Electric motor

Abstract

An electric motor (1) comprises an armature (2) that includes a printed circuit board of cylindrical shape, the printed circuit board forming a plurality of layers stacked in a radial direction of the cylindrical shape; and a field system (3) arranged with respect to the armature (2) in the direction of a central axis (AX) of the cylindrical shape. The printed circuit board includes a plurality of coils arranged circumferentially of the cylindrical shape. Each of the plurality of coils is formed from a linear conductor. Supposing that the conductor on the printed circuit board has a width, denoted by x, and a thickness in the radial direction, denoted by y, then x and y are each set to x. opt and y opt set which in combination maximize the space factor of the conductor in a cross-section of the anchor (2) that is perpendicular to the circumferential direction.

Description

Technical field

[0001] The present disclosure relates to an electric motor in which a printed circuit board is used as the armature. background

[0002] It is known that a conventional electric motor comprises a cylindrical printed circuit board for use in the armature. Patent literature 1 discloses an electric motor in which a printed circuit board rolled into a cylindrical shape is used as the armature and a plurality of coils are formed as a conductor pattern on the printed circuit board. Citation list of patent literature

[0003] Patent literature 1: Japanese patent application, publication number 2020 - 89 207 Overview of the invention Problem to be solved by the invention

[0004] It is known that an armature using a printed circuit board rolled into a cylindrical shape tends to have a smaller coil space factor than an armature comprising an iron core and magnet wires wound around the iron core. As the coil space factor decreases, copper loss increases. Therefore, the temperature rise due to heat generation caused by copper loss is a problem in electric motors that use printed circuit boards for their armature.

[0005] The present disclosure was made in view of the above explanation, and one objective of the present disclosure is to obtain an electric motor capable of reducing heat generation through copper loss. Means to solve the problem

[0006] To solve the aforementioned problem and achieve the objective, an electric motor according to the present disclosure comprises an armature that includes a printed circuit board with a cylindrical shape, wherein the printed circuit board forms a plurality of layers stacked in the radial direction of the cylindrical shape, and a field system arranged with respect to the armature along a central axis of the cylindrical shape. The printed circuit board includes a plurality of coils arranged circumferentially around the cylindrical shape. Each of the plurality of coils is formed from a linear conductor. Assuming that the conductor on the printed circuit board has a width, denoted by x, and a radial thickness, denoted by y, then x and y are each defined on x. opt and y optset which, in combination, maximize a space factor of the conductor in a cross-section of the anchor that is perpendicular to the circumferential direction. Effects of the invention

[0007] The electric motor according to the present disclosure has an effect such that heat generation due to copper losses is reduced. Brief description of the drawings Fig. Figure 1 is a diagram showing a schematic configuration of an electric motor according to a first embodiment. Fig. Figure 2 is an exploded view of the electric motor according to the first embodiment. Fig. Figure 3 is a diagram showing a printed circuit board enclosed in an armature according to the first embodiment. Fig. Figure 4 is a diagram showing part of a coil enclosed in the armature according to the first embodiment. Fig. Figure 5 is a sectional view of the anchor according to the first embodiment. Fig. Figure 6 is a diagram showing part of the anchor according to the first embodiment. Fig. Figure 7 is a diagram showing an exemplary process for manufacturing the anchor according to the first embodiment. Fig. Figure 8 is a cross-sectional view of the electric motor according to the first embodiment. Fig. Figure 9 is a first diagram showing the number of slots of the anchor according to the first embodiment. Fig. Figure 10 is a second diagram showing the number of slots of the anchor according to the first embodiment. Fig. Figure 11 is a diagram showing an exemplary relationship between a conductor width and a space factor of conductors in a slot in the anchor according to the first embodiment. Fig. Figure 12 is a cross-sectional view of the slot in the anchor according to the first embodiment. Fig. 13 is a diagram showing only cross-sections of the conductors emerging from the in Fig. The 12 cross-sections shown were extracted. Fig. Figure 14 is a diagram showing a unit structure of the electric motor according to the first embodiment. Fig. Figure 15 is a sectional view of an anchor according to a second embodiment. Fig. Figure 16 is a diagram showing a relationship between an arrangement of a coil in the armature according to the second embodiment and a winding factor. Fig. Figure 17 is a diagram showing an exemplary relationship between the width of an inner circumferential part of each coil and the copper loss coefficient in the electric motor according to the second embodiment. Fig. Figure 18 is a first diagram showing a configuration of an anchor according to a third embodiment. Fig. Figure 19 is a second diagram showing a configuration of the anchor according to the third embodiment. Fig. Figure 20 is a first diagram showing an arrangement of coils in the armature according to the third embodiment. Fig. Figure 21 is a second diagram showing an arrangement of the coils in the armature according to the third embodiment. Fig. Figure 22 is a third diagram showing the arrangement of the coils in the armature according to the third embodiment. Fig. Figure 23 is a fourth diagram showing the arrangement of the coils in the armature according to the third embodiment. Fig. Figure 24 is a fifth diagram showing the arrangement of the coils in the armature according to the third embodiment. Fig. Figure 25 is a sixth diagram showing a coil arrangement in the armature according to the third embodiment. Fig. Figure 26 is a cross-sectional view of part of an anchor according to a fourth embodiment. Fig. Figure 27 is a cross-sectional view of a coil unit in the armature according to the fourth embodiment. Fig. Figure 28 is a cross-sectional view of a coil unit in an armature according to a fifth embodiment. Fig. Figure 29 is a schematic diagram of a printed circuit board enclosed in an armature according to a sixth embodiment. Fig. Figure 30 is a schematic diagram of a printed circuit board enclosed in an armature according to a seventh embodiment. Fig. Figure 31 is a diagram showing a schematic configuration of a printed circuit board enclosed in an armature according to an eighth embodiment. Fig. Figure 32 is a cross-sectional view of part of the anchor according to the eighth embodiment. Description of the embodiments

[0008] With reference to the drawings, a detailed description of electric motors according to embodiments is provided below. First embodiment.

[0009] Fig. Figure 1 is a diagram showing a schematic configuration of an electric motor 1 according to a first embodiment. Fig. Figure 2 is an exploded view of the electric motor 1 according to the first embodiment. The electric motor 1 comprises an armature 2, which serves as the stator, and a field system 3, which serves as the rotor.

[0010] The armature 2 has a cylindrical shape. The field system 3 has a columnar shape. The field system 3 is arranged in a space surrounded by the armature 2. A central axis AX of the cylindrical armature 2 also serves as the central axis of the columnar field system 3. In other words, the armature 2 and the field system 3 are arranged coaxially with respect to each other. The field system 3 is oriented with respect to the armature 2 in the direction of the central axis AX. The field system 3 rotates about the central axis AX. A shaft 4 is attached to the field system 3 to transmit power from the field system 3 to the outside of the electric motor 1.

