Quench characteristics and mechanical responses during quench propagation in rare earth barium copper oxide pancake coils

Quench and mechanical behaviors are critical issues in high temperature superconducting(HTS)coils.In this paper,the quench characteristics in the rare earth barium copper oxide(REBCO)pancake coil at 4.2K are analyzed,and a two-dimensional(2D)axisymmetric electro-magneto-thermal model is presented.The effects of the constituent materials,background field,and coil size are analyzed.An elastoplastic mechanical model is used to study the corresponding mechanical responses during the quench propagation.The variations of the temperature and strain in superconducting layers are compared.The results indicate that the radial strain evolutions can reflect the transverse quench propagation and the tensile hoop and radial stresses in superconducting layers increase with the quench propagation.The possible damages are discussed with the consideration of the effects of the background field and coil size.It is concluded that the high background field significantly increases the maximum tensile hoop and radial stresses in quenching coils and local damage may be caused.     

Nb3Sn超导线圈力学性能精确分析的双向均质化方法

Nb₃Sn超导磁体运行时产生很高磁场, Nb₃Sn超导线圈会受到很强电磁体力的作用, 从而会产生很大的力学应变. 由于Nb₃Sn超导材料的应变敏感性, 会使得Nb₃Sn磁体线圈的临界性能退化, 这对磁体的安全稳定运行造成极大影响, 所以精确计算超导磁体在电磁体力下的力学行为具有重要的科学意义. Nb₃Sn超导磁体主要是由超导线绕制成线圈结构再经过环氧树脂固化而成, Nb₃Sn超导线是主要由多根微米级的超导芯丝、铜形成的复合结构, 所以从超导芯丝到超导磁体其尺寸跨越了几个数量级, 从而给精确分析超导线圈力学变形带来挑战. 本文首先采用代表性单元均质化方法分析了整体线圈的等效力学参数, 通过对比等效均质化模型与线圈真实结构的计算结果, 发现等效均质化模型存在很大的误差. 因此, 提出一种高精度而且计算代价低的双向均质化分析方法, 研究超导线圈内各组分材料(Nb₃Sn芯丝、铜和环氧树脂)应力-应变分布. 该方法不需要进行大规模的数值建模, 并且与真实复合线圈下的结果对比吻合很好, 由此验证了该方法的有效性和准确性. 最后基于提出的双向均质化分析方法, 详细讨论了Nb₃Sn超导线圈各层材料在电磁力作用下应力-应变随匝数和层数的变化规律.      

超导磁体等效材料参数的有限元预测

HT—7U超导托卡马克装置中纵场超导磁体是由多种材料组成的且具有周期性分布的大型复杂的重要结构，对其宏观等效材料参数的准确掌握在其结构设计阶段是十分重要的。本文着重介绍了利用小参数展开的渐近均匀化方法对其进行等效处理的过程，并采用有限元方法预测出其等效弹性模量与热膨胀系数等，这些都为纵场磁体结构的力学计算与传热分析提供了必要的参数。     

高温超导带材超导涂层局部脱黏后的电磁力学行为分析

高温超导带材因其高载流z能力、低交流损耗等优点, 在超导领域得到了广泛的关注, 然而在带材的应用中出现的力学问题严重阻碍了其应用. 基于此, 本文分析了受外部磁场激励YBCO高温超导带材在超导层局部脱黏后的电磁力学响应. 基于超导临界态Bean模型和弹性力学平面应变方法, 给出了超导薄膜内正应力与基底界面处切应力相关联的控制方程, 基于数值方法研究了超导薄膜内的正应力及基底界面处的切应力随外部磁场的变化规律. 结果显示: 在脱黏区域附近, 超导薄膜内的正应力和基底$\!-\!$薄膜界面处的切应力急剧增大, 该正应力及切应力极易引起超导层的进一步脱黏. 同时, 剪切应力在结构边缘处出现极值. 基底材料的属性, 特别是杨氏模量对结构内的应力影响显著, 在软基底材料结构中, 超导薄膜内将出现较大的正应力, 而基底材料较硬时, 在基底$\!-\!$薄膜界面处将出现较大的剪切应力, 这些因素均会引起超导涂层结构的力学及电学性能的退化. 本文研究可望为超导带材的加工制备及脱黏的处理提供一定的理论指引.      

