Alternating current motor, design method and manufacturing method thereof, and design auxiliary device

Abstract

An AC motor is provided with a rotor (22), a stator (20) having a plurality of slots (21) arranged in the circumferential direction so as to face the rotor (22), and a multi-phase winding wound around the plurality of slots (21). The number of windings of any first phase among the plurality of phases housed in each of the plurality of slots (21) periodically varies in the circumferential direction. The distribution of the number of windings of the first phase per cycle is approximated by a Fourier series having a fundamental component and a third harmonic component as main components. The approximate curve of the distribution is shaped to superimpose the positive half cycle of the sine function as the fundamental wave and the third harmonic in a phase relationship in which its value is enhanced near the peak value of the sine function and its value is cancelled near the zero value of the sine function.

Description

TECHNICAL FIELD

[0001] The present disclosure relates to an alternating-current electric machine such as a permanent magnet synchronous electric machine and an induction electric machine, a design method, a manufacturing method, and a design assistance device thereof. BACKGROUND

[0002] In order to reduce the emission of greenhouse gases, it is urgent to improve the efficiency of rotating machines that account for nearly half of the power consumption in the world.

[0003] Hitherto, various design methods for achieving the high efficiency of a rotating machine unit have been proposed. For example, Non-Patent Literatures 1 and 2 disclose a method of performing optimization by finely adjusting dimensions such as the circumferential width of slots of a stator as a variable from a widely spread basic structure model.

[0004] PRIOR ART DOCUMENTS

[0005] NON-PATENT LITERATURES

[0006] Non-Patent Literature 1: Hosokawa et al., “A Method for Efficiency Optimization Design of Permanent Magnet Motors - Optimization Design Method Using GA·SA -”, Transactions of the Institute of Electrical Engineers of Japan D (Industrial Applications), vol. 121, No. 2, 2001, pp. 171-177

[0007] Non-Patent Literature 2: Onishi et al., “Study on Design Method of IPM Motors Using Finite Element Method and Optimization Method Together”, Transactions of the Institute of Electrical Engineers of Japan D (Industrial Applications), vol. 121, No. 3, 2001, pp. 397-402 SUMMARY

[0008] PROBLEMS TO BE SOLVED BY THE INVENTION

[0009] The dimension optimization of the above Non-Patent Literatures 1 and 2 depends on the topology of the initial shape of the alternating-current electric machine, and thus, it is difficult to expect a large performance improvement. For example, regarding the structure of the stator slots and the like, since it is difficult to make a unified discussion, sometimes the optimal structure is considered to be different depending on the designer.

[0010] The present disclosure was completed in view of the above-described background, and one of the objects thereof is to provide a design method of an alternating-current motor, with respect to a stator slot, capable of uniquely determining an optimal structure regardless of a designer. Another object of the present disclosure is to provide an alternating-current motor having a structure capable of increasing an average torque on the basis of reducing torque ripple by being designed in accordance with the above-described design method.

[0011] Means for solving the problem

[0012] The design method of the alternating-current motor of one embodiment includes first to fourth steps. In the first step, a computer approximates an absolute value of a first periodic function in which a magnetic pole period of a stator of an alternating-current motor is changed in a circumferential direction, using a pulse function having a pulse width corresponding to the absolute value of the first periodic function, and determines a region in which the pulse function becomes an on-pulse as a winding arrangement region. Here, the first periodic function is a function in which a sine function as a fundamental wave and a third higher harmonic wave are superimposed in a phase relationship in which a value of the sine function is enhanced near a peak value of the sine function and a value of the sine function is canceled near a zero value of the sine function. In the second step, the computer arranges a plurality of windings of a small cross-sectional area at equal intervals in the determined winding arrangement region. In the third step, the computer enlarges a cross-sectional area of each winding, and in a case where adjacent windings overlap each other or in a case where a proportion of a portion in which the windings are arranged in the length of the circumferential direction of the stator exceeds a predetermined ratio, a new winding is generated as a winding aggregate by synthesizing the closest windings with each other. Here, the winding aggregate is a winding having a total number of the plurality of windings after the synthesis and a sum of the cross-sectional areas of the plurality of windings after the synthesis. The synthesis of a first winding and a second winding includes arranging a winding after the synthesis between the first winding and the second winding. In the fourth step, the computer determines a position at which each winding aggregate is arranged as a position at which a slot in which each winding aggregate is accommodated is arranged when a number of the winding aggregates obtained as a result of the enlargement of the cross-sectional area of each winding reaches a desired number.

[0013] The alternating-current motor of one embodiment includes a rotor, a stator having a plurality of slots arranged in a circumferential direction so as to face the rotor, and a plurality of windings of a plurality of phases wound around the plurality of slots. A number of windings of an arbitrary first phase among the plurality of phases accommodated in each of the plurality of slots changes periodically in the circumferential direction. A distribution of the number of the windings of the first phase per period is approximated by a Fourier series having a fundamental wave component and a third higher harmonic wave component as main components. An approximate curve of the distribution is a shape in which a positive half period of a sine function as a fundamental wave and a third higher harmonic wave are superimposed in a phase relationship in which a value of the sine function is enhanced near a peak value of the sine function and a value of the sine function is canceled near a zero value of the sine function.

[0014] Effects of the invention

[0015] According to the above design method, the structure of the stator slot can be uniquely determined independently of the designer while maintaining electromagnetic field characteristics of an ideal sinusoidal wave as much as possible. According to the above alternating-current motor, average torque can be increased while reducing torque ripple. BRIEF DESCRIPTION OF DRAWINGS

[0016] Figure 1 is a schematic view of the structure of a rotating machine to which the present disclosure relates.

[0017] Figure 2 is a flowchart showing steps for making a line current approximation model.

[0018] Figure 3 is a view showing specific examples of a modulation wave and a carrier wave of PWM.

[0019] Figure 4 is a view showing a step of designing a slot structure. Figure 3 is a view showing the number of windings in each region when the windings are equally arranged in each winding arrangement region in the example of

[0020] Figure 5 is a flowchart showing a step of designing a slot structure.

[0021] Figure 6 is a view for explaining a method of combining a winding of a number of turns a1 and a cross-sectional area S1 with a winding of a number of turns a2 and a cross-sectional area S2.

[0022] Figure 7 is a view showing a specific example of a slot structure.

[0023] Figure 8 is a view showing, in tabular form, the number of windings arranged in the slots SL1 to SL6 of Figure 7 , the width in the circumferential direction, and the thickness in the radial direction of each slot.