[0011] The armature 2 generates a magnetic field by exciting its coils. The field system 3 is set into rotation by the interaction between the magnetic field generated by the armature 2 and the magnets of the field system 3. In the following description, the direction of the central axis AX is referred to as the axial direction, a direction perpendicular to the central axis AX as the radial direction, and a direction that surrounds the central axis AX as the circumferential direction. The in Fig. Arrows A, B, and C shown in Figure 1 represent the radial, axial, and circumferential directions, respectively. The circumferential direction also refers to the direction of rotation in which the field system 3 rotates.

[0012] While the electric motor 1 described above comprises the armature 2 as the stator and the field system 3 as the rotor, the electric motor 1 can also comprise the armature 2 as the rotor and the field system 3 as the stator. If the armature 2 is the rotor and the field system 3 is the stator, the field system 3 is mechanically locked by an electromagnetic brake or the like. The armature 2 is rotated by the interaction between the magnetic field generated by the armature 2 and the magnets of the field system 3. In the Fig. 1 and Fig. 2 The magnetic spacing surfaces of the armature 2 and the field system 3 are arranged radially inwards; however, the magnetic spacing surfaces of the armature 2 and the field system 3 can also be arranged radially outwards.

[0013] Fig. Figure 3 is a diagram showing a printed circuit board 5 enclosed in the armature 2 according to the first embodiment. The armature 2 includes the printed circuit board 5, which is rolled into a cylindrical shape. Because the printed circuit board 5 is rolled, several layers of the printed circuit board 5 are stacked radially along the armature 2. Fig. Figure 3 is a top view showing a state in which the coils 7 are provided on a surface of a core substrate 6. Fig. 3 corresponds to the left-right direction of the circumferential direction and the up-down direction of the axial direction. When the cylindrical printed circuit board 5 is unrolled flat, it assumes an elongated shape.

[0014] The printed circuit board 5 comprises the core substrate 6, the several coils 7 formed on the core substrate 6 and an insulating layer. Fig. Figure 3 shows a portion of the printed circuit board 5 where two of the coils 7 are located. A description of the insulating layer follows later. When the printed circuit board 5 is rolled flat, the multiple coils 7 are arranged along a longitudinal direction of the printed circuit board 5. When the printed circuit board 5 is rolled into a cylindrical shape, the multiple coils 7 are arranged circumferentially.

[0015] In Fig. 3. The coils 7, which lie next to each other in the circumferential direction, are connected by a cross-wiring 8. In the Fig. In the example shown, the multiple coils 7 in the armature 2 are arranged using a so-called concentrated winding method. The multiple coils 7 in the armature 2 can also be arranged using a so-called distributed winding method.

[0016] Fig. Figure 4 is a diagram showing part of a coil 7 enclosed in the armature 2 according to the first embodiment. Fig. Figure 4 is an enlarged view of the section from frame IV in Fig. 3. Each of the coils 7 is formed from a linear conductor 10. The conductor 10, which forms the coil 7, is arranged spirally on the core substrate 6. An empty space without the conductor 10 is provided in the center of the spiral. In the following description, the empty space that forms the central space of the coil 7 is referred to as the inner circumferential part. In the Fig. In example 3, the inner circumferential part is a hexagonal region. Starting from a point next to the inner circumferential part, the conductor 10 is guided around the inner circumferential part several times. In the example shown Fig. In the example shown in Figure 3, the coil 7 has a hexagonal outer shape. The section shown in frame IV is the section of the coil 7 in which the conductor 10 extends in the axial direction.

[0017] In the Fig. In example 4, the conductor is guided around the inner circumferential part 10 times. Fig. Figure 4 shows three parallel linear sections of the conductor 10. A space 9 is provided on the core substrate 6 between adjacent linear sections to create insulation between them. It should be noted that a planar configuration of the coil 7 does not apply to the one shown in the Fig. 3 and Fig. The configuration shown in Figure 4 is limited and can be arbitrary. The coil 7 can have a different outer shape than a hexagon, for example, an elliptical shape. The conductor 10 can be wrapped around the inner circumferential part more than three times.

[0018] Fig. Figure 5 is a sectional view of anchor 2 according to the first embodiment. The one in Fig. The section shown in section 5 is the section along line VV in Fig. 3. Fig. Figure 5 shows the cross-section of the section of the printed circuit board rolled into the cylindrical shape. Fig. 5 corresponds to the left-right direction of the circumferential direction and the upward-downward direction of the radial direction. Fig. Figure 6 is a diagram showing part of the anchor 2 according to the first embodiment. Fig. Figure 6 is an enlarged view of the section from frame VI in Fig. 5.

[0019] In the Fig. 5 and Fig. In the example shown in Figure 6, the coils 7 are provided on both sides of the core substrate 6. The coils in the Fig. 5 and Fig. The printed circuit board 5 shown in Figure 6 corresponds to a so-called "double-sided mounting plate". The insulating layer 11 is provided between the radially aligned coils 7. The insulating layer 11 is, for example, a self-adhesive insulating film. The insulating layer 11 can be, for example, a self-adhesive film with insulating properties or an adhesive with insulating properties.

[0020] The one in the Fig. 5 and Fig. The armature 2 shown in Figure 6 has several stacked layers 12, each formed by placing the coil 7, the insulating layer 11, and the coil 7 between two layers of the core substrate 6. The radially stacked layers 12 of the printed circuit board 5 number N. N is a positive integer. In the following description, N is also referred to as the number of layers. In the Fig. In the example shown in Figure 5, the core substrate 6 is present at both radial ends of the printed circuit board 5; however, the insulating layer 11 may be present at at least one of these ends.

[0021] The printed circuit board 5 was described above as a "double-sided mounting board," but this is not a limitation. The printed circuit board 5 can be a "single-sided mounting board" or a "multi-layer mounting board." If the printed circuit board 5 is a "single-sided mounting board," the coils 7 are mounted on only one side of the core substrate 6. If the printed circuit board 5 is a "multi-layer mounting board," the coils 7 are stacked alternately with the insulating layer 11 on the core substrate 6.

[0022] In the first embodiment, a portion of the conductor 10, which forms the coil 7, is formed with a uniform width on the printed circuit board 5. In the following description, the width of the conductor 10 on the printed circuit board 5 is denoted by x. The conductor 10 has a thickness of y in the radial direction. The section of the coil 7 within the printed circuit board 5 is defined as x. Fig. The frame IV shown in Figure 3 has a width of W. The width of this section of the coil 7 is the circumferential width. In the following description, W, the width of the section of the coil 7, is also referred to as the slot width. The space 9 has a circumferential width c. The circumferential width of the space 9 can also be described as the distance between the linear sections of the conductors 10 in the coil 7 on the printed circuit board 5. The core substrate 6 has a radial thickness m, and the insulating layer 11 has a radial thickness h. The inner circumferential portion of each coil 7 has a width a, and the distance between adjacent coils 7 is denoted by b. The width of the inner circumferential portion is the circumferential width. The distance between the coils 7 is the circumferential distance.

