CYLINDER-SHAPED ELEMENT, CYLINDER ELEMENT WITH ATTACHED CONECULE, SURFACE MAGNET MOTOR AND METHOD FOR MANUFACTURING A SURFACE MAGNET MOTOR

Abstract

A cylindrical element (1) consists of a fiber-reinforced plastic which exhibits a relationship expressed by formula 2 when a stress-strain relationship equation in an XY plane as in formula 1 is expressed in an orthogonal coordinate system O-XYZ, where an origin O is a center point in the thickness direction of a small element (10) of the cylindrical element (1), the X-axis runs along a tangential direction of a cylinder, the Y-axis runs along the direction parallel to the axial direction of the cylinder, the Z-axis runs along the radial direction of the cylinder, σ is a stress vector, ε is a strain vector, τ is a shear stress, γ is a shear strain, and an element Q ij is an element of the i-th row and j-th column of a plane stiffness matrix Q. { σ x σ y τ xy} ≡ { σ} = [ Q 11 Q 12 Q 16 Q 12 Q 22 Q 26 Q 16 Q 26 Q 66 ] { ε x ε y γ xy} ≡ [ Q ] { ε} Q 12 Q 26 − Q 16 Q 22 ≠ 0

Description

Area

[0001] The present invention relates to a cylindrical element made of fiber-reinforced plastic, a cylindrical element with an attached conical part, a surface magnet motor using a cylindrical element, and a method for manufacturing a surface magnet motor. background

[0002] A cylindrical element molded from fiber-reinforced plastic (FRP) is already known. For example, patent document 1 describes a rotor that uses a rotor unit with a cylindrical shape molded from fiber-reinforced plastic. The rotor is configured such that a hub, serving as the core unit, is press-fitted into the inside of the rotor body unit. The rotor generates tension along the circumferential direction of the rotor body unit to create a frictional force on a contact surface between the rotor body unit and the hub. This prevents the rotor body unit from slipping relative to the hub as the rotor rotates.

[0003] Patent document 1: Japanese patent application disclosure JP2002-95208 Summary of the invention Problem to be solved by the invention

[0004] However, pressing the hub into the inner diameter side of the rotor body unit with a tightening margin, as is done for the rotor of patent document 1, requires a large pressing force and therefore large and complex equipment to generate this pressing force.

[0005] The present invention was made taking into consideration the foregoing, and it is an object of the present invention to provide a cylindrical element which enables a reduction of the pressing force for a core unit which is to be pressed into the inner diameter side of a cylindrical element. Means to solve the problem

[0006] To solve the problems mentioned above and achieve the objective, a cylindrical element according to the present invention consists of a fiber-reinforced plastic exhibiting a relationship expressed by Formula 2, where a stress-strain relationship equation in an XY plane, as in Formula 1, is expressed in an orthogonal coordinate system O-XYZ, wherein the origin O of a small element of the cylindrical element is a center point in a thickness direction, the X-axis runs along a tangential direction of a cylinder, the Y-axis runs along a direction parallel to the axial direction of the cylinder, the Z-axis runs along the radial direction of the cylinder, σ is a stress vector, ε is a strain vector, τ is a shear stress, γ is a shear strain, and an element Q ij is an element of the i-th row and j-th column of a plane stiffness matrix Q. {σxσyτxy}≡{σ}=[Q11Q12Q16Q12Q22Q26Q16Q26Q66]{εxεyγxy}≡[Q]{ε} Q12Q26−Q16Q22≠0 Effects of the invention

[0007] A cylindrical element according to the present invention offers the advantageous effect that the pressing force for a core unit that is to be pressed into the inner diameter side of a cylindrical element can be reduced. Brief description of the drawings Fig. Figure 1 is a perspective view showing a cylindrical element according to a first embodiment. Fig. Figure 2 is a perspective view showing a surface magnet motor that includes the cylindrical element according to the first embodiment. Fig. Figure 3 is a front view of the surface magnet motor, which includes the cylindrical element according to the first embodiment, viewed from the axial direction. Fig.Figure 4 is an illustrative representation showing a method for manufacturing the surface magnet motor which includes the cylindrical element according to the first embodiment. Fig. Figure 5 is an illustrative representation showing a method for manufacturing several surface magnet motors which include the cylindrical element according to the first embodiment. Fig. Figure 6 is a perspective view showing a cylindrical element according to a second embodiment. Fig. Figure 7 is a top view of the cylindrical element according to the second embodiment, seen from the cylindrical axial direction. Fig. 8 is an enlarged view of the in Fig. 7 of the area VIII shown. Fig. Figure 9 is a perspective view illustrating a specific example of the cylindrical element according to the second embodiment. Fig. 10 is an enlarged view of the in Fig. 9. Area X shown, represented with virtual cutting planes. Fig. Figure 11 is a schematic representation that schematically illustrates an example of a method for manufacturing the cylindrical element according to the second embodiment. Fig. Figure 12 is a perspective view that represents a method for evaluating a “torsional expansion property” of the cylindrical element according to the second embodiment. Fig. Figure 13 is a cross-sectional view illustrating the procedure for evaluating the “torsional expansion property” of the cylindrical element according to the second embodiment. Fig. Figure 14 is an illustrative diagram that demonstrates a method for manufacturing the surface magnet motor using a cylindrical element with an attached conical part according to a third embodiment. Fig.Figure 15 is a cross-sectional view of a part of the cylindrical element with attached conical part according to the third embodiment, which was taken along the cylindrical axial direction. Fig. Figure 16 is an illustrative diagram showing a method for manufacturing multiple surface magnet motors using the cylindrical element with attached conical part according to the third embodiment. Description of the embodiments

[0008] A cylindrical element, a cylindrical element with an attached conical part, a surface magnet motor and a method for manufacturing the surface magnet motor according to embodiments of the present invention are described in detail below with reference to the drawings. First embodiment.

[0009] Fig.Figure 1 is a perspective view illustrating a cylindrical element according to a first embodiment. To denote a direction for defining features of a cylindrical element 1, which is the material direction, the following is used in Figure 1: Fig. 1. An orthogonal coordinate system O-XYZ is defined. The orthogonal coordinate system O-XYZ is a coordinate system in which, assuming a small element 10 of the cylindrical element 1, the origin O is the center point in the thickness direction of the small element 10, the X-axis runs along a tangent direction of the cylinder, the Y-axis runs along a direction parallel to the axial direction P of the cylinder, and the Z-axis runs along the radial direction of the cylinder. Furthermore, the direction of a torsional moment M exerted on the cylindrical element 1 is also defined. T defined such that a right-hand thread direction around the cylindrical axis is the positive direction.