[0024] Figure 9 is a view showing a required specification of a motor on a torque-speed plane.

[0025] Figure 10 is a view showing, in tabular form, various elements of a 25 kW class permanent magnet synchronous motor designed as a comparative example.

[0026] Figure 11 is a view showing a cross-sectional view of the permanent magnet synchronous motor of the comparative example designed.

[0027] Figure 12A is a view showing a torque characteristic obtained with respect to a maximum output point in the permanent magnet synchronous motor of Figure 11 the comparative example.

[0028] Figure 12B is a graph showing the torque characteristics obtained with respect to the maximum output point in the permanent magnet synchronous motor of Comparative Example 1. Figure 11

[0029] Figure 12C is a graph showing the torque characteristics obtained with respect to the maximum output point in the permanent magnet synchronous motor of Comparative Example 1. Figure 11

[0030] Figure 13 is a graph showing the cross-sectional view of the 25 kW class permanent magnet synchronous motor designed by the self-organization design method 1.

[0031] Figure 14 is a graph showing the ratio of the number of turns of each phase per stator slot in the permanent magnet synchronous motor of Example 1. Figure 13

[0032] Figure 15A is a graph showing the torque characteristics obtained with respect to the maximum output point in the permanent magnet synchronous motor of Example 1 (total output torque). Figure 13 Figure 14

[0033] Figure 15B Figure 13 Figure 14

[0034] Figure 15C Figure 13 Figure 14

[0035] Figure 16 is a typical magnetic flux density vector diagram corresponding to Figures 15A-15C

[0036] Figure 17A is a graph for explaining the principle of the average torque improvement method (sine wave and 3rd harmonic wave).

[0037] Figure 17B is a graph for explaining the principle of the average torque improvement method (distribution of sine wave and distorted wave).

[0038] Figure 18 is a graph showing the current distribution based on the approximate model of the line currents of the U phase, the V phase, and the W phase before the self-organization design method 2 is performed. ​​​​​​​​​​​​

[0039] Figure 19 is a graph showing a cross-sectional view of a 25 kW class permanent magnet synchronous motor designed by the self-organizing method 2.

[0040] Figure 20 is a graph showing the ratio of the number of turns of each phase per stator slot in the permanent magnet synchronous motor shown in Figure 19

[0041] Figure 21A is a graph showing the analytical results of the torque characteristics with respect to the maximum output point in the permanent magnet synchronous motor shown in Figure 19 and Figure 20

[0042] Figure 21B is a graph showing the analytical results of the torque characteristics with respect to the maximum output point in the permanent magnet synchronous motor shown in Figure 19 and Figure 20

[0043] Figure 21C is a graph showing the analytical results of the torque characteristics with respect to the maximum output point in the permanent magnet synchronous motor shown in Figure 19 and Figure 20

[0044] Figure 22 is a flowchart showing an example of a manufacturing method of an alternating current motor.

[0045] Figure 23 is a block diagram showing an example of a structure of a computer for executing the design steps shown in Figure 2 , Figure 5

[0046] Figure 24 is a functional block diagram showing the functions of a computer as a design assistance device. DETAILED DESCRIPTION

[0047] Hereinafter, each embodiment will be described in detail with reference to the drawings. In Embodiment 1, first, a model of an ideal stator structure that ignores the shape of the stator slot (in this disclosure, referred to as a "line current approximation model") is proposed. Next, while maintaining the performance of the line current approximation model as much as possible, by continuously implementing deformation, it is shifted to an actual slot structure. Thereby, a design method of a stator of a unique slot structure that is independent of a designer (in this disclosure, referred to as a "self-organizing design method") is provided.

[0048] ​​​​​In Embodiment 2, as a specific application example of the stator design method based on the line current approximation - self-organization design method of Embodiment 1, a design of a 25 kW class permanent magnet motor for a railway is explained.

[0049] In the following description, the same reference numerals are attached to the same or corresponding parts, and the explanation thereof is not repeated.

[0050] <Embodiment 1>

[0051] [Structure of rotary machine]

[0052] Figure 1 is a schematic view of a structure of a rotary machine to which the present disclosure relates. As shown in Figure 1 , the rotary machine has a structure of an inner rotor type in which a rotor 12 is disposed in a stator 11. A space between the stator 11 and the rotor 12 is referred to as an air gap 13. A cylindrical coordinate system is adopted with a rotation axis of the rotor 12 as a z axis, and a rotation direction of the rotor 12 is set as a θ direction. Note that, hereinafter, a case where an alternating current is input to the stator 11, that is, a case where the rotary machine 10 is an alternating current motor is explained. In addition, as shown in Figure 1 , a case where the rotary machine 10 is an inner rotor type is explained, but an outer rotor type in which the rotor 12 is disposed outside the stator 11 can also be similarly addressed.

[0053] [Line current approximation model]

[0054] A distribution of a rotating magnetic field generated by a stator winding contains many high harmonic components due to the shape of a slot and disposition. Therefore, in order to approximate a spatial distribution in which an ideal rotating magnetic field distribution is realized as a target, first, with respect to the shape of the slot, the winding is assumed to be a line current, and a cross-sectional shape of the slot is ignored. With respect to the slot disposition, an idea of pulse width modulation (PWM) utilized in an inverter or the like is applied in space, and a desired magnetomotive force distribution is approximately generated. Since the magnetomotive force distribution based on one winding becomes a rectangular wave, it can be explained that a high level state of a pulse wave (that is, an on pulse) corresponds to disposition of the winding.

[0055] Figure 2 is a flowchart showing steps for making a line current approximation model. Figure 2 Each step of

[0056] In step S100, the computer accepts input of the size of the rotary machine 10, the number of poles, the modulation ratio of the PWM, and the carrier frequency, the winding interval, and the like from the user. The size of the rotary machine 10 refers to the physical size of the rotary machine 10. Specifically, as the size of the rotary machine 10, the outer diameter and the inner diameter of the rotor 12, the outer diameter and the inner diameter of the stator 11, and the length in the z direction are input. As an example, in the configuration example of the line current distribution shown in FIGS. 1 to 3, the stator outer diameter: 112 mm, the stator inner diameter: 56 mm, the rotor outer diameter: 55 mm, the rotor inner diameter: 16 mm, and the length in the z direction: 60 mm are input. Figure 3 and Figure 4 In the configuration example of the line current distribution shown in FIGS. 1 to 3, the stator outer diameter: 112 mm, the stator inner diameter: 56 mm, the rotor outer diameter: 55 mm, the rotor inner diameter: 16 mm, and the length in the z direction: 60 mm are input.

