超导磁悬浮系统有限元数值分析及其在小型风力机中的应用
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摘要
第二类高温超导体的“钉扎效应”可以实现永磁铁在超导体之上的稳定悬浮。这种超导磁悬浮可以被用来制作磁悬浮列车、磁悬浮轴承、反重力场等装置。本论文主要探讨了YBCO超导体在磁悬浮轴承方面的应用。
永磁体和超导体相互作用会在超导体内感生出涡旋电流。但由于超导体是非线性材料,其电导率不是常数,这样就使得超导体内的电流分布计算十分困难。在数值分析过程中采用Kim及磁通蠕动流动模型来对超导体的电导率进行迭代。建立满足超导体的本构方程。
矢量电位法作为电磁场分析的辅助变量适合于分析材料的涡流场分布。在超导体和永磁铁相互作用的过程中,超导体内产生的感生涡旋电流可以采用矢量电位法,将涡旋电流场的分布转变为矢量电位的空间分布。在满足一定的边界条件下,建立超导体内所满足的矢量电位微分方程。
矢量电位微分方程的求解过程采用伽辽金有限元法。首先将矢量电位微分方程转化为积分方程。连续的积分方程再进行空间和时间的离散才能进行数值分析。根据圆柱体超导块材的轴对称性,可以将超导体块材的空间网格离散为二维平面的网格。在二维平面内采用三角单元将超导体截面划分为网格和单元,并对节点和单元进行编号。在每个单元内部采用线性形函数将单元内部任意点的矢量表达为该单元顶点矢量电位的线性插值。采用形函数作为加权余量也就是伽辽金法,形成单元内部矢量电位的线性方程组。
将各单元内部的矢量电位线性方程组进行总体合成形成整个剖面的整体线性方程组,解这个线性方程组就可以得到在某一时间的所有节点的矢量电位值。再将连续时间进行离散并考虑外磁场的变化速度,就可以得到对各时间点的矢量电位分布。外磁场采用有限元软件进行计算。
根据各点的矢量电位分布,可以求得各点的电流分布,进而计算出超导体和永磁体的相互作用力。实验结果表明,数值分析的结果与实验结果基本一致,但存在一定的偏差,这主要是由于超导体的参数多为未知量。
在零场冷状态下,永磁体下降从无限远处接近超导体,然后再返回到无限远处。这个过程会出现悬浮力的滞回现象。在同一悬浮位置悬浮力不是固定值,其值的大小与永磁体的运动历史有关。
在场冷状态下,永磁体会稳定的悬浮在超导体的上方。这个稳定悬浮位置,就成为整个系统能量的势阱。当永磁体受到外力作用偏移平衡位置时就会受到反向恢复力。这个恢复力的数值与磁场强度、磁场强度的梯度、悬浮高度、超导体和永磁体相对面积相关。在偏移不是很大的情况下永磁体的运动类似于阻尼振动的弹簧。采用数值分析的方法可以计算出振动的振幅,周期和衰减特性。
风能作为重要的清洁能源是未来能源的发展趋势。本文提出一种超导磁悬浮风力发电装置,并制作了实验模型。该实验模型包括由永磁铁、YBCO超导体构成的磁悬浮系统和由线圈、永磁铁构成的发电系统。由于轴承的无摩擦性在有风的时候可以采用风轮带动磁悬浮转子旋转实现风能向机械能的转换。在无风的情况下实现飞轮储能。相比传统的风力机具有能量利用率高等优点。
影响轴承转速的衰减因素主要由悬浮高度、空气阻力、磁滞阻尼损耗、涡流损耗、陀螺效应等。
将超导磁悬浮轴承用于风力机上,轴的稳定性是非常重要的因素,本文探讨了影响轴稳定的因素,并描述了应采取的方法。超导体的摆放方式、悬浮高度、转动速度、安装精度等都对轴的稳定有重要影响。
本文提出超导磁悬浮风力机大型化的模型。这种结构可以不受超导体尺寸的限制。
对超导磁悬浮系统在小型风力机中的应用将极大提高风能的利用效率,它将成为高效清洁能源家庭中的重要成员。
The flux pinning effect of the type-II superconductor can make a permanent magnet stable levitated on the superconductors. This levitation system can be used in making maglev trains, suspension bearings, antigravity field equipments and et, al. This paper mainly describes the application of YBCO superconductors in superconducting levitation bearings.