[0010] The cylindrical element 1 consists of a fiber-reinforced plastic containing a reinforcing fiber bonded with a resin. The reinforcing fiber can be, for example, a carbon fiber or glass fiber, or an organic fiber such as a para-aramid fiber or a polyester fiber. The resin can be a thermosetting resin such as an epoxy resin, an unsaturated polyester resin, or an epoxy acrylate resin, or a thermoplastic resin such as polyamide, polypropylene, polyethylene, polystyrene, polyethylene terephthalate, polycarbonate, polyetheretherketone, or polyphenylene sulfide. The fiber can be continuous or discontinuous, as produced, for example, by injection molding or compression molding. The cylindrical element 1 consists of an anisotropic material in the orthogonal coordinate system O-XYZ.According to reference literature 1 (Japan Society of Mechanical Engineers, “Kikai Kogaku Binran DVD-ROM-ban α3-hen Zairyo Kogaku” (English equivalent: JSME Mechanical Engineers' Handbook, DVD-ROM version, Volume α3, Mechanics of Materials) (first edition), Maruzen (2014). Section 12.4, pp. 160-163), the stress-strain relationship equation in the XY plane can be expressed by equation (1.1). Formula 3: {σxσyτxy}≡{σ}=[Q11Q12Q16Q12Q22Q26Q16Q26Q66]{εxεyγxy}≡[Q]{ε}

[0011] In equation (1.1), {σ} is a stress vector in the XY plane, {ε} is a strain vector in the XY plane, and [Q] is a plane stiffness matrix. The elements in the third row and third column of equation (1.1) contain the number 6 instead of the number 3. This is because, as stated in reference 1, a three-dimensional stress-strain relationship equation has been reduced to a two-dimensional one. A similar notation is also used in the equations listed below. The solution of equation (1.1) for {ε} yields equation (1.2), and ε x can therefore be expressed by equation (1.3). Formula 4: {εxεyγxy}=[Q]−1{σxσyτxy} Formula 5: εx=[Q]11−1⋅σx+[Q]12−1⋅σy+[Q]16−1⋅τxy

[0012] In equation (1.3) [Q] ij -1an ij-th element of the inverse matrix of matrix [Q]. Assuming that only a shear stress τ caused by torsion xy is present (i.e., σ) x =σ y =0), one obtains equation (1.4). Formula 6: εx=[Q]16−1⋅τxy

[0013] In this respect, the element [Q] 16 -1 specifically described as equation (1.5). Formula 7: [Q]16−1=1detQ(Q12Q26−Q16Q22)

[0014] The symbol detQ stands for the determinant of the matrix [Q] and is expressed by equation (1.6). Formula 8: detQ=Q11Q22Q66+Q12Q26Q16+Q16Q12Q26−Q11Q26Q26−Q12Q12Q66−Q16Q22Q16

[0015] In this respect, the cylindrical element 1 according to the present first embodiment is characterized in that it satisfies equation (1.7). Formula 9: Q12Q26−Q16Q22≠0

[0016] By satisfying equation (1.7), the cylindrical element 1 exhibits the following characteristic. That is, the exertion of the torsional moment M T on the cylindrical element 1 causes the shear stress τ xy occurs on the cylindrical element 1. According to equation (1.7), which shows that [Q] 16 -1 If ≠ 0, the shear stress τ is generated. xy the perpendicular strain ε x , which is determined by equation (1.4). In the orthogonal coordinate system O-XYZ, ε x a circumferential elongation of the cylinder element 1 and represents the amount of radial deformation. If [Q] 16 -1 If >0, the exertion of the torsional moment M leads to T on the cylindrical element 1 in the in Fig. 1 direction shown to a shear stress τ xy >0, so ε x >0, causing the cylindrical element 1 to expand in the radial direction. In contrast, the application of the torsional moment M leads to Ton the cylindrical element 1 in the in Fig. 1 direction shown at [Q] 16 -1 <0 to a shear stress τ xy >0, i.e., to ε x <0, causing the cylindrical element 1 to contract radially. The application of the torsional moment M T However, acting in the opposite direction causes the cylindrical element 1 to expand in a radial direction.

[0017] Next, a metric for evaluating the extent of radial expansion when applying the torsional moment M will be developed. T It should be noted that the extent of radial expansion is referred to below as the "torsional expansion property". The extent of deformation when the torsional moment M is applied. T The effect on the cylindrical element 1 depends on its diameter and thickness. Accordingly, the extent of radial expansion can be assessed by comparing the extent of expansion per shear stress τ.xy These occur due to the torsional moment M T is generated. Equation (1.4) expresses a relationship between the shear stress τ xy and the stretching, and therefore [Q] functions 16 -1 as an evaluation metric for the "torsional expansion property". Formula 10: |[Q]16−1|=1|detQ||Q12Q26−Q16Q22|

[0018] Equations (1.4) and (1.5) show that for cylindrical elements 1 with the same inner diameter and the same thickness, a higher value obtained by equation (1.8) leads to a greater radial expansion when a torsional moment M is applied to these cylindrical elements 1. Tof the same size. The cylindrical element 1 according to the present first embodiment preferably has a right-hand side value shown in equation (1.8) of 0.002 [1 / GPa] or higher, more preferably a right-hand side value of 0.005 [1 / GPa] or higher, and more preferably a right-hand side value of 0.01 [1 / GPa] or higher. It should be noted that 1 / GPa, the unit of the above values, is the reciprocal of gigapascal (GPa), where 1 GPa = 10⁹ newtons per square meter (N / m²). 2 ) corresponds.

[0019] With reference to the Fig. 2 and Fig. 3 Next, a surface magnet motor (surface permanent magnet: SPM) 100 is described, which includes the cylindrical element 1 according to the present first embodiment. Fig. Figure 2 is a perspective view showing a surface magnet motor with the cylindrical element according to the first embodiment. Fig.Figure 3 is a front view of the surface magnet motor, seen from an axial direction, which includes the cylindrical element according to the first embodiment.

[0020] As in the Fig. 2 and Fig. As shown in Figure 3, the surface magnet motor 100 includes the cylinder element 1 described above and a rotor core unit 3 which is pressed into the inside of the cylinder element 1.

[0021] The rotor core unit 3 comprises a shaft 30, an iron core 31, permanent magnets 32, spacers 33, and a highly conductive material 34. The shaft 30 is coaxially fitted into the cylindrical bore of the iron core 31. The permanent magnets 32 are arranged circumferentially spaced from one another on an outer circumferential surface of the iron core 31. The permanent magnets 32 are not limited to those forming four poles but can be arranged in any configuration. The spacers 33 are arranged between adjacent permanent magnets 32. The highly conductive material 34 is applied to the outer circumferential surfaces of the permanent magnets 32 and the spacers 33 to reduce rotor losses. The highly conductive material 34 can be applied to the entire outer circumferential surfaces of the permanent magnets 32 and the spacers 33 or to a region of these surfaces.The cylindrical element 1 is arranged around the outer circumferential surface of the highly conductive material 34. The cylindrical element 1 is a sleeve for attaching the permanent magnets 32.

