JP6303846B2 - Vibration power generator - Google Patents
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- JP6303846B2 JP6303846B2 JP2014121036A JP2014121036A JP6303846B2 JP 6303846 B2 JP6303846 B2 JP 6303846B2 JP 2014121036 A JP2014121036 A JP 2014121036A JP 2014121036 A JP2014121036 A JP 2014121036A JP 6303846 B2 JP6303846 B2 JP 6303846B2
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Description
本発明は、錘の両端を磁歪材で支持し、該磁歪材の支点と錘との接続点に回転自由度を持たせた振動発電装置に関する。 The present invention relates to a vibration power generation apparatus in which both ends of a weight are supported by a magnetostrictive material, and a connection point between the fulcrum of the magnetostrictive material and the weight is provided with a degree of freedom of rotation.
振動を利用した発電技術としては、圧電素子を利用した発電方法がよく知られている。圧電素子を利用した発電方法の多くは、圧電素子に何らかの方法で外部から力を加えることにより、圧電素子を変形させて発電するものである。 As a power generation technique using vibration, a power generation method using a piezoelectric element is well known. Many of the power generation methods using piezoelectric elements are to generate power by deforming the piezoelectric elements by applying external force to the piezoelectric elements in some way.
圧電素子を利用した発電方法としては、例えば、下記特許文献1に記載のものがある。すなわち、下記特許文献1では、音による空気の圧力変動を利用して圧電素子により発電する音力発電装置、および、振動による圧力変動を利用して圧電素子により発電する振動力発電装置が記載されている。 As a power generation method using a piezoelectric element, for example, there is a method described in Patent Document 1 below. That is, the following Patent Document 1 describes a sound power generation device that generates electric power with a piezoelectric element using fluctuations in air pressure due to sound, and a vibration power generation device that generates electric power with piezoelectric elements using pressure fluctuations caused by vibration. ing.
また圧電素子に代えて磁歪素子を利用した発電方法も提案されている。磁歪素子を利用した発電方法としては、例えば、下記特許文献2に記載のものがある。
図13は、下記特許文献2に記載の振動を利用した発電素子の構成例を示す図である。すなわち、図13(a)は、下記特許文献2に示された発電素子の構成を示す上面図、図13(b)は、下記特許文献2に示された発電素子の構成を示す側面図である。
A power generation method using a magnetostrictive element instead of a piezoelectric element has also been proposed. As a power generation method using a magnetostrictive element, for example, there is a method described in Patent Document 2 below.
FIG. 13 is a diagram illustrating a configuration example of a power generation element using vibration described in Patent Document 2 below. That is, FIG. 13A is a top view showing the configuration of the power generating element shown in Patent Document 2 below, and FIG. 13B is a side view showing the configuration of the power generating element shown in Patent Document 2 below. is there.
図13(a)および図13(b)において発電素子100は、連結ヨーク100aおよび100bと、磁歪棒110aおよび110bと、コイル120aおよび120bと、永久磁石140aおよび140bと、パッシブヨーク150とを備えて構成されている。 13 (a) and 13 (b), the power generating element 100 includes connecting yokes 100a and 100b, magnetostrictive rods 110a and 110b, coils 120a and 120b, permanent magnets 140a and 140b, and a passive yoke 150. Configured.
図14は、図13に示した発電素子を片持ち梁構成とした場合の発電装置の構成例を示す図である。図14において発電装置は、発電素子100の連結ヨーク100aを固定部材で固定した片持ち梁構成とし、連結ヨーク100bに曲げ応力Pを印加することにより、磁歪棒110aおよび110bが曲げ変形される。これにより磁歪棒110aおよび110bに発生する逆磁歪効果により、コイル120aおよび120b(図13(a)参照)を貫く磁束が変化することで、コイル120aおよび120bに誘導電圧(または誘導電流)が発生する。これにより、発電素子100に振動を印加することで発電が可能となるものである。 FIG. 14 is a diagram illustrating a configuration example of the power generation device when the power generation element illustrated in FIG. 13 has a cantilever configuration. In FIG. 14, the power generation device has a cantilever structure in which the connecting yoke 100a of the power generating element 100 is fixed by a fixing member. By applying a bending stress P to the connecting yoke 100b, the magnetostrictive rods 110a and 110b are bent and deformed. As a result, due to the inverse magnetostrictive effect generated in the magnetostrictive rods 110a and 110b, the magnetic flux passing through the coils 120a and 120b (see FIG. 13 (a)) changes, so that an induced voltage (or induced current) is generated in the coils 120a and 120b. To do. As a result, power can be generated by applying vibration to the power generation element 100.
特許文献1に記載された圧電素子を利用する発電方法では、圧電素子を構成する圧電材料が脆性材料であり、曲げや衝撃に対して弱い材料である。そのため過度に力を加えることができず、発電量を増加させるために大きな曲げや衝撃を加えることが難しいという問題がある。また、圧電素子は低周波でインピーダンスが高く、圧電素子より低いインピーダンスを有する負荷を接続した際に、負荷に発生する電圧が小さくなるため、発電により得られる電力が小さくなり、発電の効率が低いという問題がある。 In the power generation method using the piezoelectric element described in Patent Document 1, the piezoelectric material constituting the piezoelectric element is a brittle material and is a material that is weak against bending and impact. For this reason, there is a problem that it is difficult to apply excessive bending and impact in order to increase the amount of power generation because excessive force cannot be applied. In addition, the piezoelectric element has a high impedance at a low frequency, and when a load having a lower impedance than that of the piezoelectric element is connected, the voltage generated in the load is small, so the power obtained by power generation is small and the power generation efficiency is low. There is a problem.
一方、特許文献2に記載された磁歪棒110aおよび110bを構成する磁歪材料は、延性材料であり、圧電材料に比べて曲げや衝撃に強いため、大きな曲げや衝撃を加えることで発電量を増加させることが可能である。また素子のインピーダンスが圧電材料よりも低いことから、インピーダンスの低い負荷の接続による発電効率の低下が少ないため特許文献1に記載の圧電材料の問題点を解消することができる。 On the other hand, the magnetostrictive material composing the magnetostrictive rods 110a and 110b described in Patent Document 2 is a ductile material and is more resistant to bending and impact than the piezoelectric material. Therefore, power generation is increased by applying large bending and impact. It is possible to make it. Further, since the impedance of the element is lower than that of the piezoelectric material, the problem of the piezoelectric material described in Patent Document 1 can be solved because there is little decrease in power generation efficiency due to connection of a load with low impedance.