The eddy currents will be induced in the superconductors when the permanent magnet is moved close to the superconductors. Because the superconductor is non linear material which conductivity is not constant, it is very difficult to calculate the current distribution in the superconductors. The Kim model and field flux creep-flow model are adopted to establish the constructive equations of the superconductor.
The current vector potential is an important auxiliary variable in numerical analysis of eddy current field. Through this method, the current field is changed into current potential vector field. When the current potential vectors are subjected to some boundary conditions, the differential equation is established in the superconductor-permanent magnet system.
The differential equation of the current vector potential is solved by Galerkin finite element method. The differential equation is firstly changed into integral equation. The continuous integral equation is changed into discrete equation at time and space. According to axial symmetry, the space lattice of the cylinder superconductor can be transformed into 2D plane grids. The 2D plane is divided by triangular elements. The elements and nodes are given numbers. Any current vector potential of a point in an element can be expressed by the values of the nodes using linear interpolation method. Adopting the Galerkin method, the linear equations group is established in every element.
An integral linear equations group of whole superconductor is formed by assembling all the element equations. The current vector potential of every node can be calculated through solving this linear equation group. The current potential vector distribution is obtained. The external magnetic field is calculated by finite element method soft.
The current density distribution is calculated according to the current vector potential distribution. The interaction force between superconductor and permanent magnet can be known. The results of numerical analysis results are constant with the experimental results.
Under zero field cooling condition, the permanent magnet is moved to and from the superconductors between infinite distance and superconductors. In this procedure, the levitation force-displacement curve presents hysteretic phenomenon. At the same position, the levitation force value is relevant to the permanent moving history.
Under the field cooling condition, the permanent magnet can stably suspend on the superconductors. This stability position is the lowest energy of the whole system. When the external force is acted on the permanent magnet, the permanent magnet deviate from the balancing point, the restoring force will drag the permanent magnet to the original position. The value of the restoring force is relevant to magnetic flux density, magnetic field gradient, levitation height and relative area ratio between superconductors and permanent magnet. If the displacement of the deviation is small, the processing magnet presents a comparison to the spring with damping. Using numerical analysis method, the magnitude, frequency and damping factor can be calculated.
Wind energy source is a trend of pollution-free energy in the future. A new type wind drag generator model and its experimental instrument are discrebed in this paper The superconducting levitation system can be used in small wind-driven generator to generate electricity. Because of non-contact of the bearing; small wind can drive the generator to transform wind energy to mechanical energy. At no-wind time, the generator is a power storage flywheel. The utilization ratio of wind energy is larger than traditional wind generator.
The influencing factors of rotation losses include levitate height, aerodynamic losses, damping losses and eddy current losses and et, al.
The stability of the shaft is very important factor in levitating energy system. This paper discussed the influenceing factors of the stability of the shaft and gave some advice to solve this problem. The arrangement of the superconductors, levitate height, rotational speed and installation accuracy are important for the stability of the shaft.
A new large-scale superconducting levitation model is presented in this paper. This model is not limited by the size of superconductors.
The superconducting levitation system is used in small wind-driven generators can increase largely efficiency of wind-drag generator. It must be a new important member in clear energy sources in the future.