[0022] With reference to the Fig. 4 and Fig. 5 next describes a method for manufacturing the surface magnet motor 100, which includes the cylinder element 1, including the present first embodiment. Fig. Figure 4 is an illustrative representation that demonstrates a method for manufacturing the surface magnet motor, which includes the cylindrical element 1, according to the first embodiment. As shown in Fig. As shown in Figure 4, the process for manufacturing the surface magnet motor 100 begins with the torque M T is exerted on the cylindrical element 1. By exerting the torque M T The cylindrical element 1 expands in a radial direction. Next, while the torque M is applied...T As the torque M continues to be applied to the cylinder element 1, the rotor core unit 3 is pressed into the inside of the cylinder element 1. After the rotor core unit 3 has been pressed into the inside of the cylinder element 1, the torque M applied to the cylinder element 1 is reduced. T This cancels out the constraint. As a result, the cylindrical element 1 contracts radially. However, the cylindrical element 1 is radially limited by the rotor core unit 3, which generates a circumferential stress. The response to this stress causes a distributed load to act radially on the outer circumferential surface of the rotor core unit 3. This distributed load acts in a direction that prevents centrifugal separation of the permanent magnets 32 from the iron core 31 during the rotation of the surface magnet motor 100.

[0023] Fig.Figure 5 is an illustrative representation that demonstrates a method for manufacturing multiple surface magnet motors, which includes the cylindrical element according to the first embodiment. As in Fig. As shown in Figure 5, the method for manufacturing the surface magnet motor 100 also allows several rotor core units 3 to be fitted into the single cylinder element 1. While the torsional moment M T When a force is exerted on the cylindrical element 1, the multiple rotor core units 3 are pressed into the inner surface of the cylindrical element 1. During this process, the rotor core units 3 are arranged such that adjacent rotor core units 3 do not come into contact with each other in the cylindrical axial direction X. After all rotor core units 3 have been pressed into the inner surface of the cylindrical element 1, the torsional moment M exerted on the cylindrical element 1 is reduced. TThe cylindrical element 1 is then cut according to the axial lengths of the respective rotor core units 3. This allows several surface magnet motors 100 to be manufactured simultaneously.

[0024] As described above, the cylindrical element 1 according to the present first embodiment consists of a fiber-reinforced plastic which has a relationship expressed by equation (1.7) above, where the stress-strain relationship equation in the XY plane is expressed in the orthogonal coordinate system O-XYZ as in equation (1.1) above, in which the origin O is the center point in the thickness direction of the small element 10 of the cylindrical element 1, the X-axis runs along the tangential direction of the cylinder, the Y-axis along a direction parallel to the axial direction of the cylinder, and the Z-axis along the radial direction of the cylinder, σ is a stress vector, ε is a strain vector, τ is a shear stress, γ is a shear strain, and the element Q ij is the i-th row, j-th column of the element of the plane stiffness matrix Q.

[0025] Thus, the exertion of the torsional moment M causes Ton the cylinder element 1 according to the present first embodiment, such that the cylinder element 1 is subject not only to shear deformation but also to radial expansion, thereby enabling a reduction in the pressing force for the rotor core unit 3, which is pressed into the inner diameter side of the cylinder element 1. When the torsional moment M T After the rotor core unit 3 is fitted into the cylindrical element 1, a circumferential stress is also created by a restoring force exerted when the cylindrical element 1 returns from its expanded shape to its original shape. This prevents centrifugal separation of the permanent magnets 32 from the iron core 31 during the rotation of the surface magnet motor 100. Second embodiment.

[0026] Next, a cylindrical element 2 according to the present second embodiment will be described. Fig. Figure 6 is a perspective view showing a cylindrical element according to the second embodiment. Fig. Figure 7 is a top view of the cylindrical element according to the second embodiment, seen from the cylindrical axial direction. Fig. 8 is an enlarged view of the in Fig. 7 of the area VIII shown.

[0027] To denote a direction for defining features of the cylindrical element 2, which is a material direction, in Fig.6 defines the orthogonal coordinate system O-XYZ. The orthogonal coordinate system O-XYZ is a coordinate system in which, assuming a small element 20 of the cylindrical element 2, the origin O is the center point in the thickness direction of the small element 20, the X-axis runs along the tangent direction of the cylinder, the Y-axis runs parallel to the axial direction P of the cylinder, and the Z-axis runs along the radial direction of the cylinder. Furthermore, the direction of the torsional moment M exerted on the cylindrical element 2 is T defined such that clockwise rotation around the cylinder axis is the positive direction.

[0028] As in the Fig.As shown in Figures 6 to 8, the cylindrical element 2 according to the present second embodiment is configured to include several fiber-reinforced plastic layers (hereinafter referred to as FRP layers 21), each having a cylindrical shape. Adjacent FRP layers 21 are joined together. The joining method can be, for example, adhesive bonding. If, for instance, the sheet winding technique is used to manufacture the cylindrical element 2, all layers are wound around a mandrel and stacked, and then simultaneously subjected to curing and bonding between adjacent FRP layers 21. Alternatively, the cylindrical element 2 can also be manufactured by a process in which only a portion of the adjacent FRP layers 21 is pre-formed integrally, and the integrally formed portions are then joined together using epoxy adhesive, acrylic adhesive, or the like.

[0029] The method is not limited to methods using the configurations described above. The FRP layers 21 each consist of a reinforcing fiber and a resin, wherein a region or all fibers of the reinforcing fiber, oriented in at least one direction, are continuous, and different combinations of reinforcing fiber and resin can be used in different layers of the FRP layers 21. The reinforcing fiber can be, for example, a carbon fiber or a glass fiber, as well as an organic fiber such as a para-aramid fiber or a polyester fiber. The resin can be a thermosetting resin such as an epoxy resin, an unsaturated polyester resin, or an epoxy acrylate resin, or a thermoplastic resin such as polyamide, polypropylene, polyethylene, polystyrene, polyethylene terephthalate, polycarbonate, polyetheretherketone, or polyphenylene sulfide.

