Mechanical Vibration Tests on Real-scale REBCO Coil

287QR of RTRI, Vol. 59, No. 4, Nov. 2018

Minoru TANAKAKatsutoshi MIZUNO

Mechanical Vibration Tests on Real-scale REBCO Coil

Masafumi OGATACryogenic Systems Laboratory, Maglev Systems Technology Division

Development of REBCO (Rare-Earth Barium Copper Oxide) magnets has been ongoing with the purpose of reducing the cost of operating maglev trains. On-board superconduct-ing magnets are exposed to severe vibrations due to the varying magnetic field. This paper describes mechanical vibration tests on an actual REBCO coil. The coil was vibrated at 10 G (98 m/s2) by excitation. The heat load due to vibrations was less than 2 W, which is a small percent of the total heat load. In addition, eddy current heating was evaluated with numeri-cal electromagnetic analysis.

Keywords: maglev, REBCO, vibration, eddy current

1. Introduction

Most superconducting magnets employ niobium-tita-nium, which is a low temperature superconducting (LTS) material discovered in 1961. Since the coil manufacturing process using niobium-titanium is mature, the majority of on-board superconducting magnets on maglev trains are niobium-titanium coils. These coils must be maintained at temperature below 4 K during operation. As such, liquid helium or special cryocooler is required to cool down niobi-um-titanium magnets.

A high temperature superconducting (HTS) magnet with a REBCO (Rare-Earth Barium Copper Oxide) coated conductor for the maglev and other applications has been developed. The REBCO coated conductor is suitable to be used as a magnet, because of its high-current density in high magnetic field environments. For example, at a magnetic flux density of 5 T, the current density of the REBCO coated conductor at 40 K is the same as that of niobium-titanium at 4 K [1]. In other words, the operating temperature of a superconducting magnet can be raised to 40 K without adding to coil weight. REBCO magnets have smaller cooling systems and simpler thermal insulation, which are two significant advantages in terms of energy consumption and magnet weight reduction.

In contrast to the niobium-titanium, REBCO coated conductors were only introduced to the market a few years ago, which means that there is still little feedback on large REBCO magnets in actual use. A real-scale REBCO racetrack coil has already been produced, and it has been demonstrated that it can produce a magnetomotive force of 700 kA, which is necessary for maglev operations [2], [3]. However, so far there are no examples of REBCO magnets that have been operated in conditions presenting inevitable vibration such as with the maglev. It is therefore necessary to confirm whether stable excitation when being vibrated is possible or not. In addition, heating due to vibration must be evaluated. If heating due to vibration exceeds cooling power, the REBCO magnet cannot maintain an ex-citation state. This paper reports on mechanical vibration tests performed on a real-scale REBCO coil while being vibrated. Electromagnetic heating, which is not evaluated in mechanical vibration tests, was estimated by numerical simulation.

2. Heat generated by magnetic field variation

2.1 Heating mechanism

Some research about the vibration of LTS magnets has been conducted, and the findings of this research may help towards making it possible to operate REBCO magnets while being vibrated.

When a superconducting magnet is exposed to a vary-ing magnetic field, three types of heat are generated [4]. The first one is from the eddy current due to relative dis-placement of the superconducting coil and the radiation shield (see Fig. 1. a). Vibration forces are exerted on the superconducting magnet because of the varying magnetic field. If the stiffness of the support structures is insuf-ficient, or the radiation shield is too weak, the radiation shield vibrates and is deformed. An eddy current is then in-duced on the radiation shield since the magnetic field from the superconducting coil changes. The eddy current on the radiation shield generates a varying magnetic field on the super conducting coil. Finally, the eddy current on the su-perconducting coil causes Joule heating. However, the RE-BCO coil introduced in this paper has no radiation shield because of its high operating temperature above 40 K. The relative displacement is negligible unless the stiffness of the support structures is extremely low, and therefore this type of heating does not occur.

The second type of heat is generated by penetration of the varying magnetic field through the outer vessel of the magnet (see Fig. 1. b). As with the first type of heat, the eddy current induced on the coil causes Joule heating. Al-though the outer vessel made of aluminum acts as a shield against most of the varying magnetic field, low frequency magnetic fields penetrate the vessel and the resulting Joule heat generated by the eddy current is not negligible.