しかしながら、特許文献2に記載された振動発電装置は、振動しながら磁歪棒の曲げ変形を発生させ発電するには振動源から大きな加振力を必要とするため、振動エネルギーの吸収が悪く発電効率が低下する、または錘の振動方向に直交する方向の外部振動では励振されないなどの問題点がある。 However, since the vibration power generation apparatus described in Patent Document 2 generates a bending deformation of the magnetostrictive rod while vibrating and requires a large excitation force from the vibration source to generate power, the vibration energy is not absorbed well and the power generation efficiency is low. There is a problem that the vibration is reduced, or excitation is not caused by external vibration in a direction orthogonal to the vibration direction of the weight.
そこで本発明は、従来の磁歪素子を用いた振動発電装置における下記の問題点を解決しようとするものである。すなわち、
(1)効率よく発電できる振動源の周波数範囲が狭く、特定の共振周波数から離れた振動では発電効率が低下する。
(2)加振力が小さい振動源では、磁歪素子内部に発生する伸縮ひずみが小さいため、発電効率が低い。
(3)錘の振動方向に沿った外部振動のみに励振され、錘の振動方向に直交する外部振動に対しては発電効率が低い。
Accordingly, the present invention is intended to solve the following problems in a vibration power generator using a conventional magnetostrictive element. That is,
(1) The frequency range of the vibration source capable of generating power efficiently is narrow, and the power generation efficiency is reduced when the vibration is away from a specific resonance frequency.
(2) In a vibration source with a small excitation force, the power generation efficiency is low because the expansion and contraction strain generated inside the magnetostrictive element is small.
(3) Only the external vibration along the vibration direction of the weight is excited, and the power generation efficiency is low for the external vibration perpendicular to the vibration direction of the weight.
上記課題を解決するために本発明は、2本の棒状の磁歪部材を錘体に対して回転自由度を確保する部材を介して固定し、前記2本の磁歪部材がなす角度が概略直線状になるように2本の磁歪部材の片端を支持台に対して同じく回転自由度を確保する部材を介して固定する。外部振動によって錘体が左右に振動すると、前記磁歪部材の張力が変動し磁歪部材のひずみが変化することに伴い、前記磁歪部材を通過する磁束密度も変化するため逆磁歪効果により誘導起電力がコイルの両端に発生することで発電を行うようにしたものである。 In order to solve the above-mentioned problems, the present invention fixes two rod-shaped magnetostrictive members to a weight body via a member that secures a degree of freedom of rotation, and the angle formed by the two magnetostrictive members is approximately linear. Then, one end of the two magnetostrictive members is fixed to the support base through a member that ensures the same degree of freedom of rotation. When the weight body vibrates left and right due to external vibration, the tension of the magnetostrictive member varies and the strain of the magnetostrictive member changes, so that the density of magnetic flux passing through the magnetostrictive member also changes. Electric power is generated by generating at both ends of the coil.
より具体的に示せば、請求項1に記載の発明は、振動源から振動を受ける支持台と、磁歪材料で構成された2本の棒状の磁歪部材と、該磁歪部材の間に連結されて振動する錘体と、前記磁歪部材に接続してループ状の磁気回路を構成するための棒状又は円筒状の磁性部材と、前記磁気回路にバイアス磁場を供給する永久磁石と、前記磁気回路に鎖交するように巻かれた磁気コイルで構成された振動電力変換手段とを備え、前記2本の磁歪部材を前記錘体に対して回転自由度を確保する部材を介して固定し、前記2本の磁歪部材が概略直線状となるように前記2本の磁歪部材の片端を前記支持台に対して回転自由度を確保する部材を介して固定し、前記錘体の振動に伴って前記振動電力変換手段の前記磁歪部材が伸張または収縮することにより発電することを特徴とするものである。 More specifically, the invention according to claim 1 is configured such that a support base that receives vibration from a vibration source, two rod-shaped magnetostrictive members made of a magnetostrictive material, and the magnetostrictive member are connected to each other. A vibrating weight body, a rod-shaped or cylindrical magnetic member connected to the magnetostrictive member to form a loop-shaped magnetic circuit, a permanent magnet for supplying a bias magnetic field to the magnetic circuit, and a chain connected to the magnetic circuit Vibration power conversion means composed of magnetic coils wound so as to intersect with each other, and the two magnetostrictive members are fixed to the weight body via a member that ensures a degree of freedom of rotation. One end of the two magnetostrictive members is fixed via a member that secures a degree of freedom of rotation with respect to the support base so that the magnetostrictive members are substantially linear, and the vibration power is accompanied by vibration of the weight body. When the magnetostrictive member of the converting means expands or contracts It is characterized in that conductive.
また、請求項2に記載の発明は、請求項1に記載の発明において、前記振動電力変換手段は、前記磁歪部材と前記錘体とからなる振動部分の全長が、前記支持台の2箇所の固定位置の間隔よりわずかに長く、前記支持台と前記磁歪部材との前記2箇所の固定位置を結ぶ中心軸と前記磁歪部材とがなす角度が0度より大きく5度より小さくされていることを特徴とするものである。 According to a second aspect of the present invention, in the first aspect of the present invention, the vibration power converting means is configured such that the vibration portion composed of the magnetostrictive member and the weight body has two total lengths of the support base. It is slightly longer than the interval between the fixed positions, and the angle formed between the central axis connecting the two fixed positions of the support base and the magnetostrictive member and the magnetostrictive member is larger than 0 degree and smaller than 5 degrees. It is a feature.
また、請求項3に記載の発明は、請求項1に記載の発明において、前記振動電力変換手段は、前記磁歪素子には主として圧縮力が作用するように、前記磁歪部材の両端に加わる張力を前記磁歪部材の内部で反転させて前記磁歪素子に伝達する構造を備えていることを特徴とするものである。 According to a third aspect of the present invention, in the first aspect of the present invention, the vibration power converting means applies a tension applied to both ends of the magnetostrictive member so that a compressive force mainly acts on the magnetostrictive element. The magnetostrictive member has a structure in which the magnetostrictive member is inverted and transmitted to the magnetostrictive element.
