Ac machine and designing method, manufacturing method, and design assisting device of the same

Abstract

To provide an AC machine having a structure capable of increasing average torque while reducing torque ripple.SOLUTION: An AC machine comprises: a rotor 22; a stator 20 having a plurality of slots 21 arranged in a circumferential direction facing the rotor 22; and a plural phases of windings wound around the plurality of slots 21. The number of windings of any first phase among the plural phases housed in each of the plurality of slots 21 periodically varies in the circumferential direction. A distribution of the number of windings of the first phase per period is approximated by a Fourier series having a fundamental wave component and a third harmonic component as main components. An approximate curve of the distribution has a shape formed by superimposing a positive half period of a sine function being the fundamental wave and the third harmonic in a phase relationship such that the values are enhanced near the peak value of the sine function, and the values are cancelled near the zero value of the sine function.SELECTED DRAWING: Figure 19

Description

[Technical field]

[0001] The present disclosure relates to AC machines such as permanent magnet synchronous machines and induction machines, and to design methods, manufacturing methods, and design support devices thereof. [Background technology]

[0002] In order to reduce greenhouse gas emissions, there is an urgent need to improve the efficiency of rotating machines, which account for nearly half of the world's electricity consumption.

[0003] Various design methods have been proposed to achieve high efficiency for individual rotating machines. For example, Non-Patent Documents 1 and 2 disclose a method of optimization that starts from a widely used basic structural model and finely adjusts dimensions such as the circumferential width of the stator slot as a variable. [Prior art documents] [Non-patent literature]

[0004] [Non-Patent Document 1] Hosokawa et al., "A method for optimizing the efficiency of permanent magnet motors: an optimization design method using GA and SA," IEEJ Transactions on Industrial Applications, vol. 121, No. 2, 2001, pp. 171-177 [Non-Patent Document 2] Onishi et al., "Study on Design Method of IPM Motor Using Finite Element Method and Optimization Method," IEEJ Transactions on Industrial Applications, vol. 121, No. 3, 2001, pp. 397-402 Summary of the Invention [Problem to be solved by the invention]

[0005] Size optimization such as that described in the above Non-Patent Documents 1 and 2 is difficult to expect significant performance improvement because it depends on the topology of the initial shape of the AC machine. For example, it is difficult to unify the structure of the stator slots, so the structure that is considered optimal may differ depending on the designer.

[0006] The present disclosure has been made in consideration of the above background, and one of its objectives is to provide a design method for an AC machine that can determine a unique optimum structure for the stator slots without depending on the designer. Another objective of the present disclosure is to provide an AC machine that can reduce torque ripple and increase average torque by designing according to the above design method. [Means for solving the problem]

[0007] A method for designing an AC machine according to an embodiment includes first to fourth steps. In the first step, a computer approximates an absolute value of a first periodic function that changes in the circumferential direction with the magnetic pole period of a stator of an AC machine with a pulse function having a pulse width according to the absolute value of the first periodic function, and determines a region where 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, which is a fundamental wave, and a third harmonic are superimposed in a phase relationship such that the value of the sine function is enhanced near the peak value of the sine function and the value of the sine function is offset near the zero value of the sine function. In the second step, the computer arranges a large number of windings with minute cross-sectional areas at equal intervals in the determined winding arrangement region. In the third step, the computer expands the cross-sectional area of ​​each winding, and when adjacent windings overlap each other or when the proportion of the portion of the stator circumferential length where the windings are arranged exceeds a predetermined ratio, the computer generates a new winding as a winding assembly by combining the windings that are closest to each other. Here, the winding assembly is a winding having a total number of the combined windings and a total sum of the cross-sectional areas of the combined windings. Combining the first winding and the second winding includes disposing the combined winding between the first winding and the second winding. In a fourth step, when the number of winding assemblies obtained as a result of expanding the cross-sectional areas of the windings reaches a desired number, the computer determines the placement positions of each winding assembly to be the placement positions of slots that accommodate each winding assembly.

[0008] An AC machine according to one embodiment includes a rotor, a stator having a plurality of slots arranged in a circumferential direction facing the rotor, and a plurality of phase windings wound around the plurality of slots. The number of windings of an arbitrary first phase among 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 per period is approximated by a Fourier series having a fundamental wave component and a third harmonic component as main components. The approximation curve of the distribution has a shape in which a positive half period of a sine function, which is a fundamental wave, and the third harmonic are superimposed in a phase relationship such that 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. Effect of the Invention

[0009] According to the above design method, the structure of the stator slot can be uniquely determined without depending on the designer while maintaining the ideal sinusoidal electromagnetic field characteristics as much as possible. According to the above AC machine, it is possible to increase the average torque while reducing the torque ripple. [Brief description of the drawings]

