Orthotropic hollow disk rotor for flywheel of flywheel power storage device and method for determining its optimum inner / outer diameter ratio

Abstract

To provide an orthotropic hollow disc rotor of a flywheel for flywheel power storage device that maximizes limit stored energy, and a determination method for optimum diameter ratio thereof.SOLUTION: An orthotropic hollow disc rotor 1 of a flywheel for flywheel power storage device that has an outer radius b, an inner radius a and a height h has volume πb2h of a virtual solid disk of height h having a circle of outer radius b as a bottom surface defined as "physical constitution". In this case, an optimum inner / outer diameter ratio with which maximum physical constitution limit accumulated energy density can be attained while rotating is λOPT=a / b or nearly λOPT.SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] The present invention relates to a technology for improving the stored energy of a hollow disk (including a cylinder) rotor, which is the main element of the flywheel of a flywheel energy storage device. In particular, it relates to a technology for improving the stored energy of a flywheel hollow disk rotor with orthotropy, in which the longitudinal elastic constant and tensile yield strength in the circumferential direction are higher than those in the radial direction. A typical rotor that falls into this category is a "fiber-reinforced plastic" rotor, in which high-strength fibers are wound circumferentially and the gaps between the fibers are impregnated and solidified with epoxy resin or the like, but this is not limited to this. Hereinafter, "orthotropic hollow disk (or cylindrical) rotor" may be abbreviated as simply "rotor," and "flywheel" may be abbreviated as "FW." [Background technology]

[0002] The FW power storage device is a power storage device that has the function of storing external electric power as rotational kinetic energy in the FW rotor through a means for converting electrical energy and rotational kinetic energy into each other, and conversely, supplying the rotational kinetic energy of the FW rotor to the outside as electric power.

[0003] Compared to known electrochemical storage devices (so-called secondary batteries), they function stably in both low-temperature and high-temperature environments. They have excellent features such as almost no deterioration in characteristics or lifespan even after repeated charging and discharging or when left in a charged state, the ability to easily detect the exact amount of charge, the ability to freely design input and output densities, and low internal resistance.

[0004] In recent years, there has been active development of "fiber rainforced plastics" FRP-FW rotors, which are made by wrapping high-strength fibers (carbon fiber, glass fiber, aramid fiber, etc.) around the circumference and impregnating them with plastic (as a matrix agent), as an alternative to conventional bulk metal FW rotors.

[0005] The reason is that FRP reinforced in the circumferential direction has properties that are suitable for FW rotors: "low density" and "high strength in the circumferential direction." FW energy storage devices constructed using FRP-FW rotors are expected to increase stored energy by at least several times compared to conventional FW energy storage devices using metal FW rotors.

[0006] Such FRP-FW rotors have a strong orthogonal anisotropy in structure, meaning that the Young's modulus and tensile yield strength are very large in the circumferential direction, but are significantly smaller in the perpendicular radial and axial directions.

[0007] A typical example of an FRP-FW rotor is a high-strength carbon fiber reinforced plastic (CFRP)-FW rotor as shown in FIGS. 1 and 5 of Patent Document 1 below.

[0008] The basic structure of this FW is as follows: it consists of a hollow disk CFRP-FW rotor that stores rotational energy, a rotating shaft that receives the rotational energy of the CFRP-FW rotor and transmits it to a generator / motor, and a spoke-type hub that connects the CFRP rotor and the rotating shaft.

[0009] The high-strength carbon fibers in the CFRP-FW rotor are wound and laminated in the circumferential direction, enhancing the tensile yield strength so that they can adequately withstand the strong tensile stress that occurs in the circumferential direction during rotation. The reason for this structure is that the rotational tensile stress that causes fracture occurs much stronger (typically by an order of magnitude or more) in the circumferential direction than in the radial direction.