また、請求項4に記載の発明は、請求項1に記載の発明において、前記振動電力変換手段には、前記錘体の周囲に円環状、円筒状または複数の突起物からなる振幅制限手段が配置されていることを特徴とするものである。 According to a fourth aspect of the present invention, in the first aspect of the present invention, the vibration power converting means includes an amplitude limiting means including an annular shape, a cylindrical shape, or a plurality of protrusions around the weight body. It is characterized by being arranged.
また、請求項5に記載の発明は、請求項4に記載の発明において、前記振幅制限手段が、円環又は円筒状であるとともに前記振幅制限手段が1箇所以上の突起を前記錘体と接触する面に備えるか、または、前記振幅制限手段が複数の突起からなるとともに前記支持台の固定点を結ぶ中心軸からの距離が異なる突起を1つ以上備えることを特徴とするものである。 The invention according to claim 5 is the invention according to claim 4, wherein the amplitude limiting means is an annular shape or a cylindrical shape, and the amplitude limiting means contacts one or more protrusions with the weight body. Or the amplitude limiting means includes one or more protrusions having a plurality of protrusions and different distances from a central axis connecting the fixing points of the support base.
また、請求項6に記載の発明は、請求項1に記載の発明において、前記振動電力変換手段は、前記磁歪部材を概略水平方向となるように配置するとともに前記錘体を弾性体で吊り下げることで重力による前記錘体の垂下を打ち消し、外部振動が無い場合の前記錘体の初期位置を前記中心軸上に保持させることを特徴とするものである。 According to a sixth aspect of the present invention, in the first aspect of the present invention, the vibration power converting means arranges the magnetostrictive member in a substantially horizontal direction and suspends the weight body with an elastic body. Thus, the drooping of the weight body due to gravity is canceled, and the initial position of the weight body when there is no external vibration is held on the central axis.
本発明によれば、広い周波数範囲にわたる外部振動で高い発電効率が得られる振動発電装置を得ることが可能となる。
また磁歪素子は曲げ変形のように断面で応力分布が均等でない(圧縮力と引張応力が混在する)場合には、逆磁歪効果が打ち消しあって発電効率が低下するが、本発明では磁歪素子の長さ方向にのみ力が作用して均等に近い応力分布が得られるため、応力分布に起因する発電効率の低下は原理的に殆ど発生しないため発電効率を上げることができる。
ADVANTAGE OF THE INVENTION According to this invention, it becomes possible to obtain the vibration electric power generating apparatus from which high power generation efficiency is acquired with the external vibration over a wide frequency range.
In addition, when the magnetostrictive element has a non-uniform stress distribution in the cross section like bending deformation (mixed compressive force and tensile stress), the inverse magnetostrictive effect cancels out and the power generation efficiency decreases. Since a force acts only in the length direction and a nearly uniform stress distribution is obtained, a decrease in power generation efficiency due to the stress distribution hardly occurs in principle, so that the power generation efficiency can be increased.
更に本発明では、錘体は支持台の固定点を結ぶ中心軸方向には殆ど振動できないが、中心軸に直交する任意の方向に振動することができるため、高い発電効率が得られる。従来技術では、錘体の振動に沿った1軸方向の外部振動に対してある程度高い発電効率が得られるが、本発明では2軸方向の外部振動に対して高い発電効率が得られるため、1個の振動発電装置で従来技術より外部振動を有効利用することが可能となる。 Furthermore, in the present invention, the weight body can hardly vibrate in the direction of the central axis connecting the fixed points of the support base, but can vibrate in any direction orthogonal to the central axis, so that high power generation efficiency can be obtained. In the prior art, a certain high power generation efficiency is obtained with respect to external vibration in one axial direction along the vibration of the weight body. However, in the present invention, high power generation efficiency is obtained with respect to external vibration in two axial directions. It is possible to effectively use external vibration with a single vibration power generation device as compared with the prior art.
以下、本発明の実施の形態について、詳細に説明する。
本発明の実施形態を説明する前に、本発明の基本的概念について図9を用いて説明する。図9では振動発電装置を構成する磁石、ヨーク、コイルなどの部品を図示の簡略化のために示していない。磁歪部材(磁歪素子)の両端の固定点は、自由に回転できる部材(ボールジョイント、ユニバーサルジョイント、吊り金具など)で固定する。外部振動によって錘体が左右に振動すると、磁歪部材の張力が変動し磁歪部材のひずみが変化することに伴い、逆磁歪効果により磁歪部材(磁歪素子)を通過する磁束密度も変化するため誘導起電力がコイル(図示省略)の両端に発生することで発電を行う。
Hereinafter, embodiments of the present invention will be described in detail.
Before describing the embodiment of the present invention, the basic concept of the present invention will be described with reference to FIG. In FIG. 9, parts such as a magnet, a yoke, and a coil constituting the vibration power generation apparatus are not shown for the sake of simplicity of illustration. Fixing points at both ends of the magnetostrictive member (magnetostrictive element) are fixed by a freely rotatable member (such as a ball joint, a universal joint, or a hanging metal fitting). When the weight body vibrates from side to side due to external vibration, the tension of the magnetostrictive member changes and the strain of the magnetostrictive member changes, and the magnetic flux density passing through the magnetostrictive member (magnetostrictive element) also changes due to the inverse magnetostrictive effect. Electric power is generated by generating electric power at both ends of a coil (not shown).
より具体的に説明すれば、図9において錘体を質量 m (スカラー量を表すので実際は斜体文字)の質点とみなし、錘の位置ベクトルを x (ベクトル量を表すので実際は太文字)とすれば、支持台と相対速度0で運動する観測者からみた錘体の運動方程式は、下記式(1)のように表される。 More specifically, in FIG. 9, if the weight is regarded as a mass point of mass m (actually italic letters because it represents a scalar quantity), and the weight position vector is x (actually bold because it represents a vector quantity). The equation of motion of the weight body seen from the support table and the observer moving at a relative speed of 0 is expressed as the following equation (1).