The last type of heat is frictional heating caused by deformation of the superconducting coil (see Fig. 1. c). A superconducting coil for the maglev consists of a wound su-perconducting wire and an inner vessel. The inner vessel is a gas-tight container filled with liquid helium for the cool-ing of the coil. Contact between the wound superconduct-ing wire and the inner vessel can be the source of frictional heating. In the REBCO magnet, although liquid helium is unnecessary for cooling down, the coil must be covered

PAPER

288 QR of RTRI, Vol. 59, No. 4, Nov. 2018

with a reinforced structure to endure the electromagnetic force. (In this paper, this reinforced structure in the RE-BCO magnet is referred to as the “coil case” to distinguish it from the inner vessel in the LTS magnet.)

2.2 Evaluation method of the vibration heating

There are two methods to evaluate the heating due to vibration and endurance against the vibration: electro-magnetic vibration tests and mechanical vibration tests. In the electromagnetic vibration test, conventional electric coils are lined up in front of the superconducting magnet and they generate a varying magnetic field. Now that the experimental environment is similar to the actual maglev operation, a complete superconducting magnet is neces-sary. It is impossible to evaluate a superconducting coil alone, and the whole experimental setup is huge. In addi-tion, eddy current heating and frictional heating cannot be separated.

For a mechanical vibration test, a superconducting coil is suspended from the flange of the cryostat and is directly vibrated via an electrodynamic vibrator. Only frictional

Fig. 1 Heating mechanism of a superconducting magnet vibration

(see Fig. 1. b). As with the first type of heat, the eddy current induced on the coil causes Joule heating. Although the outer vessel made of aluminum acts as a shield against most of the varying magnetic field, low frequency magnetic fields penetrate the vessel and the resulting Joule heat generated by the eddy current is not negligible.

The last type of heat is frictional heating caused by deformation of the superconducting coil (see Fig. 1. c). A superconducting coil for the maglev consists of a wound superconducting wire and an inner vessel. The inner vessel is a gas-tight container filled with liquid helium for the cooling of the coil. Contact between the wound superconducting wire and the inner vessel can be the source of frictional heating. In the REBCO magnet, although liquid helium is unnecessary for cooling down, the coil must be covered with a reinforced structure to endure the electromagnetic force. (In this paper, this reinforced structure in the REBCO magnet is referred to as the “coil case” to distinguish it from the inner vessel in the LTS magnet.)

2.2 Evaluation method of the vibration heating

There are two methods to evaluate the heating due to vibration and endurance against the vibration: electromagnetic vibration tests and mechanical vibration tests. In the electromagnetic vibration test, conventional electric coils are lined up in front of the superconducting magnet and they generate a varying magnetic field. Now that the experimental environment is similar to the actual maglev operation, a complete superconducting magnet is necessary. It is impossible to evaluate a superconducting coil alone, and the whole experimental setup is huge. In addition, eddy current heating and frictional heating cannot be separated.

For a mechanical vibration test, a superconducting coil is suspended from the flange of the cryostat and is directly vibrated via an electrodynamic vibrator. Only frictional heating can be evaluated, and the experimental setup is compact compared to the electromagnetic vibration test.

In this research, mechanical vibration tests were carried out to evaluate frictional heating and durability of the REBCO coil against vibration. The eddy current heating due to the penetration of the varying magnetic field was also estimated by electromagnetic analysis.

3. Prediction of eddy current heating by numerical

analysis The material of the coil case affects the amount of heat

generated by the eddy current. In an LTS magnet, the inner vessel must be made of welded stainless steel case to make the structure gas tight. However, the coil case for the REBCO coil itself, is just a reinforced structure, and therefore the material can be replaced with another such as aluminum alloy. The effect of the differences of the case material on the heat generated by an eddy current was evaluated through numerical analysis.

3.1 Analysis model

As the real-scale REBCO coil was designed with the aim

of reducing weight, its coil case is made of duralumin (7075 aluminum alloy). The coil body is racetrack shaped (1070 mm in length, 500 mm in height), and is packed into the coil case. Although the actual on-board magnet has four coils, the analysis model has one coil to reduce the computational cost as shown in Fig. 2. Conventional coils are lined up in front of the superconducting magnet (see Fig 3) and are excited by electromagnetic induction when the magnet goes through, and then generate the varying magnetic field. In this analysis, a commercial electromagnetic analysis software “EMsolution” was used. 3.2 Analysis results

The results of tests to examine heat generated by eddy currents at 309 Hz are compared in Table 1; one has a duralumin (7075 aluminum alloy, resistivity at 50 K: 2×10-8 Ωm) coil case and the other has a stainless steel (304, resistivity at 50 K: 4×10-

7 Ωm) coil case. The heat generated by the eddy current heating on the outer vessels was the same. This result indicates that the coil case material does not affect the eddy current on the outer vessel. Most of the varying magnetic field was shielded by the outer vessel, since the heating on the coil case was 104 times

a. Relative displacement between the radiation shield and the coil

b. Penetration of the magnetic field

c. Frictional heating between the coil and the inner vessel Fig. 1 Heating mechanism of a superconducting magnet

vibration.