[0057] In the following step S110, the computer approximates the absolute value of the first periodic function with a pulse function having a pulse width corresponding to the absolute value of the first periodic function, using the idea of the PWM, based on comparison of the first periodic function (corresponding to the modulation wave of the PWM) that changes in the circumferential direction at the pole period of the stator of the alternating-current motor and the second periodic function (corresponding to the carrier of the PWM) that has an amplitude larger than the amplitude of the first periodic function and a spatial frequency sufficiently higher than the first periodic function. The computer determines the region in which the approximated pulse function becomes the on pulse as the winding configuration region. Specifically, the interval in which the absolute value of the instantaneous value of the first periodic function is larger than the absolute value of the instantaneous value of the second periodic function as the comparison target is set as the on pulse region (i.e., the winding configuration region).

[0058] The first periodic function cites the sine wave as an example. As explained in detail in Embodiment 2, in order to increase the average torque value on the basis of reducing the torque ripple, it is preferable to superimpose a function in which the sine wave as the fundamental wave and the third-highest harmonic wave are superimposed in a phase relationship in which the peak position of the third-highest harmonic wave coincides with the peak position of the fundamental wave as the first periodic function. The second periodic function as the comparison target can be a triangular wave or a sawtooth wave, and is not particularly limited. When the number of poles of the stator is set to N, the period of the absolute value of the first periodic function is 360 / N [degrees] of mechanical angle (i.e., half of the pole period).

[0059] Figure 3 is a graph showing a specific example of the modulation wave and the carrier of the PWM. In Figure 3 , the case of 3-phase 4-pole is shown, and the winding configuration region of the U phase in the case where the modulation ratio of the PWM is set to 0.8, the modulation wave (the first periodic function) is set to the sine wave as an example (the pole period is 180 degrees of mechanical angle), and the period of the triangular wave (the second periodic function) is set to 9.0 degrees (mechanical angle) is shown. In order to easily correspond to the winding configuration, the region in which the absolute value of the instantaneous value of the modulation wave is larger than the absolute value of the instantaneous value of the carrier and the absolute value of the instantaneous value of the antiphase of the modulation wave is larger than the absolute value of the instantaneous value of the carrier is set as the region of the on pulse.

[0060] Note that the winding arrangement region of the V phase is a region in which the winding arrangement region of the U phase is shifted by 120 degrees in electrical angle (60 degrees in mechanical angle in the case of 3-phase 4-pole). Also, the winding arrangement region of the W phase is a region in which the winding arrangement region of the U phase is shifted by -120 degrees in electrical angle ( -60 degrees in mechanical angle in the case of 3-phase 4-pole). The modulation factor needs to be set to 1 or less.

[0061] Returning to Figure 2 , in the next step S120, the computer arranges a plurality of windings of small cross-sectional area at equal intervals in the winding arrangement region decided through step S110. By setting the winding intervals equally, the number of wirings in each winding arrangement region is approximately an integer. For example, in the case of Figure 3 , the half period of the sine wave is divided into 10,000 parts, and sampling and calculation are performed every 0.018 degrees of angle, so that this sampling period can be used as the arrangement interval of the windings. However, depending on the cross-sectional area of the winding, adjacent wirings overlap each other. An example in which the arrangement interval of the winding is set wider than the sampling period taking this into account is shown below.

[0062] Note that in order to reduce total harmonic distortion (THD), it is preferable to set the modulation factor to 1.0, further increase the number of windings, and further increase the spatial frequency of the carrier (further shorten the period of the triangular wave).

[0063] Figure 4 is a graph showing the number of windings of each region when windings of small cross-sectional area are arranged at equal intervals in each winding arrangement region in the example of Figure 3 . In Figure 4 , the arrangement interval of the winding is set to 0.39 degrees, the circumferential width of each winding is set to 0.01 degrees, and the radial thickness of each winding is set to 5.0 μm. In this case, the cross-sectional shape of each winding is approximately square. Note that the cross-sectional shape of each winding is not limited to square, and can be rectangular or other cross-sectional shapes. As shown in Figure 4 , 102 U-phase windings 14 are arranged in a range of 90 degrees in mechanical angle (180 degrees in electrical angle) which is the half period of the magnetic pole period. Therefore, in the range of 90 degrees in mechanical angle, 306 windings of the three phases are arranged in total.

[0064] In the case of the winding arrangement of Figure 4 , for example, if the voltage source is set to 40 V, the power source frequency is set to 10 Hz, the electrical conductivity of the stator winding is set to 5.98 x 10 7 S / m, and the relative permeability of the stator material and the rotor material is set to 10,000, the winding current density is 1.64 x 10 5 A / mm2 , which is much larger than the actual current density 4.0 A / mm 2 The following. Thus, while maintaining the size of the current flowing through the winding, the operation of continuously increasing the cross-sectional area of the winding and synthesizing the proximate windings with each other is performed. Thereby, the structure of the slot is uniquely determined.

[0065] Figure 5 is a flowchart showing the design steps of the slot structure. Figure 5 Each step of the above-described steps is realized by executing a program by a computer. Note that, at the start Figure 5 of the steps, the line current distribution is created in accordance with the flowchart of Figure 2

[0066] In step S200, the computer determines whether the windings overlap each other. In the case where the windings do not overlap each other (NO in step S200), in step S210, the computer determines whether the sum of the winding widths exceeds a prescribed proportion of the entire circumference. The prescribed proportion is, for example, 50% of the entire circumference. This condition is necessary for sufficiently ensuring the permeance between the windings.

[0067] In the case where the windings do not overlap each other (NO in step S200) and the sum of the winding widths does not exceed the prescribed proportion of the entire circumference (NO in step S210), the computer causes the process to proceed to step S220. In step S220, the computer increases the cross-sectional area of the winding by the prescribed proportion, and then causes the process to return to step S200.

[0068] On the other hand, in the case where the windings overlap each other (YES in step S200) or the sum of the winding widths exceeds the prescribed proportion of the entire circumference (YES in step S210), the computer causes the process to proceed to step S230. In step S230, the computer retrieves the winding that is most densely arranged, and in the next step S240, synthesizes the proximate windings with each other. The synthesized winding is also referred to as a winding aggregate. The winding aggregate is a winding that has the total number of the plurality of windings after the synthesis and has the sum of the cross-sectional areas of the plurality of windings after the synthesis.

