Single Tape Research Articles

Nondeterminism and the Clique Problem

The Clique problem is known to be NP-Complete [7,3] and the question whether P=NP is unresolved. This paper examines the relative power of nondeterminism versus determinism in a restricted setting. Specifically, we consider solving the clique problem using non-deterministic and deterministic Turing machines. We impose a (reasonable) format in which a problem instance is encoded. We also impose constraints on the computation of both deterministic and non-deterministic Turing machines: both have two tapes, the input tape is read-only and one-way, and once a certain stop point in the input tape is reached, no additional writing on the work tape is allowed. We consider two cases for the position of the stop point: immediately after the number of graph nodes and the size of the clique are specified, or controlled by a parameter q that indicates what portion of the graph nodes' edge specifications have been scanned. The parameter q may be arbitrarily close to 1, e.g., q=0.99999. We show, for both cases in our setting, that a non-deterministic Turing machine can solve the problem in O(n3) time whereas no deterministic Turing machine can solve the problem in polynomial time. However, we exhibit an exponential time deterministic single work tape, two-heads Turing machine that solves the clique problem in our setting.

Superconducting DC busbar with low resistive joints for all-electric aircraft propulsion system

High-temperature superconductors (HTS) can carry high currents with almost zero loss when transmitting direct current (DC). Their compact size and lower weight make them suitable for the application of all-electric aircraft. However, the current carrying capability of a single HTS tape is limited to a few hundred amps; therefore, for high-current applications, multiple HTS tapes need to be connected in parallel. The flat geometry of HTS tape and its critical current (IC) dependence on strain complicate grouping them in parallel. Furthermore, the length of HTS tape is limited by its crystal structure, necessitating low-resistance joints for extended applications. A superconducting busbar design for high-current applications is developed and tested to address these challenges. The superconducting busbar is designed in a way that it helps to reduce the effect of the self-field on critical current and also ride through the fault events. Yttrium barium copper oxide (YBCO) tapes are used to develop the busbar prototype, tested against DC currents in a liquid nitrogen environment. Joint optimization is carried out to determine the required length for efficiently joining HTS tapes. Two busbar prototypes are developed with 180° and 90° joints to join 5 HTS tapes and tested in self-field. A joint resistance of 100 nΩ is measured at self-field for the 180° joint busbar, and 800 nΩ is measured for the 90° joint busbar. Both busbar prototypes are subjected to power cycling and thermal cycling to assess joint performance in self-field and any degradation of the joint electrical parameters during testing.

A frequency-domain finite element model for simulating high temperature superconductors using the J-A and T-A formulations

Abstract The AC losses, the current density and the magnetic field are important variables to design devices made of High Temperature Superconductors (HTS). These variables are often numerically computed using a transient finite element analysis even though the interest may lay in the steady-state regime of the device. The need for solving time-dependent variables has led to improve the computation time with efficient finite element models (FEM) relying on different formulations. These transient FEM are computationally slow and demanding in terms of resources. In the present work, an alternative path is taken with the development of a frequency-domain FEM using a phasor representation to alleviate the computation burden. This model does not have the versatility of the transient models. However, it can generate the initial steady-state conditions for a subsequent transient analysis. It is perfectly adapted to study the steady-state regime of HTS devices operated in AC conditions. In this phasor modelling approach, the Root Mean Square (RMS) resistivity of the superconductor is introduced. It is subsequently approximated by an exponential function introducing a factor to ease its implementation in the commercial software COMSOL Multiphysics with the most recent and fastest formulations T-A and J-A. The case studies encompass single BSCCO and REBCO tapes as well as a CORC cable or specifically, in the present work, a CORT (Conductor on Round Tube). The results of the time- and frequency-domain FEM simulations are compared against experimental data. The comparison of the models' results is carried out comparing the current density distributions as well as the AC losses. The comparison against experimental data is only conducted on the AC losses. In the present case, it is used to quantify thoroughly the accuracy of the numerical results compared to the measurements. A reasonable agreement between those results and the experimental data was found. 