[0010] [Figure 1] FIG. 1 is a schematic diagram of a structure of a rotating machine that is addressed in the present disclosure. [Diagram 2] 10 is a flowchart showing a procedure for creating a line current approximation model. [Diagram 3] 1A and 1B are diagrams illustrating specific examples of a PWM modulated wave and a carrier wave. [Figure 4] FIG. 4 is a diagram showing the number of windings in each winding arrangement region when the windings are evenly arranged in each winding arrangement region in the example of FIG. 3. [Diagram 5] 1 is a flowchart showing a procedure for designing a slot structure. [Figure 6] 1 is a diagram for explaining a method of combining a winding having a number of turns a1 and a cross-sectional area S1 with a winding having a2 and a cross-sectional area S2. FIG. [Figure 7] FIG. 2 is a diagram showing a specific example of a slot structure. [Figure 8]FIG. 8 is a diagram showing, in tabular form, the number of windings arranged in each of the slots SL1 to SL6 in FIG. 7, and the circumferential width and radial thickness of each slot. [Figure 9] FIG. 1 is a diagram showing the required specifications of a motor on a torque-rotation speed plane. [Figure 10] FIG. 1 is a diagram showing, in table form, specifications of a 25 kW-class permanent magnet synchronous motor designed as a comparative example. [Figure 11] FIG. 2 is a cross-sectional view of a designed permanent magnet synchronous motor of a comparative example. [Figure 12] FIG. 12 is a diagram showing an analysis result of torque characteristics obtained at a maximum output point in the permanent magnet synchronous motor of the comparative example in FIG. [Figure 13] FIG. 2 is a cross-sectional view of a 25 kW-class permanent magnet synchronous motor designed by self-organization method 1. [Figure 14] FIG. 14 is a diagram showing the ratio of the number of turns of each phase for each stator slot in FIG. 13. [Figure 15] FIG. 15 is a diagram showing an analysis result of torque characteristics obtained at a maximum output point in the permanent magnet synchronous motor having the structure shown in FIGS. 13 and 14. [Figure 16] FIG. 16 is a typical magnetic flux density vector diagram corresponding to FIG. 15. [Figure 17] FIG. 4 is a diagram for explaining the principle of an average torque improvement method. [Figure 18] FIG. 13 is a diagram showing current distributions by a line current approximation model of the U-phase, V-phase, and W-phase before self-organization design method 2 is executed. [Figure 19] FIG. 1 is a cross-sectional view of a 25 kW-class permanent magnet synchronous motor designed by self-organization method 2. [Figure 20] FIG. 20 is a diagram showing the ratio of the number of turns of each phase for each stator slot in FIG. 19. [Figure 21] FIG. 21 is a diagram showing an analysis result of torque characteristics obtained at a maximum output point in the permanent magnet synchronous motor having the structure shown in FIGS. 19 and 20. [Figure 22] 4 is a flowchart showing an example of a method for manufacturing an AC machine. [Diagram 23]FIG. 6 is a block diagram showing an example of the configuration of a computer for executing the design procedures shown in FIGS. 2 and 5. [Figure 24] FIG. 2 is a functional block diagram showing functions of a computer serving as a design support device. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0011] Each embodiment will be described in detail below with reference to the drawings. In the first embodiment, first, a model of an ideal stator structure that ignores the shape of the stator slot (referred to as a "line current approximation model" in this disclosure) is proposed. Next, while maintaining the performance of the line current approximation model as much as possible, it is transformed into a realistic slot structure by continuous modification. This provides a design method for a stator with a unique slot structure that is not dependent on a designer (referred to as a "self-organizing design method" in this disclosure).

[0012] In the second embodiment, the design of a 25 kW class permanent magnet motor for railways will be described as a specific application example of the stator design method using the line current approximation-self-organizing design method of the first embodiment.

[0013] In the following description, the same or corresponding parts are given the same reference symbols and their descriptions may not be repeated.

[0014] <Embodiment 1> [Structure of Rotating Machine] FIG. 1 is a schematic diagram of the structure of a rotating machine that is handled in this disclosure. As shown in FIG. 1, the rotating machine has an inner rotor type structure in which a rotor 12 is disposed in a stator 11. The space between the stator 11 and the rotor 12 is called an air gap 13. A cylindrical coordinate system is adopted in which the rotation axis of the rotor 12 is the z-axis, and the rotation direction of the rotor 12 is the θ-direction. In the following, the case where AC power is input to the stator 11, that is, the case where the rotating machine 10 is an AC machine, is handled. In addition, the case where the rotating machine 10 is an inner rotor type as shown in FIG. 1 is described, but an outer rotor type in which the rotor 12 is disposed outside the stator 11 can also be handled in the same way.

[0015] [Line current approximation model] The distribution of the rotating magnetic field generated by the stator winding contains many harmonic components due to the influence of the slot shape and arrangement. Therefore, in order to aim for a spatial distribution that approximately realizes the ideal rotating magnetic field distribution, first, regarding the slot shape, the winding is assumed to be a line current and the cross-sectional shape of the slot is ignored. Regarding the slot arrangement, the concept of pulse width modulation (PWM) used in inverters, etc. is applied to space to generate an approximately desired magnetomotive force distribution. Since the magnetomotive force distribution by one winding is a rectangular wave, it can be interpreted that the high state of the pulse wave (i.e., on-pulse) corresponds to the arrangement of the winding.

[0016] 2 is a flowchart showing a procedure for creating a line current approximation model. Each step in FIG. 2 is realized by a computer executing a program.

[0017] In step S100, the computer accepts input of parameters such as the size of the rotating machine 10, the number of poles, the modulation rate and carrier frequency of PWM, and the winding interval from the user. The size of the rotating machine 10 refers to the physical size of the rotating machine 10. Specifically, the outer and inner diameters of the rotor 12, the outer and inner diameters of the stator 11, and the length in the z direction are input as the size of the rotating machine 10. As an example, in the arrangement example of the line current distribution shown in Figures 3 and 4, the stator outer diameter is 112 mm, the stator inner diameter is 56 mm, the rotor outer diameter is 55 mm, the rotor inner diameter is 16 mm, and the length in the z direction is 60 mm.

