Cylindrical member, cylindrical member with tapered portion, surface magnet type motor, and method for manufacturing surface magnet type motor

Abstract

In an orthogonal coordinate system O-XYZ in which the center position in the thickness direction of the minute elements (10) of the cylindrical member (1) is defined as an origin O, the tangential direction of the cylinder is defined as the X axis, the direction parallel to the axial direction of the cylinder is defined as the Y axis, and the radial direction of the cylinder is defined as the Z axis, the stress vector is set as sigma, the strain vector is set as epsilon, and the shear stress is set as tau. The cylindrical member (1) is formed from a fiber-reinforced plastic that satisfies the relationship represented by formula (2), where [gamma] is the shear strain, and Qij is the i-row j-column component of the in-plane rigid matrix (Q), and the stress-strain relational expression in the XY plane is represented by formula (1): [Mathematical formula (1)] [Mathematical formula (2)] [Mathematical formula (1)] [Mathematical formula (2)] [Mathematical formula (2)] [Mathematical formula (2)].

Description

Technical Field

[0001] The present invention relates to a cylindrical component made of fiber-reinforced plastic, a cylindrical component with a tapered portion, a surface magnet type electric motor using the cylindrical component, and a method for manufacturing the surface magnet type electric motor. Background Technology

[0002] Previously, cylindrical components made of fiber-reinforced plastics (FRP) were known. For example, Patent Document 1 discloses a rotor that uses a cylindrical rotor body made of fiber-reinforced plastic. The rotor is structured such that a bushing, serving as the core, is pressed into the inner diameter side of the rotor body with an interference fit. Tension is generated in the circumferential direction of the rotor body, and friction is generated at the contact surface between the rotor body and the bushing. As a result, slippage of the rotor body relative to the bushing is suppressed when the rotor rotates.

[0003] Patent Document 1: Japanese Patent Application Publication No. 2002-95208 Summary of the Invention

[0004] However, as with the rotor in Patent Document 1, when the bushing is pressed into the inner diameter side of the rotor body with an interference fit, a large pressing force is required, and a large device is needed to generate this pressing force.

[0005] The present invention was made in view of the above circumstances, and its object is to obtain a cylindrical component that can reduce the pressing force of the core that is pressed into the inner diameter side of the cylindrical component.

[0006] To solve the aforementioned problems and achieve the objective, the cylindrical component involved in this invention is characterized by the following: in an orthogonal coordinate system O-XYZ, where the origin O is set at the midpoint of the thickness direction of the minute elements of the cylindrical component, the tangent direction of the cylinder is set as the X-axis, the direction parallel to the axial direction of the cylinder is set as the Y-axis, and the radial direction of the cylinder is set as the Z-axis, the stress vector is set as σ, the strain vector as ε, the shear stress as τ, the shear strain as γ, and the i-th row and j-th column components of the in-plane rigidity matrix Q are set as component Q. ij When the stress-strain relationship in the XY plane is expressed as shown in Equation 1, the cylindrical component is formed of fiber-reinforced plastic to which the relationship shown in Equation 2 holds true.

Mathematical Formula 1

[0007]

Mathematical Formula 2

[0008] The effects of the invention

[0009] According to the cylindrical component of the present invention, the pressing force of the core that is pressed into the inner diameter side of the cylindrical component is reduced. Attached Figure Description

[0010] Figure 1 This is a perspective view of the cylindrical component involved in Embodiment 1.

[0011] Figure 2 This is a perspective view of a surface magnet type electric motor having the cylindrical component according to Embodiment 1.

[0012] Figure 3 This is a front view of the surface magnet type motor having the cylindrical component according to Embodiment 1, viewed from the axial direction.

[0013] Figure 4 This is an explanatory diagram illustrating a method for manufacturing a surface magnet type electric motor having the cylindrical component according to Embodiment 1.

[0014] Figure 5 This is an explanatory diagram illustrating a method for manufacturing a multi-surface magnet type electric motor having the cylindrical component according to Embodiment 1.

[0015] Figure 6 This is a perspective view of the cylindrical component involved in Embodiment 2.

[0016] Figure 7 A top view of the cylindrical component involved in Embodiment 2, viewed from the cylindrical axis.

[0017] Figure 8 yes Figure 7 An enlarged view of section VIII shown.

[0018] Figure 9 This is a perspective view showing a specific example of the cylindrical component involved in Embodiment 2.

[0019] Figure 10 It is Figure 9 The enlarged view shown is a virtual cut-off section of the X-section.

[0020] Figure 11 This is an explanatory diagram illustrating an example of a method for manufacturing a cylindrical component according to Embodiment 2.

[0021] Figure 12 This is a perspective view showing a method for evaluating the "torsional-expansion characteristics" of the cylindrical component involved in Embodiment 2.

[0022] Figure 13 This is a cross-sectional view showing a method for evaluating the "torsional-expansion characteristics" of the cylindrical component involved in Embodiment 2.

[0023] Figure 14 This is an explanatory diagram illustrating a method for manufacturing a surface magnet type electric motor using a cylindrical component with a tapered portion as described in Embodiment 3.

[0024] Figure 15 This is a cross-sectional view showing a portion of the cylindrical component with a tapered portion according to Embodiment 3 cut along the cylinder axis.

[0025] Figure 16 This is an explanatory diagram illustrating a method for manufacturing multiple surface magnet type motors using the cylindrical component with a tapered portion according to Embodiment 3. Detailed Implementation

[0026] Hereinafter, based on the accompanying drawings, a detailed description will be given of the cylindrical component, the cylindrical component with a tapered portion, the surface magnet type motor, and the manufacturing method of the surface magnet type motor according to the embodiments of the present invention.

[0027] Implementation Method 1

[0028] Figure 1 This is a perspective view showing the cylindrical component according to Embodiment 1. Figure 1 In order to show the direction used to define the features of the cylindrical component 1, i.e., the material direction, an orthogonal coordinate system O-XYZ is defined. The orthogonal coordinate system O-XYZ takes into account the minute element 10 of the cylindrical component 1, setting the origin O at the midpoint of the thickness direction of the minute element 10, setting the tangent direction of the cylinder as the X-axis, the direction parallel to the axial direction P of the cylinder as the Y-axis, and the radial direction of the cylinder as the Z-axis. Furthermore, regarding the torsional moment M applied to the cylindrical component 1... T The direction of right-hand rotation, centered on the cylindrical axis, is defined as positive.