[0010] Furthermore, the same patent document states that the FW rotor should be optimized to maximize the mass energy density (unit: Wh / kg), and that to achieve this, when the inner diameter is 2a (a is the inner radius) and the outer diameter is 2b (b is the inner radius), the inner / outer diameter ratio a / b should be within the range of 0.65 to 0.75 (the optimal value in Figure 3 of Patent Document 1 is 0.7). [Prior art documents] [Patent documents]

[0011] [Patent Document 1] Japanese Patent Application Laid-Open No. 2000-55134 Summary of the Invention [Problem to be solved by the invention]

[0012] However, the conventional FRP (CFRP)-FW rotor (outer radius b) as typified by Patent Document 1 has the problem of not being able to achieve the maximum achievable limit of stored energy. This is because optimization of the rotor structure (specifically, optimization of the inner / outer diameter ratio λ (= a / b)) was not considered, or was done inappropriately.

[0013] The "limit stored energy" mentioned here is a basic quantity for evaluating (comparing) the power storage performance of a rotor, and refers to the maximum rotational kinetic energy that can be stored in a rotor that is increasing its rotation speed just before it breaks down. Details will be given later, but the limit stored energy of an FRP rotor is strongly dependent on its shape (specifically, the inner / outer diameter ratio λ).

[0014] In view of the above, the present invention aims to provide an orthotropic hollow disk rotor for a flywheel in a flywheel energy storage device that maximizes the limit stored energy, and a method for determining the optimum inner / outer diameter ratio thereof. Note that the present invention relates to an FW rotor, which is a main element of the flywheel in a flywheel energy storage device, and can be applied regardless of the shape or structure of the other main elements, such as the hub and rotating shaft. [Means for solving the problem]

[0015] In order to achieve this object, the invention according to claim 1 provides an orthotropic hollow disk rotor for a flywheel for a flywheel energy storage device, the rotor having an outer radius of b, an inner radius of a, and a height of h. The rotor has a volume πb of a virtual solid disk having a base of a circle of outer radius b and a height of h. 2When h is defined as the "physical size", the optimum inner / outer diameter ratio that can achieve the maximum physical size limit stored energy density during rotation is λ OPT = a / b, or the λ OPT The inner and outer diameter ratios are close to each other.

[0016] The invention of claim 2 is characterized in that, in the orthogonal anisotropic hollow disk rotor of a flywheel for a flywheel energy storage device of claim 1, the orthogonal anisotropy of the orthogonal anisotropic hollow disk rotor includes at least anisotropy in which the longitudinal elastic constant and tensile yield strength in the circumferential direction are higher than the longitudinal elastic constant and tensile yield strength in the radial direction.

[0017] The invention according to claim 3 is an orthogonal anisotropic hollow disk rotor for a flywheel for a flywheel electric energy storage device according to claim 1, wherein the density is ρ and the longitudinal modulus of elasticity in the circumferential direction is E θ , the radial modulus of elasticity is E r , Poisson's ratio in the circumferential direction is ν θ , circumferential tensile yield strength is σ yθ , the radial tensile yield strength is σ yr When the optimum inner and outer diameter ratio λ OPT is E θ , E r , ν θ , σ yθ , σ yr , ρ, which is analytically determined.

[0018] The invention of claim 4 is characterized in that the orthotropic hollow disk rotor of the flywheel for the flywheel energy storage device of claim 2 is made of a composite material in which the voids of high-strength fibers wound in the circumferential direction are impregnated with a matrix agent.

[0019] The invention of claim 5 is characterized in that in the orthotropic hollow disk rotor of a flywheel for a flywheel energy storage device of claim 4, the high-strength fiber is one fiber selected from carbon fiber, boron fiber, glass fiber, aramid fiber, alumina fiber, silicon carbide fiber, and various metal fibers, or a composite fiber combining two or more of these.

[0020] The invention of claim 6 is characterized in that in the orthotropic hollow disk rotor of the flywheel for the flywheel energy storage device of claim 4, the matrix agent is various resins including epoxy resin, or lightweight, low-temperature melting metals including Al and Mg.

[0021] The invention according to claim 7 is an orthogonal anisotropic hollow disk rotor for a flywheel for a flywheel electric energy storage device according to claim 1, wherein the optimum inner and outer diameter ratio λ OPT The ratio of the inner and outer diameters in the vicinity is at least λ OPT -0.1~λ OPT +0.1, preferably λ OPT -0.05~λ OPT It is characterized by being in the range of +0.05.