高温超导带材多场特性测试系统研制进展(Ⅰ)

高温超导带材具有高的临界电流密度,高磁场下优异的载流特性以及良好的成型性在强电领域如高场磁体、超导电缆等方面应用潜力巨大。在其应用过程中,不可避免的低温-大电流-强磁场环境将对超导材料的载流能力产生影响,而加工过程中的残余应力以及洛伦兹力的存在会显著的降低超导材料的临界电流,造成相应超导装置功能性难以达到设计要求、且成为重要的安全隐患。本文介绍一种新型的适用于超导带材的力-磁-电多场耦合测试系统,该系统目前采用浸泡式制冷,可实现的主要功能有:(1)超导材料临界电流密度测试;(2)拉伸应变对超导带材临界电流的影响研究;(3)磁场对超导带材临界电流的影响研究;(4)力磁耦合情形下超导材料临界电流的变化规律;(5)超导材料磁通稳定性测试。该设备的成功研制将为我国先进超导材料研发提供基础测试平台。     

Analytic calculation of magnetic force between two current-carrying coils

Current-carrying coils are basic elements in electromagnetic equipments, for example, in high field magnets from high temperature superconducting wires or tapes. In the assembly of these systems and their current-carrying operation, unavoidable mis-alignment and shift from the original position can be induced by disturbances such as the imbalance of magnetic force due to safety problems. For two current-carrying coils with non-coplanar axes, the analytic expression of the magnetic force between the two coils is presented according to the rule of Ampere circulation and the Biot-Savart law. Based on the expression, the dependence of the magnetic force on the size and the relative position of each other is further investigated, and the variation of the magnetic force is obtained with the above parameters.     

高温超导带材多场特性测试系统研制进展(Ⅱ)

考虑到第一代高温超导带材多场特性测试系统采用液氮浸泡的方式进行材料冷却,这极大地限制了其应用范围。另外,封闭的杜瓦结构对于超导材料在变形过程中的电磁特征难以实现有效观测,这成为弄清超导材料变形导致其载流能力下降物理机制的主要瓶颈。为此,我们采用制冷机直接冷却方式,获得了最低6.59K的样品温度。采用PID温度控制,实现了从6.59K至300K样品温度的精确控制,控温精度为0.1K。采用外置式的加载装置,通过机械传动实现对试样的准静态拉伸,其最大拉伸应变可达20%。自行设计了一种高温超导导线,采用制冷机一级冷头直接冷却,实现了密闭杜瓦容器中最大可达600A的电流输入。最后,在杜瓦瓶设置直径50mm的光学观察窗,采用磁光镜像的方法实现了超导材料电磁特性的原位观测。     

Bending and buckling of superconducting partial toroidal field coils

Based on the theory of curved beams and the Biot–Savart law, a new theoretical model for magnetoelastic bending and buckling of superconducting toroidal field coils is developed and corroborated numerically. In contrast to the existing models, this model incorporates in-plane deformation of the coil. A semi-analytical approach is used to obtain the solution to the coupled problem. In order to validate the model and associated solution method, the experiment of Miya et al., 1982 is modeled. The theoretical predictions of the critical current of coils with none or one pin support are shown to be in excellent agreement with the published experimental data. It is also shown that the in-plane deformation has a significant influence on the critical current.     