Dynamic resistance of a REBCO tape carrying direct current under a mixture magnetic field of AC field with DC-biased field

Abstract When the REBCO coated conductor tape carries a direct current(DC) transport current whilst exposed to the alternating current(AC) magnetic field, a DC electrical resistance can be observed, which is called “dynamic resistance”. The High Temperature Superconducting(HTS) magnet wound by the REBCO tapes is located in the HTS electrical machine as field winding carrying DC transport current. The operational environment of the HTS electrical machine involves a complex magnetic field, encompassing both AC and DC components. The interaction between the AC magnetic field and the DC transport current induces dynamic resistance and dynamic loss in the REBCO tape which is a distinctive trait of REBCO tape. Additionally, the presence of an extra DC-biased magnetic field can decrease the critical current of the REBCO tape, thereby altering its electromagnetic properties and potentially compromising its safety. As the basis of superconducting magnets, it is particularly important to study the dynamic resistance and loss distribution of the single REBCO tape under a mixture of magnetic field backgrounds, according to the real working environments in various applications. In this paper, the electromagnetic-thermal coupling model of multilayer REBCO tape based on H-formulation is built in COMSOL Multiphysics. The electromagnetic characteristics and dynamic resistance of the tape are presented when the tape is applied AC magnetic field and carries DC transport current. The effects of perpendicular and parallel DC-biased magnetic fields on the dynamic resistance and loss distribution of the REBCO tape are investigated in the paper. And the DC transport current safety margin will be observed in different applied DC-biased magnetic fields. This study comprehensively demonstrates the variation of dynamic resistance and loss distribution under a complex background magnetic field, which is significant for exploring the electromagnetic characteristics and calculating the loss of the HTS magnets in the HTS electrical machine.

Numerical analysis of stacked HTS tapes in rotating magnetic fields using H and T-A formulations

Superconducting windings in rotating electrical machines and multi-phase transformers are subject to rotating magnetic fields. Most existing studies on the electromagnetic characteristics of stacked high-temperature superconducting (HTS) tapes focus on the influence of vertical magnetic field (VMF) and the transport current. The numerical study on characteristics of HTS stacked tapes in rotating magnetic fields (RMFs) has received less research attention. This paper presents two-dimensional models of stacked HTS tapes in RMF based on H and T-A formulations. AC losses obtained by the two formulations agree well in a single tape configuration but significantly differ in a stack configuration. The discrepancy increases as the number of stack layers and the stack interval increase. Under the same magnetic field amplitude, the RMF penetration depth in stacked tapes is higher than those of VMF and parallel magnetic field (PMF), and the parallel component of RMF causes higher AC loss in the end tapes of a stack. While the applied current increases the overall AC loss, it can significantly decrease the AC loss of the end tape. It is found that reducing the stack interval and replacing end tapes with tapes of higher critical current can significantly reduce the overall AC loss of stacked tapes in an RMF. These results are crucial for modeling superconducting machines and offer valuable insights into characterizing superconducting tapes in RMFs using numerical methods.

Electromagnetic and thermal performance study on a canted stack of REBCO tapes

Abstract Due to the critical current limitation of a single REBCO tape, stacking methods are generally employed to increase the current carrying capacity in practical high-temperature superconducting (HTS) applications. However, the overall critical current is strongly dependent on the self-magnetic field, which is influenced by the geometrical arrangement of conductors in the stack. Due to the brittle ceramic property, REBCO tapes are conventionally bent along the thickness side of the tape. However, the difference in bending radii of the outer and inner tape surfaces in the stack may lead to fracture deformation, thereby limiting the stacking number of REBCO tapes. To balance the stacking number with the bending issue, canted stack is proposed as a variant of normal stack for REBCO tapes. As a potential HTS intermediate component, it is imperative to conduct a comprehensive study on electromagnetic and thermal performance of canted stack. The unique geometrical arrangement of canted stack introduces new factors that affect critical current and transport AC loss. This paper concludes the special influencing factors of canted stack, including canted angle, stacking number, tape width, and spatial structure. The metal interleaving method is introduced for spatial distribution changing and thermal stability. Furthermore, orthogonal analysis is performed to elucidate the comprehensive correlation among these multiple factors. This study provides insights into the overall critical current and transport AC loss for different combinations of canted stack and establishes a predicting function for critical current to support the structural design of canted stack. Based on the specific case study, the improvement effect of canted stack is confirmed by both experiments and simulations.