[0022] The invention according to claim 8 provides an optimum inner / outer diameter ratio λ of the orthogonal anisotropic hollow disk rotor of the flywheel for the flywheel electric energy storage device according to claim 3. OPT A method for determining the body limit energy density U y / (πb 2 h) as a function of the inner / outer diameter ratio λ. It is characterized by:

[0023] The invention according to claim 9 is the optimum inner / outer diameter ratio λ OPT In the method of determining 1) Rotational stress σ at the radius r point of the orthogonal anisotropic hollow disk rotor θ , σ r (where the subscript θ denotes the circumferential direction and r denotes the radial direction) as a function of r with λ as a parameter; 2) The function σ θ , σ r The maximum point of σ θM , σ rM The function curve σ of λ θM -λ, σ rM -λ, and 3) The function curve σ θM -λ, σ rM Converting -λ to the critical peripheral speed bω yand the function curve bω of λ y - the process of finding λ (where ω y is the limit angular velocity of the orthotropic hollow disk rotor), and 4) Next, the function curve bω y -λ is the physique limit energy density U y / (πb 2 h) and λ function curve U y / (πb 2 h) -λ (where U y is the limit stored energy of the orthotropic hollow disk rotor), and 5) The function curve U y / (πb 2 h) - λ, the optimum value of the inner and outer diameter ratio that gives the maximum limit energy density of the body size, λ OPT and detecting The present invention is characterized by comprising:

[0024] The invention according to claim 10 is the optimum inner / outer diameter ratio λ OPT In the method of determining 1) Rotational stress σ at the radius r point of the orthogonal anisotropic hollow disk rotor θ , σ r (where the subscript θ denotes the circumferential direction and r denotes the radial direction) as a function of r with λ as a parameter; 2) The function σ θ , σ r The maximum point of σ θM , σ rM σ rM / σ θM and λ function curve σ rM / σ θM -λ, and 3) The function curve σrM / σ θM -λ to σ rM / σ θM =σ yr / σ yθ The λ value that satisfies OPT and detecting The present invention is characterized by comprising: [Brief explanation of the drawings]

[0025] [Figure 1] A diagram showing the basic structure of an FW rotor and definitions of its structural parameters. [Figure 2] FIG. 3 is a diagram showing the relationship between the rotational stress σ and the radius r of the FW rotor for explaining the first embodiment of the present invention. [Figure 3] FIG. 1 is a diagram showing the relationship between the maximum rotational stress σM and the inner / outer diameter ratio λ of the FW rotor for explaining the first embodiment of the present invention. [Figure 4] FIG. 3 is a diagram showing the relationship between the peripheral speed bωy of the FW rotor and the inner / outer diameter ratio λ for explaining the first embodiment of the present invention. [Figure 5] FIG. 3 is a diagram showing the relationship between the peripheral speed bωy and λ of an actual FW rotor for explaining the first embodiment of the present invention. [Figure 6] 1 is a diagram showing the relationship between the normalized limit energy (physical energy density) Uy / (πb2h) and λ of a FW rotor for explaining the first embodiment of the present invention. FIG. [Figure 7] FIG. 1 is a diagram showing the relationship between the radial to circumferential maximum stress ratio σrM / σθM and λ of an FW rotor for explaining a first embodiment of the present invention. [Figure 8] FIG. 2 is a diagram showing the relationship between the mass critical energy density Dy and λ of the FW rotor for explaining the first embodiment of the present invention. [Figure 9] FIG. 10 is a diagram showing the relationship between Uy / (πb2h) and λ and the relationship between σrM / σθM and λ of a FW rotor for explaining a second embodiment of the present invention. [Figure 10] FIG. 10 is a diagram showing the relationship between Uy / (πb2h) and λ and the relationship between σrM / σθM and λ of a FW rotor for explaining a third embodiment of the present invention. [Figure 11] FIG. 10 is a diagram showing the relationship between Uy / (πb2h) and λ and the relationship between σrM / σθM and λ of a FW rotor for explaining a fourth embodiment of the present invention. [Figure 12] FIG. 10 is a diagram showing the relationship between Uy / (πb2h) and λ and the relationship between σrM / σθM and λ of a FW rotor for explaining a fifth embodiment of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0026] The inventors of the present invention have conducted extensive research and studies to solve the problems of the conventional technology, and have finally analytically derived an FRP-FW rotor structure that maximizes the limit of stored energy. The details of the present invention are described below.