永磁体和超导体相互作用会在超导体内感生出涡旋电流。但由于超导体是非线性材料,其电导率不是常数,这样就使得超导体内的电流分布计算十分困难。在数值分析过程中采用Kim及磁通蠕动流动模型来对超导体的电导率进行迭代。建立满足超导体的本构方程。
矢量电位法作为电磁场分析的辅助变量适合于分析材料的涡流场分布。在超导体和永磁铁相互作用的过程中,超导体内产生的感生涡旋电流可以采用矢量电位法,将涡旋电流场的分布转变为矢量电位的空间分布。在满足一定的边界条件下,建立超导体内所满足的矢量电位微分方程。
矢量电位微分方程的求解过程采用伽辽金有限元法。首先将矢量电位微分方程转化为积分方程。连续的积分方程再进行空间和时间的离散才能进行数值分析。根据圆柱体超导块材的轴对称性,可以将超导体块材的空间网格离散为二维平面的网格。在二维平面内采用三角单元将超导体截面划分为网格和单元,并对节点和单元进行编号。在每个单元内部采用线性形函数将单元内部任意点的矢量表达为该单元顶点矢量电位的线性插值。采用形函数作为加权余量也就是伽辽金法,形成单元内部矢量电位的线性方程组。
将各单元内部的矢量电位线性方程组进行总体合成形成整个剖面的整体线性方程组,解这个线性方程组就可以得到在某一时间的所有节点的矢量电位值。再将连续时间进行离散并考虑外磁场的变化速度,就可以得到对各时间点的矢量电位分布。外磁场采用有限元软件进行计算。
根据各点的矢量电位分布,可以求得各点的电流分布,进而计算出超导体和永磁体的相互作用力。实验结果表明,数值分析的结果与实验结果基本一致,但存在一定的偏差,这主要是由于超导体的参数多为未知量。
在零场冷状态下,永磁体下降从无限远处接近超导体,然后再返回到无限远处。这个过程会出现悬浮力的滞回现象。在同一悬浮位置悬浮力不是固定值,其值的大小与永磁体的运动历史有关。
在场冷状态下,永磁体会稳定的悬浮在超导体的上方。这个稳定悬浮位置,就成为整个系统能量的势阱。当永磁体受到外力作用偏移平衡位置时就会受到反向恢复力。这个恢复力的数值与磁场强度、磁场强度的梯度、悬浮高度、超导体和永磁体相对面积相关。在偏移不是很大的情况下永磁体的运动类似于阻尼振动的弹簧。采用数值分析的方法可以计算出振动的振幅,周期和衰减特性。
风能作为重要的清洁能源是未来能源的发展趋势。本文提出一种超导磁悬浮风力发电装置,并制作了实验模型。该实验模型包括由永磁铁、YBCO超导体构成的磁悬浮系统和由线圈、永磁铁构成的发电系统。由于轴承的无摩擦性在有风的时候可以采用风轮带动磁悬浮转子旋转实现风能向机械能的转换。在无风的情况下实现飞轮储能。相比传统的风力机具有能量利用率高等优点。
影响轴承转速的衰减因素主要由悬浮高度、空气阻力、磁滞阻尼损耗、涡流损耗、陀螺效应等。
将超导磁悬浮轴承用于风力机上,轴的稳定性是非常重要的因素,本文探讨了影响轴稳定的因素,并描述了应采取的方法。超导体的摆放方式、悬浮高度、转动速度、安装精度等都对轴的稳定有重要影响。
本文提出超导磁悬浮风力机大型化的模型。这种结构可以不受超导体尺寸的限制。
对超导磁悬浮系统在小型风力机中的应用将极大提高风能的利用效率,它将成为高效清洁能源家庭中的重要成员。
The flux pinning effect of the type-II superconductor can make a permanent magnet stable levitated on the superconductors. This levitation system can be used in making maglev trains, suspension bearings, antigravity field equipments and et, al. This paper mainly describes the application of YBCO superconductors in superconducting levitation bearings.
