High Speed Spin Testing of Reinforced 2212 Coils for High Field NMR Magnets

Abstract

Bi-2212 superconductors have very good performance in field, and recent developments by Solid Materials Solutions (SMS) of Chelmsford, MA to mechanically reinforce this material will help realize the potential of this material for these highfield (> 1 GHz-class) NMR magnets. While the strength of these materials can be tested using a conventional tensile test, it is difficult-to-impossible to test coils in the high-field environment required to impose the large Lorentz stresses on the superconductor, as the available warm bore for high-field magnets is usually too small to test typical NMR insert coils, which typically have either a 60 or 80-mm winding diameter. Since it is important to test the coils—and not just wire—in the high-stress environment, as such factors as differential thermal contraction (between mandrel, wire, insulation and epoxy) and stress-concentrations (due to layer-to-layer crossover, for example) only can be tested in coil form, the objective of this study is to simulate the high-field magnet environment by spinning these coils at very high speed (up to 100,000 rpm) using the spin test facilities of Barbour-Stockwell (BSI) in Woburn, MA. By spinning coils wound on a 60-mm diameter mandrel at a speed of 100,000 rpm, the hoop stress is ~700 MPa, which is sufficient to exceed the yield strength of the reinforced Bi-2212 conductor. This paper summarizes the early stage status of this 3-year, NIH-funded project.

I. INTRODUCTION

Hightemperature superconducting (HTS) materials are an enabling technology for a new class (> 1 GHz) of NMR magnets due to their ability to transport large electrical currents in the presence of high magnetic fields beyond the limitations of low temperature superconductors (LTS). [1–7] The data in Fig. 1 describe the in-field critical current density (Je) performance of various superconducting materials at 4.2 K. It also illustrates that, among these candidate conductors, only the HTS types known as REBCO, 2212 and 2223 can break the LTS high-field (> 22 T) Je barrier. Among these, 2212 has two distinct advantages over REBCO and 2223: (1) wire geometry and (2) persistent-joining capability.

Fig. 1.

In-field critical current of various superconductors. [8]

Regarding wire geometry, only 2212 can be made into long-length, round and rectangular wires which are more suitable for fabricating NMR magnets, whereas both REBCO and 2223 are presently made in shorter-length, flat tape (i.e., not wire) format. As for persistent joining, only 2212 holds the near-term prospect of making 2212 joints, which is a key technology to achieve persistent-mode operation of NMR magnets.

As for strength, a new reinforced-version of 2212 conductor being developed by Solid Materials Solutions in Chelmsford, MA is being used. This reinforcing material has tensile strength exceeding 400 MPa, so it significantly strengthens the otherwise weak silver-based 2212 conductor.

A primary limitation in qualifying 2212 coils and other types of HTS-based coils for high-field magnet use is the high cost and limited availability of high-field background magnets. The room temperature bore size of magnets, such as the 32-mm, 45-T hybrid magnet at the National High Magnetic Field Laboratory (NHMFL) of Florida State University, are too small to accommodate the actual, full-scale size of NMR insert coils, which are typically wound on a 60-mm or 80-mm cold winding bore diameter to result in a 36-mm or 54-mm warm RT bore diameter, respectively.

As an innovative solution to this testing problem, this NIH-sponsored research project will apply an advanced form of high-speed spin testing so that it imposes large, centripetal force-based hoop stresses on these 2212 coils tha effectively simulate the Lorentz stresses that will be induced in high-field magnets, beyond the ranges that are currently available in magnet-based testing facilities. The high-speed spin testing will be performed at Barbour-Stockwell (BSI) in Woburn, MA. BSI designs custom spin pits and performs spin test services, mainly for the aircraft industry. BSI can spin coils of this nominal size at speeds of up to 200,000 rpm in their custom-designed vacuum spin pits.

II. DESIGN & ANALYSIS

A. Circumferential Hoop Stress

The circumferential hoop stress, σ_h, generated in a superconducting magnet winding, assuming a thin radial build, may be expressed in terms of the conductor current density, J, magnetic field, B, and radius, R, as:

$${\sigma }_{\text{h}}=\text{JBR}$$ (1)

For 2212 conductor, the projected current density Fig. 1 is ~500 A/mm² at a field of 45 T. Assuming a winding diameter of 30 mm (R = 0.015 m), in order to fit in the 32-mm warm bore, the corresponding hoop stress is ~340 MPa, ~50 ksi, which will not exceed the strength of the reinforced superconducting winding based on short length tensile data. This inability to test such a coil to failure prevents validation of its survivability to the required margin above maximum Lo-rentz-forced based operating stresses.