[0029] Cylindrical component 1 is made of fiber-reinforced plastic obtained by curing reinforcing fibers with resin. As reinforcing fibers, in addition to carbon fiber or glass fiber, organic fibers such as para-aramid fibers or polyester fibers can also be used. As resins, in addition to thermosetting resins such as epoxy resin, unsaturated polyester resin, and epoxy acrylate resin, thermoplastic resins such as polyamide, polypropylene, polyethylene, polystyrene, polyethylene terephthalate, polycarbonate, polyetheretherketone, and polyphenylene sulfide can also be used. As for the fiber form, in addition to continuous fibers, discontinuous fibers such as injection molded or compression molded fibers can also be used. In the orthogonal coordinate system O-XYZ, cylindrical component 1 is an anisotropic material, according to reference 1 (Japan Institute of Mechanical Engineering, *Mechanical Engineering Handbook DVD-ROM Edition α3: Mechanics of Materials* (First Edition), Maruzen (2014). 12 (Section 4, pp. 160-163) The stress-strain relationship in the XY plane can be expressed by equation (1.1).

[0030]

Mathematical Expression 3

[0031] In equation (1.1), {σ} is the stress vector in the XY plane, {ε} is the strain vector in the XY plane, and [Q] is the in-plane stiffness matrix. The reason why the subscripts of the components in the third row and third column of equation (1.1) are not 3 but 6 is, as shown in reference 1, to reduce the 3D stress-strain relationship to a 2D form, which is also the same in the following formulas. If equation (1.1) is solved for {ε}, it becomes equation (1.2), where ε x It can be expressed by equation (1.3).

[0032]

Mathematical Expression 4

[0033]

Mathematical Expression 5

[0034] In equation (1.3), [Q] ij －1 These are the ij components of the inverse matrix of [Q]. Here, if we consider that only shear stress τ is generated by torsion... xy Case (σ) x =σ y If =0), then it becomes equation (1.4).

[0035]

Mathematical Expression 6

[0036] Here, if we specifically write [Q] 16 －1 Then it becomes equation (1.5).

[0037]

Mathematical Expression 7

[0038] detQ is the determinant of matrix [Q], expressed by equation (1.6).

[0039]

Mathematical Expression 8

[0040] Here, the cylindrical component 1 according to this embodiment 1 is characterized by satisfying equation (1.7).

[0041]

Mathematical Expression 9

[0042] By satisfying equation (1.7), the cylindrical component 1 has the following characteristics. That is, when a torsional moment M is applied to the cylindrical component 1... T At that time, shear stress τ is generated in cylindrical component 1. xy However, according to equation (1.7), it becomes [Q]. 16 －1 ≠0, therefore due to the shear stress τ xy The vertical strain ε is generated by equation (1.4). x In the orthogonal coordinate system O-XYZ, ε x This represents the circumferential strain of cylindrical component 1, indicating the radial deformation. If [Q] 16 －1 >0, then through Figure 1 A torsional moment M is applied to the cylindrical component 1 in the direction shown. T Thus, it becomes the shear stress τ xy >0, therefore becomes ε x >0, cylindrical component 1 expands radially. Conversely, in [Q] 16 －1 If < 0, if Figure 1 A torsional moment M is applied to the cylindrical component 1 in the direction shown. T Then it becomes the shear stress τ xy >0, therefore becomes ε x <0, the cylindrical component 1 contracts radially, but by applying a torsional moment M in the opposite direction. T This causes the cylindrical component 1 to expand radially.

[0043] Here, consider the torsional moment M applied. T The radial expansion is an indicator used to evaluate the radial expansion. Furthermore, in the following description, the radial expansion will be referred to as the "torsional-expansion characteristic". A torsional moment M was applied to the cylindrical component 1. T The amount of deformation depends on the diameter and thickness of the cylindrical component 1. Therefore, in order to evaluate the radial expansion, it is only necessary to consider the deformation caused by the torsional moment M. T The resulting unit shear stress τ xy The strain can be compared. Equation (1.4) becomes the expression for the shear stress τ. xy The formula relating strain to [Q] 16 －1 It serves as an evaluation metric for "torsional-expansion characteristics".

[0044]

Mathematical Formula 10

[0045] According to equations (1.4) and (1.5), when comparing cylindrical components 1 with the same inner diameter and thickness, the larger value obtained by equation (1.8) indicates that if the same torsional moment M is applied to the cylindrical component 1, the value is larger. T The radial expansion increases. In the cylindrical component 1 according to Embodiment 1, the value on the right side of the preferred formula (1.8) is greater than or equal to 0.002 [1 / GPa], more preferably greater than or equal to 0.005 [1 / GPa], and even more preferably greater than or equal to 0.01 [1 / GPa]. Furthermore, 1 / GPa, the unit for the above values, is the reciprocal of GPa, where 1GPa = 10... 9 N (Newtons) / m 2 (square meters)

[0046] Next, refer to Figure 2 and Figure 3 The surface permanent magnet (SPM) 100 having the cylindrical component 1 according to Embodiment 1 will be described. Figure 2 This is a perspective view of a surface magnet type electric motor having the cylindrical component according to Embodiment 1. Figure 3 This is a front view of the surface magnet type motor having the cylindrical component according to Embodiment 1, viewed from the axial direction.

[0047] like Figure 2 and Figure 3 As shown, the surface magnet type motor 100 has a cylindrical component 1 with the above-described structure and a rotor core 3 that is pressed into the inner diameter side of the cylindrical component 1.

[0048] The rotor core 3 includes a shaft 30, an iron core 31, permanent magnets 32, spacers 33, and a high conductivity component 34. The shaft 30 is fitted concentrically inside the cylindrical iron core 31. The permanent magnets 32 are arranged circumferentially on the outer peripheral surface of the iron core 31. The permanent magnets 32 are not limited to the four poles shown in the figure and can be freely arranged. Spacers 33 are arranged between adjacent permanent magnets 32. The high conductivity component 34 is arranged on the outer peripheral surface of the permanent magnets 32 and the spacers 33 to reduce rotor losses. The high conductivity component 34 can be arranged on the entire outer peripheral surface of the permanent magnets 32 and the spacers 33, or it can be arranged on a part of the outer peripheral surface of the permanent magnets 32 and the spacers 33. The cylindrical component 1 is mounted on the outer peripheral surface of the high conductivity component 34. The cylindrical component 1 is a sleeve used to fix the permanent magnets 32.