Numerical simulations on the AC loss of REBCO stacks under rotating magnetic fields

AC loss presents a significant challenge for high-temperature superconducting (HTS) rotating machines. To date, the behaviour of total AC loss (Qtol) (with current) and magnetization loss (Qm) (without current) in a single HTS tape under rotating magnetic fields (RF) have been explored. However, a research gap remains in understanding how these findings translate to the more complex HTS windings of rotating machines. Further exploration is needed to understand the loss behaviour of more complex HTS structures, such as HTS stacks. In this work, Qtol and Qm, in the HTS stacks under RF and a perpendicular AC standing wave magnetic field are numerically investigated. Two different RF models are considered: one is the Uni-RF model, characterized by a uniform field with equal field amplitudes and phases at each position, and the other is a non-uniform field created by a rotating Halbach array, referred to as the Hal-RF model. The dependence of AC loss on parameters such as the number of tapes in the stacks, tape width (2a), and the inclination angle (α) of tapes, which refers to the angle between the normal direction of the stack and the vertical direction, have been explored. The number of tapes in the stacks ranges from 1 to 16, α ranges from 0° to 90°, and the tape width includes 4 mm and 40 mm. Additionally, different rotating field directions are also considered. Interestingly, the analytical values from Brandt and Indenbom equation for Qm of a superconducting strip (BI-strip) are close to Qm results of the stacks under the standing wave at high fields, while they are over twice as high as those in the Hal-RF model at 1 T. This suggests the BI-strip equation is not reliable for predicting Qm under RF at high fields. We also show in the Hal-RF model that different rotation directions of the field lead to varying Qm and Qtol when asymmetric Jc (B, θ) data are applied. Moreover, it has been observed that the inclination angle has no impact on Qm under uniform RF while significantly impacts both Qm and Qtol in the Hal-RF model.

Kinematics-driven design of reconfigurable bistable hinges with high stiffness and stability

Composite tape springs are curved shells with the ability to assume two energetically stable states. By carefully selecting layup and mold during manufacturing, these structures can store significant strain energy, making them ideal for deployable systems. Yet, their potential as reversible reconfigurable structures, particularly as adaptive hinges, remains largely unexplored. In structural applications, both stable states of these hinges must exhibit high stiffness to support loads while retaining the capacity for reversible reconfiguration. This paper introduces kinematics-based stacking concepts aimed at enhancing the stiffness of bistable hinges in both states, allowing for specific fold angles without compromising compliance. These designs leverage snap-through kinematics, resulting in unique architectures with customizable stiffness and stability. Additionally, the paper presents a novel energy-based semi-analytical approach for analyzing the stacking concepts. This approach involves constrained exploration of the energy landscape to assess the design space in terms of stiffness and energy barriers. Through comprehensive parametric studies, the research demonstrates significantly increased stiffness and reduced peak stresses compared to single tape spring designs. This research highlights the potential of employing tape springs as reconfigurable load-bearing structures in diverse applications, including precise adjustments of low-mass payloads like solar panels or antennas on space structures.