[0018] In the next step S110, the computer uses the concept of PWM to approximate the absolute value of the first periodic function with a pulse function having a pulse width according to the absolute value of the first periodic function based on a comparison between a first periodic function (corresponding to a modulated wave of PWM) that changes in the circumferential direction with the magnetic pole period of the stator of the AC machine and a second periodic function (corresponding to a carrier wave of PWM) that has an amplitude equal to or greater than that of the first periodic function and has a spatial frequency sufficiently higher than that of the first periodic function. The computer determines a region where the approximate pulse function becomes an on-pulse as the winding arrangement region. Specifically, a section where the absolute value of the instantaneous value of the first periodic function is greater than the absolute value of the instantaneous value of the second periodic function to be compared is set as the on-pulse region (i.e., the winding arrangement region).

[0019] An example of the first periodic function is a sine wave. As described in detail in the second embodiment, in order to increase the average torque value while reducing the torque ripple, it is preferable to use as the first periodic function a function in which a sine wave, which is a fundamental wave, and its third harmonic are superimposed in a phase relationship such that the peak position of the third harmonic coincides with the peak position of the fundamental wave. The second periodic function to be compared may be a triangular wave or a sawtooth wave, and is not particularly limited. When the number of magnetic poles of the stator is N, the period of the absolute value of the first periodic function is 360 / N [degrees] in mechanical angle (i.e., half the magnetic pole period).

[0020] Fig. 3 is a diagram showing a specific example of a PWM modulated wave and a carrier wave. Fig. 3 shows a three-phase, four-pole case, with a PWM modulation rate of 0.8, a modulated wave (first periodic function) as an example of a sine wave (magnetic pole period is 180 degrees in mechanical angle), and a triangular wave (second periodic function) with a period of 9.0 degrees (mechanical angle), and shows a winding arrangement region of the U phase. To make it easy to associate with the winding arrangement, the case where the absolute value of the instantaneous value of the modulated wave is greater than the absolute value of the carrier wave and the absolute value of the instantaneous value of the opposite phase of the modulated wave is greater than the absolute value of the carrier wave is set as an on-pulse region.

[0021] The V-phase winding layout area is shifted from the U-phase winding layout area by 120 degrees electrical angle (60 degrees mechanical angle for 3-phase, 4-pole). The W-phase winding layout area is shifted from the U-phase winding layout area by -120 degrees electrical angle (-60 degrees mechanical angle for 3-phase, 4-pole). The modulation factor must be set to 1 or less.

[0022] Returning to FIG. 2, in the next step S120, the computer places many windings with small cross-sectional areas at equal intervals in the winding arrangement area determined in step S110. By setting the winding intervals to be equal, the number of wires in each winding arrangement area is approximated to an integer. For example, in the calculation of FIG. 3, the half cycle of the sine wave is divided into 10,000 parts, and the calculation is performed by sampling every 0.018 degrees, so it is possible to use this sampling period as the winding arrangement interval. However, depending on the cross-sectional area of ​​the winding, adjacent wires may overlap. In the following, an example is shown in which the winding arrangement interval is set wider than the sampling period in consideration of this point.

[0023] In order to reduce the total harmonic distortion (THD), it is desirable to set the modulation rate to 1.0, increase the number of windings, and increase the spatial frequency of the carrier wave (shorten the triangular wave period).

[0024] FIG. 4 is a diagram showing the number of windings in each region when windings with minute cross-sectional areas are evenly arranged in each winding arrangement region in the example of FIG. 3. In FIG. 4, the winding arrangement interval is 0.39 degrees, the circumferential width of each winding is 0.01 degrees, and the radial thickness of each winding is 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 a square, and may be rectangular or another cross-sectional shape. As shown in FIG. 4, 102 U-phase windings 14 are arranged within a range of a mechanical angle of 90 degrees (electrical angle of 180 degrees), which is half the magnetic pole period. Therefore, a total of 306 windings for the three phases are arranged within a range of a mechanical angle of 90 degrees.

[0025] In the case of the winding arrangement in FIG. 4, for example, the voltage source is 40 V, the power supply frequency is 10 Hz, and the electrical conductivity of the stator winding is 5.98×107 S / m, and the relative permeability of the stator material and rotor material is 10000, the winding current density is 1.64×10 5 A / mm 2 This is a realistic current density of 4.0 A / mm 2 Therefore, while maintaining the magnitude of the current flowing through the winding, the cross-sectional area of ​​the winding is continuously increased and adjacent windings are combined. This uniquely determines the structure of the slot.

[0026] Figure 5 is a flowchart showing the design procedure of the slot structure. Each step in Figure 5 is realized by a computer executing a program. It is assumed that the line current distribution has been created according to the flowchart in Figure 2 when starting the procedure in Figure 5.

[0027] In step S200, the computer determines whether the windings overlap each other. If 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 predetermined percentage of the circumference. The predetermined percentage is, for example, 50% of the circumference. This condition is necessary to ensure sufficient magnetic permeance between the windings.

[0028] If the windings do not overlap each other (NO in step S200) and the sum of the winding widths does not exceed a predetermined percentage of the circumference (NO in step S210), the computer proceeds to step S220. In step S220, the computer increases the winding cross-sectional area by the predetermined percentage, and then returns the process to step S200.

[0029] On the other hand, if the windings overlap each other (YES in step S200) or the sum of the winding widths exceeds a predetermined percentage of the circumference (YES in step S210), the computer proceeds to step S230. In step S230, the computer searches for the windings that are most densely arranged, and in the next step S240, combines the windings that are closest to each other. The combined winding is also called a winding assembly. A winding assembly is a winding that has the total number of multiple combined windings and the sum of the cross-sectional areas of the multiple combined windings.

[0030] Specifically, the computer searches for a winding with the smallest total distance between the left and right windings for all windings (including winding assemblies) (this winding is called A). Next, the computer selects the winding that is closer to the left or right winding of winding A (this winding is called B) and combines winding A and winding B. As an example, the newly generated winding C is placed at a position that divides the distance between windings A and B in the inverse ratio of the cross-sectional areas of A and B. Winding C may be placed at another position between windings A and B. The total cross-sectional area and the total number of turns of windings A and B are inherited by winding C, and the cross-sectional shapes are maintained similar. The shape of each winding may be square, rectangular, or another shape.