[0049] Next, refer to Figure 4 and Figure 5 The manufacturing method of the surface magnet type electric motor 100 having the cylindrical component 1 according to Embodiment 1 will be described. Figure 4 This is an explanatory diagram illustrating a method for manufacturing a surface magnet type electric motor having the cylindrical component according to Embodiment 1. (As shown...) Figure 4 As shown, in the manufacturing method of the surface magnet type electric motor 100, firstly, a torsional torque M is applied to the cylindrical component 1. T If a torsional moment M is applied T Then, the cylindrical component 1 expands radially. Next, while maintaining a torsional moment M applied to the cylindrical component 1... T In this state, the rotor core 3 is inserted into the inner diameter side of the cylindrical component 1. After the rotor core 3 is inserted into the inner diameter side of the cylindrical component 1, the torsional torque M of the cylindrical component 1 is released. T Therefore, the cylindrical component 1 contracts radially, but is constrained radially by the rotor core 3, thus generating tension in the circumferential direction. Through the reaction of this tension, a distributed load acts radially on the outer circumferential surface of the rotor core 3. This distributed load acts in the direction that prevents the permanent magnet 32 ​​from separating from the iron core 31 due to centrifugal force when the surface magnet type motor 100 rotates.

[0050] Figure 5 This is an explanatory diagram illustrating a method for manufacturing a multi-surface magnet type electric motor having the cylindrical component according to Embodiment 1. (As shown...) Figure 5 As shown, in the manufacturing method of the surface magnet type electric motor 100, multiple rotor cores 3 can also be embedded into a cylindrical component 1. While maintaining a torsional torque M applied to the cylindrical component 1... T In this state, multiple rotor cores 3 are pressed into the inner diameter side of the cylindrical component 1 to embed them. At this time, the rotor cores 3 are arranged such that adjacent rotor cores 3 do not contact each other in the axial direction X of the cylinder. After all the rotor cores 3 have been pressed into the inner diameter side of the cylindrical component 1, the torsional torque M of the cylindrical component 1 is released. T Then, by cutting the cylindrical component 1 in accordance with the axial length of each rotor core 3, multiple surface magnet type motors 100 can be formed at once.

[0051] As described above, the cylindrical component 1 involved in this embodiment 1 is constructed in an orthogonal coordinate system O-XYZ, where the origin O is set at the midpoint of the thickness direction of the minute element 10 of the cylindrical component 1, the tangent direction of the cylinder is set as the X-axis, the direction parallel to the axial direction of the cylinder is set as the Y-axis, and the radial direction of the cylinder is set as the Z-axis. Furthermore, the stress vector is set as σ, the strain vector as ε, the shear stress as τ, the shear strain as γ, and the i-th row and j-th column components of the in-plane rigidity matrix Q are set as component Q. ij When expressing the stress-strain relationship in the XY plane as shown in equation (1.1) above, the fiber-reinforced plastic is formed by the relationship shown in equation (1.7) above.

[0052] Therefore, the cylindrical component 1 according to Embodiment 1 is subjected to a torsional moment M. T In this case, not only shear deformation occurs, but also radial expansion of the cylindrical component 1 occurs, thus reducing the pressing force on the rotor core 3, which is pressed into the inner diameter side of the cylindrical component 1. Furthermore, after the rotor core 3 is inserted into the cylindrical component 1, if the torsional torque M is released... T The cylindrical component 1 generates tension in the circumferential direction due to the restoring force as it attempts to return to its original state from an expanded state. As a result, when the surface magnet type motor 100 rotates, it is possible to suppress the separation of the permanent magnet 32 ​​from the iron core 31 due to centrifugal force.

[0053] Implementation Method 2

[0054] Next, the cylindrical component 2 according to this embodiment 2 will be described. Figure 6 This is a perspective view of the cylindrical component involved in Embodiment 2. Figure 7 This is a top view of the cylindrical component involved in Embodiment 2, viewed from the axial direction of the cylinder. Figure 8 yes Figure 7 An enlarged view of section VIII shown.

[0055] exist Figure 6 To illustrate the material direction used to define the features of the cylindrical component 2, an orthogonal coordinate system O-XYZ is defined. The orthogonal coordinate system O-XYZ takes into account the minute element 20 of the cylindrical component 2, setting the origin O at the midpoint of the thickness direction of the minute element 20, the tangent direction of the cylinder as the X-axis, the direction parallel to the axial direction P of the cylinder as the Y-axis, and the radial direction of the cylinder as the Z-axis. Furthermore, regarding the torsional moment M applied to the cylindrical component 2... T The direction of right-hand rotation, centered on the cylindrical axis, is defined as positive.

[0056] like Figures 6 to 8 As shown, the cylindrical component 2 according to Embodiment 2 has a structure having multiple cylindrical fiber-reinforced plastic layers (hereinafter referred to as FRP layers 21). Adjacent FRP layers 21 are bonded to each other. As a bonding method, bonding by adhesive can be used, for example. When the cylindrical component 2 is manufactured by, for example, sheet winding, all layers are wound onto a mandrel and stacked, while curing and bonding between adjacent FRP layers 21 are performed simultaneously. Alternatively, the cylindrical component 2 can also be manufactured by methods such as bonding a component obtained by pre-molding only a portion of all the FRP layers 21 in one piece using epoxy resin adhesive or acrylic adhesive.

[0057] Regarding the bonding method, the structure is not limited to that described above. Each FRP layer 21 can be composed of some or all of a continuous reinforcing fiber and resin oriented in at least one direction, with different reinforcing fibers and resins combined in each layer. As reinforcing fibers, in addition to carbon fiber or glass fiber, organic fibers such as para-aramid fibers or polyester fibers can also be used. As resins, in addition to thermosetting resins such as epoxy resin, unsaturated polyester resin, and epoxy acrylate resin, thermoplastic resins such as polyamide, polypropylene, polyethylene, polystyrene, polyethylene terephthalate, polycarbonate, polyetheretherketone, and polyphenylene sulfide can also be used.