[0069] ​Specifically, the computer retrieves, for all the windings (the winding also includes the winding aggregate), the winding whose total distance from the left and right windings is the smallest (sets this winding as A). Next, the computer selects the closer one of the left and right windings of winding A (sets this winding as B), and combines winding A and winding B. As an example, the newly generated winding C is disposed at a position that internally divides between winding A and winding B in inverse proportion to the cross-sectional areas of A and B. Winding C can be disposed anywhere between winding A and winding B, and can also be disposed at other positions. In addition, the total cross-sectional area and total number of turns of windings A and B are inherited by winding C, and the cross-sectional shape maintains a similar shape. Note that the shape of each winding can be a square, a rectangle, or another shape.

[0070] Figure 6 is a diagram for explaining a method of combining a winding of number of turns al and cross-sectional area SI (i.e., a winding aggregate) and a winding of number of turns a2 and cross-sectional area S2 (i.e., a winding aggregate). As shown in Figure 6 , the number of turns of the combined winding is al+a2, the cross-sectional area is SI+S2, and the cross-sectional shape is a shape similar to the cross-sectional shape before the combination (in this case, a substantially square shape). The position of the combined winding becomes a position that internally divides between the position of the winding of cross-sectional area SI and the position of the winding of cross-sectional area S2 in inverse proportion to the cross-sectional areas S2:SI.

[0071] Returning to Figure 5 , in the next step S250, the computer determines whether the number of winding aggregates of the entire stator is the predetermined desired slot number. In the case where the total number of winding aggregates does not reach the desired slot number (NO in step S250), the computer returns the processing to step S200, and repeatedly performs the above-described increase of the winding cross section and the combination of the closest windings with each other.

[0072] In the case where the total number of winding aggregates reaches the desired slot number (YES in step S250), the computer advances the processing to step S260. In step S260, the computer increases the radial thickness of each winding until the current density condition (i.e., the current density is 4.0 A / mm 2 , is satisfied. Through the above steps, the design step of the slot structure of the stator ends.

[0073] Next, a specific example of the slot structure made according to the flowchart of Figure 5 will be described. As an example, the modulation ratio of the PWM is set to 1.0, and the period of the triangular wave as the carrier is set to 2.0 degrees. The other parameters are the same as in Figure 3The same applies to the case of FIG. 6. In addition, the initial state inter-winding interval is set to 0.018 degrees, the winding width is set to 0.01 degrees, and the winding radial thickness is set to 5.0 μm. In this case, the cross-sectional shape of the winding is approximately square. The rotating machine is set to three-phase 4-pole, and the slot number is set to 6 per 90 degrees of mechanical angle (180 degrees of electrical angle). The winding of at least two phases is inserted in any slot, and the region of each phase in the slot corresponds to the region divided in the slot as a cross-sectional area proportional to the number of turns.

[0074] Figure 7 is a diagram showing a specific example of a slot structure. Figure 8 is a diagram showing the number of windings respectively arranged in the slots SL1 to SL6 of Figure 7 , and the width in the circumferential direction and the thickness in the radial direction of each slot. In Figure 8 , the negative number of turns indicates the opposite energization direction with respect to the positive number of turns.

[0075] As shown in Figure 7 and Figure 8 , the winding of all phases is inserted in each slot, and the inter-slot distance is approximately the same value. Note that in Figure 7 , the windings of each phase are arranged such that the phase with fewer windings is located more inward of the slot, but this is not limited thereto. For example, the windings of each phase can be arranged such that the phase with more windings is located more inward of the slot, or can be arranged in the order of U phase, V phase, and W phase from the inner side to the outer side of the slot.

[0076] Figure 7 and Figure 8 , the winding distribution is approximately as follows. Specifically, a plurality of slots formed on the stator are arranged in the circumferential direction facing the rotor. A U-phase winding, a V-phase winding, and a W-phase winding are wound in the plurality of slots. In each slot, a winding of at least two phases (all phases in the case of Figure 7 and Figure 8 ) of the U phase, the V phase, and the W phase is housed. If the number of magnetic poles of the stator is N, the number of U-phase windings housed in each slot periodically changes in the circumferential direction with a period of 360° / N of mechanical angle (half of the magnetic pole period). The change in the number of U-phase windings housed in each slot within each period is expressed by a half-period first periodic function (in the case of Figure 7 and Figure 8is a sine function). The U-phase winding for flowing the current in the same direction is arranged in the same period, and the U-phase winding for flowing the current in the opposite direction to each other is arranged in the adjacent period. The distribution of the V-phase winding housed in each slot is the distribution of the U-phase winding housed in each slot shifted by 240° / N in the mechanical angle in the circumferential direction. The distribution of the W-phase winding housed in each slot is the distribution of the U-phase winding housed in each slot shifted by -240° / N (i.e., shifted by 240° / N in the absolute value of the mechanical angle in the opposite direction to the case of the V-phase winding) in the mechanical angle.

[0077] [Effects of Embodiment 1]

[0078] As described above, according to the design method of the alternating-current motor of Embodiment 1, the configuration of the slots is determined by extending the linear current approximation model capable of obtaining an electromagnetic field distribution close to an ideal one. Specifically, each winding cross section is continuously increased, and if either of the following two conditions is satisfied in this process, the closest windings are synthesized with each other.

[0079] Condition 1: The winding cross sections overlap each other.

[0080] Condition 2: The total of the winding cross section widths exceeds a prescribed ratio of the entire inner circumference of the stator.

[0081] Thus, since each winding approximating a linear current forms a slot structure according to the distance from the adjacent left and right windings by self-judgment, it can be said that the slot structure of the stator is determined by self-organization. Therefore, the structure of the stator slots can be uniquely determined without depending on the designer on the basis of maintaining the ideal electromagnetic field characteristics as much as possible.

[0082] [Embodiment 2]

[0083] In Embodiment 2, as a design example of an alternating-current motor using the self-organization design method explained in Embodiment 1, the design of a 25 kW-class permanent magnet synchronous motor for a railway is explained. Hereinafter, first, the design specifications are explained, and then, as a comparative example, the design result in the case where the self-organization design method is not used is explained. Next, the design result in the case where the self-organization design method is used is explained. In the following explanation, the case where a sine wave is used as the above first periodic function (corresponding to the modulation wave of PWM) is referred to as self-organization design method 1, and the case where a function obtained by superimposing the third highest harmonic wave on the sine wave is used as the above first periodic function is referred to as self-organization design method 2.