[0031] 6 is a diagram for explaining a method of combining a winding (i.e., a winding assembly) with a winding having a number of turns a1 and a cross-sectional area S1 and a winding (i.e., a winding assembly) with a winding a2 and a cross-sectional area S2. As shown in FIG. 6, the combined winding has a number of turns a1+a2, a cross-sectional area S1+S2, and a cross-sectional shape similar to the cross-sectional shape before the combination (in this case, approximately square). The position of the combined winding is a position obtained by dividing the distance between the position of the winding with the cross-sectional area S1 and the position of the winding with the cross-sectional area S2 by the inverse ratio of the cross-sectional areas S2:S1.

[0032] 5, in the next step S250, the computer determines whether the total number of winding assemblies in the entire stator is equal to the predetermined desired number of slots. If the total number of winding assemblies does not reach the desired number of slots (NO in step S250), the computer returns to step S200 and repeats the above-mentioned increase in the winding cross section and the combination of the most adjacent windings.

[0033] If the total number of the winding assemblies has reached the desired number of slots (YES in step S250), the computer proceeds to step S260. In step S260, the computer determines the current density condition (i.e., the current density is 4.0 A / mm 2 The radial thickness of each winding is increased until the following condition is satisfied. This completes the design procedure for the stator slot structure.

[0034] Next, a specific example of a slot structure created according to the flowchart of FIG. 5 will be described. As an example, the modulation rate of PWM is 1.0, and the period of the triangular wave, which is the carrier wave, is 2.0 degrees. The other parameters are the same as those in FIG. 3. Also, the initial winding interval is 0.018 degrees, the winding width is 0.01 degrees, and the radial thickness of the winding is 5.0 μm. In this case, the cross-sectional shape of the winding is approximately square. The rotating machine is three-phase and four-pole, and the number of slots is six per 90 mechanical degrees (180 electrical degrees). At least two phase windings are inserted in each slot, and the area of ​​each phase in the slot corresponds to the internal division of the slot as a cross-sectional area proportional to the number of turns.

[0035] Fig. 7 is a diagram showing a specific example of the slot structure. Fig. 8 is a diagram showing, in table form, the number of windings arranged in each of the slots SL1 to SL6 in Fig. 7, and the circumferential width and radial thickness of each slot. In Fig. 8, a negative number of turns indicates that the current flows in the opposite direction to a positive number of turns.

[0036] As shown in Figures 7 and 8, windings of all phases are inserted into each slot, and the distance between the slots is approximately equal. Note that in Figure 7, the windings of each phase are arranged so that the phase with the fewer number of windings is closer to the inside of the slot, but this is not limited to this. For example, the windings of each phase may be arranged so that the phase with the greater number of windings is closer to the inside of the slot, or may be arranged from the inside to the outside of the slot in the order of U phase, V phase, and W phase.

[0037] The winding distribution shown in Figs. 7 and 8 is generally as follows. Specifically, a plurality of slots formed in 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 around the plurality of slots. Each slot houses windings of at least two phases of the U-phase, V-phase, and W-phase (all phases in the case of Figs. 7 and 8). If the number of magnetic poles of the stator is N, the number of U-phase windings housed in each slot changes periodically in the circumferential direction with a period of 360° / N mechanical angle (half the magnetic pole period). The change in the number of U-phase windings housed in each slot within each period is approximated by a first periodic function of a half period (a sine function in the case of Figs. 7 and 8). Within the same period, U-phase windings for passing current in the same direction are arranged, and in adjacent periods, U-phase windings for passing current in opposite directions are arranged. The distribution of the V-phase windings housed in each slot is obtained by shifting the distribution of the U-phase windings housed in each slot in the circumferential direction by 240° / N in mechanical angle. The distribution of the W-phase windings housed in each slot is obtained by shifting the distribution of the U-phase windings housed in each slot by -240° / N in mechanical angle (i.e., 240° / N in absolute mechanical angle in the opposite direction from the V-phase winding).

[0038] [Advantages of the First Embodiment] As described above, according to the design method of the AC machine of the first embodiment, the slot arrangement is determined by expanding the line current approximation model that obtains an electromagnetic field distribution close to the ideal. Specifically, the cross section of each winding is continuously increased, and if either of the following two conditions is satisfied in the process, the windings that are closest to each other are combined.

[0039] Condition 1: The winding cross sections overlap each other. Condition 2: The total winding cross-sectional width exceeds a specified ratio of the entire inner circumference of the stator.

[0040] In this way, each winding that has been approximated by line current determines the distance between the adjacent windings on the left and right and forms the slot structure by itself, so the stator slot structure is determined by self-organization, so to speak. Therefore, the stator slot structure can be uniquely determined without relying on the designer, while maintaining ideal electromagnetic field characteristics as much as possible.

[0041] <Embodiment 2> In the second embodiment, the design of a 25kW-class permanent magnet synchronous motor for railways will be described as an example of designing an AC machine using the self-organizing design method described in the first embodiment. In the following, first, the design specifications will be described, and then, as a comparative example, the design result when the self-organizing design method is not used will be described. After that, the design result when the self-organizing design method is used will be described. In the following description, the case where a sine wave is used as the first periodic function (corresponding to the modulated wave of PWM) will be referred to as self-organizing design method 1, and the case where a function obtained by superimposing a sine wave with its third harmonic is used as the first periodic function will be referred to as self-organizing design method 2.