[0058] Here, as Figure 6 As shown, the fiber direction (tangential direction on the cylinder) of FRP layer 21 is defined as the L direction, and the direction orthogonal to the L direction is defined as the T direction. The L direction is represented by the rotation angle θ from the X-axis counterclockwise through the orthogonal coordinate system O-XYZ. The total number of FRP layers 21 is defined as N, and they are sequentially referred to as layer 1, layer 2, layer 3, layer 4, layer 5, layer 6, layer 7, layer 8, layer 9, layer 10, layer 11, layer 11, layer 11, layer 12, layer 13, layer 14, layer 15, layer 16, layer 17, layer 18, layer 19, layer 10 ... The kth layer The Nth layer. If the L direction of the kth layer is set as θk, then according to the classical stacking theory shown in Reference 1 above, the resultant force-strain relationship in the XY plane of the cylindrical component 2 can be expressed by Equation (2.1).

[0059]

Mathematical Expression 11

[0060] Here, {N} = {N} x N y N xy} T It is the resultant force vector. {ε} = {ε} x ε y γ xy} T It is the strain vector. Additionally, the components A of the in-plane stiffness matrix [A] are... ij This is expressed by equation (2.2).

[0061]

Mathematical Expression 12

[0062] Here, as Figure 8 As shown, z k It is the Z-coordinate of the radial boundary of the k-th layer. Additionally, in equation (2.2), (Q (overlined)) ij ) k The component Q (underlined) in the stress-strain equation for the k-th layer. ij(i, j = 1, 2, 6), specifically, assigned by equation (2.3). In addition, Q (overline) is Q with an overline attached above it.

[0063]

Mathematical Expression 13

[0064] In equation (2.3), Q 11 Q 22 Q 12 Q 66 This is expressed by equation (2.4).

[0065]

Mathematical Expression 14

[0066] In equation (2.4), E L E is the tensile modulus of elasticity in the L direction of the k-th layer. T ν is the tensile modulus of elasticity in the T direction of the k-th layer. LT G is the Poisson's ratio in the LT direction of the k-th layer. LT It is the shear modulus in the LT direction.

[0067] If we solve equation (2.1) for {ε}, it becomes equation (2.5), and we get equation (2.6).

[0068]

Mathematical Expression 15

[0069]

Mathematical Expression 16

[0070] In equation (2.6), [A] ij －1 These are the ij components of the inverse matrix of [A]. Here, if we consider that only the shear resultant force N is generated by torsion... xy Case (N) x =N y If = 0), then it becomes equation (2.7). [A] 16 －1 This is expressed by equation (2.8).

[0071]

Mathematical Expression 17

[0072]

Mathematical Expression 18

[0073] In equation (2.8), detA is the determinant of matrix [A], which is represented by equation (2.9).

[0074]

Mathematical Expression 19

[0075] The cylindrical component 2 according to this embodiment 2 is characterized in that it satisfies equation (2.10).

[0076]

Mathematical Expression 20

[0077] By satisfying equation (2.10), the cylindrical component 2 thus possesses the characteristics shown below. That is, when a torsional moment M is applied to the cylindrical component 2... T At that time, a shear force N is generated in the cylindrical component 2. xy However, according to equation (2.10), it becomes [A]. 16 －1 ≠0, therefore due to the resultant shear force N xy The vertical strain ε is generated by equation (2.7). x In the orthogonal coordinate system O-XYZ, ε x This represents the circumferential strain of cylindrical component 2, indicating the radial deformation. In [A] 16 －1 If > 0, then Figure 6 A torsional moment M is applied to the cylindrical component 2 in the direction shown. T Then it becomes the resultant shear force N. xy >0, therefore becomes ε x >0, cylindrical component 2 expands radially. Conversely, in [A] 16 －1 If < 0, if Figure 6 A torsional moment M is applied to the cylindrical component 2 in the direction shown. T Then it becomes the resultant shear force N. xy >0, therefore becomes ε x <0, the cylindrical component 2 contracts radially, but by applying a torsional moment M in the opposite direction. T This causes it to expand radially.

[0078] Here, N xy The shear stress τ of each FRP layer 21 in the thickness direction is... xy This is obtained by integration, therefore it will make N xy The value obtained by dividing by the plate thickness t of cylindrical component 2 is set as equation (2.11), if the average shear stress τ (underlined) is defined. xy Then equation (2.7) becomes equation (2.12), which can convert t / detA×(A) into t / detA×(A) 12 A 26 -A 16 A 22) is used as an evaluation index for "torsional-expansion characteristics". In addition, τ (overline) is τ with an overline attached above it.

[0079]

Mathematical Expression 21

[0080]

Mathematical Expression 22

[0081]

Mathematical Expression 23

[0082] According to equation (2.12), when comparing cylindrical components 2 of the same size, the larger value obtained by equation (2.13) indicates that if the same torsional moment M is applied to the cylindrical component 2, the value is larger. T The radial expansion increases. In the cylindrical component 2 according to Embodiment 2, the value on the right side of the preferred formula (2.13) is greater than or equal to 0.002 [1 / GPa], more preferably greater than or equal to 0.005 [1 / GPa], and even more preferably greater than or equal to 0.01 [1 / GPa]. Furthermore, 1 / GPa, the unit for the above values, is the reciprocal of GPa, where 1GPa = 10... 9 N (Newtons) / m 2 (square meters)

[0083] Next, refer to Figure 6 And refer to Figure 9 and Figure 10 Specific examples of the cylindrical component 2 involved in this embodiment 2 will be described. Figure 9 This is a perspective view showing a specific example of the cylindrical component involved in Embodiment 2. Figure 10 It is Figure 9 The enlarged view shown is a virtual cut-off section of the X-section.

[0084] Table 1 shows the material, thickness, and fiber orientation of each FRP layer 21 in the cylindrical component 2. Table 2 shows the material constants and physical properties of material A shown in Table 1, which is a unidirectional reinforced prepreg material composed of high-strength PAN-type carbon fiber and epoxy resin. PAN (Polyacrylonitrile) is a polyacrylonitrile compound.

[0085] Table 1

[0086] Table 2

[0087] In the cylindrical component 2 shown in Tables 1 and 2, if we calculate t / |detA|×|A 12 A 26 -A 16 A 22 |, then as shown in equation (2.14).

[0088]

Mathematical Expression 24

[0089] like Figure 6 As shown, if the diameter of the central part of the plate thickness of cylindrical component 2 is set as D... m The torsional moment M will be used to achieve this. T The resulting diameter D m The expansion amount is set as ΔD m Then the average shear stress τ (underlined) xy It can be approximately calculated as shown in equation (2.15).