Fig. 1 Heating mechanism of a superconducting magnet vibration.



c. Frictional heating between the coil and the inner vessel









heating can be evaluated, and the experimental setup is compact compared to the electromagnetic vibration test.

In this research, mechanical vibration tests were car-ried out to evaluate frictional heating and durability of the REBCO coil against vibration. The eddy current heating due to the penetration of the varying magnetic field was also estimated by electromagnetic analysis.

3. Prediction of eddy current heating by numerical analysis

The material of the coil case affects the amount of heat generated by the eddy current. In an LTS magnet, the in-ner vessel must be made of welded stainless steel case to make the structure gas tight. However, the coil case for the REBCO coil itself, is just a reinforced structure, and therefore the material can be replaced with another such as aluminum alloy. The effect of the differences of the case material on the heat generated by an eddy current was evaluated through numerical analysis.

3.1 Analysis model

As the real-scale REBCO coil was designed with the aim of reducing weight, its coil case is made of duralumin (7075 aluminum alloy). The coil body is racetrack shaped (1070 mm in length, 500 mm in height), and is packed into the coil case. Although the actual on-board magnet has four coils, the analysis model has one coil to reduce the computational cost as shown in Fig. 2. Conventional coils are lined up in front of the superconducting magnet (see Fig 3) and are excited by electromagnetic induction when the magnet goes through, and then generate the varying magnetic field. In this analysis, a commercial electromag-netic analysis software “EMsolution” was used.

3.2 Analysis results

The results of tests to examine heat generated by eddy currents at 309 Hz are compared in Table 1; one has a du-ralumin (7075 aluminum alloy, resistivity at 50 K: 2 × 10-8 Ωm) coil case and the other has a stainless steel (304, resis-tivity at 50 K: 4 × 10-7 Ωm) coil case. The heat generated by the eddy current heating on the outer vessels was the same. This result indicates that the coil case material does not affect the eddy current on the outer vessel. Most of the varying magnetic field was shielded by the outer vessel, since the heating on the coil case was 104 times lower than that on the outer vessel. However, as the coil case is lo-cated in the cryogenic region, even a small amount of heat is not negligible. The static heat road to the superconduct-ing magnet contains thermal conduction and Joule heating at the current leads, thermal conduction of the support structures and radiation. In the REBCO coil which is the subject of this research, the current lead heating is approx. 13 W per coil [5], and thermal conduction of the support structures and the radiation is approx. 15 W in total. The total heat load is less than 30 W, which is significantly larger than the eddy current heating of 0.7 W in the stain-less steel coil case.

The differences in heat generated by the eddy current


between different coil case materials can be explained as follows: Basically, as the coil case material has lower resis-tivity, the eddy current increases. If the coil case is made of an insulating material, the eddy current falls to zero and Joule heating does not occur. (In this case, the vary-ing magnetic field is not shielded by the coil case. The eddy current is generated in the superconducting wire which forms the coil.) However, in the high frequency region where the reactance is much higher than the resistance of the coil case, the eddy current peaks out regardless of the resistance. Of course, at the same eddy current, lower re-sistivity is preferable to reduce Joule heating. Under these analysis conditions, the reactance dominates the eddy cur-rent. Therefore, eddy current heating in the duralumin coil case is lower than that in the stainless steel coil case.

Fig. 2 Superconducting magnet model for the evaluation of the eddy current heating by varying magnetic fields

Fig. 3 Position of the superconducting coil and the coils which generate the varying magnetic fields

lower than that on the outer vessel. However, as the coil case is located in the cryogenic region, even a small amount of heat is not negligible. The static heat road to the superconducting magnet contains thermal conduction and Joule heating at the current leads, thermal conduction of the support structures and radiation. In the REBCO coil which is the subject of this research, the current lead heating is approx. 13 W per coil [5], and thermal conduction of the support structures and the radiation is approx. 15 W in total. The total heat load is less than 30 W, which is significantly larger than the eddy current heating of 0.7 W in the stainless steel coil case. The differences in heat generated by the eddy current between different coil case materials can be explained as follows: Basically, as the coil case material has lower resistivity, the eddy current increases. If the coil case is made of an insulating material, the eddy current falls to zero and Joule heating does not occur. (In this case, the varying magnetic field is not shielded by the coil case. The eddy current is generated in the superconducting wire which forms the coil.) However, in the high frequency region where the reactance is much higher than the resistance of the coil case, the eddy current peaks out regardless of the resistance. Of course, at the same eddy current, lower resistivity is preferable to reduce Joule heating. Under these analysis conditions, the reactance dominates the eddy current. Therefore, eddy current heating in the duralumin coil case is lower than that in the stainless steel coil case.