Numerical Simulation of Heat Transfer Enhancement of a Heat Exchanger Tube Fitted with Single and Double-Cut Twisted Tapes

Numerical Simulation of Heat Transfer Enhancement of a Heat Exchanger Tube Fitted with Single and Double-Cut Twisted Tapes

Enhancing electric field calculation in HTS tape simulations for currents exceeding the critical limit using full HTS tape modeling

Superconducting devices are an interesting technological option for improvement of efficiency of energy systems. High-temperature superconducting tapes are among the best choices for power applications. Because of their high non-linearity, the design of devices with superconducting tape requires specific simulation models and methods to correctly represent the superconducting behavior. The J-A formulation has been investigated as an efficient tool to represent the electromagnetic behavior of such devices. It is based on the current density (J) and magnetic vector potential (A), and able to represent both superconducting materials and ferromagnetic materials. With regards to the tapes, the use of thin-film approximation can be successful with the J-A formulation. Usually, only representations considering the superconducting layer of tapes have been investigated. This becomes a problem for operations where the current in the superconductor surpasses the critical current, for example in transient analysis. This paper presents an analysis of the effects the inclusion of all of the tapes’ layers have on simulations with the J-A formulation with thin-film approximations. By considering all layers of the tape, one represents the transition between superconducting and high-loss states of the tape. A simple system, consisting of a single tape with applied current, has been studied as benchmark and simulated with J-A and the more established T-A formulation in two cases: considering all layers; and only the superconducting layers. Results show that results for the J-A and T-A formulations are compatible and the inclusion of all layers improves the stability of the simulation and provides correct assessment of the electric field in the tapes.

Effect of sintering time on the characteristics of YBCO coated-conductor joints using nano-silver paste

Jointing YBa2Cu3O7-z (YBCO) superconducting coated-conductor (CC) tapes is becoming increasingly significant for magnet applications because of the limited length of single tapes. In this work, YBCO CC tapes stabilized by silver were connected by low-temperature sintering of nano-silver paste. The effect of sintering time and lapped length on the electrical properties of YBCO joints were systematically investigated. And the correlation between microstructure and bonding force of the joints with extending the sintering time was established. It is found that joints sintered within 1∼5 min exhibit relatively lower resistance, while the maximum axial tensile strength at room temperature (RT) was improved with increasing sintering time. Considering the electromechanical properties, ten min is selected as the optimal sintering time for nano-silver paste. The joint by this efficient technology possesses closely connected interface, similar critical current and axial tensile strength (RT) to the single CC tape. The joint resistivity is as low as ∼12.5 nΩ·cm2, which is much less than the traditional soldering joint.

Qualification and test of space compatible superconducting current leads (REBCO) designed for adiabatic demagnetization refrigerators

Many astrophysics observations require space telescopes, either to reduce atmospheric perturbation or simply to make these detections possible (in the X-Ray spectrum for example). One of these missions, Athena, is led by the European Space Agency (ESA), with additional international contributions, dedicated to X-Ray observation. Two instruments will be part of this mission and among them, X-IFU, will use Transition Edge Sensors (TES) to detect and precisely measure the energy of X-Ray photons. These sensors require a temperature of 50 mK to reach their ambitious sensitivity goals. In space, this temperature can be reached using Adiabatic Demagnetization Refrigeration (ADR) and such a cooling system is currently being developed for the X-IFU instrument. ADR utilizes magnetocaloric materials which, upon variation in magnetic fields, can produce a cooling effect. The magnetic field of the order of 1 T in a volume of 10s of cm3 is produced by a superconducting coil with high winding number and current limited to approximately 2 A. Even though this current is low compared to most earth-based systems, metallic current leads to link the high- and low-temperature stages would cause high thermal loads, unacceptable for the limited capacity of the cryogenic cooling chain of the spacecraft. Therefore, a harness consisting of superconducting current leads is planned to reduce the thermal loads at the low-temperature stage. As part of an ESA contract, our team designed, built and tested such a space-compatible harness. This harness includes the electrical interfaces at both ends as well as mechanical support. Its development is capable of operating between interfaces at 80 K and 4 K. The harness is based on industrially available Rare-Earth-Barium-Copper-Oxide (REBCO) High-Temperature Superconductor (HTS) tapes. The tapes were laser-cut by our group to fulfill our specifications, Parylene coated and reinforced with Kapton laminate tape for mechanical and insulating purposes. After characterization of the single tapes, the assembled harness has been subjected to an extensive qualification sequence including thermal cycling and mechanical testing based on launch loads requirements. This paper will summarize the technical design choices for this HTS harness. It will discuss the test results and propose some perspectives for the next iteration of the development.