[0023] Fig. Figure 7 is a diagram showing an exemplary process for manufacturing the anchor 2 according to the first embodiment. Fig. Figure 7 schematically shows how the armature 2, which encompasses the cylindrical printed circuit board 5, is formed by rolling up the printed circuit board 5 from a flat, expanded state. Although either the core substrate 6 or the insulating layer 11 is present on an inner surface of the cylindrical printed circuit board 5, the core substrate 6 or the insulating layer 11 is located on this surface in Fig. 7 omitted. In the description above, the outer shape of coil 7 is hexagonal; in Fig. However, the outer shape of coil 7 is simplified to an elliptical shape.

[0024] Each component of the printed circuit board 5 must be flexible enough to prevent breakage during the rolling process. Furthermore, the components of the printed circuit board 5 must not exhibit any significant changes in their electrical properties, such as insulation performance, as a result of the rolling process. The armature 2 is not limited to being formed by rolling the printed circuit board 5. The armature 2 can also be formed by mounting the coils 7 on a core substrate 6 that has been previously formed into a cylindrical shape.

[0025] Fig. Figure 8 is a cross-sectional view of the electric motor 1 according to the first embodiment. The Fig. The cross-section shown in Figure 8 is the section taken perpendicular to the axial direction at a midpoint of the armature 2. The armature 2 is described below by an outer diameter D and an inner diameter d. Both D, the outer diameter, and d, the inner diameter, are diameters. The slots, i.e., the areas of the armature 2 in which the coils 7 are arranged, number n, and the number of turns of the coils 7 is T per slot. The number of slots in the armature 2 is determined based on the specifications of the electric motor 1.

[0026] Fig. Figure 9 is a first diagram showing the number of slots of the anchor 2 according to the first embodiment. Fig. Figure 10 is a second diagram showing the number of slots of the armature 2 according to the first embodiment. Here, the slot counting method is applied to the concentrated winding arrangement of the multiple coils 7, and the distributed winding arrangement of the multiple coils 7 is unified. Fig. Figure 9 schematically shows an arrangement of the coils 7 in the case of a concentrated winding. Fig. Figure 10 schematically shows an arrangement of the coils 7 in the case of a distributed winding. Fig. 9 and Fig. Figure 10 shows the areas in which the coils 7 for phases U, V, and W are arranged. A mark in each area indicates a direction of current flow through the coil 7. Identical marks indicate the same direction of current flow. Different marks indicate opposite directions of current flow.

[0027] In the case of the in Fig. In the concentrated winding shown in Figure 9, coils 7, through which current flows in opposite directions, are arranged in two adjacent circumferential regions. In the case of the concentrated winding, each of these regions is defined as a slot. A Fig. The area shown in Figure 13 is an example of the single slot.

[0028] In the case of the in Fig. In the distributed winding shown in section 10, areas with the same current flow direction are arranged adjacent to each other circumferentially. For each phase, two areas where the current flows in opposite directions are positioned with a plurality of areas in between. In the case of the distributed winding, each of these areas is defined as a slot. A Fig. Area 13 shown in section 10 is an example of the single slot.

[0029] Next, a first procedure for determining the width x and the thickness y is described. Fig. Figure 11 is a diagram showing an exemplary relationship between the width of the conductor 10 and a space factor of the conductor 10 in the slot in the anchor 2 according to the first embodiment. Fig. Figure 11 shows a graph illustrating the relationship between the width x of conductor 10 and the volume factor of conductor 10. Fig. In figure 11, the vertical axis represents the space factor. The horizontal axis represents the width x of conductor 10. Due to manufacturing limitations of the printed circuit board 5, the thickness y of conductor 10 is limited to a value between 0.03 mm and 0.12 mm inclusive. The in Fig. Diagram 11 shows the relationship between the width x and the volume factor when the thickness y is in the range from 0.03 mm inclusive to 0.12 mm inclusive.

[0030] x and y are each set to x opt and y optset which, in combination, maximize the space factor of the conductor 10 in a cross-section of the anchor 2 that runs perpendicular to the circumferential direction. In the Fig. The graph shown in 11 refers to x opt on the x that maximizes the space factor. Since y is limited to a value between 0.03 mm and 0.12 mm inclusive, y opt limited to a value between 0.03 mm and 0.12 mm inclusive.

[0031] Details of the theoretical formulas that show the relationship between the width x of conductor 10 and the space factor of conductor 10 are described here. The width x can be derived once the slot width W is determined. The slot width W is expressed by the following formula (1) based on the design specifications of the printed circuit board 5. Formula 1: W=TƒNx+(TƒN−1)c

[0032] The slot width W is also expressed by the following formula (2), which is based on different dimensions of the anchor 2. Formula 2: W=π(D+d)2n−a2

[0033] By combining formulas (1) and (2) we obtain the following formula (3), which expresses the width x. Formula 3: x=ƒNT{π(D+d)2n−a2−(TƒN−1)c}

[0034] For the width a of the inner circumferential part, a=a is used in formula (3) in the case of a concentrated winding, while a=0 is used in formula (3) in the case of a distributed winding.

[0035] To obtain the width x of conductor 10, the number of layers N of armature 2 must be determined. The number of layers N can be obtained once the thickness y of conductor 10 has been determined. The thickness y is expressed by the following formula (4). Formula 4: y=D−d−2hN−2m(N+1)2ƒN

[0036] As described above, the thickness y is limited to a value between 0.03 mm and 0.12 mm inclusive due to the manufacturing constraints of the printed circuit board 5. The number of layers N is a positive integer. The number of layers N can be obtained by increasing or decreasing its value so that the value of y falls within the range of 0.03 mm to 0.12 mm inclusive. Once the thickness y and the number of layers N are determined, the width x can be obtained using formula (3).

[0037] Fig. Figure 12 is a cross-sectional view of the slot in the anchor 2 according to the first embodiment. Fig. 13 is a diagram showing only cross-sections of the conductor 10, which comes from the in Fig. The 12 cross-sections shown were extracted. Fig. Figure 12 shows the cross-section of area 13, which shows the single slot.

[0038] The cross-sectional area S of the conductor 10 in the slot is expressed by the following formula (5). The cross-sectional area S can be derived once the width x and the thickness y have been determined. Formula 5: S=(y׃N)×(x×TƒN)=xyT

[0039] Formulas (3) to (5) show that the cross-sectional area S is determined once the number of layers N is determined.

[0040] The space factor of the conductor 10 in the slot is maximized by forming the printed circuit board 5 such that each conductor 10 has the width x and the thickness y that maximize the cross-sectional area S. The width x and the thickness y are each adjusted to the width x opt and the thickness y optThe parameters are defined which, in combination, maximize the space factor of the conductor 10. By maximizing the space factor of the conductor 10, the electrical resistance and the loss of the conductor 10 are reduced. Accordingly, the electric motor 1 can reduce copper loss, thereby reducing heat generation due to copper loss.

[0041] The first method for determining the width x and the thickness y has been described. Next, an alternative method for determining the width x and the thickness y is described as the second method. In the second example, it is assumed that the electric motor 1 comprises one or more unit structures. Here, a group of a certain number of magnetic poles, encompassed in the field system 3, and a certain number of slots, which are the areas of the armature 2 in which the coils 7 are arranged, is referred to as a unit structure of the electric motor 1.