[0042] [Required specifications] There are two types of permanent magnet synchronous motors: a surface magnet type in which permanent magnets are attached to the surface of the rotor core, and an interior magnet type in which permanent magnets are installed inside the rotor core. The latter makes it possible to utilize reluctance torque during high-speed driving when it becomes difficult to maintain output as the back electromotive force increases. However, interior magnet type motors have problems such as a decrease in power factor, and high-speed rotation is not anticipated for 25kW-class permanent magnet synchronous motors for railways. Therefore, a surface magnet type motor was selected for the motor design described below.

[0043] Fig. 9 is a diagram showing the required specifications of a motor on a torque-rotational speed plane, in which the vertical axis represents torque (unit: Nm) and the horizontal axis represents rotational speed (unit: rpm (revolutions per minute)).

[0044] As shown in Fig. 9, the maximum torque value in the low speed region is set to 98.4 Nm, and the output exceeds the maximum output of 25 kW at a rotation speed of 2581 rpm (26.6 kW in the case of Fig. 9). Also, the maximum torque in a region higher than the rotation speed of 2581 rpm that gives the maximum output is set to have a constant output characteristic so as to maintain the above maximum output, i.e., torque ∝ rotation speed -1 On the other hand, the most frequent driving condition is set to (torque, rotation speed) = (80.7 Nm, 2581 rpm), and this condition is set as the steady-state output point (i.e., continuous rating).

[0045] [Comparative example: when self-organizing design method is not used] First, as a comparative example, a design result of a permanent magnet synchronous motor designed using a method that does not use the self-organizing design method will be described so as to satisfy the required specifications in FIG.

[0046] Fig. 10 is a table showing the specifications of a 25 kW class permanent magnet synchronous motor designed as a comparative example, and Fig. 11 is a cross-sectional view of the designed permanent magnet synchronous motor as a comparative example.

[0047] As shown in Fig. 11, 36 stator slots 21 are formed in the stator core 20. Windings of different phases are wound in every three slots. In addition, four permanent magnets 23 are attached to the surface of the rotor core 22. Adjacent permanent magnets 23 have opposite polarities.

[0048] Fig. 12 is a diagram showing an analysis result of the torque characteristics obtained at the maximum output point in the permanent magnet synchronous motor of the comparative example in Fig. 11. An electromagnetic field calculation program based on the finite element method was used for the analysis.

[0049] Figure 12(A) shows the time change of the output torque (Nm). As shown in Figure 12(A), an average torque of 104.30 Nm is obtained at the maximum output point, and an output of more than 25 kW is realized. However, the peak value of the torque ripple is 18.68 Nm, which is more than 10% of the average torque value. To investigate the cause of the torque ripple, the fundamental wave component and the third harmonic component of the torque ripple were extracted.

[0050] Fig. 12(B) is a diagram showing the time change of the fundamental wave component of the torque ripple in Fig. 12(A). Fig. 12(C) is a diagram showing the third harmonic component of the torque ripple in Fig. 12(A). In Fig. 12(B), the total output torque ripple is shown by a solid line, and the fundamental wave component of the torque ripple is shown by a dashed line. In Fig. 12(C), the total output torque ripple is shown by a solid line, and the third harmonic component of the torque ripple is shown by a dashed line.

[0051] As shown in Figures 12(B) and 12(C), the amplitude value of the fundamental wave component is 3.07 Nm, while the amplitude value of the third harmonic component is 6.03 Nm, which is approximately twice the amplitude value of the fundamental wave component. This finding will be used for comparison with the design results using the self-organizing design method.

[0052] [Self-organizing design method 1: When the modulating wave is a sine wave] Next, a description will be given of the result of designing a motor with the specifications in Fig. 10 using the self-organizing design method 1. In the self-organizing design method 1, a sine wave is used as the above-mentioned first periodic function (corresponding to the modulated wave of PWM).

[0053] Fig. 13 is a diagram showing a cross section of a 25 kW class permanent magnet synchronous motor designed by self-organization method 1. Fig. 14 is a diagram showing the ratio of the number of turns of each phase for each stator slot in Fig. 13.

[0054] As shown in Figures 13 and 14, for a magnetic pole number N = 4, the spatial distribution of the number of turns of each phase winding changes periodically to correspond to the positive half cycle of a sine wave every 360° / N = 90° mechanical angle. In adjacent cycles, the windings are arranged so that current flows in the opposite direction to each other. For example, the current direction in the U-phase windings in slot numbers 1 to 9 is opposite to that of the U-phase windings in slot numbers 10 to 18, is the same as that of the U-phase windings in slot numbers 19 to 27, and is opposite to that of the U-phase windings in slot numbers 28 to 36.

[0055] The spatial distribution of the V-phase winding is obtained by shifting the spatial distribution of the U-phase winding in the circumferential direction by a mechanical angle of 240° / N = 60° (when N = 4). The spatial distribution of the W-phase winding is obtained by shifting the spatial distribution of the U-phase winding in the opposite direction to the V-phase winding by a mechanical angle of 240° / N = 60° (when N = 4). Windings of all phases, U, V, and W, are arranged in each slot.

[0056] Fig. 15 is a diagram showing the analysis results of the torque characteristics obtained at the maximum output point in the permanent magnet synchronous motor having the structure shown in Fig. 13 and Fig. 14. For the analysis, an electromagnetic field calculation program using the finite element method was used.