4. Mechanical vibration tests on REBCO coil Analysis of frictional heating is not realistic because of the

complicated coil structure. Frictional heating must therefore be evaluated experimentally. Reports exist on the frictional heating of a superconducting magnet, and some countermeasures have already been suggested [6]. It is possible for frictional heat to be generated between the coil case and the coil body in REBCO magnets. Therefore, countermeasures were taken to reduce the frictional heating before the vibration tests.

4.1 Resin filling

The REBCO coil in this research consists of stacked pancake coils and a coil case capable of withstanding hoop stress (as shown in Fig. 4). Because of the machining accuracy or clearance for the assembly of the coil, some small gaps remain between the pancake coils and the coil case. When the coil is vibrated, components shift relative to each other generating frictional heat. One countermeasure was to fill the inside of the coil case with DCP (Dicyclopentadiene). DCP is a suitable filling resin, since it has a viscosity of less than 10 mPa･s, which means it easily infiltrates small gaps. In addition, its mechanical strength at low temperature is as high as that of epoxy resin [7].

4.2 Mechanical vibration test apparatus

Resonance phenomena are used in these vibration tests. Since the REBCO coil is approximately 140 kg, it is quite difficult to vibrate the coil to a high vibration acceleration. Hence, the REBCO coil was suspended from the flange of the cryostat to vibrate freely. The Eigen modes were determined by frequency response. The coil was then vibrated at its Eigen frequencies with a vibration acceleration of 10 G (98 m/s2).

The mechanical vibration test apparatus was designed to represent the actual maglev operation; the coil was cooled to below 40 K, and excited with a magnetomotive force of 700 kA during the vibration tests. The cryostat had a single-stage GM cryocooler, and the cryocooler was connected to the coil through multi-layer high-purity aluminum plates to separate the vibration. The vibrator was connected to the coil through a rigid rod. As the vibrator is located outside the cryostat, a bellows between the rod and the cryostat maintained the vacuum, and the vibration force was only transferred to the coil. Figure 5 shows the appearance of the apparatus. As shown in Fig. 5, two vibrators could be used in the vibration tests. This setup resolved the imbalance in the coil deformation due to the mass

Fig. 2 Superconducting magnet model for the evaluation of the eddy current heating by varying magnetic fields.

Fig. 3 Position of the superconducting coil and the coils which generate the varying magnetic fields.

Table 1 Analytical results of eddy current heating depending on coil case material

Coil case material

Resistivity at 50 K

Heat load Outer vessel

Coil case (per single

pole) 7075 aluminum alloy

2×10-8 Ωm 7470 W 0.31 W

304 stainless steel

4×10-7 Ωm 7470 W 0.66 W

lower than that on the outer vessel. However, as the coil case is located in the cryogenic region, even a small amount of heat is not negligible. The static heat road to the superconducting magnet contains thermal conduction and Joule heating at the current leads, thermal conduction of the support structures and radiation. In the REBCO coil which is the subject of this research, the current lead heating is approx. 13 W per coil [5], and thermal conduction of the support structures and the radiation is approx. 15 W in total. The total heat load is less than 30 W, which is significantly larger than the eddy current heating of 0.7 W in the stainless steel coil case. The differences in heat generated by the eddy current between different coil case materials can be explained as follows: Basically, as the coil case material has lower resistivity, the eddy current increases. If the coil case is made of an insulating material, the eddy current falls to zero and Joule heating does not occur. (In this case, the varying magnetic field is not shielded by the coil case. The eddy current is generated in the superconducting wire which forms the coil.) However, in the high frequency region where the reactance is much higher than the resistance of the coil case, the eddy current peaks out regardless of the resistance. Of course, at the same eddy current, lower resistivity is preferable to reduce Joule heating. Under these analysis conditions, the reactance dominates the eddy current. Therefore, eddy current heating in the duralumin coil case is lower than that in the stainless steel coil case.

4. Mechanical vibration tests on REBCO coil Analysis of frictional heating is not realistic because of the

complicated coil structure. Frictional heating must therefore be evaluated experimentally. Reports exist on the frictional heating of a superconducting magnet, and some countermeasures have already been suggested [6]. It is possible for frictional heat to be generated between the coil case and the coil body in REBCO magnets. Therefore, countermeasures were taken to reduce the frictional heating before the vibration tests.