[0042] Fig. Figure 14 is a diagram showing the unit structure 15 of the electric motor 1 according to the first embodiment. Fig. Figure 14 schematically shows a section of the anchor 2 and a section of the field system 3, which together form the single unit structure 15. In Fig. 14 corresponds to the left-right direction of the circumferential direction and the up-down direction of the radial direction. In the section of anchor 2 that is encompassed in the single unit structure 15, the multiple slots are arranged circumferentially. One in Fig. Rectangle 16, shown in 14, represents one of the several slots. In the section of the field system 3 encompassed by the unit structure 15, the multiple magnetic poles are arranged circumferentially. One in Fig. Rectangle 17 shown in Figure 14 represents one of the multiple magnetic poles.

[0043] Suppose that the electric motor 1 has a total of six magnetic poles and a total of nine slots. In this case, the unit structure 15 of the electric motor 1 consists of a set of two magnetic poles and three slots, and the electric motor 1 comprises three such unit structures 15. It should be noted that the unit structure 15 can comprise any number of magnetic poles and any number of slots. Furthermore, the electric motor 1 can comprise any number of unit structures 15. In the following description, the number of slots in the unit structure 15 is denoted by n', the section of the armature 2 enclosed in the unit structure 15 has a circumferential length of L, and the slots each have a radial length of H.

[0044] As with the first method, the second method also uses a combination of width x opt and the thick y optderived once the slot width W is determined. Formula (1) also applies to the second method.

[0045] The slot width W is expressed using different dimensions of the anchor 2 by the following formula (6). Formula 6: W=Ln'−a2

[0046] By combining formulas (1) and (6) we obtain the following formula (7), which expresses the width x. Formula 7: x=ƒNT{Ln'−a2−(TƒN−1)c}

[0047] For the width a of the inner circumferential part, a=a is used in formula (7) in the case of a concentrated winding, while a=0 is used in formula (7) in the case of a distributed winding.

[0048] The thickness y is expressed by the following formula (8). Formula 8: y=H−hN−m(N+1)ƒN

[0049] The number of layers N can be obtained by increasing or decreasing its value so that the value of y falls within the range of 0.03 mm to 0.12 mm inclusive. Once the thickness y and the number of layers N are determined, the width x can be obtained using formula (7). The cross-sectional area S can be derived once the width x and the thickness y are determined.

[0050] The space factor of the conductor 10 in the slot is maximized by designing the printed circuit board 5 such that each conductor 10 has the width x and the thickness y that maximize the cross-sectional area S. The width x and the thickness y are each adjusted to the width x opt and the thickness y optThe parameters are defined which, in combination, maximize the space factor of the conductor 10. By maximizing the space factor of the conductor 10, the electrical resistance and the loss of the conductor 10 are reduced. Accordingly, the electric motor 1 can reduce copper loss and thereby reduce heat generation due to copper loss. Second embodiment.

[0051] Fig. Figure 15 is a sectional view of the anchor 2 according to a second embodiment. The second embodiment mainly describes how its configuration differs from that of the first embodiment. Fig. Figure 15 shows the cross-section of a section of a printed circuit board 5, which is rolled into a cylindrical shape. Fig. 15 corresponds to the left-right direction of the circumferential direction and the up-down direction of the radial direction. The in Fig. The configuration shown in 15 is similar to the one in Fig. 5 configuration shown. A cross-section of each area, which serves as the slot of anchor 2, resembles that shown in Fig. 6 cross-section shown. In the second embodiment, it is assumed that several coils 7 are arranged in a concentrated winding arrangement.

[0052] In the Fig. In the configuration shown in Figure 15, an inner circumferential portion of each coil 7 has a width a', and a distance between adjacent coils 7 is denoted by b'. The width of the inner circumferential portion is the width in the circumferential direction. The distance between the coils 7 is the distance in the circumferential direction. In the second embodiment, a' and b' are each located on a' opt and b' opt set, which in combination maximize a winding factor of coil 7.

[0053] It is known that the copper loss generated in the electric motor 1 is essentially inversely proportional to the winding factor k. w is. The winding factor k wis a coefficient that is determined, for example, by a combination of the number of magnetic poles and the number of slots of the electric motor 1, or by an arrangement of the multiple coils 7 in the electric motor 1. The copper loss of the electric motor 1, which is a three-phase motor, is proportional to the phase resistance R. p and to the square of the phase current. With increasing winding factor k w The induced voltage of the electric motor 1 increases. Therefore, it decreases with increasing winding factor k. w the phase current required to generate the same torque.

[0054] Here, a component is extracted that is proportional to the square of the reciprocal of the winding factor k. w is, and the extracted component is called the copper loss coefficient k Cu denoted by the copper loss coefficient k. Cu is expressed by the following formula (9). Formula 9: kCu=3×Rp×1kw2

[0055] Furthermore, it is known that the winding factor k w proportional to a short-step size factor k p is. The short-step size factor k p k is a coefficient that indicates the ratio by which the flux linkage decreases when the slot spacing and the magnetic pole spacing differ. Although factors such as the distribution factor are also proportional to the winding factor k w Their details are omitted here.

[0056] Fig. Figure 16 is a diagram showing a relationship between the arrangement of a coil 7 in the armature 2 according to the second embodiment and the winding factor. In a diagram shown in Fig. In graph 16, the vertical axis represents the winding factor k. w, and the horizontal axis represents an electrical angle θ of the coil 7 and the width x of the conductor 10. A configuration of the coil 7 is shown schematically above the graph in Fig. 16 shown.

[0057] The short step size factor k p of the electric motor 1, which drives the in Fig. The amount of magnetic flux associated with the coil 7, as shown in Figure 15, can be derived from the amount of magnetic flux associated with the coil 7 at an inner circumferential position P1 and an outer circumferential position P2. The inner circumferential position P1 refers to a point on the inner circumference of the coil 7 adjacent to the inner circumferential portion. The outer circumferential position P2 refers to a point on the outer circumference of the coil 7. The amount of flux linkage in the coil 7 is small at the inner circumferential position P1 and at the outer circumferential position P2 and reaches its maximum at a midpoint between the inner circumferential position P1 and the outer circumferential position P2. The ratio between the amount of magnetic flux generated by a magnet and the amount of flux linkage corresponds to the short-step factor k. p Let φ magnet The amount of magnetic flux of each magnet. Let φ n_maxThe maximum value of the flux linkage in each slot. Let θ1 be an electric angle at the inner circumferential position P1 of coil 7 of each phase. Let θ2 be an electric angle at the outer circumferential position P2 of coil 7 of each phase. The short-step factor k p is expressed by the following formula (10). Formula 10: kp=1n∫1nΦn_maxdnΦmagnet=(cos θ1−cos θ2)θ2−θ1

[0058] The electric angle θ1 is given by the following formula (11) based on the one in Fig. The electric angle θ2 is expressed by the following formula (12) based on the configuration shown in 15. Fig. The configuration shown in Figure 15 is expressed as follows. Let p be the number of magnetic poles applied to electric motor 1, and let τ be the number of magnetic poles applied to electric motor 1. p The spacing at which the multiple magnetic poles are arranged. Formula 11: θ1=a'2τp×180 Formula 12: θ2=pnτp−b'2τp×180

[0059] Formulas (9) to (12) show that the width a' and the distance b' are each related to the copper loss coefficient k Cu are related.