Effectiveness of various cast covers in the pediatric population

BackgroundKeeping casts dry is a challenge in pediatric orthopedics. A wet cast risks skin complications, and generally requires a cast change resulting in unplanned visits and increased healthcare costs in patients undergoing cast immobilization. Previous research on the effectiveness of cast covers has only reviewed adult models. We evaluated the efficacy of different commercially available cast covers and do-it-yourself (DIY) methods for keeping casts dry in different sized pediatric arm models and compared relative costs of using each method. MethodsShort arm casts were applied to plastic mannequin arms representing pediatric patients ages 3, 6 and 12 years old. Different cast covers or DIY methods were applied over each cast and the limbs were then submerged in water for 1 minute. Water absorption was calculated by comparing the mass before and after submersion as measured with a digital scale. Each test group had 6 trials as determined by a power analysis. Statistical analysis was done using a non-parametric test with additional post-hoc analysis. Cost effectiveness was estimated for typical materials needed for use over a 6-week period. ResultsA plastic bag and duct tape was the most effective in keeping a cast dry. Other DIY methods (plastic bag and rubber bands, adhesive film) were not effective. There were several highly effective commercial cast covers across age groups, including Bloccs, Seal-Tight, and DryPro. Other commercial cast covers tested had inferior performance. Of the effective methods, a single plastic bag and duct tape was most cost-effective. Discussion / ConclusionA plastic bag and duct tape was overall the most clinically and cost effective method of avoiding a wet cast, with good to excellent results across arm size/age groups. Findings from this study may better inform patients about ways to keep casts dry, avoid unnecessary visits for cast changes, and decrease associated costs and risk of complications.

Numerical simulation at the micro-scale for the heat transfer modelling in the thermoplastic composites laser-assisted AFP process

Laser-assisted Automated Fibre Placement for thermoplastic composites has shown its potential to process complex shaped parts with high productivity rates but many challenges, both physical and technical, still need to be addressed in order to achieve proper in-situ consolidation. Ensuring high quality bonding of the laid tapes relies on perfect control of their thermal history throughout the process, and heat transfer has long proven essential to achieve this. Numerous heat transfer models account for optical interaction between the laser and composite at a macroscopic scale. Here, a thermo-optical model at the micro-scale is designed and differentiates the fibres from matrix domain, accounting for their respective properties. A single tape is modelled in a static configuration. Based on a composite material realistic microstructure, a ray-tracing algorithm highlights the laser heat absorption depth dependency to laser incidence angle and fibre distribution. Numerical surface temperatures are compared to experimental data obtained with a specific set-up leading to an overall accurate approximation. Finally, the microstructure model relevance is assessed with 1D homogenised models considering either ideal surface heating or a volumetric heat source. The surface heating model leads to inaccurate approximation of surface temperatures, whereas volumetric heat source absorption substantially limits temperature errors. As a result, this model gives a satisfactory compromise between model complexity, computational time and temperature prediction.