[0027] Consider an orthotropic FW rotor 1 (Figure 1) with outer radius b, inner radius a, and length h, rotating at an angular velocity ω around the z axis of a (r, θ, z) cylindrical coordinate system. The radial equilibrium equation (equation of balance) at the point of radius r of such a FW rotor 1 is as follows:

[0028]

number

[0029] It is known that the unit system is the SI unit system, and the variable σ θ , σ r are the rotational stresses occurring in the circumferential and radial directions, respectively, and ρ is the density of the material of the FW rotor 1. This differential equation is given by two boundary conditions: When r=a, σr(a)=0 When r=b, σr(b)=0 Taking this into consideration, we can analytically solve the general solution:

[0030]

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[0031]

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[0032]

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[0033]

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[0034] is derived. E θ , E r are the Young's modulus (modulus of longitudinal elasticity) of the FW rotor 1 in the circumferential and radial directions, respectively, and ν θ is the Poisson's ratio of the rotor 1 in the θ direction. σ r , σ θ It can be seen that is a function of the relative radius variable r / b with the inner / outer diameter ratio λ as a parameter.

[0035] The stored energy U (= rotational kinetic energy) of the FW rotor 1 with the shape shown in Figure 1 is

[0036]

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[0037]

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[0038] Here, the variables and constants are the same as in the previous equation. (bω) 2 is a function that increases with the square of the peripheral speed bω, (1-λ 4 ) is a function that rapidly decreases from 1 to 0 (zero) near λ=1 as λ (0<λ<1) goes from 0 to 1.

[0039] Next, specific elastic constants are given to calculate the σ of the orthotropic FRP-FW rotor 1. r and σ θ After checking the function form of on the graph, the limit stored energy U y A method for realizing a structure of the FW rotor 1 that maximizes the above will be described.

[0040] [First embodiment] Carbon fiber T1000G (Toray Industries, Inc.) is a material widely known in industry and academia as a carbon fiber with extremely high tensile yield strength. The first column of Table 1 shows the elastic constants (Young's modulus E) of the CFRP-FW rotor 1 reinforced in the circumferential direction with T1000G. θ , E r, Poisson's ratio ν θ ) and tensile yield strength (σ yθ , σ yr ), and density ρ.

[0041] [Table 1]

[0042] The matrix material used is epoxy resin 470-36S (Ashland Inc.). The literature on which these values are based is MA Conteh, EC Nsofor, J. Appl. Res. Tech., 14 (2016), pp. 184-190 (Reference 1).

[0043] Figure 2 shows the stress σ calculated using equations (2) and (3). θ and σ r The vertical axis of the graph shows the radial profile of stress σ θ and σ r ρ(bω) 2 The parameter of each curve is the inner / outer diameter ratio λ=a / b. Looking closely at the graph,

[0044] 1) σ θ Curves also have σ r The curve also has a maximum value σ θM , σ rM (↓ mark) 2) The relationship between these two values is always σ θM > σ rM That is, 3) As λ increases, σ θM increases and σ rM is decreasing, 4) Even more interestingly, for some λ, σ θM The position of the switch from the peak to the inner end of the FW, I understand.

[0045] Considering the above 1) to 4), we can obtain many σ by making the increment of λ (increment δλ) smaller. θ curve, σ rσ from each curve θM , σ rM If we extract and plot each time, we can get σ as shown in Figure 3. θM , σ rM A curve showing the relationship between δλ and λ (δλ=0.01) is obtained.

[0046] The condition for FW rotor 1 to yield is σ θM =σ yθ or σ rM =σ yr Therefore, using the data in Figure 3 and equations (2) and (3), the critical peripheral speed bω corresponding to each λ can be calculated. y Once the critical peripheral speed bω is determined, as shown in Figure 4, the critical peripheral speed bω when yielding occurs in the circumferential direction is obtained. θy The curve between and λ (solid line), and the critical peripheral speed bω when yielding occurs in the radial direction. ry A curve (dashed line) between λ and λ is obtained.