[0090]

Mathematical Expression 25

[0091] Furthermore, if we define the circumference of the central portion of the plate thickness of the cylindrical component 2 as L, and the elongation of the circumference L as ΔL, then we have equation (2.16). Therefore, the diameter expansion ΔD m It becomes equation (2.17).

[0092]

Mathematical Expression 26

[0093]

Mathematical Expression 27

[0094] In equation (2.17), the torsional moment M T The value is 500 Nm (Newton-meter), and the diameter is D. m When the diameter is 100mm, the diameter expansion ΔD can be calculated. m It is 0.119mm.

[0095] Next, different specific examples of the cylindrical component 2 according to Embodiment 2 will be described. Table 3 shows the material, thickness and fiber orientation of each FRP layer 21 in the cylindrical component 2. Table 4 shows the material constants and physical properties of material B shown in Table 3, which is a unidirectional reinforced prepreg material composed of highly elastic pitch-based carbon fiber and epoxy resin.

[0096] Table 3

[0097] Table 4

[0098] For the cylindrical component 2, if the elastic modulus of the FRP layer 21 is large, the tension after it is installed on the outer peripheral surface of the rotor core 3 will increase. Therefore, relative to the centrifugal force generated by the high-speed rotation of the surface magnet type motor 100, a force can be generated to prevent the permanent magnet 32 ​​from separating from or scattering from the cylindrical component 2. Therefore, the fiber used as the FRP layer 21 is preferably a highly elastic pitch-based carbon fiber. In addition, the tensile elastic modulus of the fiber in the fiber direction is preferably greater than or equal to 300 GPa. In the cylindrical component 2 as described above, if the calculated parameter t / |detA|×|A 12 A 26 -A 16 A 22 | Then we can find equation (2.18).

[0099]

Mathematical Expression 28

[0100] Additionally, in equation (2.17), the torsional moment M T The value is 500 Nm (Newton-meter), and the diameter is D. m When the diameter is 100mm, the diameter expansion ΔD can be calculated. m It is 0.113mm.

[0101] Next, refer to Figure 11 The manufacturing method of the cylindrical component 2 according to Embodiment 2 will be described. Figure 11 This is an explanatory diagram schematically illustrating an example of a method for manufacturing the cylindrical component according to Embodiment 2. As a method for manufacturing the cylindrical component 2, when the resin is a thermosetting resin, methods such as sheet winding or fiber winding exist. Figure 11 As shown, the sheet winding method involves pre-impregnating resin into unidirectional continuous fibers, then curing the semi-cured prepreg 22 after winding it around a cylindrical or cylindrical mandrel 23. The fiber winding method involves impregnating a pre-cured thermosetting resin in a liquid state into a fiber bundle, then curing the thermosetting resin after winding it around a mandrel. In addition, when the resin is a thermoplastic resin, the ATP (Automated Tape Placement) method also exists as a manufacturing method for the cylindrical component 2. The ATP method involves heating and pressurizing a strip or sheet substrate pre-impregnated with resin into unidirectional continuous fibers, while winding the substrate around a mandrel clamp and bonding it. Furthermore, the manufacturing method for the cylindrical component 2 is not limited to the sheet winding method, fiber winding method, or ATP method; other methods may also be used.

[0102] Next, refer to Figure 12 and Figure 13 This describes a method for evaluating the "torsional-expansion characteristics" of cylindrical component 2. Figure 12 This is a perspective view showing a method for evaluating the "torsional-expansion characteristics" of the cylindrical component involved in Embodiment 2. Figure 13 This is a cross-sectional view showing a method for evaluating the "torsional-expansion characteristics" of the cylindrical component according to Embodiment 2. For example... Figure 12 and Figure 13 As shown, strain gauges 200 are bonded to the outer and inner circumferential surfaces of the cylindrical component 2. The strain gauges 200 transmit the torsional torque M. T The circumferential vertical strain ε applied to cylindrical component 2 x Measurements are performed. The strain measurement direction of strain gauge 200 is the circumferential direction of cylindrical component 2. The number of measurement points of strain gauge 200 is not limited to... Figure 13 Of the two points shown, any one point greater than or equal to the other is acceptable. Circumferential vertical strain ε x It is obtained from equations (2.16) and (2.17) through equation (2.19). By comparing the value obtained through equation (2.19) with the measured value of strain gauge 200, the "torsional-expansion characteristics" can be evaluated.

[0103]

Mathematical Expression 29

[0104] Furthermore, in the cylindrical component 2 of this embodiment 2, based on the above-described manufacturing method of the surface magnet type motor 100, it is also possible to form a surface magnet type motor 100 that is pressed into the inner diameter side of the cylindrical component 2 and embedded in the rotor core 3.

[0105] As described above, the fiber-reinforced plastic forming the cylindrical component 2 according to Embodiment 2 is composed of multiple FRP layers 21, some or all of which are composed of continuous fibers. The resultant force vector of the FRP layers 21 is set to N, and the i-th row and j-th column component of the equivalent in-plane rigidity matrix A calculated using classical lamination theory is set as component A. ij When expressing the resultant force-strain relationship in the XY plane as shown in equation (2.1) above, component A ij As shown in equation (2.2) above, if the fiber direction of the FRP layer 21 is defined as the L direction, the direction orthogonal to the L direction is defined as the T direction, and the L direction is represented by a counterclockwise rotation angle θ from the X-axis, then the component Q shown in equation (2.2) above... ij (Overline) As shown in equations (2.3) and (2.4) above, the cylindrical component 2 is formed in such a manner that the relationship shown in equation (2.10) above holds.

[0106] Therefore, the cylindrical component 2 according to this embodiment 2 is subjected to a torsional moment M. T In this case, not only shear deformation occurs, but also radial expansion of the cylindrical component 2 occurs, thus reducing the pressing force on the rotor core 3, which is pressed into the inner diameter side of the cylindrical component 2. Furthermore, after the rotor core 3 is inserted into the cylindrical component 2, if the torsional torque M is released... T The cylindrical component 2 generates tension in the circumferential direction due to the restoring force as it attempts to return to its original state from an expanded state. As a result, when the surface magnet type motor 100 rotates, it is possible to suppress the separation of the permanent magnet 32 ​​from the iron core 31 due to centrifugal force.