なお、U(x)(ベクトル量を表すので実際は太文字)は、固定点の位置ベクトルp1,p2から錘の位置ベクトルx に向かう単位ベクトルの平均値である。図9で水平方向以外の変位および減衰を無視し(y=z=c=0)(これらはスカラー量を表すので実際は斜体文字)、固定点の位置ベクトルp1およびp2と錘の位置ベクトルx がなす角をθ、x軸方向の単位ベクトルをexとすれば、 Note that U (x) (actually bold because it represents a vector quantity) is an average value of unit vectors from the fixed point position vectors p 1 and p 2 toward the weight position vector x. In FIG. 9, displacements and attenuations other than in the horizontal direction are ignored (y = z = c = 0) (these represent scalar quantities and are actually italic letters), and the fixed point position vectors p 1 and p 2 and the weight position vector If the angle formed by x is θ and the unit vector in the x-axis direction is e x ,
(イ)振幅が小さいほど低い周波数で共振する(θ→0のとき、f→0)(fはスカラー量を表すので実際は斜体文字)
(ロ)角度θが増加するにつれて共振周波数が高くなる(最大値√(2k/m))(k,mはスカラー量を表すので実際は斜体文字)
上記(イ)の効果により、非常に低い周波数でも小さい振幅で共振することがわかる。また上記(ロ)の効果により周波数に応じて振幅と共振周波数が変化するため、広い範囲の周波数で励振することが可能である。
(B) Resonance at a lower frequency as the amplitude is smaller (when θ → 0, f → 0).
(B) The resonance frequency increases as the angle θ increases (maximum value √ (2k / m)) (k and m represent scalar quantities, so they are actually italic letters)
It can be seen that the effect (a) resonates with a small amplitude even at a very low frequency. Further, since the amplitude and the resonance frequency change according to the frequency due to the effect (b), excitation can be performed in a wide range of frequencies.
通常のバネ−錘系では共振周波数は√(k/m)(k,mはスカラー量を表すので実際は斜体文字)で変化しないため、共振周波数を小さくするには、k (スカラー量を表すので実際は斜体文字)を小さくする(柔らかいバネを使う)か、m (スカラー量を表すので実際は斜体文字)を大きくする(錘を重くする)ことが必要だが、本発明では低周波数でもθが小さくなることで自動的に共振する。また外部振動の周波数が一定である場合、上記式(6)の共振周波数で決まるθより振動が大きくなると共振しなくなるため、装置の破壊につながる無制限な振幅の増大が生じないという効果を有する。 In a normal spring-weight system, the resonance frequency does not change with √ (k / m) (k, m represents a scalar quantity, so it is actually an italic character), so to reduce the resonance frequency, k (scalar quantity) Actually, it is necessary to reduce (use italic letters) (use a soft spring) or increase m (actually italic letters because it represents a scalar quantity) (heavier weight), but in the present invention θ is reduced even at low frequencies. Automatically resonates. Further, when the frequency of the external vibration is constant, resonance does not occur when the vibration becomes larger than θ determined by the resonance frequency of the above formula (6), so that there is an effect that an unlimited increase in amplitude leading to destruction of the apparatus does not occur.
さらに本発明の構造では、磁歪部材が錘体に及ぼす力のうち、図9の上下方向の成分が互いに打ち消しあって小さな振幅でも大きな力が発生するため、弱い振動から効果的に発電することができる。 Furthermore, in the structure of the present invention, among the forces exerted by the magnetostrictive member on the weight body, the vertical components in FIG. 9 cancel each other and a large force is generated even with a small amplitude, so that it is possible to generate power effectively from weak vibrations. it can.
[実施形態1]
図1は、本発明の第1の実施形態に係る振動発電装置の構成を示す図である。図1において、本発明の第1の実施形態に係る振動発電装置は、一例として、2本の磁歪部材(磁歪素子)1の間に錘体2を固定し、磁歪部材1の残りの端を支持台3に固定する。磁歪部材1を固定する部材としてボールジョイント4を用いて回転自由度を持たせるようにしている。磁歪部材1とボールジョイント4との間は、ねじ込み、溶接、拡散摩擦接合など任意の方法で強固に固定する。
[Embodiment 1]
FIG. 1 is a diagram illustrating a configuration of a vibration power generation apparatus according to a first embodiment of the present invention. In FIG. 1, the vibration power generation apparatus according to the first embodiment of the present invention includes, as an example, a weight body 2 fixed between two magnetostrictive members (magnetostrictive elements) 1, and the remaining end of the magnetostrictive member 1 is connected. Fix to the support 3. A ball joint 4 is used as a member for fixing the magnetostrictive member 1 to provide a degree of freedom of rotation. The magnetostrictive member 1 and the ball joint 4 are firmly fixed by an arbitrary method such as screwing, welding, or diffusion friction bonding.
回転自由度を有する部材としては、ボールジョイントやユニバーサルジョイント、吊り金具などを使用することができる。本実施形態で必要な特性は以下のとおりである。
(a)強い引張力を加えても変形が少ない。
(b)摩擦が少なく、滑らかに回転できる。
(c)長い期間が経過しても磨耗が少なく、ガタつきがない。
(d)張力だけでなく圧縮力も伝達できる(後述する第2の実施形態で必要となる)。
As a member having a degree of freedom of rotation, a ball joint, a universal joint, a hanging metal fitting, or the like can be used. The characteristics required in this embodiment are as follows.
(A) Even if a strong tensile force is applied, the deformation is small.
(B) There is little friction and it can rotate smoothly.
(C) Even after a long period of time, there is little wear and there is no backlash.
(D) Not only tension but also compressive force can be transmitted (necessary for the second embodiment described later).
ジョイントの接合面は潤滑油や潤滑性のある素材を使用して摩擦を軽減することが望ましく、ボールベアリングを使用するのも良い。
図1では、中心軸が垂直方向となるように描かれているが、本装置は、中心軸が水平方向になるように配置しても発電可能である。しかし重力により錘体が下方向に変位した状態で安定するため共振が生じにくくなる。このような横置きの場合でも、図12に示すように錘体2を弱いバネで吊り下げて重力を打ち消すことにより、縦置きの場合に近い発電特性を得ることができる。
It is desirable to reduce friction by using lubricating oil or a lubricious material for the joint surface of the joint, and a ball bearing may be used.
In FIG. 1, the central axis is drawn in the vertical direction, but this apparatus can generate power even when the central axis is arranged in the horizontal direction. However, resonance is less likely to occur because the weight is stabilized in a state where it is displaced downward due to gravity. Even in the case of such horizontal placement, power generation characteristics close to those in the case of vertical placement can be obtained by suspending the weight body 2 with a weak spring and canceling gravity as shown in FIG.