[0060] Fig. Figure 17 is a diagram showing an exemplary relationship between the width of the inner circumferential part of each coil 7 and the copper loss coefficient in the electric motor 1 according to the second embodiment. The vertical axis of a Fig. The graph shown in Figure 17 represents the copper loss coefficient k. Cu The horizontal axis of the graph represents the width a' of the inner circumference portion. The in Fig. Graph 17 shows the relationship between the width a' and the copper loss coefficient k. Cu for cases where the distance b' between adjacent coils 7 takes on a value of 0, 1, 2 or 3.

[0061] According to Fig. 17 is the copper loss coefficient k CuThe smaller the value of the distance b', the smaller the coefficient of copper loss. Cu This means less copper loss. Furthermore, according to Fig. 17 even when the distance b' takes on one of the values ​​0, 1, 2 and 3, a value for the width a' that leads to a local minimum of the copper loss coefficient k Cu leads to the combination of the width a' and the distance b', for which the copper loss coefficient k Cu Reaching its local minimum corresponds to the combination of a' opt and b' opt , which determines the winding factor k w The coil 7 is maximized.

[0062] According to Fig. As the width a' approaches 0, the area of ​​the part of coil 7 facing the magnet increases, thereby increasing the flux linkage of coil 7. With increasing flux linkage of coil 7, the short-step factor k also increases. p to and the copper loss coefficient k Cuab. When the width a' increases to approximately τp / 2, the coil 7 is no longer located at the point where the magnetic flux density of the magnet reaches its maximum, leading to a significant reduction in the short-step width factor k. p leads to this. Therefore, the width a' satisfies opt preferably the following formula (13). Formula 13: 0 <a'opt<τp2

[0063] The above description of the width a' opt This also applies to the distance b' opt . For a range of possible values ​​of the electric angle θ2 in formula (12), the distance b' satisfies opt preferably the following formula (14). Formula 14: 0 <b'opt<(pn−12)τp

[0064] The copper loss of the electric motor 1 is reduced when the multiple coils 7 are designed such that they have a width a' opt and the distance b' opt fulfilling the winding factor k wmaximize coil 7. Furthermore, if the width a' opt the formula (13) is satisfied and the distance b' opt If formula (14) is satisfied, the copper loss coefficient k can be calculated. Cu This can be reduced, leading to a further reduction in the copper loss of electric motor 1. Accordingly, electric motor 1 can reduce copper loss and thereby reduce heat generation due to copper loss. Third embodiment.

[0065] Fig. Figure 18 is a first diagram showing a configuration of anchor 2 according to a third embodiment. Fig. Figure 19 is a second diagram showing a configuration of anchor 2 according to the third embodiment. The third embodiment mainly describes how the configurations differ from those of the first or second embodiments.

[0066] The Fig. 18 and Fig. Figures 19 each schematically show how a printed circuit board 5 is rolled from a flat state into a cylindrical shape. In the Fig. 18 and Fig. Figure 19 shows coil units 14 parts of the layers 12, each comprising two coils 7 stacked with the insulating layer 11 between the two coils 7. Each coil unit 14 refers to a region of the layer 12 in which the coils 7 are formed and can be described as the region in which a slot is formed. Fig. 18 and Fig. Figure 19 shows the core substrate 6 in simplified form. In the Fig. 18 and Fig. In the third embodiment, the insulating layer 11 is omitted. It is assumed that the multiple coils 7 are arranged in a concentrated winding arrangement.

[0067] The armature 2 with the N layers 12 is formed by rolling the printed circuit board 5 into a cylindrical shape. In the third embodiment, N is an integer greater than or equal to 2. For each slot of the armature 2, it is advantageous to align several coil units 14 radially. However, if all the multiple coils 7 are arranged on the core substrate 6 at a fixed distance b, positional offsets occur between the coil units 14 within each slot in the circumferential direction. These positional offsets result in the slot having a shape that deviates from the ideal shape. The ideal shape of the slot is the shape that results when the coils 7 from the layers 12 within the slot are radially aligned.

[0068] Here, M is an integer greater than or equal to 1 and less than N. Let b'' be a distance between the coils 7 closest to a rolling end of the cylindrical shape in an M-th layer 12, measured from the central axis AX of the cylindrical shape among the multiple layers 12 of the printed circuit board 5, and the coils 7 closest to a rolling start of the cylindrical shape in an (M+1)-th layer 12, measured from the central axis AX of the cylindrical shape among the multiple layers 12 of the printed circuit board 5. In the Fig. 18 and Fig. In Equation 19, the distance between a coil unit 14 closest to the rolling end of the cylindrical shape in the M-th layer 12 and a coil unit 14 closest to the rolling start of the cylindrical shape in the (M+1)-th layer 12 is denoted by b''. If the distance b'' has the same length as the distance b between the coils 7 in each of the multiple layers 12 of the printed circuit board 5, the coils 7 in the (M+1)-th layer 12 are theoretically offset circumferentially relative to the coils 7 in the M-th layer 12.

[0069] In the third embodiment, as in Fig. As shown in Figure 18, the positions of the coils 7 on the core substrate 6 are determined such that the distance b'' is greater than the distance b. By making the distance b'' greater than the distance b, the positional offset of the coils 7 in the (M+1)th layer 12 relative to the coils 7 in the Mth layer 12 can be eliminated. In other words, the coils 7 in the (M+1)th layer 12 can be aligned radially with the coils 7 in the Mth layer 12. Fig. Figure 19 shows how the coil units 14 in the (M+1)th layer 12 are aligned radially with the coil units 14 in the Mth layer 12 by extending a section of the core substrate 6 corresponding to the distance b'' from the layer shown in Fig. The condition shown in Figure 18 is bent. By making the distance b'' larger than the distance b and adjusting the circumferential positions of the coil units 14 accordingly, the coil units 14 in one layer 12 can be aligned radially with the coil units 14 in layer 12 on an outer circumferential side of this layer 12. By aligning the coil units 14 radially across the radially adjacent layers 12, each slot obtains the ideal shape.

[0070] In the third embodiment, the distance b'' satisfies the following formula (15). Formula 15: b≤b'' <b2+(h+yƒ+2m)2−2b(h+yƒ+2m)cos ((2−n)π2n−NWMD+d{N−(M−12)})

[0071] This section describes how formula (15) is derived. Fig. Figure 20 is a first diagram showing an arrangement of the coils 7 in the armature 2 according to the third embodiment. Fig. Figure 21 is a second diagram showing an arrangement of the coils 7 in the armature 2 according to the third embodiment.