[0047] The rotational angular velocity ω (or outer diameter peripheral velocity bω) of the FW rotor 1 gradually increases, and the maximum circumferential stress value σ θM and the maximum value of the radial stress σ rM increases, and eventually one of them reaches its respective tensile yield strength, σ yθ , σ yr When this maximum stress fracture model is exceeded, the FW rotor 1 yields (breaks). According to this maximum stress fracture model, reconsidering Figure 4, the actual bω of the FW rotor y It is understood that the relationship between λ and λ is as shown in Figure 5.

[0048] Each point (λ, bω y ) into equation (4), the limit energy U of FW rotor 1 is y The relationship between the inner and outer diameter ratio λ and the diameter ratio λ is obtained as shown in Figure 6. The vertical axis of Figure 6 is U y πb 2 The limiting energy normalized (divided) by h. 2 h is the volume of a virtual cylinder with a height of h and a base of a circle with a radius of b, that is, it corresponds to the size of the FW rotor 1. y / (πb 2 h) is the amount that can be called the "physical limit energy density" of FW rotor 1.

[0049] The true volume of the FW rotor 1 with a hollow part is π(ba) 2 h, so the so-called volumetric limiting energy density U y / (π(ba) 2 h) and physique limit energy density U y / (πb 2 h) is a different quantity and should not be confused with the other.

[0050] As is clear from FIG. 6, the maximum limit energy U yOPT is the inner / outer diameter ratio λ OPT = 0.8 (optimal value), and this value is obtained when U yOPT / (πb 2 h) = 200 kWh / m 3 The limiting peripheral speed is bω yOPT =1719 m / s.

[0051] For example, if the FW rotor 1 is a cylinder with an outer diameter b = 0.15 m and a height h = 1 m, the maximum limit energy U yOPT =14.1kWh. The inner and outer diameter ratio of the FW rotor 1 is λ OPT =0.8, so the inner diameter is a=0.12m.

[0052] By following the above process, the optimum inner and outer diameter ratio λ OPT In addition to the method to obtain λ (called the first method), OPT There is a method for obtaining this (called the second method), which will be explained below.

[0053] Referring to Figure 4, λ OPT is the curve bω θy and the curve bω ry At this point λ, circumferential yielding and radial yielding occur simultaneously, so

[0054]

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[0055]

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[0056]

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[0057] At the stage shown in Figure 3, σ rM and σ θM Instead of plotting separately, σ rM / σ θM When plotted, it looks like Figure 7. Here, because of the relationship of equation (7), σ yr / σ yθ If we draw a horizontal line at (=constant), σ rM / σ θM -λ curve and an intersection point is generated. The λ value of this intersection point is λ OPT is.

[0058] Next, the effects of the first embodiment of the present invention will be described. Patent Document 1 states that λ = 0.7 is the optimum inner / outer diameter ratio for a CFRP-FW rotor (see Figure 3 of Patent Document 1). However, referring to Figure 6 obtained in the present invention, the limit stored energy (normalized limit stored energy in this case) of the conventional FW rotor when λ = 0.7 is not the maximum, and U y / (πb 2 h)=128kWh / m 3 The 200 kWh / m 3 It's much lower compared to.

[0059] The FW rotor 1(λ OPT = 0.8) is clearly superior to the conventional FW rotor according to Patent Document 1. In other words, it can be said that the FW rotor 1 of the first embodiment of the present invention solves the problem of the conventional FW rotor represented by Patent Document 1, that "the maximum achievable limit of stored energy cannot be realized."

[0060] If the outer radius b and height h that determine the size of the FW rotor 1 are given, then πb 2 I would like to add that since the actual limiting stored energy is multiplied by h, this conclusion does not change even if we consider limiting stored energy (Wh) rather than normalized limiting stored energy (= physical limiting stored energy density).

[0061] In order to clarify why such a result is obtained, the conventional optimization method of the FW rotor structure in Patent Document 1 is examined, and it is found that Patent Document 1 is based on the idea of maximizing the mass limit energy density (Wh / kg) and a trial-and-error method.