[0084] [Required Specifications]

[0085] In a permanent magnet synchronous motor, there are two types of surface magnet type in which permanent magnets are attached to the surface of a rotor core and buried magnet type in which permanent magnets are provided inside a rotor core. The latter can effectively utilize reluctance torque at the time of high speed driving in which output is difficult to maintain accompanying rise of counter electromotive force. However, in the buried magnet type motor, there are problems such as reduction of power factor, and in addition, high speed rotation is not assumed in a 25 kW class permanent magnet synchronous motor for railway. Therefore, in the motor design described below, the surface magnet type motor is selected.

[0086] Figure 9 is a graph showing a required specification of the motor on a torque-speed plane. Figure 9 The vertical axis of Figure 9 indicates torque (unit: Nm), The horizontal axis of

[0087] indicates speed (unit: rpm (revolutions per minute)). Figure 9 As shown in Figure 9 , the maximum torque value in a low speed region is set to 98.4 Nm, and becomes an output (26.6 kW in the case of ) exceeding the maximum output of 25 kW at a speed of 2581 rpm. In addition, a constant output characteristic is set, that is, torque ∝ speed -1 is set so that the maximum torque in a high speed region higher than the speed of 2581 rpm at which the maximum output is provided is maintained to the above maximum output. On the other hand, as a most frequent driving condition, (torque, speed) = (80.7 Nm, 2581 rpm) is set, and this condition is set as a stable output point (that is, a continuous rating).

[0088] [Comparative Example: Case where Self-organization Design Method is not Used]

[0089] In order to satisfy the required specification of Figure 9 , first, as a comparative example, a design result of a permanent magnet synchronous motor designed by a method in which the self-organization design method is not used is described.

[0090] Figure 10 is a graph showing various elements of the 25 kW class permanent magnet synchronous motor designed as the comparative example in a table form. Figure 11 is a graph showing a cross-sectional view of the permanent magnet synchronous motor of the designed comparative example.

[0091] As shown in Figure 11 , 36 stator slots 21 are formed on a stator core 20. Windings of different phases are wound every 3 slots. In addition, 4 permanent magnets 23 are attached to the surface of a rotor core 22. Adjacent permanent magnets 23 are different in polarity from each other.

[0092] Figures 12A-12C is a graph showing a cross-sectional view of the permanent magnet synchronous motor of the designed comparative example. Figure 11Fig. 6 is a graph showing the analytical result of the torque characteristics at the maximum output point in the permanent magnet synchronous motor of Comparative Example 1. In the analysis, an electromagnetic field calculation program based on the finite element method was used.

[0093] Figure 12A indicates the time variation of the output torque (Nm). As shown in Fig. 6, the average torque 104.30 Nm is obtained at the maximum output point, and an output exceeding 25 kW is achieved. However, the peak-to-peak value of the torque ripple is 18.68 Nm, which exceeds 10% of the average torque value. In order to investigate the cause of the torque ripple, the fundamental component and the third-highest harmonic component of the torque ripple were extracted. Figure 12A

[0094] Fig. 7 is a graph showing the time variation of the fundamental component of the torque ripple of Figure 12B Figure 12A Fig. 8 is a graph showing the third-highest harmonic component of the torque ripple of Figure 12C Figure 12A In Fig. 7, the full output torque ripple is indicated by a solid line, and the fundamental component of the torque ripple is indicated by a single-dot chain line. In Fig. 8, the full output torque ripple is indicated by a solid line, and the third-highest harmonic component of the torque ripple is indicated by a broken line. Figure 12B Figure 12C As shown in Figs. 7 and 8, the amplitude value of the fundamental component is 3.07 Nm, and, in contrast, the amplitude value of the third-highest harmonic component is 6.03 Nm, which is about twice the amplitude value of the fundamental component. This finding is used for comparison with the design result based on the self-organization design method.

[0095] Figure 12B Figure 12C [Self-organization design method 1: case where modulation wave is sine wave]

[0096] Next, the results of the motor in which various elements of the 25 kW class permanent magnet synchronous motor were designed by the self-organization design method 1 will be described. In the self-organization design method 1, a sine wave was used as the above-mentioned first periodic function (corresponding to the modulation wave of the PWM).

[0097] Figure 10

[0098] Figure 13 Fig. 15 is a graph showing a cross-sectional view of the 25 kW class permanent magnet synchronous motor designed by the self-organization method 1. Figure 14 Fig. 16 is a graph showing the ratio of the number of turns of each phase in each stator slot in Figure 13

[0099] As shown in Figs. 15 and 16, the fundamental component of the torque ripple has an amplitude value of 1.48 Nm, and, in contrast, the third-highest harmonic component of the torque ripple has an amplitude value of 2.97 Nm, which is about twice the amplitude value of the fundamental component. This finding is used for comparison with the design result based on the self-organization design method 2. Figure 13 Figure 14 ​​​​​​​​​As shown, the spatial distribution of the number of turns of each phase winding is periodically changed in a manner corresponding to the positive half cycle of a sine wave per 360° / N = 90° of mechanical angle with respect to the number of magnetic poles N = 4. In adjacent cycles, the windings are arranged so that the current flows in opposite directions to each other. For example, the current direction of the U-phase winding of slots Nos. 1 to 9 is opposite to that of the U-phase winding of slots Nos. 10 to 18, the same as that of the U-phase winding of slots Nos. 19 to 27, and opposite to that of the U-phase winding of slots Nos. 28 to 36.

[0100] The spatial distribution of the V-phase winding is a distribution obtained by shifting the spatial distribution of the U-phase winding by 240° / N = 60° (in the case of N = 4) of mechanical angle in the circumferential direction. The spatial distribution of the W-phase winding is a distribution obtained by shifting the spatial distribution of the U-phase winding by 240° / N = 60° (in the case of N = 4) of mechanical angle in the opposite direction to the case of the V-phase winding. The windings of all the phases of U, V, and W are arranged in each slot.