Anterior cruciate ligament reconstruction with a single hamstring tendon graft and tape locking screw (TLS) fixation leads to good clinical outcome in two years of follow-up

BackgroundThere are many fixation methods for hamstring tendon autograft available for anterior cruciate ligament (ACL) reconstruction. The intention of this study was to report clinical follow-up data of the Tape Locking Screw (TLS) reconstruction technique. HypothesisDoes TLS method give good long term results in patient satisfaction and in clinical knee tests. Patients and methodsWe selected 119 prospectively collected patients with a two-year follow-up who had an ACL reconstruction using TLS technique. A total of 114 cases were available for follow-up two years postoperatively. The evaluation methods were instrumented laxity measurements, clinical examination and knee scores. ResultsThe Lysholm and IKDC scores improved from preoperative 76 and 50 to 95 and 90, respectively. Tegner activity level before surgery was 3 and improved to 6 at 2 years postoperatively. DiscussionACL reconstruction with TLS technique showed good objective outcome at the 2-year follow-up. We confirmed improvement in all evaluation method variables. Level of evidenceCase series; level of evidence, 4. Trial registrationISRCTN registry, study ID ISRCTN34011837. Registered retrospectively April 29, 2020.

Electromechanical characteristic of stacked REBCO tapes under tension deformation

Stacking REBCO tapes is an effective way to increase the current-carrying capacity of the cable. Various loading conditions, including combined tension-bend, are applied to these tapes during fabrication and operation of the magnets. This paper investigates the degradation behaviors of critical current (Ic) in stacked rare earth–barium–copper–oxide (REBCO) coated conductor (CC) tapes under tension loading through experimental. Uniaxial tension experiments are conducted on single tapes and 4-tape cables with different stacking at 77 K. The critical current degrades rapidly when strain exceeds an irreversible threshold around 0.4-0.5%. A 3D finite element model analyzes the non-uniform stress distribution in the cable cross-section under tension, causing different degradation behaviors. An empirical model combining the Ekin law and Weibull distribution is proposed to relate Ic and axial strain. By fitting experimental data, the key parameters are determined. The Ic of a single tape reduces 20% at 0.4% strain. Face-to-face stacking decays at 0.45% irreversible strain, while back-to-back decays at 0.38%. The model provides an effective way to optimize the electromechanical performance of stacked REBCO cables.

Non-uniform current distribution in parallel-wound no-insulation high-temperature superconductor coil during ramping and fast discharging operations

A parallel-wound no-insulation (PWNI) high-temperature superconductor (HTS) coil is a kind of pancake-shaped no-insulation (NI) coil wound with parallel-stacked HTS tapes, which combines the characteristics of a NI coil and non-twisted stacked-tape cable. It shows a significant advantage in accelerating the ramping response compared with traditional NI HTS coils wound by a single tape, and is a promising alternative for large-scale high-field magnets. The stacked cable approach can lead to current redistribution between parallel tapes during ramping operations. It couples with the turn-to-turn current redistribution and leads to a much more complicated current redistribution inside the PWNI coil, the mechanism of which remains unclear so far. The aim of this work is to investigate electromagnetic behavior of a PWNI HTS coil in ramping and fast discharging process. A simulation model was developed by integrating an equivalent circuit network model and an improved T–A model. A three-tape PWNI coil and its insulated counterpart were wound and tested, and this model was validated by charging and discharging tests. Results show that there is a significant non-uniform current distribution on parallel tapes in the same turn during ramping operations and the maximum azimuthal current (transport current) can be 2.26 times the minimum one in the three-tape PWNI coil in this study. Meanwhile, the radial current shows a considerable accumulation in the tape near turn-to-turn contacts and the radial current through the turn-to-turn contacts can be 4.16 times of that the flow through tape-to-tape contacts (parallel tapes) in the same turn. During the fast discharging process, a significant coupling current is generated in the PWNI coil, leading to a large opposite transport current in local areas; the amplitude of variation of this can be 4.66 times the initial operating current. The radial current shows a similar distribution but opposite direction to that during ramping, and its amplitude is two orders of magnitude higher. These results provide practical guidelines for the design of large-scale high-field HTS magnets.

Does Suture Type or Configuration Matter in Percutaneous Achilles Tendon Repairs?