[0057] FIG. 15(A) shows the change in output torque (Nm) over time. As shown in FIG. 15(A), the peak-to-peak value of the torque ripple is 12.22 Nm, which is reduced from 18.68 Nm in the comparative example shown in FIG. 12(A). This is believed to be because the winding arrangement by the self-organizing design method is a distributed winding arrangement. Meanwhile, the average torque at the maximum output point is 87.46 Nm, which is reduced from 104.30 Nm in the comparative example shown in FIG. 12(A). The cause of this will be described later with reference to FIG. 16.

[0058] Fig. 15(B) is a diagram showing the time change of the fundamental wave component of the torque ripple in Fig. 15(A). Fig. 15(C) is a diagram showing the third harmonic component of the torque ripple in Fig. 15(A). In Fig. 15(B), the total output torque ripple is shown by a solid line, and the fundamental wave component of the torque ripple is shown by a dashed line. In Fig. 15(C), the total output torque ripple is shown by a solid line, and the third harmonic component of the torque ripple is shown by a dashed line.

[0059] As shown in Figures 15(B) and 15(C), the amplitude value of the fundamental wave component is 0.46 Nm, while the amplitude value of the third harmonic component is 5.91 Nm. Compared to the conventional example shown in Figures 12(B) and 12(C), the amplitude value of the fundamental wave component is significantly reduced from 3.07 Nm to 0.46 Nm, while the amplitude value of the third harmonic component is almost unchanged from 6.03 Nm to 5.91 Nm. Therefore, the reduction effect of the total torque ripple by the self-organizing design method is realized as a reduction effect of the fundamental wave component, and it is considered that the contribution of the third harmonic component to the reduction of the torque ripple is small.

[0060] Figure 16 is a typical magnetic flux density vector diagram corresponding to Figure 15. Only the magnetic flux density component that forms the N pole is plotted in Figure 16. Magnetic flux cancellation occurs in the area surrounded by the dashed line, and this magnetic flux cancellation is thought to be the cause of the decrease in average torque.

[0061] [Self-organizing design method 2: When the modulating wave is a sine wave + third harmonic] Next, a method for improving the average torque while maintaining the torque ripple reduction effect by effectively utilizing the third harmonic component, which has a small contribution to the torque ripple, will be described.

[0062] Fig. 17 is a diagram for explaining the principle of the average torque improvement method. As shown in Fig. 17(A), it is assumed that the third harmonic distribution (solid line), which has a low contribution rate to the torque ripple reduction effect, is superimposed on the sinusoidal current density distribution (dashed line) used in the self-organization design method 1.

[0063] Here, if the sinusoidal distribution is expressed as K1·sinθ with the electrical angle θ, the third harmonic distribution can be expressed as K2·sin(3θ-π). In this case, the current density is increased by the overlap near the peak of the sinusoidal distribution, which is the central region of the magnetic pole, and the current density is canceled near the zero of the sinusoidal distribution, which is the boundary region of the magnetic pole. As mentioned above, the magnetic flux cancels out in the boundary region of the magnetic pole where the magnetic flux density is zero, but the current density of the third harmonic component is canceled by the overlap, so an improvement in the average torque is expected as a result. The amplitude K2 of the third harmonic is set to, for example, about 20% of the amplitude K1 of the sine wave.

[0064] Therefore, as shown by the solid line in Fig. 17(B), a distorted wave-like spatial current distribution in which the third harmonic component is added to the sine wave distribution is set as the initial distribution for generating a line current approximation model. Then, the self-organizing design method is used for this initial distribution to design the stator slots. In this disclosure, the case in which the distorted wave current distribution is set as the initial distribution is referred to as self-organizing design method 2. Below, the results of designing a motor with the specifications in Fig. 10 using self-organizing design method 2 will be described.

[0065] Fig. 18 is a diagram showing current distribution by a line current approximation model of the U-phase, V-phase, and W-phase before executing self-organization design method 2. Fig. 19 is a diagram showing a cross-sectional view of a 25 kW-class permanent magnet synchronous motor designed by self-organization method 2. Fig. 20 is a diagram showing the ratio of the number of turns of each phase for each stator slot in Fig. 19.

[0066] As shown in Fig. 19 and Fig. 20, the spatial distribution of the number of turns of each phase winding for the number of magnetic poles N=4 changes periodically every 360° / N=90° of mechanical angle. In this case, the spatial distribution of the number of turns reflects the shape of the first periodic function used in the line current approximation model, and is approximated by a Fourier series with the fundamental wave component and the third harmonic component as the main components. Specifically, the approximation curve approximating the distribution of the number of turns for each phase period is a shape in which the positive half period of the fundamental sine wave and the third harmonic are superimposed in a phase relationship in which the sine wave is enhanced near its peak value and offset near its zero value. The windings are arranged so that current flows in the same direction in the windings within a common period, and current flows in opposite directions in adjacent periods. For example, the direction of current in the U-phase windings in slot numbers 1 to 9 is opposite to the direction of current in the U-phase windings in slot numbers 10 to 18, is the same as the direction of current in the U-phase windings in slot numbers 19 to 27, and is opposite to the direction of current in the U-phase windings in slot numbers 28 to 36.

[0067] The spatial distribution of the V-phase winding is obtained by shifting the spatial distribution of the U-phase winding in the circumferential direction by 240° / N=60° mechanical angle (when N=4). The spatial distribution of the W-phase winding is obtained by shifting the spatial distribution of the U-phase winding by -240° / N=-60° mechanical angle (when N=4) (i.e., 240° / N=60° (when N=4) in absolute mechanical angle in the opposite direction to that of the V-phase winding).

[0068] At least two phase windings are arranged in each slot. For example, in the example shown in Fig. 20, windings of all three phases are accommodated in the stator slots with slot numbers 2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, and 35. Windings of any two phases are arranged in the stator slots with other slot numbers.