[0062] The mass limit energy density D of the hollow disk FW rotor defined in Fig. 1 y (Wh / kg) is

[0063]

number

[0064] D of the FW rotor 1 of the first embodiment y The results are plotted as a function of λ in Figure 8. Here, the vertical axis bω y D y Converted to D y As is clear from Figure 8, is a function that continues to increase monotonically throughout the effective range of the inner / outer diameter ratio, 0<λ<1. The closer ba is to zero, the smaller D y becomes higher.

[0065] That is, in the range λ=0.7 described in Patent Document 1 (and also in the range 0.65<λ<0.75), D y This means that the λ value and λ interval claimed in Patent Document 1 actually have no rational meaning.

[0066] According to the inventors' intensive research, such D yThe monotonically increasing property of is not limited to the FRP material of the first embodiment, but is widely recognized in other FRP materials (including the FRP materials of the embodiments described below). Therefore, it should be said that the structural optimization design method of Patent Document 1 that maximizes the mass limit energy density is almost never applicable to FRP-FW rotors that are actually manufactured.

[0067] Now, it goes without saying that it is important to reduce the manufacturing cost of a flywheel electric energy storage device (not shown) as a product, but even in the design of the FW, which is the unit, there is always a demand to configure the FW using existing parts (hubs and rotating shafts of electric energy storage devices FW that have already been commercialized) in order to realize an inexpensive FW. In order to meet this demand (for example, by using an existing hub), it is necessary to set the inner / outer diameter ratio of the FW rotor to the above-mentioned optimum value λ OPT It is often difficult to precisely align the

[0068] The compromises made to meet this demand are as follows: Optimal inner / outer diameter ratio λ OPT and the compromised design value of outer diameter ratio λ DSN The absolute value of the deviation of Δλ(=|λ OPT -λ DSN |) and referring to Figure 6 above, as Δλ increases, the physique limit energy density decreases, but when Δλ = 0.05, the decrease is limited to about 20%, and when Δλ = 0.1, the decrease is limited to about 40%.

[0069] However, if Δλ becomes much larger than 0.1, the reduction in the body size limit energy density becomes so severe that it is no longer acceptable. Therefore, it can be said that a realistic compromise point for deviation is Δλ = 0.1, and preferably Δλ = 0.05. This view also applies to the second and subsequent embodiments.

[0070] [Second embodiment] To date, prototype FW rotors have been produced that are not only strongly reinforced in the circumferential direction but also slightly reinforced in the radial direction, motivated by the need to reduce the inner diameter a of the CFRP-FW rotor 1. An example of this is "H. Hiroshima et al., Composite Structures, Vol. 131, (2015) pp. 304-311" (Reference 2).

[0071] The second column of Table 1 lists the elastic constants (E θ , E r , ν θ ) and tensile yield strength (σ yθ , σ yr ) and density ρ. The carbon fiber is T1000G and the matrix material is epoxy resin.

[0072] The second embodiment is a CFRP-FW rotor 1 (FIG. 1) that is designed to maximize the limit stored energy in the material of the FW rotor.

[0073] The methods (first and second methods) for deriving the optimum structure of the FW rotor 1 are exactly the same as those in the first embodiment, so the same explanations will be omitted and only the final results will be shown. This also applies to the third and subsequent embodiments.

[0074] Figure 9 shows the physique energy density U calculated by the first method. y / (πb 2 h)-λ curve and σ obtained by the second method rM / σ θM The optimal value λ is shown in Fig. 1. OPT = 0.53. In this case, the maximum normalized limiting stored energy is U y / (πb 2 h) - 195 kWh / m from the λ curve 3 This value is almost the same as in the first embodiment.

[0075] As is already clear from the results of the first and second embodiments, the optimum value λ of the inner / outer diameter ratio OPT is the physical property value of the FW rotor material (E θ , Er , ν θ , σ yθ , σ yr , ρ), and is not localized in the interval 0.65<λ<0.75 as claimed in Patent Document 1.

[0076] [Third embodiment] The present invention is not limited to CFRP, but is applicable to all FRPs. The third embodiment of the present invention is an example of the optimization of the structure of a BFRP-FW rotor 1 made of boron fiber B(4) (manufacturer unknown) and epoxy resin 5505 (SICOMIN). The third column of Table 1 shows the material properties of this circumferentially reinforced BFRP material. The literature showing these material properties is "Miki Mitsunori, Materials 30 (1981) pp.943-948" (Reference 3).