4.1 Resin filling

The REBCO coil in this research consists of stacked pancake coils and a coil case capable of withstanding hoop stress (as shown in Fig. 4). Because of the machining accuracy or clearance for the assembly of the coil, some small gaps remain between the pancake coils and the coil case. When the coil is vibrated, components shift relative to each other generating frictional heat. One countermeasure was to fill the inside of the coil case with DCP (Dicyclopentadiene). DCP is a suitable filling resin, since it has a viscosity of less than 10 mPa･s, which means it easily infiltrates small gaps. In addition, its mechanical strength at low temperature is as high as that of epoxy resin [7].


Resonance phenomena are used in these vibration tests. Since the REBCO coil is approximately 140 kg, it is quite difficult to vibrate the coil to a high vibration acceleration. Hence, the REBCO coil was suspended from the flange of the cryostat to vibrate freely. The Eigen modes were determined by frequency response. The coil was then vibrated at its Eigen frequencies with a vibration acceleration of 10 G (98 m/s2).

The mechanical vibration test apparatus was designed to represent the actual maglev operation; the coil was cooled to below 40 K, and excited with a magnetomotive force of 700 kA during the vibration tests. The cryostat had a single-stage GM cryocooler, and the cryocooler was connected to the coil through multi-layer high-purity aluminum plates to separate the vibration. The vibrator was connected to the coil through a rigid rod. As the vibrator is located outside the cryostat, a bellows between the rod and the cryostat maintained the vacuum, and the vibration force was only transferred to the coil. Figure 5 shows the appearance of the apparatus. As shown in Fig. 5, two vibrators could be used in the vibration tests. This setup resolved the imbalance in the coil deformation due to the mass

Fig. 2 Superconducting magnet model for the evaluation of the eddy current heating by varying magnetic fields.

Fig. 3 Position of the superconducting coil and the coils which generate the varying magnetic fields.

Table 1 Analytical results of eddy current heating depending on coil case material

Coil case material

Resistivity at 50 K

Heat load Outer vessel

Coil case (per single

pole) 7075 aluminum alloy

2×10-8 Ωm 7470 W 0.31 W

304 stainless steel

4×10-7 Ωm 7470 W 0.66 W

Table 1 Analytical results of eddy current heating de-pending on coil case material

Coil casematerial

Resistivityat 50 K

Heat loadOutervessel

Coil case(per single

pole)7075 aluminumalloy

2 × 10-8 Ωm 7470 W 0.31 W

304 stainlesssteel

4 × 10-7 Ωm 7470 W 0.66 W

4. Mechanical vibration tests on REBCO coil

Analysis of frictional heating is not realistic because of the complicated coil structure. Frictional heating must therefore be evaluated experimentally. Reports exist on the frictional heating of a superconducting magnet, and some countermeasures have already been suggested [6]. It is possible for frictional heat to be generated between the coil case and the coil body in REBCO magnets. Therefore, countermeasures were taken to reduce the frictional heat-ing before the vibration tests.

4.1 Resin filling

The REBCO coil in this research consists of stacked pancake coils and a coil case capable of withstanding hoop stress (as shown in Fig. 4). Because of the machining ac-curacy or clearance for the assembly of the coil, some small gaps remain between the pancake coils and the coil case. When the coil is vibrated, components shift relative to each other generating frictional heat. One countermeasure was to fill the inside of the coil case with DCP (Dicyclopentadi-ene). DCP is a suitable filling resin, since it has a viscosity of less than 10 mPa･s, which means it easily infiltrates small gaps. In addition, its mechanical strength at low temperature is as high as that of epoxy resin [7].


Resonance phenomena are used in these vibration tests. Since the REBCO coil is approximately 140 kg, it is quite difficult to vibrate the coil to a high vibration accel-eration. Hence, the REBCO coil was suspended from the flange of the cryostat to vibrate freely. The Eigen modes were determined by frequency response. The coil was then vibrated at its Eigen frequencies with a vibration accelera-tion of 10 G (98 m/s2).