In a spin test, this same circumferential hoop stress, σ_h, may be expressed in terms of the density, ρ, angular velocity, ω, and radius, R, as:

$${\sigma }_{\text{h}}={\text{ρω}}^2{\text{R}}^2$$ (2)

By equating Eqs. (1) and (2), we can establish a relationship between the test speed, ω, in terms of the magnetic field, B, current density, J, winding density, ρ, and radius, R, as:

$$\text{ω}=\sqrt{\frac{\text{JB}}{\text{ρR}}}$$ (3)

By using the proposed spin test method, two (2) distinct test problems are solved:

1. Size-There is no arbitrary limit to the spin test coil diameter. Therefore, it is possible to spin coils wound on either 60-mm or 80-mm winding diameters, which are standard sizes for the cold winding diameter of conven-tional NMR magnets. For this initial experiment, 60-mm diameter will be used as it simplifies the high-speed dynamic design.

2. Failure Testing-Unlike the magnetically-applied Lo-rentz stress, the spin test stress can be increased past failure by simply increasing the spin test velocity.

Using Eq. (3), the speed required to simulate the 500 A/mm² 45 T condition for a winding density of 7800 kg/m³ at a radius of 0.03 m was determined to be ~9800 rad/s, or ~94,000 rpm. From Eq. (2) this corresponds to a hoop stress of ~675 MPa (or ~100 ksi), which should be sufficient to surpass the failure of present prototype 2212 winding. This stress point is shown by the dotted red line in Fig. 2.

Fig. 2.

Relationship between 2212 test coil hoop stress (MPa) and spin test velocity (rpm).

At a spin test velocity of 100,000 rpm, the corresponding hoop stress is ~800 MPa (almost double that achievable using the 45 T, 30 mm hybrid magnet). Therefore, it will be possible to test a representative size 2212 coil to failure using this method.

The conceptual design of the test configuration for this new test is provided in Fig. 3, along with the stress plot for the 94,000 rpm test, which is equivalent to 500 A/mm² at 45 T at a 60-mm winding diameter, showing maximum imposed stresses of ~650 MPa, which should be sufficient to cause mechanical failure. Note that the coil will need to be located sufficiently removed from the ends of the mandrel to avoid bending stresses and end effects.

Fig. 3.

Conceptual design of spin test assembly.

B. Spin Test Mandrel Design

During this initial phase, a group of WIT students designed and built a prototype spin test mandrel . The design consists of a thin-walled, Inconel tube with a machined outer groove for attaching the 2212 winding. The mandrel is connected to an Inconel spindle via a transitional arbor piece, which is thermally shrunk-fit into the mandrel.

The thin–walled mandrel design was chosen to minimize the difference between the wire stress and the peak stress in the mandrel, thereby the design coil stress to be achieved without excessively stressing or yielding the spin test mandrel. Extensive finite element analysis was performed to optimize the mandrel dimensions. The wire is assumed to be epoxy-bonded in the groove. These FEA results provided in Fig. 4 show how the thin mandrel section with the embedded coil has a relatively uniform peak stress region compared to the arbor and spindle.

Fig. 4.

FEA results for prototype spin test mandrel design.

At this time, the first 2212 coil windings have been fabricated and are awaiting heat treatment. A photograph of one of these coils, along with the prototype spin test assembly is provided in Fig. 5.

Fig. 5.

Photograph of coil winding, along with spin test assembly.

III. TESTING

A. Instron Mechanical Testing

In addition to the spin testing, conventional stress-strain wire testing has been performed on the reinforcing strips using a video extensometer to measure the strain. A typical room-temperature stress–strain curve is provided in Fig. 6, showing a yield strength of over 400 MPa and a high failure strain of ~10%. Data will also be taken on reinforced samples of 2212 wires, including testing at ~100 K in an available cryogenic environmental chamber.

Fig. 6.

Stress-strain curve for reinforcing strip material.

B. Electrical Testing in Solid Nitrogen

The critical temperature of the 2212 wire is very close to the boiling temperature of liquid nitrogen (77 K). Therefore, it will be necessary to test wires and coils in a sub-cooled vacuum environment, ranging from 63 K (solid nitrogen temperature) to 77 K. Some data taken on a 2212 stranded cable show the temperature-dependence on temperature in this range is provided in Fig. 7.

Fig. 7.

Critical current of 2212 cable measured in subcooled nitrogen.

Since this test method is much simpler and less expensive to perform than liquid helium testing, this method will be used to check the critical current in-between spin test runs at BSI, using a portable solid nitrogen test station.

IV. SUMMARY

A new spin test method for qualifying a reinforced 2212 conductor for high–field superconducting magnets has been designed. A preliminary spin test mandrel and coil winding have been fabricated. While this initial design will focus on a single layer geometry, subsequent designs and tests may incorporate multi–layer coils.

Over the next year, initial spin tests will be performed, and the coil critical current will be checked at solid nitrogen temperature (63 K) after each spin test, in an effort to determine the critical winding stress. For the selected coil design, successful spin testing to 70,000 rpm will correspond to a 500 A/mm² and 45 T condition.