[0077] FIG. 10 shows the physique energy density U y / (πb 2 h)-λ curve and σ obtained by the second method rM / σ θM -λ curve. The optimal value λ OPT = 0.66 was obtained. At this time, the maximum physique energy density (normalized limit stored energy) is U y / (πb 2 h) - 85.7 kWh / m from the λ curve 3 becomes.

[0078] [Fourth embodiment] The fourth embodiment of the present invention is an example of optimizing the structure of a GFRP-FW rotor 1 made of glass fiber Scotchply (3M) and epoxy resin 1002 (3M). The fourth column of Table 1 shows the material properties (according to Reference 3) of this circumferentially reinforced GFRP material.

[0079] FIG. 11 shows the energy density U of the GFRP-FW rotor 1 obtained by the first method of the present invention. y / (πb 2 h)-λ curve and σ obtained by the second method rM / σ θM-λ curve. The optimal value λ OPT = 0.74. At this time, the maximum physique energy density (normalized limit stored energy) is U y / (πb 2 h) - 56.6 kWh / m from the λ curve 3 becomes.

[0080] [Fifth embodiment] The fifth embodiment of the present invention is an example of optimizing the structure of an AFRP-FW rotor 1 made of aramid fiber Kevlar 49 (DuPont) and epoxy resin. The physical properties of this circumferentially reinforced AFRP material (based on the aforementioned Reference 3) are shown in the fifth column of Table 1.

[0081] FIG. 12 shows the physique energy density U y / (πb 2 h)-λ curve and σ obtained by the second method rM / σ θM -λ curve. The optimal value λ OPT = 0.86. In this case, the maximum physique energy density (normalized limit stored energy) is U y / (πb 2 h) - 46.3 kWh / m from the λ curve 3 becomes.

[0082] [Other embodiments] The FW orthotropic hollow disk rotor 1 according to the present invention is not limited to the materials used in the above-described embodiments, but can be applied to rotors using various orthotropic materials. For example, alumina fiber, silicon carbide fiber, and various metal fibers can be used as high-strength fiber materials.

[0083] Furthermore, various fibers of the above-described embodiments or composite fibers combining two or more of these fibers may be used.

[0084] As the matrix material, resins other than epoxy resins, as well as lightweight, low-melting metals such as Al and Mg, can also be used. [Explanation of symbols]

[0085] 1...Flywheel orthotropic hollow disk rotor (FW rotor) b...Outer radius of FW rotor a...FW rotor inner radius h…FW rotor length r...radius (variable) θ...azimuth angle (variable) z…Central axis

Claims

1. An orthotropic hollow disk rotor for a flywheel for a flywheel energy storage device, having an outer radius of b, an inner radius of a, and a height of h, The orthogonal anisotropic hollow disk rotor has a volume πb of a virtual solid disk with a base of a circle of outer radius b and a height h. 2 The rotor has an optimum inner / outer diameter ratio λ OPT that can maximize the normalized limit stored energy normalized by h, or when the optimum inner / outer diameter ratio λ OPT is the inner / outer diameter ratio that can maximize the normalized limit stored energy normalized by the volume πb 2 h of a virtual solid disk having a base of a circle with an outer radius b and a height h, the inner / outer diameter ratio of the orthotropic hollow disk rotor is at least in the range of optimum inner / outer diameter ratio λ OPT -0.1 to optimum inner / outer diameter ratio λ OPT +0.1, and preferably in the range of optimum inner / outer diameter ratio λ OPT -0.05 to optimum inner / outer diameter ratio λ OPT +0.

05. An orthogonal anisotropic hollow disk rotor for a flywheel for a flywheel power storage device, characterized by:

2. 2. The orthogonal anisotropic hollow disk rotor for a flywheel for a flywheel electric energy storage device according to claim 1, The orthogonal anisotropy of the orthogonal anisotropic hollow disk rotor includes at least anisotropy in which the longitudinal elastic constant and tensile yield strength in the circumferential direction are higher than the longitudinal elastic constant and tensile yield strength in the radial direction.