The mechanical vibration test apparatus was designed to represent the actual maglev operation; the coil was cooled to below 40 K, and excited with a magnetomotive force of 700 kA during the vibration tests. The cryostat had a single-stage GM cryocooler, and the cryocooler was connected to the coil through multi-layer high-purity alu-minum plates to separate the vibration. The vibrator was connected to the coil through a rigid rod. As the vibrator is located outside the cryostat, a bellows between the rod and the cryostat maintained the vacuum, and the vibra-tion force was only transferred to the coil. Figure 5 shows the appearance of the apparatus. As shown in Fig. 5, two vibrators could be used in the vibration tests. This setup resolved the imbalance in the coil deformation due to the mass of the rod, and offered another advantage: for coils with Eigen frequencies that are close together, they can be separated by adjusting the combination of the vibration points and the phase control of the vibrators.

Acceleration sensors were attached to the surface of the coil to evaluate not only the vibration acceleration, but also the mode shape. Temperature sensors were also attached to the coil surface, some of which were in the fill-ing resin inside the coil case. The location of the vibration heating could then be identified.

Experiments were performed in the following sequence:


First, a sweep vibration test was carried out to determine the Eigen modes (frequency response). Then, the coil was vibrated continuously at the Eigen frequencies. The vibra-tion acceleration was set at 10 G, and the heat value and the durability were evaluated (continuous vibration test). This paper describes the results of two-point-vibration. The vibration tests were carried out with and without excita-tion to reveal the influence of excitation on the heat gener-ated through vibration.

4.3 Frequency response

The REBCO coil was cooled down to 35 K and vibrated while not being excited. The vibration frequency was swept from 50 Hz to 400 Hz. The vibration points were the cor-ners on the lower side as shown in Fig. 6. The two vibra-tors were controlled to vibrate the coil in the same-phase or the reverse-phase. Figure 7 shows the dependence of the vibration acceleration per vibration force on the vibration frequency (frequency response function). Each peak indi-cates the Eigen frequency. Peaks appeared at 170 Hz and 295 Hz in the same-phase vibration and at 119 Hz in the reverse-phase vibration. The peak intensities depended on the sensor locations (a1~a12 in Fig. 6). A small peak meant that the sensor was close to a node. In addition, mode shapes were determined using the phase information of each sensor. The Eigen mode at 117 Hz was the torsional primary mode, at 170 Hz the bending primary mode and at 295 Hz the tor-sional secondary mode as shown in Table 2. Figure 8 shows the mode shapes. In the bending primary mode and in the torsional secondary mode, the vibration points (the corners on the lower side) underwent deformation in the same-phase. Conversely, they underwent deformation in the reverse-phase in the torsional primary mode. These results are consistent with the vibrator phases and confirm that the Eigen modes can be separated by controlling the phase of the vibration force.

Next, a frequency response test was carried out again with excitation at 700 kA. The frequency response func-tions were similar to those when not excited. However, the peaks had slightly higher frequencies, as shown in Table 2. When a coil is excited, compression forces are exerted on each of the pancake coils along with hoop stress. These stresses created a binding force on the contact faces of the

Fig. 4 Internal constitution of the real-scale REBCO coil

of the rod, and offered another advantage: for coils with Eigen frequencies that are close together, they can be separated by adjusting the combination of the vibration points and the phase control of the vibrators.

Acceleration sensors were attached to the surface of the coil to evaluate not only the vibration acceleration, but also the mode shape. Temperature sensors were also attached to the coil surface, some of which were in the filling resin inside the coil case. The location of the vibration heating could then be identified.

Experiments were performed in the following sequence: First, a sweep vibration test was carried out to determine the Eigen modes (frequency response). Then, the coil was vibrated continuously at the Eigen frequencies. The vibration acceleration was set at 10 G, and the heat value and the durability were evaluated (continuous vibration test). This paper describes the results of two-point-vibration. The vibration tests were carried out with and without excitation to reveal the influence of excitation on the heat generated through vibration. 4.3 Frequency response

The REBCO coil was cooled down to 35 K and vibrated

while not being excited. The vibration frequency was swept from 50 Hz to 400 Hz. The vibration points were the corners on the lower side as shown in Fig. 6. The two vibrators were controlled to vibrate the coil in the same-phase or the reverse-phase. Figure 7 shows the dependence of the vibration acceleration per vibration force on the vibration frequency (frequency response function). Each peak indicates the Eigen frequency. Peaks appeared at 170 Hz and 295 Hz in the same-phase vibration and at 119 Hz in the reverse-phase vibration. The peak intensities depended on the sensor locations (a1~a12 in Fig. 6). A small peak meant that the sensor was close to a node. In addition, mode shapes were determined using the phase information of each sensor. The Eigen mode at 117 Hz was the torsional primary mode, at 170 Hz the bending primary mode and at 295 Hz the torsional secondary mode as shown in Table 2. Figure 8 shows the mode shapes. In the bending primary mode and in the torsional secondary mode, the vibration points

(the corners on the lower side) underwent deformation in the same-phase. Conversely, they underwent deformation in the reverse-phase in the torsional primary mode. These results are consistent with the vibrator phases and confirm that the Eigen modes can be separated by controlling the phase of the vibration force.