磁歪部材1の周囲に導線を巻いたコイル5を設置し、コイル5の外側に磁石6を配置する。磁石6の極性はN-S方向が中心軸に沿うようにする。磁石6の両端には磁性体(磁性部材)7を固定して、磁石6から磁歪部材1を通る磁気回路を形成する。磁石6としてはネオジウム、フェライトなど任意の永久磁石を用いることができる。磁性体(磁性部材)7としては鉄やその合金など任意の強磁性体を用いることができる。 A coil 5 in which a conducting wire is wound around the magnetostrictive member 1 is installed, and a magnet 6 is arranged outside the coil 5. The polarity of the magnet 6 is set so that the NS direction is along the central axis. A magnetic body (magnetic member) 7 is fixed to both ends of the magnet 6 to form a magnetic circuit passing from the magnet 6 through the magnetostrictive member 1. As the magnet 6, any permanent magnet such as neodymium or ferrite can be used. As the magnetic body (magnetic member) 7, an arbitrary ferromagnetic body such as iron or an alloy thereof can be used.
図1では、磁石6の長さとコイル5の長さをほぼ等しくしているが、磁気回路の磁束密度と磁石のコストを勘案して磁石6の長さを短くし、その代わりに磁性体(磁性部材)7を延長することもできる。実際にはコイル5の任意の場所から導線と接続端子により外部に電力を取り出すが、図1では導線や接続端子を省略している。 In FIG. 1, the length of the magnet 6 and the length of the coil 5 are substantially equal, but the length of the magnet 6 is shortened in consideration of the magnetic flux density of the magnetic circuit and the cost of the magnet. The magnetic member 7 can be extended. Actually, power is taken out from an arbitrary place of the coil 5 by a conducting wire and a connecting terminal, but the conducting wire and the connecting terminal are omitted in FIG.
磁性体(磁性部材)7のいずれか片方は磁歪部材1に固定するが、もう片方は磁歪部材1との間にわずかな隙間を開けて磁歪部材1の伸縮を妨げないようにする。同様にコイル5も磁歪部材1に固着させない。 Either one of the magnetic bodies (magnetic members) 7 is fixed to the magnetostrictive member 1, but the other is opened with a slight gap between the magnetostrictive member 1 so as not to prevent expansion and contraction of the magnetostrictive member 1. Similarly, the coil 5 is not fixed to the magnetostrictive member 1.
支持台3は高い剛性を持ち、変形しにくい材質と構造を選定する。この例ではステンレス(SUS304)の中空円筒としている。支持台3は実際には複数の部品から構成されるが、図1では部品の詳細については省略している。 The support 3 is selected from a material and a structure that have high rigidity and are difficult to deform. In this example, a hollow cylinder of stainless steel (SUS304) is used. The support base 3 is actually composed of a plurality of parts, but details of the parts are omitted in FIG.
上記した本発明の第1の実施形態における運動方程式(上述した式(2)参照)の数値解を図10に示している。図10の左側が加振から5秒後までの錘体の位置座標と磁歪部材の応力(引張応力が正の値)、右側が錘体のx−y座標の軌跡である。計算条件は磁歪部材φ2×50mm、錘体の質量0.2kg、減衰比1%、外部振動による加速度はF/m=(Fdir/|Fdir|)gGsin(2πft)で与え(Fdir:振動方向ベクトル、m:質量、g:重力加速度=9.80665[m2/s]、G:最大加速度、f:周波数[Hz]、t:時刻[s])(なお、m,g,G,f,tはスカラー量を表すので実際は斜体文字)、Fdir(振動方向ベクトル)は(1,1,0)で中心軸(Z軸)に直交する方向とした。 FIG. 10 shows a numerical solution of the equation of motion (see the above-described equation (2)) in the first embodiment of the present invention described above. The left side of FIG. 10 is a position coordinate of the weight body and the stress of the magnetostrictive member (tensile stress is a positive value) from 5 seconds after the vibration, and the right side is a locus of the xy coordinate of the weight body. Calculation conditions are magnetostrictive member φ2 × 50mm, weight 0.2kg, damping ratio 1%, acceleration by external vibration is given by F / m = (F dir / | F dir |) gGsin (2πft) (F dir : vibration Direction vector, m: mass, g: gravitational acceleration = 9.80665 [m 2 / s], G: maximum acceleration, f: frequency [Hz], t: time [s]) (m, g, G, f, Since t represents a scalar quantity, it is actually an italic character), and F dir (vibration direction vector) is (1,1,0) and a direction orthogonal to the central axis (Z axis).
図10Aは本発明の第1の実施形態に係る振動発電装置を説明するための運動方程式の数値解を示す図(その1)であり、外部振動の周波数3Hz、最大加速度0.3G、重力が -Z 方向(縦置き)の場合であって、最大応力振幅は14.7MPaとなった。図10Bは本発明の第1の実施形態に係る振動発電装置を説明するための運動方程式の数値解を示す図(その2)であり、周波数3Hz、最大加速度0.1Gの場合であって、最大応力振幅は9.9MPaとなり、最大加速度が1/3に低下しても応力振幅は2/3程度にしか低下しない。図10Cは本発明の第1の実施形態に係る振動発電装置を説明するための運動方程式の数値解を示す図(その3)であり、周波数1Hz、最大加速度0.3Gの場合であって、最大応力振幅は11.7MPaとなり、低い周波数でも発電可能であることが分かる。また周波数1Hzの外部振動より高い周波数で応力が変化しているため、低周波数でも高い発電出力が得られる。 FIG. 10A is a diagram (part 1) illustrating a numerical solution of an equation of motion for explaining the vibration power generation apparatus according to the first embodiment of the present invention. The frequency of external vibration is 3 Hz, the maximum acceleration is 0.3 G, and gravity is − In the case of the Z direction (vertical placement), the maximum stress amplitude was 14.7 MPa. FIG. 10B is a diagram (part 2) illustrating a numerical solution of the equation of motion for explaining the vibration power generation apparatus according to the first embodiment of the present invention, in the case of a frequency of 3 Hz and a maximum acceleration of 0.1 G, and the maximum The stress amplitude is 9.9 MPa, and even if the maximum acceleration is reduced to 1/3, the stress amplitude is only reduced to about 2/3. FIG. 10C is a diagram (part 3) illustrating a numerical solution of the equation of motion for explaining the vibration power generation apparatus according to the first embodiment of the present invention, in the case where the frequency is 1 Hz and the maximum acceleration is 0.3 G, and the maximum The stress amplitude is 11.7 MPa, indicating that power generation is possible even at low frequencies. Moreover, since the stress changes at a higher frequency than the external vibration with a frequency of 1 Hz, a high power generation output can be obtained even at a low frequency.