[0030] As in Fig.As shown in Figure 6, let L-direction be the fiber direction of each of the FRP layers 21 (i.e., the tangent direction on the cylinder) and T-direction the direction perpendicular to L-direction. The L-direction is expressed by a counterclockwise rotation angle θ from the X-axis of the orthogonal coordinate system O-XYZ. The FRP layers 21 have a total of N layers, which are designated, in order from the inside out, as first layer, second layer, ..., k-th layer, ... and N-th layer. If θk denotes the L-direction of the k-th layer, the relation between resultant and strain in the XY-plane of the cylindrical element 2 can be expressed by equation (2.1) according to classical lamination theory, as described in the preceding reference literature 1. Formula 11: {N}={NxNyNxy}=[A]{ε}=[A11A12A16A12A22A26A16A26A66]{εxεyγxy}

[0031] In the equation, {N} = {N x N y Nxy} T a resultant force vector and {ε}={ε x ε y γ xy} T a strain vector. Additionally, an element A is used. ij a plane stiffness matrix [A] expressed by equation (2.2). Formula 12: Aij=∑k=1N(Q¯ij)k(zk−zk−1)(i,j=1,2,6)

[0032] In the equation, z k , as in Fig. Figure 8 shows a Z-coordinate at a radial boundary of the k-th layer. Furthermore, (Q(bar) ij ) k in equation (2.2) an element Q(bar) ij (i, j=1, 2, 6) of the stress-strain relationship equation for the k-th layer and is specifically given by equations (2.3). Note that Q(bar) represents the letter Q with a line over it. Formula 13: Q¯11=c4Q11+s4Q22+2(Q12+2Q66)c2s2¶Q¯22=s4Q11+c4Q22+2(Q12+ 2Q66)c2s2¶Q¯12=(c4+s4)Q12+(Q11+Q22−4Q66)c2s2¶Q¯66=(c4+s4 )Q66+(Q11+Q22−2Q12−2Q66)c2s2¶Q¯16=(Q11−Q12−2Q66)c3s+(Q11−Q22+2Q66)cs3¶Q¯26=(Q11−Q12−2Q66)cs3+(Q12−Q22+2Q66)c3s¶wo c=cosθk and s=sinθk¤

[0033] In equations (2.3) Q 11 , Q 22 , Q 12 and Q 66 expressed by equations (2.4). Formula 14: Q11=mELQ22=mETQ12=−mνLTETQ66=mGLTm=1 / (1−νLT2ET / EL)

[0034] In equations (2.4) E L a tensile module in the L-direction of the k-th layer, E T a tensile module in the T-direction of the k-th layer, v LT a Poisson number in the LT direction of the k-th layer and G L,T a shear modulus in the LT direction.

[0035] Solving equation (2.1) for {ε} yields equation (2.5) and thus equation (2.6). Formula 15: {εxεyγxy}=[A]−1{NxNyNxy} Formula 16: εx=[A]11−1⋅Nx+[A]12−1⋅Ny+[A]16−1⋅Nxy

[0036] In equation (2.6) [A] ij -1 an ij-th element of the inverse matrix of matrix [A]. Assuming that only a shear force N caused by torsion xy occurs (i.e., N x = N y =0), we obtain equation (2.7). The element [A] 16 -1 is expressed by equation (2.8). Formula 17: εx=[A]16−1⋅Nxy Formula 18: [A]16−1=1detA(A12A26−A16A22)

[0037] In equation (2.8) detA is the determinant of the matrix [A] and is expressed by equation (2.9). Formula 19: detA=A11A22A66+A12A26A16+A16A12A26−A11A26A26−A12A12A66−A16A22A16

[0038] The cylindrical element 2 according to the present second embodiment is characterized in that it satisfies equation (2.10). Formula 20: A12A26−A16A22≠0

[0039] By satisfying equation (2.10), the cylindrical element 2 exhibits the following characteristic. That is, the exertion of the torsional moment M T on the cylindrical element 2 causes the shear force N xy acts on the cylindrical element 2. According to equation (2.10), which shows that [A] 16 -1 ≠0, generates the shear force N xy the perpendicular strain ε x , which is determined by equation (2.7). In the orthogonal coordinate system O-XYZ, ε x a circumferential elongation of the cylindrical element 2 and represents the extent of the radial deformation. If [A] 16 -1 If >0, the exertion of the torsional moment M leads to T on the cylindrical element 2 in the Fig.6 shown direction to a shear force N xy >0, so ε x >0, causing the cylindrical element 2 to expand radially. In contrast, the application of the torsional moment M leads to T on the cylindrical element 2 in the Fig. 6 direction shown at [A] 16 -1 <0 to a shear force N xy >0, so ε x <0, causing the cylindrical element 2 to contract radially. The application of the torsional moment M T However, acting in the opposite direction causes the cylindrical element 2 to expand in a radial direction.

[0040] In this respect, N xy an integrated value of the shear stress τ xy Each of the FRP layers 21 along the plate thickness direction. If the average shear stress τ(bar) xy as the quotient of N xyThe value defined by dividing by a plate thickness “t” of the cylindrical element 2 according to equation (2.11) can be rewritten as equation (2.12), and t / detA×(A 12 A 26 -A 16 A 22 ) can be used as a measure of the "torsional expansion property". Note that τ(bar) represents the letter τ with a line over it. Formula 21: τ¯xy=Nxyt Formula 22: εx=[A−1]16⋅t⋅τ¯xy={tdetA(A12A26−A16A22)}⋅τ¯xy Formula 23: |[A]16−1⋅t|=t|detA||A12A26−A16A22|

[0041] Equation (2.12) shows that for cylindrical elements 2 with the same dimensions, a higher value obtained by equation (2.13) leads to a greater radial extension when a torsional moment M is applied to these cylindrical elements 2. Tof the same size. The cylindrical element 2 according to the present second embodiment preferably has a right-hand side value shown in equation (2.13) of 0.002 [1 / GPa] or higher, more preferably a right-hand side value of 0.005 [1 / GPa] or higher, and more preferably a right-hand side value of 0.01 [1 / GPa] or higher. It should be noted that 1 / GPa, the unit of the above values, is the reciprocal of GPa, where 1 GPa = 10⁹ newtons per square meter (N / m²). 2 ) is.

[0042] With reference to the Fig. 9 and Fig. 10 as well as on Fig. Section 6 will next describe a specific example of the cylinder element 2 according to the present second embodiment. Fig. Figure 9 is a perspective view showing a specific example of the cylindrical element according to the second embodiment. Fig. 10 is an enlarged view of the in Fig.9. Area X shown, represented with virtual cutting planes.

[0043] Table 1 contains information on the material of each of the FRP layers 21, the thickness of each of the FRP layers 21, and the fiber directions in the cylindrical element 2. Table 2 contains the types of material constants and the values ​​of the physical properties of material A specified in Table 1, which is a unidirectionally reinforced prepreg formed from a high-strength PAN-based carbon fiber and an epoxy resin. PAN stands for polyacrylonitrile. [Table 1] FRP layers material Thickness (mm) ok first shift Material A 0.125 60° second Schiobt -25° third layer 60° fourth shift -25° fifth layer -25° sixth shift 60° seventh shift -25° eighth layer 60° [Table 2] material constant Physical property value E L 130.1 GPa E T 8.03 GPa v LT 0.31 G LT 4.8GPa

[0044] The cylindrical element 2 given in Tables 1 and 2 has a value of t / |detA| × |A 12 A 26 -A 16 A 22 |, which is calculated as in equation (2.14). Formula 24: t|detA||A12A26−A16A22|=0.0373(1 / GPa)

[0045] The average shear stress τ(bar) xy can be approximately determined according to equation (2.15), where D m the diameter of a plate thickness mid-region of the cylindrical element 2 and ΔD m the extent of the diameter D m due to the torsional moment M T illustrates how in Fig. 6 shown. Formula 25: τ¯xy≅MT2(πDm24)t=2MTπDm2t

[0046] Furthermore, L, which represents the circumferential length of the plate thickness region of the cylindrical element 2, and ΔL, which represents the magnitude of the extension of the circumferential length L, have the relationship according to equation (2.16), and the magnitude of the diameter expansion ΔD m is therefore given by equation (2.17). Formula 26: εx=ΔLL=πΔDmπDm=ΔDmDm Formula 27: ΔDmDm=t|detA||A12A26−A16A22|⋅2MTπDm2t∴ΔDm=t|detA||A12A26−A16A22|⋅2MTπDmt

[0047] From equation (2.17) the measure of the diameter expansion ΔD can be determined. m determine to 0.119 mm if the torsional moment M T 500 Newton meters (Nm) and the diameter D m 100 mm.