The eddy currents will be induced in the superconductors when the permanent magnet is moved close to the superconductors. Because the superconductor is non linear material which conductivity is not constant, it is very difficult to calculate the current distribution in the superconductors. The Kim model and field flux creep-flow model are adopted to establish the constructive equations of the superconductor.
The current vector potential is an important auxiliary variable in numerical analysis of eddy current field. Through this method, the current field is changed into current potential vector field. When the current potential vectors are subjected to some boundary conditions, the differential equation is established in the superconductor-permanent magnet system.
The differential equation of the current vector potential is solved by Galerkin finite element method. The differential equation is firstly changed into integral equation. The continuous integral equation is changed into discrete equation at time and space. According to axial symmetry, the space lattice of the cylinder superconductor can be transformed into 2D plane grids. The 2D plane is divided by triangular elements. The elements and nodes are given numbers. Any current vector potential of a point in an element can be expressed by the values of the nodes using linear interpolation method. Adopting the Galerkin method, the linear equations group is established in every element.
An integral linear equations group of whole superconductor is formed by assembling all the element equations. The current vector potential of every node can be calculated through solving this linear equation group. The current potential vector distribution is obtained. The external magnetic field is calculated by finite element method soft.
The current density distribution is calculated according to the current vector potential distribution. The interaction force between superconductor and permanent magnet can be known. The results of numerical analysis results are constant with the experimental results.
Under zero field cooling condition, the permanent magnet is moved to and from the superconductors between infinite distance and superconductors. In this procedure, the levitation force-displacement curve presents hysteretic phenomenon. At the same position, the levitation force value is relevant to the permanent moving history.
Under the field cooling condition, the permanent magnet can stably suspend on the superconductors. This stability position is the lowest energy of the whole system. When the external force is acted on the permanent magnet, the permanent magnet deviate from the balancing point, the restoring force will drag the permanent magnet to the original position. The value of the restoring force is relevant to magnetic flux density, magnetic field gradient, levitation height and relative area ratio between superconductors and permanent magnet. If the displacement of the deviation is small, the processing magnet presents a comparison to the spring with damping. Using numerical analysis method, the magnitude, frequency and damping factor can be calculated.
Wind energy source is a trend of pollution-free energy in the future. A new type wind drag generator model and its experimental instrument are discrebed in this paper The superconducting levitation system can be used in small wind-driven generator to generate electricity. Because of non-contact of the bearing; small wind can drive the generator to transform wind energy to mechanical energy. At no-wind time, the generator is a power storage flywheel. The utilization ratio of wind energy is larger than traditional wind generator.
The influencing factors of rotation losses include levitate height, aerodynamic losses, damping losses and eddy current losses and et, al.
The stability of the shaft is very important factor in levitating energy system. This paper discussed the influenceing factors of the stability of the shaft and gave some advice to solve this problem. The arrangement of the superconductors, levitate height, rotational speed and installation accuracy are important for the stability of the shaft.
A new large-scale superconducting levitation model is presented in this paper. This model is not limited by the size of superconductors.
The superconducting levitation system is used in small wind-driven generators can increase largely efficiency of wind-drag generator. It must be a new important member in clear energy sources in the future.
引文
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55. J. Ogawa, M. Iwamoto. Interaction between trapped magnetic field and AC loss in HTS bulk[J], Physica C,2002,372-376:1754-1757
56. T. Sugiura, T. Inoue. Nonlinear vibration of a coupled high-Tc superconducting levitation system[J], Physica C,2004,412-414:778-783
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70..韩羽中,李艳,余江.超导电力磁储能系统研究进展(一)：超导储能装置[J],电力系统自动化,2001,25(12)：63-68
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77. Y. Komano. Numerical simulation of levitation force and magnetic field in levitated bulk superconductor[J], Physica C,2004,412-414:729-733
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91.梁振光,杨志坚.基于T-TO-Q的三维有限元法及电力变压器计算[J].高压电工技术,2006,32(2)：18-20.
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