図10Dは本発明の第1の実施形態に係る振動発電装置を説明するための運動方程式の数値解(横置き)を示す図(その4)であり、図10Aと同じ外部振動で水平配置した場合であって、-Y 方向の重力が外部振動より強いため、錘体はx=0mm、y=-1mm付近でほぼ安定するため、最大応力振幅は4.2MPaと垂直配置の場合の1/4程度に低下する。横置きでの発電効率を高めるには、重力による錘体の垂下を防ぐための図12に示すように錘体を弱いバネで吊り下げる構成を採用することが望ましい。この方法を採用すれば重力の影響がなくなるため、図10Aと同等の最大応力振幅が得られる。 FIG. 10D is a view (No. 4) showing a numerical solution (horizontal placement) of the equation of motion for explaining the vibration power generator according to the first embodiment of the present invention, and is horizontally arranged with the same external vibration as FIG. 10A. Since the gravity in the -Y direction is stronger than the external vibration, the weight is almost stable near x = 0mm and y = -1mm, so the maximum stress amplitude is 1 / 4MPa and 1/4 To a degree. In order to increase the power generation efficiency in the horizontal position, it is desirable to employ a configuration in which the weight body is suspended by a weak spring as shown in FIG. 12 for preventing the weight body from drooping due to gravity. If this method is adopted, the influence of gravity is eliminated, so that the maximum stress amplitude equivalent to that in FIG. 10A can be obtained.
[実施形態2]
図2は、本発明の第2の実施形態に係る振動発電装置の構成を示す図である。図2において、本発明の第2の実施形態に係る振動発電装置は、磁歪部材(磁歪素子)1と錘体2とからなる振動部分の全長が、支持台3の2箇所の固定位置の間隔よりわずかに長く、2本の磁歪部材1がなす角度が180度より小さくなる構造とする。
[Embodiment 2]
FIG. 2 is a diagram illustrating a configuration of a vibration power generation apparatus according to the second embodiment of the present invention. In FIG. 2, the vibration power generation device according to the second embodiment of the present invention is configured such that the entire length of the vibration portion composed of the magnetostrictive member (magnetostrictive element) 1 and the weight body 2 is an interval between two fixed positions of the support 3 The structure is slightly longer and the angle formed by the two magnetostrictive members 1 is smaller than 180 degrees.
この構造では、励振された錘体2が支持台3の2箇所の固定位置を結ぶ中心軸に接近すると、磁歪部材1には圧縮力が作用する。このため磁歪部材1に作用する応力振幅(圧縮力と引張応力の絶対値の合計)が大きくなり、発電出力が増加する。また、磁歪素子1の疲労破壊の原因となる最大引張応力が図1に示した構造より小さくなるため、磁歪部材1の耐久性が向上する。 In this structure, when the excited weight body 2 approaches the central axis connecting the two fixed positions of the support base 3, a compressive force acts on the magnetostrictive member 1. For this reason, the stress amplitude (the sum of absolute values of compressive force and tensile stress) acting on the magnetostrictive member 1 is increased, and the power generation output is increased. Further, since the maximum tensile stress that causes fatigue failure of the magnetostrictive element 1 is smaller than that shown in FIG. 1, the durability of the magnetostrictive member 1 is improved.
図9に示すように、錘体2の初期位置を(x0,0,0)(x0はスカラー量を表すので実際は斜体文字)とすると、望ましい角度範囲はx0/L(なお、x0,Lはスカラー量を表すので実際は斜体文字)が1〜3%となる範囲である(Lは磁歪部材1の無荷重時の長さ)(Lはスカラー量を表すので実際は斜体文字)。中心軸と磁歪部材1がなす角度をθとすると、θ=tan-1(x0/L)=0.5〜2.0度である(なお、x0,Lはスカラー量を表すので実際は斜体文字)。望ましい角度範囲は材質や構造により変化するが、最大でも5度程度が上限と考えられ。角度θが大きすぎると錘体2が中心軸付近に移動できなくなって発電効率が低下し、θが小さいと磁歪部材1に作用する圧縮応力が小さくなり実施形態1と同じになってしまう。 As shown in FIG. 9, when the initial position of the weight body 2 is (x 0 , 0,0) (x 0 represents a scalar quantity, so it is actually an italic character), the desired angle range is x 0 / L (where x 0 0 and L represent scalar quantities, so the actual italic letters) are in the range of 1 to 3% (L is the length of the magnetostrictive member 1 when no load is applied) (L is the italic letters because L represents the scalar quantity). Assuming that the angle formed by the central axis and the magnetostrictive member 1 is θ, θ = tan −1 (x 0 /L)=0.5 to 2.0 degrees (note that x 0 , L represents a scalar quantity, so it is actually an italic character). The desired angle range varies depending on the material and structure, but a maximum of about 5 degrees is considered the upper limit. If the angle θ is too large, the weight body 2 cannot move near the central axis and power generation efficiency is reduced, and if θ is small, the compressive stress acting on the magnetostrictive member 1 becomes small and becomes the same as in the first embodiment.
本実施形態における運動方程式(上述した式(2))の数値解を図11に示している。計算条件は図10に示したのと同じに設定し、さらにx0/L(なお、x0,Lはスカラー量を表すので実際は斜体文字)は1.5%とした。 FIG. 11 shows a numerical solution of the equation of motion (formula (2) described above) in the present embodiment. The calculation conditions were set to be the same as those shown in FIG. 10, and x 0 / L (note that it is actually italic letters because x 0 and L represent scalar quantities) is 1.5%.
図11Aは本発明の第2の実施形態に係る振動発電装置を説明するための運動方程式の数値解を示す図(その1)であり、外部振動の周波数3Hz、最大加速度0.3G、重力がZ軸方向(縦置き)の場合であって、最大応力振幅は29.2MPaと図10Aの約2倍に増加し、圧縮応力(負の値)が生じることが分かる。 FIG. 11A is a diagram (part 1) illustrating a numerical solution of an equation of motion for explaining a vibration power generator according to a second embodiment of the present invention, in which the frequency of external vibration is 3 Hz, the maximum acceleration is 0.3 G, and the gravity is Z In the case of the axial direction (vertical placement), it can be seen that the maximum stress amplitude is 29.2 MPa, which is about twice as large as that in FIG. 10A, and compressive stress (negative value) is generated.