[0048] Next, another specific example of the cylindrical element 2 according to the present second embodiment is described. Table 3 contains information on the material of each of the FRP layers 21, the thickness of each of the FRP layers 21, and the fiber directions in the cylindrical element 2. Table 4 contains information on the material constants and physical properties of the material B specified in Table 3, which is a unidirectionally reinforced prepreg formed from a highly elastic, pitch-based carbon fiber and an epoxy resin. [Table 3] FRP layers material Thickness (mm) 8 k first shift Material A 0.125 -20° second layer 55° third layer -20° fourth shift 55° fifth layer 55° sixth shift -20° seventh shift 55° eighth layer -20° [Table 4] material constant Physical property value E L 350 GPa E T 5GPa v LT 0.33 G LT 4.2GPa

[0049] A high elastic modulus of the FRP layers 21 results in a high stress acting on the cylinder element 2 after the cylinder element 2 has been arranged around the outer circumferential surface of the rotor core unit 3. This can generate a force that prevents the permanent magnets 32 from detaching or flying off the cylinder element 2 due to the centrifugal force caused by the high-speed rotation of the surface magnet motor 100. The fiber to be used for the FRP layers 21 is therefore preferably a highly elastic, pitch-based carbon fiber. In addition, the fiber preferably has a tensile modulus in the fiber direction of 300 GPa or more. The parameter t / |detA| × |A 12 A 26 -A 16 A 22 | is calculated for such a cylindrical element 2 according to equation (2.18). Formula 28: t|detA||A12A26−A16A22|=0.0356(1 / GPa)

[0050] Furthermore, the diameter expansion ΔD can be determined from equation (2.17). m can be determined to be 0.113 mm if the torsional moment M T 500 Newton meters (Nm) and the diameter D m 100 mm.

[0051] With reference to Fig. 11 next describes a method for manufacturing the cylinder element 2 according to the present second embodiment. Fig. Figure 11 is a schematic representation illustrating an example of a method for producing the cylindrical element according to the second embodiment. In a case where the resin is a thermosetting resin, examples of the method for producing the cylindrical element 2 include the sheet winding technique and the filament winding technique. As shown in Fig.As shown in Figure 11, the sheet winding process is a method in which a unidirectionally oriented continuous fiber is pre-impregnated with resin, a semi-cured prepreg 22 is wound around a cylindrical cylinder or mandrel 23, and the prepreg 22 is subsequently cured. In the filament winding technique, fiber bundles are impregnated with an uncured liquid thermosetting resin, wound around a mandrel, and then cured. Alternatively, if the resin is a thermoplastic resin, the process for producing the cylindrical element 2 includes, for example, an automated tape placement technique (ATP). In the ATP technique, tapes or sheet-shaped matrices, produced by pre-impregnating a unidirectionally oriented continuous fiber with a resin, are wound around a mandrel under heat and pressure to ensure adhesion.It should be noted that the method for manufacturing the cylinder element 2 is not limited to a manufacturing process that uses the sheet winding technique, the filament winding technique or the ATP technique, but can also be another method.

[0052] With reference to the Fig. 12 and the Fig. 13 Next, a procedure for evaluating the “torsional expansion property” of the cylindrical element 2 is described. Fig. Figure 12 is a perspective view illustrating a method for evaluating the “torsional expansion property” of the cylindrical element according to the second embodiment. Fig. Figure 13 is a cross-sectional view illustrating the procedure for evaluating the “torsional expansion property” of the cylindrical element according to the second embodiment. As shown in the Fig. 12 and Fig.Figure 13 shows strain gauges 200 attached to the outer and inner circumferential surfaces of the cylindrical element 2. The strain gauges 200 each measure the circumferential strain ε. x , if the torsional moment M T is exerted on the cylindrical element 2. The strain gauges 200 measure the strain in the circumferential direction of the cylindrical element 2. The measuring points used by the strain gauges 200 are not located on the two in Fig. The number of points shown is limited to 13; the use of one or more points is sufficient. The circumferential and perpendicular strain ε x The torsional expansion property can be determined by equation (2.19) below, using equations (2.16) and (2.17). The torsional expansion property can be evaluated by comparing the measured value of strain gauge 200 with the value determined by equation (2.19). Formula 29: εx=[A−1]16⋅t⋅τ¯xy={tdetA(A12A26−A16A22)}⋅τ¯xy={tdetA(A12A26−A16A22)}⋅2MTπDm2t

[0053] It should be noted that, according to the present second embodiment, the cylinder element 2 also enables the manufacture of the surface magnet motor 100, in which the rotor core unit 3 is pressed into the inner diameter side of the cylinder element 2 using the above method for manufacturing the surface magnet motor 100.

[0054] As described above, the fiber-reinforced plastic forming the cylindrical element 2 according to the present second embodiment comprises the multiple FRP layers 21 in which a region or all fibers are formed from continuous fibers. The fiber-reinforced plastic is designed to satisfy a relationship expressed by equation (2.10) above, where the element A ijas expressed in the equation (2.2) above, where N represents a resultant force vector of the FRP layers 21, the element A ij The i-th row, j-th column of the equivalent plane rigidity matrix A, calculated according to classical lamination theory, and the resulting force-strain relationship equation in the XY plane are expressed as in equation (2.1) above. The element Q shown in equation (2.2) above ij (bar) is expressed as in the equations (2.3) and (2.4) above, where an L-direction is the fiber direction of each of the FRP layers 21, a T-direction is the direction perpendicular to the L-direction, and the L-direction is expressed by a rotation angle θ counterclockwise from the X-axis.

[0055] Thus, the exertion of the torsional moment M causes TOn the cylinder element 2 according to the present second embodiment, the cylinder element 2 is subject not only to shear deformation but also to radial expansion, thereby enabling a reduction in the pressing force for the rotor core unit 3, which is pressed into the inner diameter side of the cylinder element 2. When the torque M T After the rotor core unit 3 is fitted into the cylindrical element 2, a circumferential stress is also created by a restoring force exerted when the cylindrical element 2 returns from its expanded shape to its original shape. This prevents centrifugal separation of the permanent magnets 32 from the iron core 31 during the rotation of the surface magnet motor 100. Third embodiment.

