points Fig. 10, Comparison of the proposed methods to reduce torque ripple at different operating points. (a) Torque vs. speed efficiency map (b) Power vs. speed efficiency map Fig. 11 Efficiency maps of the optimized IPM machine Consequently, the results demonstrate that skewing is not the best method to reduce the torque ripple in this case where large skewing angel is needed. Even though the usage and design of notches can be complicated in the design stage, it is worth using them in mass production instead of skewing. V. INVESTIGATION OF IPM MOTOR PERFORMANCE IN THE WHOLE RANGE OF OPERATION To investigate the performance of the selected design on the whole range of operation, efficiency maps versus average torque and power are presented in this section. In these efficiency maps, the maximum speed of the machine is considered to be 10,000 r/min with maximum input current of 120 Arms (equal to 8.47 A/mm2). Efficiency maps are shown in Fig. 11. Considered losses comprised of DC and AC winding loss, core loss and 50 Watts of mechanical loss at the maximum speed. As seen in Fig. 11, the selected machine delivers a 24.8 Nm maximum torque and can deliver 6.2 kW power at 3600 r/min. However, the power drops to 3 kW at 10,000 r/min. It should be noted that this motor is designed for traction, thereby, initial high torque is essential and required power at the maximum speed is related to the actual application of the vehicle. However, according to calculations, if 6 kW at 10,000 0 4 8 12 16 20 24 8,20 8,50 8,70 7,20 7,50 6,20 6,70 5,20 4,20 Average Torque [Nm] Current density [A/mm2], Current Angle [deg] Original selected design Using notch1 and notch 2 Using semi magnetic wedge Using rotor skew notches 1,2 and sem magnetic wedge 0 5 10 15 20 25 30 8,20 8,50 8,70 7,20 7,50 6,20 6,70 5,20 4,20 Torque ripple [%] Current density [A/mm2], Current Angle [deg] r/min is needed then input current needs to be increased to 135 Arms. VI. CONCLUSION IPM motors with TCW machines are attractive for traction applications because, they have shorter end windings and thereby the active length of the machine can be increased which will lead to higher power and torque density. However, higher torque ripples are seen in IPM-TCW machines due to the existence of high order harmonics in airgap. Furthermore, torque ripple changes at various current densities and current angles. Hence, in this study an effective optimization method to design an IPM-TCW motor for traction application was proposed. In the proposed methodology, the performance of the machine at several operating points of current angle and current density are gathered to create an objective function and optimization algorithm tries to maximize the average torque and minimize the torque ripple and magnet mass in all the considered operating points simultaneously. Results showed that the optimization method can effectively guide the design in the correct direction and suggest several designs for the machine geometry which can be selected based on requirements of torque, torque ripple and magnet mass. Additionally, to further decrease the torque ripple, usage of notches and semi magnetic wedges are investigated, and the results compared with the effects of using rotor skewing. In this regard, it was found out that both notches and semi magnetic wedges can reduce the torque ripple to values lower than 7% in the whole range of operation which is lower than what was achieved by rotor skewing. Finally, efficiency maps of the selected machine were calculated up to the maximum speed of 10,000 r/min. The results showed that the designed motor can reach the maximum power of 6.2 kW with initial torque of 24.8 Nm with 120 Arms input current and 48 V battery voltage limit. Furthermore, the ratio of maximum to base speed is 4.54 which is considerable. VII. 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