図11Bは本発明の第2の実施形態に係る振動発電装置を説明するための運動方程式の数値解を示す図(その2)であり、周波数1Hz、最大加速度0.1Gの場合であって、最大応力振幅は6.0MPaとなり、図10Bより低くなった。これは錘体2が円を描くように中心軸の周囲を回転するためであり、振幅制限用に突起を配置(図3、請求項5参照)してこうした回転運動を防ぐことで応力振幅を増加させることができる。 FIG. 11B is a diagram (part 2) illustrating a numerical solution of the equation of motion for explaining the vibration power generation apparatus according to the second embodiment of the present invention, in the case of a frequency of 1 Hz and a maximum acceleration of 0.1 G. The stress amplitude was 6.0 MPa, which was lower than that in FIG. 10B. This is because the weight body 2 rotates around the central axis so as to draw a circle, and by arranging a protrusion for limiting the amplitude (see FIG. 3 and claim 5), the stress amplitude can be reduced by preventing such rotational movement. Can be increased.
[実施形態3]
図3および図4は、本発明の第3の実施形態に係る振動発電装置の構成を示す図である。図3および図4において、本発明の第3の実施形態に係る振動発電装置は、金具8により磁歪部材1に作用する力の向きを反転させ、圧縮応力が加わるように構成している。このように構成することで、磁歪部材1には疲労破壊の要因となる引張応力が作用しなくなり、耐久性が向上する。磁歪部材1は固定ピン10で金具8に強固に固定(図4参照)され圧縮応力と引張応力の双方の力を受けるため、磁歪部材1と錘体2とからなる振動部分の全長を支持台3の2箇所の固定位置の間隔よりわずかに長く、また支持台3と磁歪部材1との前記2箇所の固定位置を結ぶ中心軸と磁歪部材1とがなす角度を0度より大きく5度より小さく構成する(請求項2参照)を同時に採用することも可能である。
[Embodiment 3]
3 and 4 are diagrams showing the configuration of the vibration power generator according to the third embodiment of the present invention. 3 and 4, the vibration power generation apparatus according to the third embodiment of the present invention is configured such that the direction of the force acting on the magnetostrictive member 1 is reversed by the metal fitting 8 so that compressive stress is applied. By comprising in this way, the tensile stress which becomes a factor of fatigue failure does not act on the magnetostrictive member 1, and durability improves. Since the magnetostrictive member 1 is firmly fixed to the metal fitting 8 by the fixing pin 10 (see FIG. 4) and receives both compressive stress and tensile stress, the entire length of the vibrating portion composed of the magnetostrictive member 1 and the weight body 2 is supported by the support base. 3 is slightly longer than the interval between the two fixed positions, and the angle formed between the central axis connecting the two fixed positions of the support base 3 and the magnetostrictive member 1 and the magnetostrictive member 1 is greater than 0 degree and greater than 5 degrees. It is also possible to adopt a small configuration (see claim 2) at the same time.
錘体2は、錘体外周リング2aに錘体ジョイントベース2cを入れた状態で錘体ジョイントカバー2bをねじ込むことにより、ボールジョイント4と一体化する。支持台筐体3aの内径を適切に設定することで、錘体2の振幅を制限することができる。 The weight body 2 is integrated with the ball joint 4 by screwing the weight joint cover 2b with the weight joint base 2c inserted into the weight outer ring 2a. By appropriately setting the inner diameter of the support base housing 3a, the amplitude of the weight body 2 can be limited.
また突起9aは図11Bのような回転運動を阻害するためのものである。支持台ジョイントカバー3bと支持台ジョイントベース3cはネジ11で支持台筐体3aに結合しているが、当然ながら他の方法で結合させても構わない。支持台スペーサ3dにはボールジョイント4の動きと支持台3全体の長さを調整する作用がある。 Further, the projection 9a is for inhibiting the rotational movement as shown in FIG. 11B. The support base joint cover 3b and the support base joint base 3c are coupled to the support base casing 3a with screws 11, but may be coupled by other methods. The support base spacer 3d has an effect of adjusting the movement of the ball joint 4 and the overall length of the support base 3.
[実施形態4]
図5および図6は、本発明の第4の実施形態に係る振動発電装置の構成を示す図である。図5および図6において、本発明の第4の実施形態に係る振動発電装置は、上記した本発明の第3の実施形態に係る振動発電装置と同様に、磁歪部材1に作用する力を反転させているが、磁歪部材1と磁性体(磁性部材)7を円筒状の入れ子構造とすることで、上記した本発明の第3の実施形態に係る振動発電装置よりも部品数が少なくなるようにしている。
[Embodiment 4]
5 and 6 are diagrams showing the configuration of the vibration power generator according to the fourth embodiment of the present invention. 5 and 6, the vibration power generation apparatus according to the fourth embodiment of the present invention reverses the force acting on the magnetostrictive member 1 in the same manner as the vibration power generation apparatus according to the third embodiment of the present invention described above. However, since the magnetostrictive member 1 and the magnetic body (magnetic member) 7 have a cylindrical nested structure, the number of components is smaller than that of the vibration power generation apparatus according to the third embodiment of the present invention described above. I have to.
また磁石6を上下に分割し、磁極の向きを中心軸から外側に向かう方向と内側に向かう方向にすることで、磁歪部材1から磁性体(磁性部材)7を通る磁気回路を形成する。磁石6が十分に強ければ片方の磁石を磁性体(磁性部材)7に置き換えることもできる。 Further, the magnet 6 is divided into upper and lower parts, and the magnetic poles are directed from the central axis toward the outside and toward the inside, thereby forming a magnetic circuit passing from the magnetostrictive member 1 to the magnetic body (magnetic member) 7. If the magnet 6 is sufficiently strong, one of the magnets can be replaced with a magnetic body (magnetic member) 7.
また金具8および磁歪部材1の内側にあるボールジョイント4からつながっている棒は、磁束が磁歪部材1以外の部分を通らないようにするため、ステンレスなど磁性のない金属(非磁性部材)とする必要がある。 Further, the rod connected from the metal joint 8 and the ball joint 4 inside the magnetostrictive member 1 is made of a non-magnetic metal such as stainless steel (nonmagnetic member) so that the magnetic flux does not pass through portions other than the magnetostrictive member 1. There is a need.