[0056] Next, a cylindrical element 4 with an attached conical part according to the present third embodiment and the surface magnet motor 100, which was manufactured using the cylindrical element 4 with an attached conical part, are described. Fig. Figure 14 is an illustrative representation demonstrating a method for manufacturing the surface magnet motor using a cylindrical element with an attached conical part according to the third embodiment. As shown in Fig.As shown in Figure 14, the cylindrical element 4 with attached conical part, according to the present third embodiment, comprises a straight body section 41, which consists of the cylindrical element 1 of the first embodiment or the cylindrical element 2 of the second embodiment, and a conical part 42 with a cylindrical shape, which is connected to an end face in the cylindrical axial direction X of the straight body section 41 and has an inner diameter that widens along the cylindrical axial direction X from the end face where the connection with the straight body section 41 is made. The rotor core unit 3 of the surface magnet motor 100 is pressed into the straight body section 41. Therefore, it is necessary that at least the straight body section 41 satisfies equation (1.7) or equation (2.10). It should be noted that the conical part 42 can also satisfy equation (1.7) or equation (2.10).The straight body section 41 and the conical cone part 42 are formed in one piece. The conical cone part 42 is designed to accommodate a later described twisting device 51b.

[0057] If the straight body section 41 corresponds to the cylindrical element 2 of the second embodiment, the cylindrical element 4, provided with a cone-like cone part, is manufactured, for example, using sheet metal winding technology. In this case, semi-hardened prepreg layers are wound and layered around a combination of a mandrel with an outer diameter in the shape of the straight body section 41 and a mandrel with an outer diameter corresponding to the inner diameter of the cone part 42, and the prepreg layers adjacent in the lamination direction are simultaneously hardened and bonded. This enables the production of the cylindrical element 4 with an attached cone part, which includes the straight body section 41 and the cone part 42.

[0058] Fig. Figure 15 is a cross-sectional view of a portion of the cylindrical element with an attached conical part according to the third embodiment, taken along the cylindrical axial direction. As in Fig.As shown in Figure 15, a doubler 43a is provided for reinforcement on the outer circumferential surface near an opening in the cylindrical body of the straight body section 41. Additionally, a doubler 43b is provided for reinforcement on the outer circumferential surface near an opening in the cylindrical body of the conical part 42. As a result, the straight body section 41 and the conical part 42 have a greater plate thickness near the cylindrical openings where the doubler 43a and the doubler 43b are provided than in the area where neither the doubler 43a nor the doubler 43b is provided. The doubler 43a and the doubler 43b can be formed, for example, by increasing the number of prepreg layers used in the manufacturing process.Alternatively, another method for forming the doubler 43a and the doubler 43b involves gluing and joining separately manufactured cylindrical elements to the outer circumferential surface of the straight body section 41 and to the outer circumferential surface of the conical part 42. The doubler 43a and the doubler 43b need not satisfy equation (1.7) or equation (2.10), and their materials can be chosen arbitrarily. For improved processability, a fabric material can be used on the surfaces of the doubler 43a and the doubler 43b. It should be noted that the cylindrical element 4 with attached conical part is not limited to an element configured to include reinforcements on both the straight body section 41 and the conical part 42, but can be configured to include reinforcement on at least one of the parts, the straight body section 41 and the conical part 42.

[0059] Furthermore, the conical part 42 has several cone angles that gradually increase along the cylindrical axial direction X, starting at one end where the connection with the straight body region 41 is made. The in Fig.The conical region 42 shown in Figure 15 includes, for example, a first conical region 44 with a cone angle θ1, which is connected to the straight body region 41, and a second conical region 45 with a cone angle θ2 that is larger than the cone angle θ1. The cone angle θ1 of the first conical region 44 is, for example, 1°, 2°, or 5°. The cone angle θ2 of the second conical region 45 is, for example, 10°, 20°, 30°, or 45°. It should be noted that the cone angle θ1 of the first conical region 44 and the cone angle θ2 of the second conical region 45 are not limited to the angles mentioned above; it is only required that the cone angle θ1 be smaller than the cone angle θ2. Furthermore, the cone part 42 is not limited to one with two cone angles, the cone angle θ1 and the cone angle θ2, but can also be designed with one cone angle or three or more cone angles.

[0060] Furthermore, the doubler 43b provided on the conical part 42 is not located in a region near the straight body section 41 of the first conical section 44, but is arranged continuously over a region of the first conical section 44 and the entire length of the second conical section 45. In the first conical section 44, the doubler 43b is preferably provided such that it includes a region “a” with a plate thickness identical to the plate thickness of the straight body section 41, a region “b” with a plate thickness identical to the plate thickness of the second conical section 45 on which the doubler 43b is provided, and an intermediate region “c” with a continuously varying plate thickness. If the cylindrical element with the attached conical part 42 has a large cone angle, the application of the torsional moment M leads to TThis can lead to the cylindrical element 4 being subjected to an anomalous condition in which high stress occurs at the junction between the straight body section 41 and the conical section 42, potentially resulting in fracture at this junction. The cylindrical element 4 with attached conical section according to the present third embodiment includes a first conical section 44 with a small cone angle. This prevents the occurrence of anomalous stress at the junction between the straight body section 41 and the conical section 42. Furthermore, the cylindrical element 4 with attached conical section includes a reinforcement 43b over a portion of the first conical section 44 and the second conical section 45, thereby improving the strength of the conical section 42.This allows the cylindrical element 4 with attached conical part to prevent a fracture point at the connection between the first conical area 44 and the second conical area 45, even if an unusually high stress occurs at this connection point.

[0061] Next, a method for manufacturing the surface magnet motor 100 using the cylindrical element 4 with attached conical part according to the present third embodiment is described. As in Fig.As shown in Figure 15, a cylindrical rotating device 51a is provided in the cylinder bore of the straight body section 41. Additionally, a cylindrical rotating device 51b is provided in the cylinder bore of the conical part 42. The rotating device 51a provided in the cylinder bore of the straight body section 41 is arranged such that it faces at least partially towards the doubler 43a provided on the outer circumferential surface and is fixed by tightening a bolt 52a through the doubler 43a and the straight body section 41. By tightening the bolt 52a through a section that includes the doubler 43a, the stress concentration caused by tightening the bolt can be reduced.Furthermore, the rotating device 51b provided in the cylinder bore of the conical part 42 is arranged such that it faces at least partially towards the doubler 43b provided on the outer circumferential surface of the second conical region 45 and is fastened by tightening a bolt 52b through the doubler 43b and the second conical region 45. Tightening the bolt 52b through a region comprising the doubler 43b reduces the stress concentration caused by tightening the bolt 52b. In this respect, the rotating device 51b provided in the cylinder bore of the conical part 42 is designed to have an inner diameter larger than the outer diameter of the rotor core unit 3, so that the rotor core unit 3 can pass through the cylinder bore of the rotating device 51b.It should be noted that the twisting devices 51a and 51b are not limited to those configured to be attached in the cylindrical bore of the straight body section 41 and the cylindrical bore of the conical part 42, but can also be attached to the outer circumferential surface of the straight body section 41 and the outer circumferential surface of the conical part 42. Furthermore, the twisting devices 51a and 51b can be attached to the straight body section 41 and the conical part 42, for example, by a bonding method using an adhesive such as an epoxy or acrylic adhesive, a frictional fastening method, or a method combining one of these methods with the tightening of screws.