[0069] Fig. 21 is a diagram showing the analysis results of the torque characteristics obtained at the maximum output point in the permanent magnet synchronous motor having the structure shown in Fig. 19 and Fig. 20. For the analysis, an electromagnetic field calculation program based on the finite element method was used.

[0070] Figure 21(A) shows the time change of the output torque (Nm). As shown in Figure 21(A), the average torque value at the maximum output point is 97.97 Nm, which is an improvement of more than 10 Nm from the average torque value of 87.46 Nm in the case of self-organizing design method 1 shown in Figure 15(A). On the other hand, the peak-to-peak value of the torque ripple is 12.36 Nm, which is almost unchanged from the peak-to-peak value of 12.22 Nm in the case of self-organizing design method 1 shown in Figure 15(A). Therefore, it can be seen that the influence of the superposition of the third harmonic component on the torque ripple is small.

[0071] Fig. 21(B) is a diagram showing the time change of the fundamental wave component of the torque ripple in Fig. 21(A). Fig. 21(C) is a diagram showing the third harmonic component of the torque ripple in Fig. 21(A). In Fig. 21(B), the total output torque ripple is shown by a solid line, and the fundamental wave component of the torque ripple is shown by a dashed line. In Fig. 21(C), the total output torque ripple is shown by a solid line, and the third harmonic component of the torque ripple is shown by a dashed line.

[0072] As shown in Figures 21(B) and 21(C), the amplitude value of the fundamental wave component is 0.27 Nm, while the amplitude value of the third harmonic component is 6.14 Nm. It was confirmed that the amplitude values ​​of both the fundamental wave component and the third harmonic component did not change significantly, as compared with the case of self-organizing design method 1 shown in Figures 15(B) and 15(C).

[0073] [Summary of the second embodiment] According to the above self-organizing design method 2, the first periodic function (corresponding to the modulated wave of PWM) described in the first embodiment is a function in which a sine function, which is a fundamental wave, and the third harmonic are superimposed in a phase relationship in which the peak value of the sine function is enhanced near the peak value and the values ​​are offset near the zero value of the sine function. By designing the stator slots by the self-organizing design method using such a first periodic function, it is possible to reduce the torque ripple and improve the average torque.

[0074] In a stator actually manufactured according to the above design method, the distribution of the number of windings of any first phase housed in each of the multiple slots changes periodically in the circumferential direction and is approximated by a Fourier series with the fundamental wave component and the third harmonic component as the main components. That is, the circumferential distribution of the number of windings of each phase reflects the shape of the above first periodic function. Specifically, the approximation curve of the distribution of the number of windings of the first phase for each period is a shape in which a sine function, which is the fundamental wave, and the third harmonic are superimposed in a phase relationship in which the peak value of the sine function is enhanced near the peak value and the values ​​are canceled near the zero value of the sine function.

[0075] <Manufacturing method of AC machine> By using the self-organizing design method 2 described in the above first and second embodiments, an AC machine having a large output torque and a small torque ripple can be manufactured. The AC machine is not limited to the permanent magnet synchronous motor described in the second embodiment. For example, the AC machine may be an induction machine or a synchronous machine. The AC machine may be a generator or an electric motor.

[0076] Fig. 22 is a flow chart showing an example of a method for manufacturing an AC machine. Specifically, as shown in Fig. 22, a stator and a rotor are designed as one unit in step S300, a stator is manufactured based on the design in step S310, and a rotor is manufactured in step S320. Here, the stator slots are designed using the self-organizing design method 2 described in the first and second embodiments. In the next step S330, the stator and rotor are assembled to manufacture an AC machine.

[0077] <Design support equipment> Fig. 23 is a block diagram showing an example of the configuration of a computer for executing the design procedures shown in Fig. 2 and Fig. 5. As shown in Fig. 23, a 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 a reader only), a recording medium 35, a communication device 36, an input device 37, and a display device 38. These components are connected to each other via a bus 39.

[0078] The function of the computer 30 as a design support device is realized by the CPU 31 executing a program. The RAM 32 is used as a main memory for the CPU 31. The non-volatile memory 33 stores the program executed by the CPU 31. The program is provided in a recording medium 35, and is read into the computer 30 via a reader / writer 34. Alternatively, the program may be provided via a network, and taken into the computer 30 via a communication device 36.

[0079] The input device 37 includes a keyboard and a mouse for receiving input from a user. The display device 38 includes a liquid crystal display, an organic EL (Electroluminescence) display, etc. The input device 37 and the display device 38 may be integrated into a touch panel.

[0080] Fig. 24 is a functional block diagram showing the functions of the computer 30 as a design support device. With reference to Fig. 24, from a functional perspective, the design support device 40 includes a winding arrangement region determination unit 41, a minute winding arrangement unit 42, and a winding synthesis unit 43. These elements can be considered to correspond to modules of a program executed by the computer 30. Note that the division of modules is for convenience, and for example, the winding arrangement region determination unit 41 and the minute winding arrangement unit 42 may be configured as a common module.

[0081] Specifically, the winding arrangement region determination unit 41 approximates the absolute value of a first periodic function that changes in the circumferential direction with the magnetic pole period of the stator of the AC machine with a pulse function having a pulse width according to the absolute value of the first periodic function. The winding arrangement region determination unit 41 determines the region where the pulse function becomes an on-pulse as the winding arrangement region. Here, the first periodic function is a function in which a sine function, which is a fundamental wave, and the third harmonic are superimposed in a phase relationship such that the peak value of the sine function is enhanced near the peak value and the values ​​are offset near the zero value of the sine function.

[0082] The minute winding arrangement section 42 arranges a large number of windings, each having a minute cross-sectional area, at equal intervals in the determined winding arrangement region.