Next, a frequency response test was carried out again with excitation at 700 kA. The frequency response functions were similar to those when not excited. However, the peaks had slightly higher frequencies, as shown in Table 2. When a coil is excited, compression forces are exerted on each of the pancake coils along with hoop stress. These stresses created a binding force on the contact faces of the pancake coils or between the pancakes coils and the coil case. As the pancake coils and the coil case may behave like a single mass due to these binding forces, the stiffness of the REBCO coil increases and the Eigen frequencies also drift upward.

4.4 Continuous vibration test

The REBCO coil was continuously vibrated at the Eigen

frequencies observed in the frequency response tests. This section describes the heat load in the continuous vibration test in the bending primary mode (170 Hz or 172 Hz) at a vibration acceleration of 10 G (98 m/s2). Figure 9 shows the temperature


Fig. 5 Mechanical vibration test apparatus

Fig. 6 Location of Acceleration and temperature sensors on REBCO coil

pancake coils or between the pancakes coils and the coil case. As the pancake coils and the coil case may behave like a single mass due to these binding forces, the stiffness of the REBCO coil increases and the Eigen frequencies also drift upward.


The REBCO coil was continuously vibrated at the Ei-gen frequencies observed in the frequency response tests. This section describes the heat load in the continuous vi-bration test in the bending primary mode (170 Hz or 172 Hz) at a vibration acceleration of 10 G (98 m/s2). Figure 9 shows the temperature trends when excited and when not excited. For the first 5 minutes, the coil was not vibrated, to confirm that the coil was in a thermally static state. After that, the maximum vibration acceleration was set to be 10 G (98 m/s2) and the coil was vibrated for 20 minutes. The coil voltage between the electrodes is also shown in the graph for when the coil was excited (see Fig. 9. b). The ini-tial temperature difference is caused by the Joule heating of the current leads. Although the coil temperatures were measured at several points, only the average temperature is shown here to clarify the heat load. The heat load can be calculated based on the heat capacity of the coil and the ca-pacity map of the cryocooler. The heat load when not excit-ed was approx. 1.3 W, and when excited was approx. 1.7 W. Considering the accuracy of the heat load calculation, these






























results indicate that the excitation had little or no effect on frictional heating due to vibration. In addition, the coil voltage did not change with the vibration. This confirmed that coil excitation remained stable while being vibrated.

5. Summary

The REBCO coated conductor, which is one of the HTS wires, raises the operating temperature of the magnet of the maglev. Introducing the REBCO magnets in practice, would help save energy, cut operating costs and reduce the weight of the magnet. In order for REBCO magnets to be introduced into service, it is essential to demonstrate that excitation remains stable even during vibration. Therefore, mechanical vibration tests were carried out using a full-scale REBCO coil with a magnetomotive force of 700 kA.

The inside of the REBCO coil was filled with DCP (Di-cyclopentadiene) to reduce frictional heating due to vibra-tion. When the coil was vibrated at a vibration acceleration of 10 G (98 m/s2) by using resonation, the heat load was less than 2 W whether the coil was excited or not. This confirmed that excitation has little effect on the frictional

Fig. 7 Frequency response functions at 35 K when not excited

Fig. 8 Mode shape of the REBCO coil

trends when excited and when not excited. For the first 5 minutes, the coil was not vibrated, to confirm that the coil was

in a thermally static state. After that, the maximum vibration acceleration was set to be 10 G (98 m/s2) and the coil was vibrated for 20 minutes. The coil voltage between the electrodes is also shown in the graph for when the coil was excited (see Fig. 9. b). The initial temperature difference is caused by the Joule heating of the current leads. Although the coil temperatures were measured at several points, only the average temperature is shown here to clarify the heat load. The heat load can be calculated based on the heat capacity of the coil and the capacity map of the cryocooler. The heat load when not excited was approx. 1.3 W, and when excited was approx. 1.7 W. Considering the accuracy of the heat load calculation, these results indicate that the excitation had little or no effect on frictional heating due to vibration. In addition, the coil voltage did not change with the vibration. This confirmed that coil excitation remained stable while being vibrated.