HT-7U超导托卡马克装置极向场线圈的等效弹性常数及其残余刚度

HT－7装置的超导极向场线圈由导管，超导材料和绝缘体组合而成，具有复杂的正交各向异性的性质。本文从微观力学的观点出发，将极向场线圈整体作为一种复合材料来考虑，采用微观力学的复合律和损伤力学的细观损伤模型，求出了极向场线圈的等效弹性常数和残余刚度；并且，残余刚度的计算结果已得到了实验验证。这些材料特性已被用于有限元分析的输入数据。     

静水压作用下Nb3Sn多晶体超导临界温度退化的耦合模型

Nb3Sn超导材料主要用于强磁场超导磁体的制造。力学变形诱导的其超导临界性能退化给强磁场超导磁体装置的电磁性能指标和安全运行造成了极其不利的影响。针对静水压作用下，Nb3Sn单晶体和多晶体表现出的不同退化行为，本文基于Maki De Gennes（MDG）关系式，建立了描述Nb3Sn单晶体变形-超导临界温度耦合响应的本构关系，并借助于多晶体有限元方法，对静水压作用下Nb3Sn多晶体超导临界温度退化响应进行了预测，预测结果与实验结果定性吻合。模型实现了从Nb3Sn单晶体到Nb3Sn多晶体变形-超导临界温度退化响应曲线的一致性预测。研究结果有助于提高对Nb3Sn高场超导材料变形-超导电性能耦合行为的认识，为发展描述运行工况下Nb3Sn超导材料力-电磁-热多物理场多尺度耦合行为的建模与数值计算方法提供了一定的基础；同时，相关结果对于特殊工况下高场超导磁体性能的评估和高应变耐受性超导材料的制备也具有一定的指导作用。     

静水压作用下Nb3Sn多晶体超导临界温度退化的耦合模型

Nb3Sn超导材料主要用于强磁场超导磁体的制造。力学变形诱导的其超导临界性能退化给强磁场超导磁体装置的电磁性能指标和安全运行造成了极其不利的影响。针对静水压作用下,Nb3Sn单晶体和多晶体表现出的不同退化行为,本文基于Maki De Gennes（MDG）关系式,建立了描述Nb3Sn单晶体变形-超导临界温度耦合响应的本构关系,并借助于多晶体有限元方法,对静水压作用下Nb3Sn多晶体超导临界温度退化响应进行了预测,预测结果与实验结果定性吻合。模型实现了从Nb3Sn单晶体到Nb3Sn多晶体变形-超导临界温度退化响应曲线的一致性预测。研究结果有助于提高对Nb3Sn高场超导材料变形-超导电性能耦合行为的认识,为发展描述运行工况下Nb3Sn超导材料力-电磁-热多物理场多尺度耦合行为的建模与数值计算方法提供了一定的基础;同时,相关结果对于特殊工况下高场超导磁体性能的评估和高应变耐受性超导材料的制备也具有一定的指导作用。     

Nb3Sn高场复合超导体临界性能力学变形效应的多尺度模拟

A15型Nb₃Sn超导体是制造高场( > 10 T)超导磁体线圈的主要材料, 被广泛应用于磁约束可控核聚变、高能物理等强磁场超导磁体装备制造领域. 力学变形诱导的Nb₃Sn超导临界性能退化给高场超导磁体装备的电磁性能指标和安全稳定运行造成了极其不利的影响. 鉴于Nb₃Sn超导体具有复杂的多尺度结构特征, 不同尺度下变形与超导电性能耦合行为是相互关联的, 本文建立了考虑微/细/宏观关联的非线性力电磁耦合本构模型, 提出了从原子尺度A15晶体结构到超导体微结构到宏观非均质Nb₃Sn复合超导体的多尺度模拟模型. 基于多晶体有限元方法, 对静水压加载条件下Nb₃Sn多晶体超导临界温度衰退和单轴拉压加载条件下Nb₃Sn复合多晶体临界性能衰退行为进行了模拟预测, 预测结果与实验观测结果定性吻合. 该模型揭示了Nb₃Sn复合超导体变形-超导电性能多尺度耦合机理, 实现对高场超导体力、电、磁、热耦合行为的预测, 有助于提高对A15型金属间化合物高场超导复合材料力、电、磁、热多尺度耦合行为的认识和描述能力, 为强磁场超导磁体的设计与制造提供有力的理论支撑.      