支持台筐体3aの形状は本実施形態4では直方体とし、振幅制限手段9として円形の穴を開けた板を内部に配置している。また突起9aは第3の実施形態と同様に錘体2の回転運動を防ぐためのものである(図5セクションC-C参照)。 In the fourth embodiment, the shape of the support base housing 3a is a rectangular parallelepiped, and a plate with a circular hole is disposed inside as the amplitude limiting means 9. Further, the projection 9a is for preventing the rotational movement of the weight body 2 as in the third embodiment (see section CC in FIG. 5).
[実施形態5]
図7および図8は、本発明の第5の実施形態に係る振動発電装置の構成を示す図である。図7および図8において、本発明の第5の実施形態に係る振動発電装置は、上記した本発明の第1及び第2の実施形態に係る振動発電装置と同様に、磁歪部材1には主に引張応力が作用する。磁歪部材1を円筒状にして内部にコイル5、磁石6、磁性体(磁性部材)7を収納することでコンパクトな振動発電部としたものである。
[Embodiment 5]
7 and 8 are diagrams showing the configuration of the vibration power generator according to the fifth embodiment of the present invention. 7 and 8, the vibration power generation apparatus according to the fifth embodiment of the present invention is mainly composed of the magnetostrictive member 1 like the vibration power generation apparatuses according to the first and second embodiments of the present invention described above. Tensile stress acts on. The magnetostrictive member 1 is formed into a cylindrical shape, and the coil 5, the magnet 6, and the magnetic body (magnetic member) 7 are accommodated therein, thereby forming a compact vibration power generation unit.
また回転自由度を有して固定可能とする部材としてユニバーサルジョイント4a,4bを用いている。錘体2を中央のユニバーサルジョイント軸4bに固定することでユニバーサルジョイントの総数は3個となり、ボールジョイントを用いた他の実施形態よりジョイント数を1個少なくすることができる(図8参照)。 The universal joints 4a and 4b are used as members that can be fixed with a degree of freedom of rotation. By fixing the weight body 2 to the central universal joint shaft 4b, the total number of universal joints becomes three, and the number of joints can be reduced by one as compared with other embodiments using ball joints (see FIG. 8).
本実施形態5では、支持台3を籠状として錘体2の振動状況を観察できるようにしている。支持台3は十分な剛性があれば任意の形状で良く、例えば、コの字型や上記した第3及び第4の実施形態の支持台を部分的にカットした形状とすることも可能である。 In the fifth embodiment, the support base 3 is shaped like a bowl so that the vibration state of the weight body 2 can be observed. The support base 3 may have any shape as long as it has sufficient rigidity. For example, a U-shape or a shape obtained by partially cutting the support bases of the third and fourth embodiments described above can be used. .
上述した本発明の振動発電装置をワイヤレスセンサの電源装置として適用することで、ワイヤレスセンサにおける電力供給に関する問題点を克服することが可能となる。ワイヤレスセンサは、振動を計測するセンセとして、高速道路や鉄道、建物、回転機などの構造ヘルスモニタリング用の振動センサや加速度センサ、タイヤ圧のモニタリングセンサ等に既に実用されている。 By applying the vibration power generation apparatus of the present invention described above as a power supply apparatus for a wireless sensor, it is possible to overcome problems related to power supply in the wireless sensor. Wireless sensors have already been put to practical use as vibration sensors for structural health monitoring such as highways, railways, buildings, and rotating machines, acceleration sensors, tire pressure monitoring sensors, and the like as sensors for measuring vibration.
1 磁歪部材(磁歪素子)
2 錘体
2a 錘体外周リング
2b 錘体ジョイントカバー
2c 錘体ジョイントベース
3 支持台
3a 支持台筐体
3b 支持台ジョイントカバー
3c 支持台ジョイントベース
3d 支持台スペース
4 ボールジョイント(回転自由度を確保する部材)
4a ユニバーサルジョイント継手
4b ユニバーサルジョイント軸
5 磁気コイル
6 磁石
7 磁性体(磁性部材)
8 金具(力の方向反転手段)
9 振幅制限手段
9a 突起
10 固定ピン
11 ネジ
12 バネ(弾性体)
1 Magnetostrictive member (magnetostrictive element)
2 Weight body 2a Weight body outer ring 2b Weight body joint cover 2c Weight body joint base 3 Support base 3a Support base housing 3b Support base joint cover 3c Support base joint base 3d Support base space 4 Ball joint (to ensure rotational freedom) Element)
4a Universal joint joint 4b Universal joint shaft 5 Magnetic coil 6 Magnet 7 Magnetic body (magnetic member)
8 Bracket (Force direction reversing means)
9 Amplitude limiting means 9a Protrusion 10 Fixing pin 11 Screw 12 Spring (elastic body)
Claims (6)
前記磁歪部材に接続してループ状の磁気回路を構成するための棒状又は円筒状の磁性部材と、前記磁気回路にバイアス磁場を供給する永久磁石と、前記磁気回路に鎖交するように巻かれた磁気コイルで構成された振動電力変換手段とを備え、
前記2本の磁歪部材を前記錘体に対して回転自由度を確保する部材を介して固定し、前記2本の磁歪部材が概略直線状となるように前記2本の磁歪部材の片端を前記支持台に対して回転自由度を確保する部材を介して固定し、前記錘体の振動に伴って前記振動電力変換手段の前記磁歪部材が伸張または収縮することにより発電することを特徴とする振動発電装置。 A support base that receives vibration from a vibration source, two rod-shaped magnetostrictive members made of a magnetostrictive material, and a weight that is connected between the magnetostrictive members to vibrate;
A rod-shaped or cylindrical magnetic member for connecting to the magnetostrictive member to form a loop-shaped magnetic circuit, a permanent magnet for supplying a bias magnetic field to the magnetic circuit, and a winding to be linked to the magnetic circuit Vibration power conversion means composed of a magnetic coil,
The two magnetostrictive members are fixed to the weight body via a member that secures a degree of freedom of rotation, and one end of the two magnetostrictive members is fixed so that the two magnetostrictive members are substantially linear. A vibration that is fixed to a support base via a member that secures a degree of freedom of rotation, and generates power when the magnetostrictive member of the vibration power conversion means expands or contracts with the vibration of the weight body. Power generation device.
The vibration power converting means arranges the magnetostrictive member in a substantially horizontal direction and suspends the weight body by an elastic body to cancel the drooping of the weight body due to gravity, and the weight when there is no external vibration The vibration power generation apparatus according to claim 1, wherein an initial position of a body is held on the central axis.
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