3. 2. The orthogonal anisotropic hollow disk rotor for a flywheel for a flywheel electric energy storage device according to claim 1, Density is ρ, circumferential longitudinal elastic modulus is Eθ, radial longitudinal elastic modulus is E r , circumferential Poisson's ratio is νθ, circumferential tensile yield strength is σ y θ, radial tensile yield strength σ yr When the optimum inner and outer diameter ratio λ OPT is Eθ, E r , νθ, σ y θ, σ yr , be analytically determined using ρ An orthogonal anisotropic hollow disk rotor for a flywheel for a flywheel power storage device, characterized by:

4. 3. The orthogonal anisotropic hollow disk rotor for a flywheel for a flywheel electric energy storage device according to claim 2, It is made up of a composite material in which the voids between circumferentially wound high-strength fibers are impregnated with a matrix material. An orthogonal anisotropic hollow disk rotor for a flywheel for a flywheel power storage device, characterized by:

5. 5. The orthogonal anisotropic hollow disk rotor for a flywheel for a flywheel electric energy storage device according to claim 4, The high-strength fiber is one fiber selected from carbon fiber, boron fiber, glass fiber, aramid fiber, alumina fiber, silicon carbide fiber, and various metal fibers, or a composite fiber made by combining two or more of these fibers. An orthogonal anisotropic hollow disk rotor for a flywheel for a flywheel power storage device, characterized by:

6. 5. The orthogonal anisotropic hollow disk rotor for a flywheel for a flywheel electric energy storage device according to claim 4, The matrix material is a resin containing an epoxy resin or a lightweight, low-melting metal containing Al or Mg. An orthogonal anisotropic hollow disk rotor for a flywheel for a flywheel power storage device, characterized by:

7. 4. The optimum inner / outer diameter ratio λ of the orthogonal anisotropic hollow disk rotor of the flywheel for the flywheel electric energy storage device according to claim 3. OPT A method for determining At least the limiting stored energy U y is normalized by the volume πb 2 h of a virtual solid disk with a base of a circle of outer radius b and a height h, y / (πb 2 h) as a function of the inner / outer diameter ratio λ. A method for determining an optimum inner / outer diameter ratio of an orthogonal anisotropic hollow disk rotor of a flywheel for a flywheel power storage device, characterized by the above.

8. 8. The method for determining an optimum inner / outer diameter ratio according to claim 7, 1) Rotational stresses σθ, σ at the radius r point of the orthogonal anisotropic hollow disk rotor r (where the subscript θ denotes the circumferential direction and r denotes the radial direction) as a function of r with λ as a parameter; 2) The functions σθ, σ r The maximum point of σθ M , σ rM The function curve σθ of λ M -λ, σ rM -λ, and 3) The function curve σθ M -λ, σ rM Converting -λ to limit peripheral speed bω y and the function curve bω of λ y -λ calculation process (where ω y is the limit angular velocity of the orthotropic hollow disk rotor), and 4) Next, the function curve bω y -λ is the normalized limit storage energy U y / (πb 2 h) and λ function curve U y / (πb 2 h) -λ conversion step (where U y is the limit stored energy of the orthotropic hollow disk rotor), and 5) The function curve U y / (πb 2 h) -λ to obtain the optimum value λ of the inner / outer diameter ratio that gives the maximum value of the normalized limit stored energy Uy / (πb2h). OPT and detecting A method for determining an optimum inner / outer diameter ratio of an orthotropic hollow disk rotor of a flywheel for a flywheel electric storage device, comprising:

9. 8. The method for determining an optimum inner / outer diameter ratio according to claim 7, 1) Rotational stresses σθ, σ at the radius r point of the orthogonal anisotropic hollow disk rotor r (where the subscript θ denotes the circumferential direction and r denotes the radial direction) as a function of r with λ as a parameter; 2) The functions σθ, σ r The maximum point of σθ M , σ rM σ rM / σθ M and λ function curve σ rM / σθ M -λ, and 3) The function curve σrM / σθ thus obtained M -λ to σ rM / σθ M = σ yr / σ y The λ value that satisfies θ, i.e., λ OPT and detecting A method for determining an optimum inner / outer diameter ratio of an orthotropic hollow disk rotor of a flywheel for a flywheel electric storage device, comprising:

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