[0072] In the Fig. 20 and Fig. 21 is a coil unit 14 nM The nM-th coil unit 14, counted from the roll start of the printed circuit board 5. The coil unit 14 nM refers to the coil unit 14 that is closest to the rolling end of the cylindrical shape in the M-th layer 12. A coil unit 14 nM+1 is the (nM+1)th coil unit 14, counted from the roll start of the printed circuit board 5. The coil unit 14 nM+1 refers to the coil unit 14 that is closest to the roll start of the cylindrical shape in the (M+1)th layer 12. A coil unit 14 n(M-1)+1 is the {n(M-1)+1}th coil unit 14, counted from the roll start of the printed circuit board 5. The coil unit 14 n(M-1)+1is the coil unit 14 that is closest to the roll start of the cylindrical shape in an (M-1)th layer 12.

[0073] Fig. Figure 20 shows a case where the distance b'' satisfies formula (15) and is shortest, meaning that the distance b'' has the same length as the distance b. In this case, the coil units 14nM+1 and 14nM are arranged on the same circle, the center of which is the central axis AX. The theoretical description above states that if the distance b'' has the same length as the distance b, the coils 7 in the (M+1)th layer 12 are offset circumferentially relative to the coils 7 in the Mth layer 12. However, if the printed circuit board 5 is rolled into a cylindrical shape, the cylindrical shape may bulge radially, or the printed circuit board 5 may deform due to the stress applied to it.Even if the distance b'' is the same length as the distance b, the coils 7 in the (M+1)th layer 12 could still be radially aligned with the coils 7 in the Mth layer 12 due to a bulge in the cylindrical shape or a deformation of the printed circuit board 5. Therefore, formula (15) includes the case where the distance b'' is equal to the distance b.

[0074] Fig. Figure 21 shows a case in which the distance b'' satisfies formula (15) and is the longest.

[0075] Fig. Figure 22 is a third diagram showing the arrangement of the coils 7 in the armature 2 according to the third embodiment. Fig. Figure 23 is a fourth diagram showing the arrangement of the coils 7 in the armature 2 according to the third embodiment. Fig. Figure 24 is a fifth diagram showing the arrangement of the coils 7 in the armature 2 according to the third embodiment.

[0076] Fig. Figure 22 schematically shows the arrangement of the coil units 14 n(M-1)+1 , 14 nM and 14 nM+1 in armature 2, when the distance b'' is greatest. An expression on the right-hand side of “<” in formula (15) represents the case where the coil units 14 n(M-1)+1 and 14 nM are arranged on the same circle, the center of which is the central axis AX.

[0077] The in Fig. The triangle shown in figure 23 represents a triangle formed by the coil units 14. n(M-1)+1 , 14 nM+1 and 14 nM in Fig. 22 is defined. That in Fig. The triangle shown in Figure 23 comprises a first side with a length equal to the distance b'', a second side with a length equal to the distance b, and a third side with a length of h+yf+2m. Fig. 23 is an angle θ, the angle formed by the second side and the third side, i.e., the angle opposite the first side.

[0078] The distance b'' is expressed by the following formula (16). Formula 16: b''=b2+(h+yƒ+2m)2−2b(h+yƒ+2m)cos θ

[0079] A radius r is the radius of the circle on which the coil units 14 n(M-1)+1 and 14 nM are arranged and whose center point is the central axis AX. The in Fig. The angle θ' shown in 24 is the angle that results when the third side of the Fig. The triangle shown in Figure 23 is extended in the direction of the central axis AX. The angle θ' is a supplementary angle to the angle between the second and third sides. The angle θ' is expressed by the following formula (17). Formula 17: θ'=π−θ

[0080] An angle between a straight line passing through the central axis AX and a circumferential center of the coil unit 14 n(M-1)+1runs, and a straight line passing through the central axis AX and a circumferential center of the coil unit 14 nM The path formed is expressed as 2π / n. The width of the coil unit 14, namely the slot width W, can be expressed using the radius r. Accordingly, the angle θ' is expressed by the following formula (18). Formula 18: θ'=π2−12(2πn−Wr)

[0081] Fig. Figure 25 is a sixth diagram showing an arrangement of coils 7 in the armature 2 according to the third embodiment. Fig. 25 shows the N coil units 14 n1 , 14 n2 , ..., 14 nM , ... and 14 nN , which form one of the slots. The coil unit 14 n1 The coil unit 14 is located in the first layer 12. The coil unit 14 n2 The coil unit 14 is located in the second layer 12. The coil unit 14 nMThe coil unit 14 is located in the M-th layer 12. The coil unit 14 nN The coil unit 14 is located in the Nth layer 12. The radial length of a single layer 12 is expressed as (Dd) / 2N. The radius r is expressed by the following formula (19). Formula 19: r=d2+D−d2N(M−12)

[0082] Substituting formulas (17) to (19) into formula (16) yields the expression on the right-hand side of “<” in formula (15). However, rolling the printed circuit board 5 into the cylindrical shape does not lead to the assumed situation where the distance b'' corresponds to the expression on the right-hand side of “<” in formula (15) due to the bulging of the cylindrical shape or the deformation of the printed circuit board 5. Therefore, formula (15) excludes the case where the distance b'' corresponds to the expression on the right-hand side of “<” in formula (15).

[0083] In the third embodiment, the coil units 14 can be aligned radially across the radially adjacent layers 12 if the distance b'' satisfies formula (15). This allows each slot in the armature 2 to have the ideal shape. Fourth embodiment.

[0084] Fig. Figure 26 is a cross-sectional view of part of the anchor 2 according to a fourth embodiment. Fig. Figure 26 shows the cross-section of area 13, which illustrates an example of a single slot. The fourth embodiment mainly describes how its configuration differs from those of the first to third embodiments. The in Fig. The cross-section shown in section 26 is the section perpendicular to the central axis AX. Fig. Figure 26 shows N coil units 14. In the fourth embodiment, N is an integer greater than or equal to 2.

[0085] An almost trapezoidal shape is an ideal shape for the slot in the Fig. The cross-section shown in Figure 26 is obtained when the armature 2 is manufactured. In the fourth embodiment, each of the coil units 14 is longer in the circumferential direction on an outer circumferential side of the cylindrical shape than on an inner circumferential side of the cylindrical shape, thereby bringing the slot closer to the ideal shape.

[0086] Fig. Figure 27 is a cross-sectional view of the coil unit 14 in the armature 2 according to the fourth embodiment. The Fig. The cross-section shown in section 27 is the section perpendicular to the central axis AX.

[0087] Let W1 be the circumferential width of an end of the coil unit 14 (i.e., the region of layer 12 in which the coils 7 are formed) that is closer to the central axis AX, and let W2 be the circumferential width of an opposite end of the coil unit 14 with respect to the central axis AX. W1 and W2 satisfy the following formula (20). Formula 20: 1 <W2W1<1.05

[0088] In each of the coil units 14 that form the slot, the width W2 is approximately 0% to 5% larger than the width W1. This gives the slot its ideal shape, which is nearly trapezoidal. By forming the slot in this ideal shape, the deformation of the armature 2 during its manufacture can be reduced. Fifth embodiment.