Category: Trauma; Sports Introduction/Purpose: The human Achilles tendon is functionally important for dynamic activities and is a common site of injury, resulting in pain, weakness, and removal from sport. While treatment options vary and the opinions regarding optimal management are not uniform, percutaneous repair through commercially available guides is one option that has been used in the United States. The purpose of this study was to test the mechanical properties of four suture permutations. Methods: This biomechanical study included Porcine toe flexor tendons as an analogue for the human Achilles tendon. Simulated rupture was performed and tendons repaired using a percutaneous guide. Technique was uniform with pre-determined allotment into one of four groups based on suture configuration (single or double locked) and type (round or flat) with a total of 10 specimens in each group. Specimen then underwent static creep test, a dynamic load creep test, and finally load to failure test. An analysis of variance test was performed, followed by pairwise comparisons using independent t-tests to assess inter-group differences if significant effects were found, adjusted for multiple comparisons. Results: No significant differences were seen between conditions for the creep tests. The suture configuration used was determined to have a significant effect on the maximum load to failure of the constructs (p = 0.018) and maximum stress in the construct during the load to failure test (p = 0.019). Double Tape had a significantly greater load to failure than the Single Round (66N (0.021, [25, 107]) and Single Tape (72N (0.037, [18, 126]) conditions, and reached greater stresses before failure (0.1N/mm^2 (0.04, [0.03, 0.17] and 0.1N/mm^2 (0.04, [0.02, 0.18], respectively). No significant differences were found between the double tape and double round techniques, nor the Double Round and either of the Single techniques for any of the load to failure variables. Conclusion: Currently, there is no compelling data to support surgical over non-surgical management of Achilles tendon ruptures. However, by patient or surgeon preference, many patients undergo operative intervention, and percutaneous repair through a guide is a popular modality. The results of this study, using a porcine model to simulate a minimally invasive technique for Achilles tendon repairs, suggest that the use of a double locked tape suture configuration leads to a stronger overall construct. The clinical implications of these findings will be the subject of future work.

Analysis and tests of non-uniform wrapping process of tape spring

A tape spring, which has a high ratio of retraction and deployment, is a type of basic deployable member that plays an important role in deployable structures. This paper is focused on the non-uniform wrapping process of a tape spring that the fixed end section preserves the initial shape. A theoretical method is presented to predict the non-uniform wrapping process of a metallic tape spring based on classical theories about the bending behavior of this type of tape spring. There are two possible shapes for a tape spring after the non-uniform wrapping process, namely a polygon or a continuous curve. The boundary lines of the two possible shapes are studied, and it is shown that the shape depends on the radius of the central cylindrical hub. A finite element model is built using the commercial software ABAQUS to verify the reliability of the theoretical model. Experimental measurement is also conducted to record the shape change process of a tape spring. The comparisons of the results of the three different methods show that they are in good agreement with each other, which means that the theoretical model can be used to predict the non-uniform wrapping behavior of the tape spring. Additionally, the behavior of four tape springs during the non-uniform wrapping process is studied, and the results show that the shapes of multiple tape springs in a coiled state correspond to that of a single tape spring.

Bending characteristics of stacked REBCO cable under different stacking modes

High-temperature superconducting tapes provide new materials for various high-current applications. The stacked tape cable (STC) is one of the promissing structure, which is based on the idea to stack single REBCO tapes. However, stacking the tapes increases the thickness of the cable and reduces its bending performance. In order to study the bending behavior of stacked tapes, bending tests of single tape was first made to analyze the strain of the REBCO layer at different bending radii, and the strain-current curves were obtained by empirical equations. The cables were stacked in both back-to-back and face-to-face modes. The strains of the REBCO layers in the tapes are calculated, and the critical currents of the cables are experimentally measured at various bending radii. The bending characteristics of the cable are analyzed using the fitted equation, and the experimental results demonstrate good agreement with the calculated results. The results indicate that the REBCO layer exhibits improved bending performance under compression, and thinner cables perform better. Therefore, we added copper tape to adjust the position of the neutral axis to optimize the bending performance. The results show that this method can effectively reduce the bending radius of the stacked cable.