[0083] The winding combining unit 43 expands the cross-sectional area of ​​each winding, and when adjacent windings overlap each other or when the proportion of the circumferential length of the stator where the windings are arranged exceeds a predetermined ratio, combines the most adjacent windings to generate a new winding as a winding assembly. The winding assembly is a winding having a total number of multiple combined windings and a total cross-sectional area of ​​the multiple combined windings. Combining the first winding and the second winding includes placing the combined winding between the first winding and the second winding. When the number of winding assemblies obtained as a result of expanding the cross-sectional area of ​​each winding reaches a desired number, the winding combining unit 43 determines the placement position of each winding assembly to the placement position of the slot that houses each winding assembly.

[0084] The embodiments disclosed herein should be considered to be illustrative and not restrictive in all respects. The scope of this application is defined by the claims, not the above description, and is intended to include all modifications within the meaning and scope of the claims. [Explanation of symbols]

[0085] 10 rotating machine, 11 stator, 12 rotor, 13 air gap, 20 stator core, 21 stator slot, 22 rotor core, 23 permanent magnet, 25kW maximum output, 30 computer, 31 CPU, 32 RAM, 33 non-volatile memory, 34 reader / writer, 35 recording medium, 36 communication device, 37 input device, 38 display device, 39 bus, 40 design support device, 41 winding placement area determination unit, 42 microwinding placement unit, 43 winding synthesis unit, SL1 to SL6 slots.

Claims

1. A rotor; a stator having a plurality of slots arranged in a circumferential direction facing the rotor; a plurality of phase windings wound in the plurality of slots, the number of windings of any first phase among the plurality of phases housed in each of the plurality of slots varies periodically in the circumferential direction; an AC motor in which a distribution of the number of windings of the first phase per period is approximated by a Fourier series whose main components are a fundamental wave component and a third harmonic component, and an approximation curve of the distribution has a shape in which a positive half cycle of a sine function, which is a fundamental wave, and the third harmonic are superimposed in a phase relationship in which the value of the sine function is enhanced near its peak value and is canceled out near its zero value.

2. 2. The AC machine according to claim 1, wherein the windings of the first phase are arranged such 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, the two windings pass current in the same direction, and when the two windings are included in adjacent periods, the two windings pass current in opposite directions.

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

4. 4. The AC machine according to claim 1, wherein windings of at least two phases are arranged in the same slot.

5. 1. A method for designing an AC machine, comprising: a step in which a computer approximates an absolute value of a first periodic function that changes in a circumferential direction with a magnetic pole period of a stator of the AC machine with a pulse function having a pulse width according to the absolute value of the first periodic function, and determines a region where the pulse function becomes an on-pulse as a winding arrangement region; the first periodic function is a function obtained by superposing a sine function, which is a fundamental wave, and a third harmonic wave in a phase relationship such that the value of the sine function is enhanced near a peak value of the sine function and is canceled out near a zero value of the sine function, The design method further comprises: a step in which the computer arranges a large number of windings each having a small cross-sectional area at equal intervals in the determined winding arrangement region; the computer enlarges the cross-sectional area of ​​each of the windings, and when adjacent windings overlap or when the proportion of the portion of the circumferential length of the stator where the windings are arranged exceeds a predetermined ratio, combines the windings that are closest to each other to generate a new winding as a winding assembly; The winding assembly has a total number of a plurality of combined windings and a total cross-sectional area of ​​the combined plurality of windings, and combining the first winding and the second winding includes disposing the combined winding between the first winding and the second winding, and further and when the number of winding assemblies obtained as a result of enlarging the cross-sectional area of ​​each of the windings reaches a desired number, determining by the computer an arrangement position of each of the winding assemblies to be an arrangement position of a slot that houses each of the winding assemblies.

6. 6. The method for designing an AC machine according to claim 5, wherein combining the first winding and the second winding includes arranging the combined winding at a position obtained by dividing the area from the first winding to the second winding in an inverse ratio of a cross-sectional area of ​​the first winding to a cross-sectional area of ​​the second winding.

7. manufacturing a stator by forming the slots at the slot placement positions determined according to the method for designing an AC machine according to claim 5 or 6; and manufacturing a rotor.

8. A design support device for an AC machine, comprising: a winding arrangement region determination unit that approximates an absolute value of a first periodic function that changes in a circumferential direction with a magnetic pole period of a stator of the AC machine with a pulse function having a pulse width according to the absolute value of the first periodic function, and determines a region where the pulse function becomes an on-pulse as a winding arrangement region; the first periodic function is a function obtained by superposing a sine function, which is a fundamental wave, and a third harmonic wave in a phase relationship such that the value of the sine function is enhanced near a peak value of the sine function and is canceled out near a zero value of the sine function, The design support device further comprises: a minute winding arrangement section that arranges a large number of windings with minute cross-sectional areas at equal intervals in the determined winding arrangement region; a winding combining unit that enlarges the cross-sectional area of ​​each of the windings, and combines the windings that are closest to each other when adjacent windings overlap or when the proportion of the portion of the circumferential length of the stator where the windings are arranged exceeds a predetermined ratio, thereby generating a new winding as a winding assembly; the winding assembly has a total number of a plurality of combined windings and a total cross-sectional area of ​​the combined plurality of windings, and combining the first winding and the second winding includes disposing the combined winding between the first winding and the second winding; When the number of winding assemblies obtained as a result of enlarging the cross-sectional area of ​​each of the windings reaches a desired number, the winding synthesis unit determines the arrangement position of each of the winding assemblies to be the arrangement position of a slot that accommodates each of the winding assemblies.

Images