[0089] Fig. Figure 28 is a cross-sectional view of a coil unit 14 in the armature 2 according to a fifth embodiment. The Fig. The cross-section shown in Figure 28 is the section perpendicular to the central axis AX. The fifth embodiment mainly describes how its configuration differs from those of the first to fourth embodiments.

[0090] Let W1 be the circumferential width of an end of the coil unit 14 (i.e., the region of layer 12 in which the coils 7 are formed) that is closer to the central axis AX, let W2 be the circumferential width of an opposite end of the coil unit 14 with respect to the central axis AX, and let W3 be a circumferential width measured at a radial center point of the coil unit 14. W1 and W3 satisfy the following formula (21). W2 and W3 satisfy the following formula (22). Formula 21: 1 <W3W1<1.025 Formula 22: 1 <W2W3<1.025

[0091] The width W3 can be described as the representative circumferential width of the coil unit 14. The width W1 is smaller than the representative width W3, and the width W2 is larger than the representative width W3. This allows the slot to have an ideal, nearly trapezoidal shape. By shaping the slot into this ideal form, the deformation of the armature 2 during its manufacture can be reduced. Sixth embodiment.

[0092] Fig. Figure 29 is a schematic diagram of a printed circuit board 5 enclosed in the armature 2 according to a sixth embodiment. The sixth embodiment mainly describes how its configuration differs from those of the first through fifth embodiments. In the sixth embodiment, pins 21 are provided on one side of a core substrate 6, which are radially erect. The core substrate 6 includes holes 22 formed on an opposite side. Each of the holes 22 is shaped to fit the pin 21. Fig. Figure 29 shows a portion of the core substrate 6 in which two of the coils 7, one of the pins 21, and one of the holes 22 are provided. The pins 21 and the holes 22 are each located in a region of the core substrate 6 that differs from the regions in which the coils 7 are formed.

[0093] If errors in the alignment of the coils 7 that form slots can be reduced when the printed circuit board 5 is rolled into a cylindrical shape, the slots can be brought closer to their ideal shape. In the sixth embodiment, the pins 21 are inserted into the holes 22 when the printed circuit board 5 is rolled to form the multiple stacked layers 12. The relative positions of the pins 21 and the holes 22 are determined such that each pin 21 can be inserted into the corresponding hole 22 when the printed circuit board 5 is rolled into multiple stacked layers 12. In the core substrate 6, the areas for the pins 21 and the holes 22 are assigned axial positions relative to the areas where the coils 7 are formed.This prevents the printed circuit board 5 from becoming longer in the circumferential direction, and the pins 21 and the holes 22 can be provided without reducing the space factor.

[0094] The radial length of pin 21 is greater than the thickness y of coil 7. The radial depth of hole 22 is greater than the difference between the radial length of pin 21 and the thickness y. Pin 21 is not on the in Fig. The column shape shown in Figure 29 is limited. The pin 21 can have any shape that reduces errors in the alignment of the coils 7, for example, an elliptical cylinder that is long in the axial or circumferential direction. The hole 22 is shaped according to the shape of the pin 21. Each pin 21 and the corresponding hole 22 can be in any relative position that reduces errors in the alignment of the coils 7. The position of the hole 22 can be offset in the axial or circumferential direction relative to the position of the pin 21.

[0095] The pins 21 can be made of any material. The pins 21 can be made of the same material as one of the components of the printed circuit board 5, or of a material that is not used for any of the components of the printed circuit board 5. The pins 21 can be attached during the installation of the components of the printed circuit board 5 or added after the components of the printed circuit board 5 have been installed.

[0096] During the manufacture of the armature 2, the pins 21 are inserted into the holes 22, thereby reducing errors in the alignment of the coils 7 that form the slots. In this way, a reduction in the performance of the electric motor 1 can be prevented. Seventh embodiment.

[0097] Fig. Figure 30 is a schematic diagram of a printed circuit board 5 enclosed in the armature 2 according to a seventh embodiment. The seventh embodiment mainly describes how its configuration differs from those of the first to sixth embodiments. In the seventh embodiment, the multiple coils 7 are provided on one side of a core substrate 6. The core substrate 6 includes recesses 23 on an opposite side, each shaped to fit the corresponding coil 7. Fig. Figure 30 shows part of the core substrate 6, where two of the coils 7 and two of the recesses 23 are provided.

[0098] In the seventh embodiment, the coils 7 are inserted into the recesses 23 when the printed circuit board 5 is rolled to form the multiple stacked layers 12. Each recess 23 is shaped according to the form of the coil 7. The position of each recess 23 is determined such that the corresponding coil 7 can be inserted into the recess 23 when the printed circuit board 5 is rolled into multiple stacked layers 12.

[0099] During the manufacture of the armature 2, the coils 7 are inserted into the recesses 23, thereby reducing errors in the alignment of the coils 7 that form slots. In this way, a deterioration in the performance of the electric motor 1 can be prevented. In the seventh embodiment, the core substrate 6 has larger contact areas with the coils 7 than in the sixth embodiment. As a result, the heat transfer coefficient between the stacked layers 12 is improved in the seventh embodiment compared to the sixth embodiment. With the improved heat transfer coefficient between the stacked layers 12, the electric motor 1 enables a reduction in the temperature rise of the coils 7 during excitation. Eighth embodiment.

[0100] Fig. Figure 31 is a diagram showing a schematic configuration of a printed circuit board 5 enclosed in the armature 2 according to an eighth embodiment. The eighth embodiment mainly describes how its configuration differs from those of the first to seventh embodiments. Fig. Figure 31 shows a part of the printed circuit board 5, which has been rolled flat from its cylindrical shape.

[0101] In the eighth embodiment, the circumferential positions of the coils 7 for each layer 12 are offset over the majority of layers 12. In this configuration, the electrical angles of radially adjacent coils 7 differ. Fig. Figure 31 shows the coils 7 provided in one of the layers 12. Fig. Figure 31 represents, for illustration purposes, the coils 7 of a layer 12, which are arranged in a depth direction of a paper surface behind this layer 12, as shown in dashed lines.

[0102] Fig. Figure 32 is a cross-sectional view of part of the anchor 2 according to the eighth embodiment. Fig. Figure 32 shows the cross-section of area 13, which is an example of a single slot. The one in Fig. The cross-section shown in Figure 32 is the section perpendicular to the central axis AX. Fig. 32 corresponds to a left-right direction of the circumferential direction and an up-down direction of the axial direction. As in Fig. As shown in Figure 32, the circumferential positions of the coils 7 are offset based on their radial positions. The majority of the coils 7 are mounted on the printed circuit board 5 such that their circumferential positions are offset based on their radial positions.

[0103] By shifting the circumferential positions of the coils 7 for each layer 12, the armature 2 can be formed with a so-called skewed orientation. This allows the electric motor 1 to reduce the torque ripple or shear ripple in one drive direction of the electric motor 1.