[0107] Implementation Method 3

[0108] Next, the cylindrical component 4 with a tapered portion according to Embodiment 3 and the surface magnet type motor 100 manufactured using the cylindrical component 4 with a tapered portion will be described. Figure 14 This is an explanatory diagram illustrating a method for manufacturing a surface magnet type electric motor using the cylindrical component with a tapered portion according to Embodiment 3. (As shown) Figure 14 As shown, the cylindrical component 4 with a tapered portion according to Embodiment 3 has: a straight body portion 41 formed by the cylindrical component 1 of Embodiment 1 or the cylindrical component 2 of Embodiment 2; and a cylindrical tapered portion 42 connected to one end of the straight body portion 41 along the cylindrical axial direction X, the inner diameter of which expands from the end connected to the straight body portion 41 along the cylindrical axial direction X. The rotor core 3 of the surface magnet type motor 100 is pressed in and embedded into the straight body portion 41. Therefore, at least the straight body portion 41 needs to satisfy formula (1.7) or formula (2.10). In addition, the tapered portion 42 can also satisfy formula (1.7) or formula (2.10). The straight body portion 41 and the tapered portion 42 are integrally formed. The tapered portion 42 is provided for mounting the torsion clamp 51b described later.

[0109] In the case where the straight portion 41 corresponds to the cylindrical component 2 of Embodiment 2, the cylindrical component 4 with a tapered portion is manufactured, for example, by a sheet winding method. In this case, semi-cured prepreg is wound around a mandrel and laminated, while adjacent prepregs in the lamination direction are cured and bonded. This mandrel is formed by combining a mandrel with an outer diameter shape of the straight portion 41 and a mandrel with an outer diameter shape corresponding to the inner diameter of the tapered portion 42. Thus, a cylindrical component 4 with a tapered portion having a straight portion 41 and a tapered portion 42 can be formed.

[0110] Figure 15 This is a cross-sectional view showing a portion of the tapered cylindrical component according to Embodiment 3 cut along the cylinder's axial direction. (e.g.) Figure 15As shown, in the straight section 41, a reinforcing multiplier 43a is provided on the outer peripheral surface near the opening of the cylindrical body. Similarly, in the conical section 42, a reinforcing multiplier 43b is provided on the outer peripheral surface near the opening of the cylindrical body. Therefore, in the straight section 41 and the conical section 42, the plate thickness near the cylindrical opening where the multipliers 43a and 43b are provided is greater than the plate thickness of the portion where the multipliers 43a and 43b are not provided. The multipliers 43a and 43b are formed, for example, by increasing the number of sheets of prepreg used in the sheet winding method during manufacturing. Alternatively, as another method, the multipliers 43a and 43b can be formed by bonding a separately manufactured cylindrical component to the outer peripheral surface of the straight section 41 and the outer peripheral surface of the conical section 42. The materials of the multipliers 43a and 43b do not need to satisfy formula (1.7) or formula (2.10), and can be arbitrarily selected. Multipliers 43a and 43b can also be made of fabric material on their surfaces, taking into account processability. Furthermore, the cylindrical component 4 with the tapered portion is not limited to a structure in which multipliers are provided in both the straight portion 41 and the tapered portion 42, but can also be a structure in which at least one of the straight portion 41 and the tapered portion 42 is provided with a multiplier.

[0111] Furthermore, the tapered portion 42 has multiple tapered angles that gradually increase in size along the cylindrical axial direction X from one end connected to the straight portion 41. As an example, Figure 15 The cone portion 42 shown has a first cone portion 44 connected to the straight portion 41, consisting of a cone angle θ1, and a second cone portion 45 consisting of a cone angle θ2 larger than the cone angle θ1. As an example, the cone angle θ1 of the first cone portion 44 is 1°, 2°, or 5°. As an example, the cone angle θ2 of the second cone portion 45 is 10°, 20°, 30°, or 45°. Furthermore, the cone angles θ1 of the first cone portion 44 and θ2 of the second cone portion 45 are not limited to the aforementioned angles, as long as the cone angle θ1 is smaller than the cone angle θ2. Additionally, the cone portion 42 is not limited to a structure having two cone angles θ1 and θ2; it can also be a structure with one cone angle, or a structure with three or more cone angles.

[0112] Furthermore, the multiplier 43b disposed on the conical portion 42 is not disposed in the portion of the first conical portion 44 close to the straight portion 41, but is disposed continuously with a portion of the first conical portion 44 and the entire area of ​​the second conical portion 45. Preferably, in the first conical portion 44, the multiplier 43b is disposed in a manner having portions a, b, and c, wherein portion a has the same plate thickness as the straight portion 41, portion b has the same plate thickness as the second conical portion 45 on which the multiplier 43b is disposed, and the plate thickness of portion c varies continuously between portions a and b. Regarding the cylindrical component 4 with the conical portion, if the cone angle of the conical portion 42 is large, then when a torsional moment M is applied... TIn this case, the stress at the junction of the straight portion 41 and the tapered portion 42 exhibits high specificity, and this junction may become the starting point of failure. In the cylindrical member 4 with a tapered portion according to Embodiment 3, since it has a first tapered portion 44 with a small cone angle, the specificity of the stress at the junction of the straight portion 41 and the tapered portion 42 can be suppressed. Furthermore, the cylindrical member 4 with a tapered portion is provided with a multiplier 43b in a part of the first tapered portion 44 and the second tapered portion 45, thereby increasing the strength of the tapered portion 42. Thus, even when highly specific stress is generated at the junction of the first tapered portion 44 and the second tapered portion 45, the cylindrical member 4 with a tapered portion can suppress failure at that junction.

[0113] Next, the manufacturing method of the surface magnet type electric motor 100 using the cylindrical component 4 with a tapered portion according to Embodiment 3 will be described. Figure 15 As shown, a cylindrical torsion clamp 51a is provided inside the cylinder of the straight body portion 41. Similarly, a cylindrical torsion clamp 51b is provided inside the cylinder of the conical portion 42. The torsion clamp 51a inside the cylinder of the straight body portion 41 is configured such that at least a portion faces the multiplier 43a provided on the outer peripheral surface, and is fastened and fixed together with the multiplier 43a and the straight body portion 41 by bolts 52a. Fastening the portion where the multiplier 43a is provided by bolts 52a helps to alleviate stress concentration caused by bolt tightening. Similarly, the torsion clamp 51b inside the cylinder of the conical portion 42 is configured such that at least a portion faces the multiplier 43b provided on the outer peripheral surface of the second conical portion 45, and is fastened and fixed together with the multiplier 43b and the second conical portion 45 by bolts 52b. Fastening the portion where the multiplier 43b is provided by bolts 52b helps to alleviate stress concentration caused by bolt tightening. Here, the inner diameter of the torsion clamp 51b installed inside the cylinder of the cone portion 42 is set to be larger than the outer diameter of the rotor core 3, so that the rotor core 3 can pass through the inside of the cylinder of the torsion clamp 51b. Furthermore, the torsion clamps 51a and 51b are not limited to structures fixed inside the cylinder of the straight body portion 41 and the cylinder of the cone portion 42; they can also be fixed to the outer peripheral surfaces of the straight body portion 41 and the cone portion 42. Additionally, the torsion clamps 51a and 51b can be fixed to the straight body portion 41 and the cone portion 42 using methods such as bonding with adhesives like epoxy resin or acrylic adhesives, fixing by friction, or a combination of these methods with bolt fastening.