[0101] Figures 15A-15C is a graph showing the time variation of the torque ripple of Figure 13 and Figure 14 is a graph showing the time variation of the torque ripple of

[0102] Figure 15A indicates the time variation of the output torque (Nm). As shown in Figure 15A , the peak-to-peak value of the torque ripple is 12.22 Nm, which can be reduced compared to 18.68 Nm in the case of the comparative example shown in Figure 12A . The reason can be considered to be that the winding arrangement based on the self-organization design method is a distributed winding arrangement. On the other hand, the average torque at the maximum output point is 87.46 Nm, which is reduced compared to 104.30 Nm in the case of the comparative example shown in Figure 12A . With regard to the reason, reference will be made to Figure 16 to be described later.

[0103] Figure 15B is a graph showing the time variation of the fundamental component of the torque ripple of Figure 15A Figure 15C is a graph showing the third-highest harmonic component of the torque ripple of Figure 15A . In Figure 15B , the solid line indicates the total output torque ripple, and the single-dot chain line indicates the fundamental component of the torque ripple. In Figure 15C , the solid line indicates the total output torque ripple, and the broken line indicates the third-highest harmonic component of the torque ripple.

[0104] As shown in Figure 15B and Figure 15C ​As shown, the amplitude value of the fundamental component is 0.46 Nm, and, in contrast, the amplitude value of the third highest harmonic component is 5.91 Nm. In comparison with the case of the prior example shown in FIG. 6, the amplitude value of the fundamental component is greatly reduced from 3.07 Nm to 0.46 Nm, and, in contrast, the amplitude value of the third highest harmonic component hardly changes from 6.03 Nm to 5.91 Nm. Therefore, the reduction effect of the total torque ripple based on the self-organization design method is realized as a reduction effect of the fundamental component, and it can be considered that the contribution to the reduction of the torque ripple of the third highest harmonic component is small. Figure 12B and Figure 12C In comparison with the case of the prior example shown in FIG. 6, the amplitude value of the fundamental component is greatly reduced from 3.07 Nm to 0.46 Nm, and, in contrast, the amplitude value of the third highest harmonic component hardly changes from 6.03 Nm to 5.91 Nm. Therefore, the reduction effect of the total torque ripple based on the self-organization design method is realized as a reduction effect of the fundamental component, and it can be considered that the contribution to the reduction of the torque ripple of the third highest harmonic component is small.

[0105] Figure 16 is a typical magnetic flux density vector diagram corresponding to Figures 15A-15C In Figure 16 , only the magnetic flux density component forming the N pole is plotted. In the region enclosed by the dotted line, cancellation of magnetic flux occurs, which can be considered as a cause of the reduction of the average torque.

[0106] [Self-organization design method 2: case where modulation wave is sine wave + third highest harmonic]

[0107] Next, a method of effectively utilizing the third highest harmonic component having a small contribution to the torque ripple to increase the average torque while maintaining the reduction effect of the torque ripple will be described.

[0108] Figure 17A and Figure 17B is a diagram for explaining the principle of the average torque increasing method. As shown in Figure 17A , it is assumed that a third highest harmonic distribution (solid line) having a low contribution rate to the torque ripple reduction effect is superimposed on the sine wave current density distribution (dotted line) used in the self-organization design method 1.

[0109] Here, if the sine wave distribution is expressed as K1•sinθ in terms of the electrical angle θ, the third highest harmonic distribution is expressed as K2•sin(3θ-π). In this case, in the vicinity of the peak of the sine wave distribution in the central region of the magnetic pole, the current density is enhanced due to the superposition, and in the vicinity of zero of the sine wave distribution in the boundary region of the magnetic pole, the current density is cancelled. As described above, in the boundary region of the magnetic pole where the magnetic flux density is zero, cancellation of magnetic flux occurs, but for the third highest harmonic component, the current density is cancelled by the superposition, and as a result, improvement of the average torque can be expected. Note that the amplitude K2 of the third highest harmonic is set to, for example, about 20% of the amplitude K1 of the sine wave.

[0110] Therefore, as shown in Figure 17Bthe solid line, the spatial current distribution of the distorted wave, which is given a third harmonic component to the sine wave distribution, is taken as an initial distribution for generating a line current approximation model. Then, the stator slot is designed using the self-organizing design method for the initial distribution. In the present disclosure, the case where the distorted wave current distribution is taken as the initial distribution like this is referred to as the self-organizing design method 2. Hereinafter, the results of the motor of various elements designed by the self-organizing design method 2 are described. Figure 10

[0111] Figure 18 is a graph showing the current distribution based on the line current approximation model of the U phase, the V phase, and the W phase before the self-organizing design method 2 is executed. Figure 19 is a graph showing a cross-sectional view of the 25 kW class permanent magnet synchronous motor designed by the self-organizing method 2. Figure 20 is a graph showing the ratio of the number of turns of each phase in each stator slot in Figure 19

[0112] As shown in Figure 19 and Figure 20 , the spatial distribution of the number of turns of each phase winding periodically changes with a period of 360° / N = 90° in mechanical angle with respect to the number of magnetic poles N = 4. The spatial distribution of the number of turns in this case reflects the shape of the first periodic function used in the line current approximation model, which is approximated by a Fourier series with the fundamental component and the third harmonic component as the principal components. Specifically, the approximate curve that approximates the winding number distribution of each period of each phase is a shape in which the positive half cycle of the sine wave as the fundamental wave and the third harmonic wave are superimposed in a phase relationship in which the peak of the sine wave is enhanced and the zero of the sine wave is canceled. The windings are arranged in a manner that the current flows in the same direction in the windings within a common period, and the current flows in opposite directions to each other in adjacent periods. For example, the current direction of the U phase winding of the slot numbers 1 to 9 is opposite to that of the U phase winding of the slot numbers 10 to 18, the same as that of the U phase winding of the slot numbers 19 to 27, and opposite to that of the U phase winding of the slot numbers 28 to 36.

[0113] The spatial distribution of the V phase winding is a distribution in which the spatial distribution of the U phase winding is shifted by 240° / N = 60° (in the case of N = 4) in the circumferential direction in mechanical angle. The spatial distribution of the W phase winding is a distribution in which the spatial distribution of the U phase winding is shifted by -240° / N = -60° (in the case of N = 4) in mechanical angle (i.e., shifted by 240° / N = 60° (in the case of N = 4) in the absolute value of the mechanical angle in the opposite direction to the case of the V phase winding).

[0114] The windings of at least two phases are arranged in each slot. For example, in Figure 20 ​​In the example shown, in the stator slots with slot numbers 2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, 35, the windings of all three phases are accommodated. In the stator slots with other slot numbers, the windings of any two phases are arranged.