[0062] The process for manufacturing the surface magnet motor 100 is carried out such that the torsional torque M Tis exerted on the twisting device 51a and the twisting device 51b, as shown in Fig. 14 shown by holding the twisting devices 51a and 51b provided on both sides, thereby controlling the torsional moment M T is transferred to the cylindrical element with the attached conical part. This causes the straight body section 41 to expand radially. While the torsional moment M TAs the torsional moment M is exerted on the cylindrical element with attached conical part, the rotor core unit 3 is inserted into the inner diameter side of the rotating device 51b attached to the conical part 42 and then pressed into the straight body section 41. In the cylindrical element 4 with attached conical part, the rotating device 51b attached to the conical part 42 has an inner diameter that is larger than the outer diameter of the rotor core unit 3. This allows the rotor core unit 3 to be installed in the cylinder bore of the cylindrical element 4 with attached conical part without any interference between the rotor core unit 3 and the rotating device 51b. After the rotor core unit 3 has been inserted into the straight body section 41, the torsional moment M exerted on the rotating device 51a and the rotating device 51b is reduced. TThe tension is released. This creates a circumferential stress on the cylindrical element 4 with the attached conical part. The reaction to this stress causes a distributed load to act radially on the outer circumferential surface of the rotor core unit 3. This distributed load acts in a direction that prevents centrifugal separation of the permanent magnets 32 from the iron core 31 during rotation of the surface magnet motor 100. The rotating device 51a and the rotating device 51b are then released from the cylindrical element 4 with the attached conical part. Subsequently, the conical part 42 is separated from the straight body section 41, thus enabling the surface magnet motor 100 to be manufactured.

[0063] Fig. Figure 16 is an illustrative representation demonstrating a method for manufacturing multiple surface magnet motors using the cylindrical element with attached conical part according to the third embodiment. As shown in Fig.As shown in Figure 16, the method for manufacturing the surface magnet motor 100 also allows several rotor core units 3 to be fitted into the single cylinder element 4 with attached conical part. By exerting the torsional moment M T The torsional moment M is applied to the twisting device 51a and the twisting device 51b. T The torque is transferred to the cylindrical element 4 with the attached conical part and causes the straight body section 41 to expand in a radial direction. While the torque M TAs the torque M is exerted on the cylindrical element with attached conical part 4, the multiple rotor core units 3 are inserted into the inner diameter side of the rotating device 51b attached to the conical part 42 and then pressed into the straight body section 41. During this process, the rotor core units 3 are arranged such that adjacent rotor core units 3 do not come into contact with each other in the cylindrical axial direction X. After all rotor core units 3 have been fitted into the straight body section 41, the torque M exerted on the rotating device 51a and the rotating device 51b is released. TThe rotating device 51a and the rotating device 51b are then detached from the cylindrical element 4 with the attached conical part. The cylindrical element 4 with the attached conical part is then cut according to the axial lengths of the respective rotor core units 3. In this way, several surface magnet motors 100 can be manufactured simultaneously.

[0064] As described above, the cylindrical element with attached conical part 4, according to the present third embodiment, comprises the straight body section 41, which consists of a cylindrical element corresponding to the cylindrical element 1 of the first embodiment or the cylindrical element 2 of the second embodiment, and the conical part 42 with a cylindrical shape, which is connected to an end face in the cylindrical axial direction X of the straight body section 41 and extends along the cylindrical axial direction X. That is to say, the straight body section 41 is configured such that it satisfies a relationship expressed by equation (1.7) or equation (2.10) above.

[0065] Thus, the exertion of the torsional moment M causes TIn the present third embodiment, the cylindrical element 4 with the attached conical part undergoes not only shear deformation but also radial expansion of the straight body section 41, thereby reducing the pressing force required for the rotor core unit 3, which is to be pressed into the inner diameter side of the straight body section 41. Furthermore, in the cylindrical element 4 with the attached conical part, the rotating device 51b, attached to the conical part 42, has an inner diameter larger than the outer diameter of the rotor core unit 3. This allows the rotor core unit 3 to be installed in the cylinder bore of the cylindrical element 4 with the attached conical part without any interference between the rotor core unit 3 and the rotating device 51b. When the torsional moment M TAfter the rotor core unit 3 is fitted into the straight body section 41, a circumferential stress is also generated by a restoring force exerted when the straight body section 41 is in the process of returning from its expanded shape to its original shape. This prevents centrifugal separation of the permanent magnets 32 from the iron core 31 during the rotation of the surface magnet motor 100.

[0066] The configurations described in the preceding embodiments are merely examples. These configurations can be combined with other known technologies, and configurations of different embodiments can be combined with one another. Furthermore, such configurations can be omitted and / or modified in one area without deviating from the essential features. List of reference symbols

[0067] 1, 2 Cylindrical element; 3 Rotor core unit; 4 Cylindrical element with attached conical part; 10, 20 Small element; 21 FRP layer; 22 Prepreg; 23 Mandrel; 30 Shaft; 31 Iron core; 32 Permanent magnet; 33 Spacer; 34 Highly conductive material; 41 Straight body section; 42 Conical part; 43a, 43b Doubler; 44 First conical section; 45 Second conical section; 51a, 51b Twisting device; 52a, 52b Bolt; 100 Surface magnet motor; 200 Strain gauges; θ1, θ2 Conical angles. 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 2002-95208

[0003] Cited non-patent literature

[0000] JSME Mechanical Engineers' Handbook, DVD-ROM version, Volume α3, Mechanics of Materials) (first edition), Maruzen (2014). Section 12.4, pp. 160-163

[0010]