Buckling behavior of a superconducting magnet coil

The buckling behavior of a superconducting magnet coil has been investigated for out of plane perturbations. It has been shown that such a coil becomes unstable due to its own magnetic field for out of plane bending at the operating values of electric currents. A technique devised by the author that computes the inductance change due to deformation, has been incorporated in this study. The evaluation shows that although the magnetic fields external to the coil are important and that there is additional structural stiffness provided by the surrounding structure, the effects of the self magnetic field should be evaluated and incorporated in the design of such coils. However, based on previous studies, both analytical and experimental, it has been established that the out-of-plane deformation is the most critical mode from a stability standpoint. Therefore, this mode has been exclusively addressed in this study.     

A general perturbation method for inhomogeneities in anisotropic and piezoelectric solids with applications to quantum-dot nanostructures

By introducing a homogeneous piezoelectric material and its Green’s function, we present a new semi-analytical three-dimensional perturbation method for general inhomogeneity problems in anisotropic and piezoelectric solids. This method removes the limitations associated with previous analytical methods, which often ignore the anisotropic properties or the difference between the material properties of the inhomogeneity and its surrounding matrix. As an important application, the proposed theory is employed to calculate the elastic and electric fields in a truncated pyramidal InAs/GaAs quantum-dot (QD) nanostructure. Numerical results demonstrate that the anisotropy of the materials and the difference between the material constants of the QD and the matrix have a significant influence on the strain and electric fields. The relative differences of the strain and electric field inside the QD between the simplified isotropic and homogeneous model and the real anisotropic and heterogeneous one may reach 22% and 53%, respectively. The accuracy of the calculated elastic strain and electric fields is improved greatly by a second order approximate solution (OAS). Since the third OAS nearly coincides with the second one, good convergence of the iteration procedure is demonstrated. Moreover, contours of the hydrostatic strain and electric potential within and around the QD are also presented and analyzed.     

Transient multi-physics behavior of an insert high temperature superconducting no-insulation coil in hybrid superconducting magnets with inductive coupling

A transient multi-physics model incorporated with an electromagneto-thermomechanical coupling is developed to capture the multi-field behavior of a single-pancake (SP) insert no-insulation (NI) coil in a hybrid magnet during the charging and discharging processes. The coupled problem is resolved by means of the finite element method (FEM) for the magneto-thermo-elastic behaviors and the Runge-Kutta method for the transient responses of the electrical circuits of the hybrid superconducting magnet system. The results reveal that the transient multi-physics responses of the insert NI coil primarily depend on the charging/discharging procedure of the hybrid magnet. Moreover, a reverse azimuthal current and a compressive hoop stress are induced in the insert NI coil during the charging process, while a forward azimuthal current and a tensile hoop stress are observed during the discharging process. The induced voltages in the insert NI coil can drive the currents flowing across the radial turns where the contact resistance exists. Therefore, it brings forth significant Joule heat, causing a temperature rise and a uniform distribution of this heat in the coil turns. Accordingly, a thermally/mechanically unstable or quenching event may be encountered when a high operating current is flowing in the insert NI coil. It is numerically predicted that a quick charging will induce a compressive hoop stress which may bring a risk of buckling instability in the coil, while a discharging will not. The simulations provide an insight of hybrid superconducting magnets under transient start-up or shutdown phases which are inevitably encountered in practical applications.     