[0114] In the manufacturing method of the surface magnet type electric motor 100, the torsion on both sides is gripped by clamps 51a and 51b, such as Figure 14 As shown, a torsional torque M is applied to the torsion clamps 51a and 51b. T This will reduce the torsional torque MT The cylindrical component 4 with tapered section is transmitted to the cylindrical component 4, and the straight section 41 expands radially. A torsional moment M is maintained on the cylindrical component 4 with tapered section. T In the state of being inserted, the rotor core 3 is inserted from the inner diameter side of the torsion clamp 51b fixed to the cone 42 and pressed into the interior of the straight body 41. In the cylindrical component 4 with the cone, the inner diameter of the torsion clamp 51b fixed to the cone 42 is larger than the outer diameter of the rotor core 3, so the rotor core 3 and the torsion clamp 51b will not interfere with each other, and the rotor core 3 can be installed inside the cylindrical component 4 with the cone. After the rotor core 3 is inserted into the interior of the straight body 41, if the torsional torque M applied to the torsion clamp 51a and the torsion clamp 51b is removed... T This generates tension in the circumferential direction of the tapered cylindrical component 4. The reaction force of this tension distributes the load radially onto the outer circumferential surface of the rotor core 3. This distributed load acts in the direction that suppresses the separation of the permanent magnet 32 ​​from the iron core 31 due to centrifugal force when the surface magnet motor 100 rotates. Subsequently, the torsion clamps 51a and 51b are removed from the tapered cylindrical component 4. Then, by cutting the tapered portion 42 from the straight portion 41, the surface magnet motor 100 can be formed.

[0115] Figure 16 This is an explanatory diagram illustrating a method for manufacturing multiple surface magnet type electric motors using the cylindrical component with a tapered portion according to Embodiment 3. (As shown...) Figure 16 As shown, in the manufacturing method of the surface magnet type electric motor 100, multiple rotor cores 3 can also be embedded into a cylindrical component 4 with a tapered portion. A torsional torque M is applied to the torsion clamps 51a and 51b. T This will reduce the torsional torque M T The cylindrical component 4 with tapered section is transmitted to the cylindrical component 4, and the straight section 41 expands radially. A torsional moment M is maintained on the cylindrical component 4 with tapered section. T In this state, multiple rotor cores 3 are inserted from the inner diameter side of the torsion clamp 51b fixed to the cone portion 42 and pressed into the interior of the straight body portion 41. At this time, the rotor cores 3 are arranged such that adjacent rotor cores 3 do not contact each other in the cylindrical axial direction X. After all rotor cores 3 are embedded into the interior of the straight body portion 41, the torsional torque M applied to the torsion clamps 51a and 51b is released. T Furthermore, the torsion clamps 51a and 51b are removed from the tapered cylindrical component 4. Then, by cutting the tapered cylindrical component 4 in accordance with the axial length of each rotor core 3, multiple surface magnet type motors 100 can be formed at once.

[0116] As described above, the cylindrical component 4 with a tapered portion according to Embodiment 3 includes: a straight portion 41, which is composed of a cylindrical component equivalent to the cylindrical component 1 of Embodiment 1 or the cylindrical component 2 of Embodiment 2; and a cylindrical tapered portion 42, which is connected to one end of the straight portion 41 along the cylindrical axial direction X and extends along the cylindrical axial direction X. That is, the straight portion 41 is formed in such a manner that the relationship shown in the above formula (1.7) or formula (2.10) is established.

[0117] Therefore, the cylindrical component 4 with a tapered portion according to Embodiment 3, when subjected to a torsional moment M, T In this case, not only shear deformation occurs, but radial expansion also occurs in the straight body portion 41, thus reducing the pressing force on the rotor core 3, which is pressed into the inner diameter side of the straight body portion 41. Furthermore, in the cylindrical component 4 with a tapered portion, the inner diameter of the torsion clamp 51b fixed to the tapered portion 42 is larger than the outer diameter of the rotor core 3, so the rotor core 3 and the torsion clamp 51b do not interfere with each other, allowing the rotor core 3 to be installed inside the cylindrical component 4 with the tapered portion. Moreover, after the rotor core 3 is inserted into the straight body portion 41, if the torsional torque M is released... T The tension in the circumferential direction is generated due to the restoring force of the straight body 41 as it attempts to return from its expanded state to its original state. As a result, when the surface magnet type motor 100 rotates, it is possible to suppress the separation of the permanent magnet 32 ​​from the iron core 31 due to centrifugal force.

[0118] The structure shown in the above embodiments is an example and can be combined with other known technologies. The embodiments can also be combined with each other, and parts of the structure can be omitted or changed without departing from the spirit of the subject.

[0119] Explanation of the label

[0120] 1, 2 Cylindrical components, 3 Rotor core, 4 Cylindrical component with tapered section, 10, 20 Micro-elements, 21 FRP layer, 22 Prepreg, 23 Mandrel, 30 Shaft, 31 Iron core, 32 Permanent magnet, 33 Spacer, 34 High conductivity component, 41 Straight body, 42 Tapered section, 43a, 43b Multiplier, 44 First tapered section, 45 Second tapered section, 51a, 51b Torsional clamps, 52a, 52b Bolts, 100 Surface magnet type motor, 200 Strain gauge, θ1, θ2 Cone angle.