Claims

[1] cylindrical element, wherein The cylindrical element is formed from a fiber-reinforced plastic, which exhibits a relationship expressed by Formula 2 when a stress-strain relationship equation in an XY plane, as in Formula 1, is expressed in an orthogonal coordinate system O-XYZ, where an origin O is a center point in a thickness direction of a small element of the cylindrical element, the X-axis runs along a tangential direction of a cylinder, the Y-axis runs along a direction parallel to an axial direction of the cylinder, the Z-axis runs along a radial direction of the cylinder, σ is a stress vector, ε is a strain vector, τ is a shear stress, γ is a shear strain, and an element Q ij is an element of the i-th row and j-th column of a plane rigidity matrix Q. {σxσyτxy}≡{σ}=[Q11Q12Q16Q12Q22Q26Q16Q26Q66]{εxεyγxy}≡[Q]{ε} Q12Q26−Q16Q22≠0 [2] Cylinder element according to claim 1, wherein the element Q ij a relationship is fulfilled which is expressed by the following formula. 1|detQ||Q12Q26−Q16Q22|≥0.002(1 / GPa) [3] Cylindrical element according to claim 1, wherein the element Q ij a relationship is fulfilled which is expressed by the following formula. 1|detQ||Q12Q26−Q16Q22|≥0.005(1 / GPa) [4] Cylinder element according to claim 1, wherein the element Q ij a relationship is fulfilled which is expressed by the following formula. 1|detQ||Q12Q26−Q16Q22|≥0.01(1 / GPa) [5] Cylindrical element according to claim 1, wherein The fiber-reinforced plastic comprises a multitude of fiber-reinforced plastic layers in which an area or all fibers are formed from continuous fibers, and the fiber-reinforced plastic is designed such that it satisfies a relationship expressed by formula 10, where the element A ij as expressed in formula 7, where N represents a resultant force vector of the fiber-reinforced plastic layers, the element A ij an element of the i-th row and j-th column of an equivalent plane rigidity matrix A calculated according to classical lamination theory, and a resulting force-strain relation equation in the XY plane as expressed in Equation 6, and in which the element Q shown in Equation 7 ij (bar) as expressed in formulas 8 and 9, where an L-direction is a fiber direction of each of the fiber-reinforced plastic layers, a T-direction is a direction perpendicular to the L-direction, and the L-direction is expressed by a rotation angle θ counterclockwise from the X-axis. {N}={NxNyNxy}=[A]{ε}=[A11A12A16A12A22A26A16A26A66]{εxεyγxy} Aij=∑k=1N(Q¯ij)k(zk−zk−1) (i,j=1,2,6) where in formula 7 the element Q ij (bar) is a stress-strain relationship equation in a k-th layer of the fiber-reinforced plastic layers and z k a Z-coordinate at a radial boundary of the k-th layer. Q¯11=c4Q11+s4Q22+2(Q12+2Q66)c2s2¶Q¯22=s4Q11+c4Q22+2(Q12+ 2Q66)c2s2¶Q¯12=(c4+s4)Q12+(Q11+Q22−4Q66)c2s2¶Q¯66=(c4+s4 )Q66+(Q11+Q22−2Q12−2Q66)c2s2¶Q¯16=(Q11−Q12−2Q66)c3s+(Q12−Q22+2Q66)cs3¶Q¯26=(Q11−Q12−2Q66)cs3+(Q12−Q22+2Q66)c3s¶wo c=cos θk and s=sin θk¤ Q11=mELQ22=mETQ12=mvLTETQ66=mGLTm=1 / (1−vLT2ET / EL) where in Formula 9 E L a tensile elasticity modulus in the L-direction of the k-th layer is, E T a tensile elasticity modulus in the T-direction of the k-th layer is, v LT the Poisson number in the LT direction of the k-th layer is and G LT a thrust module in the LT direction. A12A26−A16A22≠0 [6] Cylinder element according to claim 5, wherein the element A ij a relationship is satisfied which is expressed by the following formula, where t represents the plate thickness of the cylinder. 1|detA||A12 A26−A16 A22|≥0.002(1 / GPa) [7] Cylindrical element according to claim 5, wherein the element A ij a relationship is satisfied which is expressed by the following formula, where t represents the plate thickness of the cylinder. 1|detA||A12 A26−A16 A22|≥0.005(1 / GPa) [8] Cylindrical element according to claim 5, wherein the element A ij a relationship is satisfied which is expressed by the following formula, where t represents the plate thickness of the cylinder. 1|detA||A12 A26−A16 A22|≥0.01(1 / GPa) [9] Cylindrical element according to any one of claims 5 to 8, wherein a region of the fibers of the fiber-reinforced plastic has a tensile modulus in the fiber direction of greater than or equal to 300 gigapascals (GPa). [10] The cylinder element according to claim 9, wherein part of the fibers of the fiber-reinforced plastic consist of carbon fibers. [11] Cylindrical element with attached conical part comprising the following: a straight body region comprising the cylindrical element according to any one of claims 1 to 10; and a conical part with a cylindrical shape, wherein the conical part is connected to an end side in the cylindrical axial direction of the straight body region and has an inner diameter that widens along the cylindrical axial direction from an end side where the connection to the straight body region is made. [12] Cylindrical element with attached conical part according to claim 11, wherein the conical part has a plurality of conical angles which gradually increase along the cylindrical axial direction, starting from the one end side where the connection with the straight body region is made. [13] Cylindrical element with attached conical part according to claim 11 or 12, wherein at least one of the straight body regions or the conical part has a region where a doubler is provided for reinforcement in order to increase the plate thickness. [14] Cylindrical element with attached conical part according to claim 13, wherein the conical part has a region whose plate thickness changes continuously along the cylindrical axial direction. [15] Surface magnet motor comprising the following: the cylindrical element according to any one of claims 1 to 10; and a rotor core unit that is pressed into the inside of the cylinder element. [16] Method for manufacturing the surface magnet motor according to claim 15, wherein the method comprises the following steps: a step of applying a torque to the cylinder element; a step of pressing the rotor core unit into the inner diameter side of the cylinder element, while the torque continues to be applied to the cylinder element; and a step of removing the torque applied to the cylinder element after the rotor core unit has been pressed into the inner diameter side of the cylinder element. [17] Method for manufacturing the surface magnet motor according to claim 16, wherein a large number of rotor core units are pressed into the inner diameter side of the cylinder element, and The method further includes a step of cutting the cylinder element according to the length of each of the rotor core units after removing the torque applied to the cylinder element. [18] Method for manufacturing a surface magnet motor using the cylinder element with attached cone part according to any one of claims 11 to 14, wherein the method comprises the following steps: one step of attaching a twisting device to each, the straight body section and the conical part; a step of applying a torsional moment to the twisting device to cause the torsional moment to be transferred to the cylindrical element with attached conical part; a step of inserting the rotor core unit from a side where the cone part is located and pressing the rotor core unit into an inner diameter side of the straight body area, with the torque continuing to be applied to the cylindrical element with attached cone part; a step of removing the torque applied to the cylindrical element with attached conical part after the rotor core unit has been pressed into the inner diameter side of the straight body area; a step of releasing the twisting device from the straight body section and the conical part; and a step of separating the conical part from the straight body area. [19] Method for manufacturing a surface magnet motor according to claim 18, wherein a large number of rotor core units are pressed into the inner diameter side of the straight body area, and The method further includes a step of cutting the straight body area according to a length of each of the rotor core units after removing the torsional moment exerted on the cylindrical element with attached conical part.

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