[0115] Figures 21A-21C is a graph showing the time variation of the torque ripple of Figure 19 and Figure 20 In the structure shown, the analytical results of the torque characteristics at the maximum output point in the permanent magnet synchronous motor. In the analysis, an electromagnetic field calculation program based on the finite element method was used.

[0116] Figure 21A indicates the time variation of the output torque (Nm). As shown in Figure 21A , the average torque value at the maximum output point is 97.97 Nm, which is more than 10 Nm higher than the average torque value in the case of the self-organizing design method 1 shown in Figure 15A , which is 87.46 Nm. On the other hand, the peak-to-peak value of the torque ripple is 12.36 Nm, which is almost the same as the peak-to-peak value of the torque ripple in the case of the self-organizing design method 1 shown in Figure 15A , which is 12.22 Nm. Therefore, it is known that the superposition of the third harmonic component has little effect on the torque ripple.

[0117] Figure 21B is a graph showing the time variation of the fundamental component of the torque ripple of Figure 21A Figure 21C is a graph showing the third harmonic component of the torque ripple of Figure 21A In Figure 21B , the full output torque ripple is indicated by a solid line, and the fundamental component of the torque ripple is indicated by a single-dot chain line. In Figure 21C , the full output torque ripple is indicated by a solid line, and the third harmonic component of the torque ripple is indicated by a dotted line.

[0118] As shown in Figure 21B and Figure 21C , the amplitude value of the fundamental component is 0.27 Nm, and in contrast, the amplitude value of the third harmonic component is 6.14 Nm. As compared with the case of the self-organizing design method 1 shown in Figure 15B and Figure 15C , it is confirmed that the amplitude values of the fundamental component and the third harmonic component do not change greatly.

[0119] [Summary of Embodiment 2]

[0120] ​According to the self-organizing design method 2 described above, the first periodic function (corresponding to the modulation wave of the PWM) explained in Embodiment 1 is a function in which a sine function as a fundamental wave and a third harmonic wave are superimposed in a phase relationship in which the peak value is enhanced near the peak value of the sine function and the value is canceled near the zero value of the sine function. By designing the stator slot using the self-organizing design method using such a first periodic function, it is possible to increase the average torque while reducing the torque ripple.

[0121] In the stator actually manufactured according to the design method described above, the distribution of the number of windings of the arbitrary first phase accommodated in each of the plurality of slots varies periodically in the circumferential direction and is approximated by a Fourier series in which the fundamental wave component and the third harmonic component are main components. That is, the circumferential distribution of the number of windings of each phase reflects the shape of the first periodic function described above. Specifically, the approximate curve of the distribution of the number of windings of the first phase for each period is a shape in which a sine function as a fundamental wave and a third harmonic wave are superimposed in a phase relationship in which the peak value is enhanced near the peak value of the sine function and the value is canceled near the zero value of the sine function.

[0122] <Manufacturing method of alternating-current motor>

[0123] Using the self-organizing design method 2 explained in Embodiments 1 and 2 described above, it is possible to manufacture an alternating-current motor that outputs a large torque and has a small torque ripple. Note that the alternating-current motor is not limited to the permanent magnet synchronous motor explained in Embodiment 2. For example, the alternating-current motor can be an induction motor or a synchronous motor. In addition, the alternating-current motor can be a generator or a motor.

[0124] Figure 22 is a flowchart showing an example of a manufacturing method of an alternating-current motor. Specifically, as shown in Figure 22 , in step S300, a stator and a rotor are designed as one body, and based on the design, the stator is manufactured in step S310, and the rotor is manufactured in step S320. Here, the stator slot is designed using the self-organizing design method 2 explained in Embodiments 1 and 2. In the following step S330, the alternating-current motor is manufactured by assembling the stator and the rotor.

[0125] <Design support device>

[0126] Figure 23 is a block diagram showing an example of the structure of a computer for executing the design steps shown in Figure 2 , Figure 5 . As shown in Figure 23As shown, the computer 30 includes a CPU (Central Processing Unit) 31, a RAM (Random Access Memory) 32, a non-volatile memory 33, a reader / writer 34 (may be only a reader), a recording medium 35, a communication device 36, an input device 37, and a display device 38. These constituent elements are connected to each other via a bus 39.

[0127] The functions of the computer 30 as a design support device are realized by a program executed by the CPU 31. The RAM 32 is used as a main memory of the CPU 31. The non-volatile memory 33 stores the program executed by the CPU 31. The program is provided in the recording medium 35 and read into the computer 30 via the reader / writer 34. Alternatively, the program can be provided via a network and imported into the computer 30 via the communication device 36.

[0128] The input device 37 includes a keyboard and a mouse or the like for accepting an input of a user. The display device 38 includes a liquid crystal display or an organic EL (Electroluminescence) display or the like. The input device 37 and the display device 38 can also be configured as an integrated touch panel.

[0129] Figure 24 is a functional block diagram showing the functions of the computer 30 as a design support device. Referring to Figure 24 From a functional viewpoint, the design support device 40 is provided with a winding arrangement region deciding section 41, a minute winding arrangement section 42, and a winding synthesis section 43. It can be considered that these elements correspond to modules of the program executed by the computer 30. Note that the division of the modules is for convenience, and, for example, the winding arrangement region deciding section 41 and the minute winding arrangement section 42 can be configured as a common module.

[0130] Specifically, the winding arrangement region deciding section 41 approximates an absolute value of a first periodic function that varies in a circumferential direction of a magnetic pole period of a stator of an alternating-current motor, using a pulse function having a pulse width corresponding to the absolute value of the first periodic function. The winding arrangement region deciding section 41 decides a region in which the pulse function becomes an on-pulse as a winding arrangement region. Here, the first periodic function is a function in which a sine function as a fundamental wave and a third harmonic wave are superimposed in a phase relationship in which a peak value of the third harmonic wave is enhanced near a peak value of the sine function and a value of the third harmonic wave is canceled near a zero value of the sine function.

[0131] The minute winding arrangement section 42 arranges a plurality of windings of a minute cross-sectional area at intervals in the decided winding arrangement region.