[0104] The configurations shown above in the embodiments illustrate the content of this disclosure. The configurations of the embodiments can be combined with other publicly known techniques. The configurations of the embodiments can be combined with one another as needed. The configurations of the embodiments can be partially omitted or modified without departing from the core of this disclosure. Reference symbol list 1 electric motor; 2 anchors; 3 field system; 4 wave; 5 printed circuit boards; 6 core substrate; 7 coils; 8 Cross-wiring; 9 rooms; 10 ladders; 11 Insulating layer; 12 layers; 13 area; 14, 14 n1 , 14 n2 , 14 n(M-1)+1 , 14 nM , 14 nM+1 , 14 nN Coil unit; 15 Unit structure; 16, 17 Rectangle; 21 pens; 22 holes; 23 recesses; AX center axis. QUOTES INCLUDED IN THE DESCRIPTION

[0000] This list of documents cited by the applicant was automatically generated and is included solely for the reader's convenience. The list is not part of the German patent or utility model application. The DPMA accepts no liability for any errors or omissions. Cited patent literature

[0000] JP 2020 - 89 207

[0003]

Claims

[1] Electric motor, comprising: an armature comprising a printed circuit board of cylindrical shape, the printed circuit board forming a plurality of layers stacked in a radial direction of the cylindrical shape; and a field system that is arranged in relation to the anchor in the direction of a central axis of the cylindrical shape, wherein the printed circuit board comprises a plurality of coils arranged in a circumferential direction of the cylindrical shape, wherein each of the plurality of coils is formed from a linear conductor, wherein the conductor on the printed circuit board has a width designated x and a thickness designated y in the radial direction, and where x and y are each on x opt and y opt are set which, in combination, maximize a space factor of the conductor in a cross-section of the anchor, where the cross-section is perpendicular to the circumferential direction. [2] Electric motor according to claim 1, wherein the printed circuit board further comprises a core substrate on which the majority of coils are formed and an insulating layer provided between the coils across the majority of layers, where x opt the following formula (1) is satisfied: Formula 1: xopt=ƒNT{π(D+d)2n−a2−(TƒN−1)c} where y opt the following formula (2) is satisfied: Formula 2: yopt=D−d−2hN−2m(N+1)2ƒN where c is a distance between linear sections of the conductor in the coil on the printed circuit board, where f is a number of conductors per slot formed in each of the layers of the printed circuit board, where h is the thickness of the core substrate in the radial direction, where m is the thickness of the insulating layer in the radial direction, where n is a number of slots that are areas of the armature in which the coils are arranged, where T is a number of coil turns per slot, where N is a number of radially stacked layers of the printed circuit board in the armature, where D is an outer diameter of the anchor, where d is an inner diameter of the anchor, and where a is a width in the radial direction of an inner circumferential part that serves as a central space of the coil. [3] Electric motor according to claim 1, wherein the electric motor comprises one or more unit structures, wherein each of the unit structures is a set of a specific number of magnetic poles encompassed in the field system and a specific number of slots, where the slots are areas of the armature in which the coils are arranged, wherein the printed circuit board further comprises a core substrate in which the majority of coils are formed and an insulating layer provided between the coils across the majority of layers, where x opt the following formula (3) is satisfied: Formula 3: xopt=ƒNT{Ln'−a2−(TƒN−1)c} where y opt the following formula (4) is satisfied: Formula 4: yopt=H−hN−m(N+1)ƒN where c is a distance between linear sections of the conductors in the coil on the printed circuit board, where f is a number of conductors per slot formed in each of the layers of the printed circuit board, where h is the thickness of the core substrate in the radial direction, where m is the thickness of the insulating layer in the radial direction, where n' is the number of slots in the unit structure, where T is a number of coil turns per slot, where N is a number of radially stacked layers of the printed circuit board in the armature, where L is a circumference length of a section of the anchor that is encompassed in the unit structure, where H is a radial length of each of the slots, and where a is a width in the radial direction of an inner circumferential part that serves as a central space of the coil. [4] Electric motor according to any one of claims 1 to 3, wherein y opt a thickness that is limited to a value between inclusive 0.03 mm and inclusive 0.12 mm. [5] Electric motor according to one of claims 2 to 4, wherein the plurality of coils are arranged in a concentrated winding arrangement, wherein the inner circumferential part serving as a central space of the coil has a width in the radial direction which is designated by a', where a distance between adjacent coils is denoted by b', and where a' and b' each point to a' opt and b' opt are set, which in combination maximize the winding factor of the coil. [6] Electric motor according to claim 5, where a' opt the following formula (5) is satisfied: Formula 5: 0 <a'opt<τp2 where b' opt the following formula (6) is satisfied: Formula 6: 0 <b'opt<(pn−12)τp where p is a number of magnetic poles applied to the electric motor, and where τ p is an arrangement distance for arranging the majority of magnetic poles. [7] Electric motor according to claim 2 or 3, wherein the majority of coils are arranged in a concentrated winding arrangement, and where b'' satisfies the following formula (7): Formula 7: b≤b'' <b2+(h+yƒ+2m)2−2b(h+yƒ+2m)cos ((2−n)π2n−nwmd+d{n−(m−12)})where M is an integer greater than or equal to 1 and less than N, where b'' is a distance between the coils closest to a rolling end of the cylindrical shape in an M-th layer, counted from the central axis of the cylindrical shape under the plurality of layers of the printed circuit board, and the coils closest to a rolling start of the cylindrical shape in an M+1-th layer, counted from the central axis of the cylindrical shape under the plurality of layers of the printed circuit board, where b is a distance between the coils in each of the plurality of layers of the printed circuit board, and where W is a width in the circumferential direction of each of the slots. [8] Electric motor according to claim 7, where W1 and W2 satisfy the following formula (8): Formula 8: 1 <w2w1<1.05where W1 is a width c in the circumferential direction of an end of a coil unit that is closer to the central axis, where W2 is a width in the circumferential direction of an opposite end of the coil unit with respect to the central axis, and where the coil unit is a coil formation area of ​​each of the layers. [9] Electric motor according to claim 7 or 8, where W1 and W3 satisfy the following formula (9): Formula 9: 1 <w3w1<1.025where W2 and W3 satisfy the following formula (10): Formula 10: 1 <w2w3<1.025where W1 is a width in the circumferential direction of an end of a coil unit that is closer to the central axis, where W2 is a width in the circumferential direction of an opposite end of the coil unit with respect to the central axis, where W3 is a width in the circumferential direction, measured at a radial center of the coil unit, and where the coil unit is a coil formation area of ​​each of the layers. [10] Electric motor according to any one of claims 1 to 4, wherein the printed circuit board further comprises the core substrate on which the majority of coils are formed, wherein pins are provided on one side of the core substrate, which stand upright in the radial direction, and where holes are formed on the opposite side of the core substrate and are shaped to fit the pins. [11] Electric motor according to any one of claims 1 to 4, wherein the printed circuit board further comprises the core substrate on which the majority of coils are formed, where the majority of coils are provided on one side of the core substrate, and wherein recesses are formed on an opposite side of the core substrate, which are shaped to fit the coils. [12] Electric motor according to one of claims 1 to 4, wherein circumferential positions of the coils for each of the layers are offset over the plurality of layers.

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