基于拓扑优化的均匀磁场励磁结构设计方法

在一定限度的空间内设计励磁结构以使在所需要的区域内产生足够强度和均匀度的磁场,是实现重要的医学诊断设备设计的关键。本文基于拓扑优化方法,建立了能够产生均匀磁场的核磁共振成像仪器中超导励磁线圈空间排布形式的优化设计方法。以励磁线圈在给定区域内的分布参数为设计变量,以在所需区域内磁场的均方差为均匀性描述指标,建立了包含线圈体积和磁场强度要求的均匀磁场设计优化问题的数学模型。基于所建立的优化模型,给出了具体的均匀磁场的励磁结构设计方案。该设计方案的仿真分析,验证了磁场的均匀性以及所建立的方法的有效性。     

The construction of a coil to produce high pulsed magnetic fields

Summary In this paper we describe a pulse apparatus for producing strong magnetic fields by discharging a capacitor bank through a coil. A new construction technique for specially reinforced coils, wound with copper wires, allows us to produce a magnetic field of 570 kOe, with a pulse time of 5 ms.Finally we mention some calculations of the field homogeneity in the coils.     

轴向脉冲磁场增强金属射流侵彻穿深能力的因素

为掌握轴向脉冲磁场对金属射流的作用规律,基于破甲弹金属射流对目标的作用原理及磁场与金属射流之间的相互作用关系,设计了励磁线圈对破甲弹金属射流作用的试验系统,并开展了相关实弹试验,突破了金属射流形成和励磁线圈脉冲电流产生之间时序匹配的关键技术,得出了使金属射流发生有效变形的合理储能电容器组电参数和励磁线圈结构参数。试验结果表明,当电容器电压为5 kV、电容为1 200 μF、励磁线圈长度为50 mm时,破甲弹金属射流对目标靶板的侵彻穿深增量最大,破甲效果最佳;各因素对破甲弹金属射流侵彻穿深能力影响程度由大到小分别是电容器组充电电压、电容器组电容、线圈长度。研究成果为破甲弹威力电磁增强技术可行性论证、原理试验及励磁线圈结构设计提供了重要的理论和技术支撑。     

电感式磨粒监测传感器的磁场均匀性研究

在介绍电感式磨粒监测传感器结构原理的基础上 ,提出可采用检测线圈内部磁场均匀性的方法来弥补颗粒运动轨迹和流型变化带来的检测误差 ,以提高检测灵敏度 .通过分析不同几何尺寸的线圈中轴线上磁场的变化情况 ,并借助直螺线管的径向和轴向公式 ,对轴外磁场均匀性进行了探讨 .数学模型和优化结果表明 :在检测传感器线圈中部范围内为非匀强磁场 ,且呈非线性变化 ,细长管磁场相对均匀 ;当选取 R/ L <0 .2 ,磁场在线圈轴向长度范围内 ,径向在90 %范围内可近似看作均匀磁场 .所得结果可以确定传感器检测区域的磁场均匀性范围 ,为设计电感式磨粒监测传感器提供依据 .     

Continuous versus discrete (invariant) representations of fibrous structure for modeling non-linear anisotropic soft tissue behavior

The non-linear anisotropic mechanical response of soft tissue is largely dependent on the structure of the underlying collagen network. Collagen structure has been successfully quantified for various tissue types in terms of a locally defined fiber orientation distribution function. The continuous distribution function derived from structural data can be directly incorporated into an integral representation of the strain energy function for modeling tissue behavior. Alternatively, non-integral (often invariant-based) strain energy functions have been developed in which the collagen network structure is approximated using a discrete set of fiber classes. The advantage of such an approach is increased computational efficiency since the values of the strain energy and its derivatives (e.g. stress) can be evaluated without numerical integration. However, because of the structural simplifications such models are presumably unable to predict mechanical data as accurately as the models which incorporate a continuous orientation distribution function. In this work the ability of discrete versus continuous fiber models to capture the non-linear anisotropic response of soft tissue is critically analyzed. Both unimodal and bimodal fiber distributions are considered. A general formulation has been developed in terms of an arbitrary fiber strain energy function, such that the analysis can be performed for any suitable fiber material model. For tissue structures in which a discrete representation is suitable, techniques are presented for establishing the range of loading conditions in which model accuracy is not significantly compromised, thus justifying the use of an invariant-based modeling approach.