[0132] The winding synthesis section 43 expands the cross-sectional area of each winding, and in a case where adjacent windings overlap each other or in a case where the proportion of the portion in which the winding is arranged in the length of the circumference of the stator exceeds a prescribed ratio, a new winding as a winding aggregate is generated by synthesizing the closest windings with each other. The winding aggregate is a winding having the total number of windings after the synthesis and the sum of the cross-sectional areas of the windings after the synthesis. Synthesizing the first winding and the second winding includes arranging the winding after the synthesis between the first winding and the second winding. The winding synthesis section 43 determines the arrangement position of each winding aggregate as the arrangement position of the slot in which each winding aggregate is accommodated when the number of winding aggregates obtained as a result of expanding the cross-sectional area of each winding reaches a desired number.

[0133] It should be understood that the embodiments disclosed herein are illustrative only and the scope of the present application is not limited by the foregoing description. The scope of the present application is shown by the claims rather than the foregoing description, and is intended to include all modifications equivalent within the meaning and scope of the claims.

[0134] Explanation of Reference Numerals

[0135] 10 rotating machine, 11 stator, 12 rotor, 13 air gap, 20 stator core, 21 stator slot, 22 rotor core, 23 permanent magnet, 25 kW maximum output, 30 computer, 31 CPU, 32 RAM, 33 nonvolatile memory, 34 reader / writer, 35 recording medium, 36 communication device, 37 input device, 38 display device, 39 bus, 40 design support device, 41 winding arrangement region determination section, 42 minute winding arrangement section, 43 winding synthesis section, SL1 to SL6 slots.

Claims

1. An AC motor, wherein: The AC motor has: rotor; a stator having a plurality of slots arranged in a circumferential direction facing the rotor; as well as a multi-phase winding, the winding being wound on the plurality of slots, The number of windings of any first phase of the plurality of phases housed in each of the plurality of slots changes periodically in the circumferential direction. The distribution of the number of windings of the first phase in each cycle is approximated by a Fourier series with a fundamental wave component and a third harmonic component as main components, and the approximate curve of the distribution is a shape in which the positive half cycle of the sine function as the fundamental wave and the third harmonic are superimposed with a phase relationship in which the value of the sine function is enhanced near the peak value of the sine function and is offset near the zero value of the sine function.

2. The AC motor according to claim 1, wherein The windings of the first phase are configured so that when any two windings of the first phase are included in a common period of the distribution of the number of windings of the first phase, current flows through the two windings in the same direction; and when any two windings of the first phase are included in adjacent periods to each other, current flows through the two windings in opposite directions.

3. The AC motor according to claim 2, wherein: The AC motor is a 3-phase N-pole AC motor. The number of windings of the first phase housed in each of the plurality of slots periodically changes in the circumferential direction at a period of a mechanical angle of 360° / N. The distribution of the second-phase winding accommodated in each of the plurality of slots is a distribution obtained by shifting the distribution of the first-phase winding accommodated in each of the plurality of slots by 240° / N in absolute value of the mechanical angle in the circumferential direction. The distribution of the third-phase winding accommodated in each of the plurality of slots is obtained by shifting the distribution of the first-phase winding in the opposite direction to that of the second-phase winding by an absolute value of a mechanical angle of 240° / N.

4. The AC motor according to any one of claims 1 to 3, wherein: At least two phase windings are arranged in the same slot.

5. A method for designing an AC motor, wherein: The design method comprises the steps of approximating the absolute value of a first periodic function that changes in the circumferential direction at the magnetic pole period of the stator of the AC motor using a pulse function by a computer, and determining a region where the pulse function becomes an on pulse as a winding arrangement region, wherein the pulse function has a pulse width corresponding to the absolute value of the first periodic function. The first periodic function is a function in which a sine function as a fundamental wave and a third higher harmonic wave are superimposed in a phase relationship in which a value of the sine function is enhanced near a peak value of the sine function and is canceled near a zero value of the sine function. The design method also has: a step of arranging a plurality of windings having a small cross-sectional area at equal intervals in the determined winding arrangement area; and The computer increases the cross-sectional area of ​​each winding and, when adjacent windings overlap or when the proportion of the portion where the windings are arranged in the circumferential length of the stator exceeds a predetermined ratio, generates a new winding as a winding assembly by combining the closest windings. The winding assembly is a winding having the total number of windings after being combined and the total cross-sectional area of ​​the plurality of windings after being combined, and combining the first winding and the second winding includes arranging the combined winding between the first winding and the second winding. The design method further includes the step of: when the number of winding assemblies obtained as a result of increasing the cross-sectional area of ​​each winding reaches a desired number, the computer determines the arrangement position of each winding assembly as the arrangement position of a slot for accommodating each winding assembly.

6. The design method of an AC motor according to claim 5, wherein: Combining the first winding and the second winding includes arranging the combined winding at a position where the distance from the first winding to the second winding is internally divided in inverse proportion to the cross-sectional area of ​​the first winding and the cross-sectional area of ​​the second winding.

7. A method for manufacturing an AC motor, wherein: The manufacturing method of the AC motor comprises: A step of manufacturing a stator by forming the slots at the slot arrangement positions determined according to the design method of the AC motor according to claim 5 or 6; and Steps for manufacturing the rotor.

8. A design aid for an AC motor, wherein: The design support device includes a winding arrangement region determining unit that approximates the absolute value of a first periodic function that changes in a circumferential direction at the magnetic pole period of the stator of the AC motor using a pulse function, and determines a region where the pulse function becomes an on pulse as the winding arrangement region, wherein the pulse function has a pulse width corresponding to the absolute value of the first periodic function. The first periodic function is a function in which a sine function as a fundamental wave and a third higher harmonic wave are superimposed in a phase relationship in which a value of the sine function is enhanced near a peak value of the sine function and is canceled near a zero value of the sine function. The design assistance device further comprises: a minute winding arrangement portion for arranging a plurality of windings having a minute cross-sectional area at equal intervals in the determined winding arrangement region; and a winding assembly unit that increases the cross-sectional area of ​​each of the windings and, when adjacent windings overlap or when the proportion of the portion where the windings are arranged in the circumferential length of the stator exceeds a predetermined ratio, combines the closest windings to generate a new winding as a winding assembly; The winding assembly is a winding having the total number of windings after being combined and the total cross-sectional area of ​​the plurality of windings after being combined, and combining the first winding and the second winding includes arranging the combined winding between the first winding and the second winding. When the number of winding assemblies obtained as a result of increasing the cross-sectional area of ​​each winding reaches a desired number, the winding assembly unit determines the arrangement position of each winding assembly to be the arrangement position of the slot for accommodating each winding assembly.

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