Claims

1. A cylindrical component, characterized in that, In an orthogonal coordinate system O-XYZ, with the origin O located at the midpoint of the thickness direction of the minute elements of the cylindrical component, the tangent direction of the cylinder defined as the X-axis, the direction parallel to the axial direction of the cylinder defined as the Y-axis, and the radial direction of the cylinder defined as the Z-axis, and with the stress vector defined as σ, the strain vector as ε, the shear stress as τ, the shear strain as γ, and the i-th row and j-th column components of the in-plane rigidity matrix Q defined as component Q... ij When the stress-strain relationship in the XY plane is expressed as shown in Equation 1, the cylindrical component is formed of fiber-reinforced plastic to which the relationship shown in Equation 2 holds true. 【Mathematical Formula 1】 【Mathematical Formula 2】 。 2. The cylindrical component according to claim 1, characterized in that, Regarding the component Q ij The following relationship holds true: 【Mathematical Expression 3】 。 3. The cylindrical component according to claim 1, characterized in that, Regarding the component Q ij The following relationship holds true: 【Mathematical Expression 4】 。 4. The cylindrical component according to claim 1, characterized in that, Regarding the component Q ij The following relationship holds true: 【Mathematical Expression 5】 。 5. The cylindrical component according to claim 1, characterized in that, The fiber-reinforced plastic is composed of multiple fiber-reinforced plastic layers, wherein some or all of the fibers in each fiber-reinforced plastic layer are continuous fibers. Let N be the resultant force vector of the fiber-reinforced plastic layer, and let the i-th row and j-th column component of the equivalent in-plane rigidity matrix A calculated by classical lamination theory be component A. ij When expressing the resultant force-strain relationship in the XY plane as shown in Equation 6, the component A ij As shown in Equation 7, if the fiber direction of the fiber-reinforced plastic layer is defined as the L direction, and the direction orthogonal to the L direction is defined as the T direction, and the L direction is represented by a counterclockwise rotation angle θ from the X-axis, then the component Q shown in Equation 7... ij (Underlined) As shown in mathematical formulas 8 and 9, the cylindrical component is formed in a manner that holds true according to the relationship shown in mathematical formula 10. 【Mathematical Expression 6】 【Mathematical Expression 7】 In mathematical expression 7, component Q ij (Underlined) represents the stress-strain relationship of the k-th layer of the fiber-reinforced plastic layer, z k It is the Z-coordinate of the radial boundary of the k-th layer. 【Mathematical Expression 8】 【Mathematical Expression 9】 In Equation 9, E L E is the tensile modulus of elasticity in the L direction of the k-th layer. T ν is the tensile modulus of elasticity in the T direction of the k-th layer. LT G is the Poisson's ratio in the LT direction of the k-th layer. LT It is the shear modulus in the LT direction. 【Mathematical Formula 10】 。 6. The cylindrical component according to claim 5, characterized in that, Regarding component A ij When the thickness of the cylindrical plate is set to t, the following relationship holds: 【Mathematical Expression 11】 。 7. The cylindrical component according to claim 5, characterized in that, Regarding component A ij When the thickness of the cylindrical plate is set to t, the following relationship holds: 【Mathematical Expression 12】 。 8. The cylindrical component according to claim 5, characterized in that, Regarding component A ij When the thickness of the cylindrical plate is set to t, the following relationship holds: 【Mathematical Expression 13】 。 9. The cylindrical component according to any one of claims 5 to 8, characterized in that, The tensile modulus of elasticity in the fiber direction of a portion of the fibers of the fiber-reinforced plastic is greater than or equal to 300 GPa.

10. The cylindrical component according to claim 9, characterized in that, A portion of the fibers in the fiber-reinforced plastic is carbon fiber.

11. A cylindrical component with a tapered portion, characterized in that, have: A straight body portion, which is composed of a cylindrical component as described in any one of claims 1 to 10; and The cylindrical conical portion is connected to one end of the cylindrical body portion along the cylindrical axis, and its inner diameter expands from the end connected to the cylindrical body portion along the cylindrical axis.

12. The cylindrical component with a tapered portion according to claim 11, characterized in that, The conical portion has multiple cone angles that increase in stages along the axial direction of the cylinder from one end connected to the straight portion.

13. The cylindrical component with a tapered portion according to claim 11 or 12, characterized in that, At least one of the straight portion and the tapered portion has a portion where the plate thickness increases due to the installation of a multiplier for reinforcement.

14. The cylindrical component with a tapered portion according to claim 13, characterized in that, The thickness of the tapered portion includes a portion that varies continuously along the axial direction of the cylinder.

15. A surface magnet type electric motor, characterized in that, have: The cylindrical component as described in any one of claims 1 to 10; and The rotor core is pressed in and embedded into the inner diameter side of the cylindrical component.

16. A method for manufacturing a surface magnet type electric motor, which is the method for manufacturing a surface magnet type electric motor as described in claim 15. The manufacturing method of this surface magnet type electric motor is characterized by having the following steps: Apply a torsional moment to the cylindrical component; While maintaining a torsional torque applied to the cylindrical component, the rotor core is pressed into the inner diameter side of the cylindrical component; and After the rotor core is embedded by pressing it into the inner diameter side of the cylindrical component, the torsional torque of the cylindrical component is removed.

17. The method for manufacturing a surface magnet type electric motor according to claim 16, characterized in that, It also includes the following steps: pressing a plurality of rotor cores into the inner diameter side of the cylindrical component to embed them, and cutting the cylindrical component in a manner that matches the length of each rotor core after the torsional torque of the cylindrical component is removed.

18. A method for manufacturing a surface magnet type electric motor, wherein the surface magnet type electric motor is manufactured using a cylindrical component with a tapered portion as described in any one of claims 11 to 14. The manufacturing method of this surface magnet type electric motor is characterized by having the following steps: The torsion clamp is used to fix the straight part and the conical part; A torsional torque is applied to the torsion clamp, and the torsional torque is transmitted to the cylindrical component with the tapered portion; While maintaining a torsional torque applied to the cylindrical component with the tapered portion, the rotor core is inserted from the tapered portion side and pressed into the inner diameter side of the straight body portion to embed the rotor core; After the rotor core is inserted into the inner diameter side of the straight body, the torsional torque of the cylindrical component with the tapered portion is removed. Remove the twisting clamp from the straight part and the tapered part; as well as The conical portion is cut off from the straight portion.

19. The method for manufacturing a surface magnet type electric motor according to claim 18, characterized in that, It also includes the following steps: pressing a plurality of rotor cores into the inner diameter side of the straight body portion to embed them; and after removing the torsional torque of the cylindrical component with the tapered portion, cutting the straight body portion in a manner that matches the length of each rotor core portion.

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