a. Same-phase vibration

b. Reverse-phase vibration


a. Torsional primary mode b. Bending primary mode c. Torsional secondary mode


Table2 Eigen frequencies of the REBCO coil at 35 K

Torsional primary mode (Reverse-phase)

Bending primary mode (Same-phase)

Torsional secondary mode (Same-phase)

170 Hz 295 Hz Excited (Magnetomotive force of 700 kA)

124 Hz 172 Hz 298 Hz

trends when excited and when not excited. For the first 5 minutes, the coil was not vibrated, to confirm that the coil was

in a thermally static state. After that, the maximum vibration acceleration was set to be 10 G (98 m/s2) and the coil was vibrated for 20 minutes. The coil voltage between the electrodes is also shown in the graph for when the coil was excited (see Fig. 9. b). The initial temperature difference is caused by the Joule heating of the current leads. Although the coil temperatures were measured at several points, only the average temperature is shown here to clarify the heat load. The heat load can be calculated based on the heat capacity of the coil and the capacity map of the cryocooler. The heat load when not excited was approx. 1.3 W, and when excited was approx. 1.7 W. Considering the accuracy of the heat load calculation, these results indicate that the excitation had little or no effect on frictional heating due to vibration. In addition, the coil voltage did not change with the vibration. This confirmed that coil excitation remained stable while being vibrated.

a. Same-phase vibration

b. Reverse-phase vibration


a. Torsional primary mode b. Bending primary mode c. Torsional secondary mode


Table2 Eigen frequencies of the REBCO coil at 35 K

Torsional primary mode (Reverse-phase)

Bending primary mode (Same-phase)

Torsional secondary mode (Same-phase)

170 Hz 295 Hz Excited (Magnetomotive force of 700 kA)

124 Hz 172 Hz 298 Hz

Table 2 Eigen frequencies of the REBCO coil at 35 K

Torsionalprimarymode(Reverse-phase)

Bendingprimarymode(Same-phase)

Torsional secondarymode(Same-phase)

170 Hz 295 HzExcited (Magnetomotiveforce of 700 kA)

124 Hz 172 Hz 298 Hz


heating due to vibration. The coil voltage was stable during the vibration. These results demonstrate that it is highly probable that REBCO magnets could be operated in a vi-brating environment, such as a maglev train.

Eddy current heating, which cannot be evaluated through mechanical vibration tests, was estimated using FEM. Aluminum alloy and stainless steel were compared as coil case material. The aluminum alloy coil case gener-ated lower levels of heat due to the eddy current. However, heat due to the eddy current was less than 1 W in both the materials and had little effect on the cooling of the magnet.

Fig. 9 Temperature and voltage trends during continuous vibration

5. Summary

The REBCO coated conductor, which is one of the HTS wires, raises the operating temperature of the magnet of the maglev. Introducing the REBCO magnets in practice, would help save energy, cut operating costs and reduce the weight of the magnet. In order for REBCO magnets to be introduced into service, it is essential to demonstrate that excitation remains stable even during vibration. Therefore, mechanical vibration tests were carried out using a full-scale REBCO coil with a magnetomotive force of 700 kA.

The inside of the REBCO coil was filled with DCP (Dicyclopentadiene) to reduce frictional heating due to vibration. When the coil was vibrated at a vibration acceleration of 10 G (98 m/s2) by using resonation, the heat load was less than 2 W whether the coil was excited or not. This confirmed that excitation has little effect on the frictional heating due to vibration. The coil voltage was stable during the vibration. These results demonstrate that it is highly probable that REBCO magnets could be operated in a vibrating environment, such as a maglev train.

Eddy current heating, which cannot be evaluated through mechanical vibration tests, was estimated using FEM. Aluminum alloy and stainless steel were compared as coil case material. The aluminum alloy coil case generated lower levels of heat due to the eddy current. However, heat due to the eddy

current was less than 1 W in both the materials and had little effect on the cooling of the magnet.

Acknowledgement

This work was financially supported by the Japanese Ministry of Land, Infrastructure, Transport and Tourism.

The authors would like to thank M. Takeuchi and N. Kishi from RIMTEC CO. for their technical cooperation in the resin filling process using DCP (Dicyclopentadiene) resin. References [1] Nagashima K., Ogata M., Mizuno K., Arai Y., Hasegawa H. and Sasakawa T., “Study on Component of Superconducting Magnet for Maglev Using High-temperature Superconducting Wire Based on Rare Earth Barium Copper Oxide,” RTRI Report, Vol.25，No.3，pp.17-22, 2011 (in Japanese). [2] Mizuno K., Sugino M., Tanaka M. and Ogata M., “Experimental Production of a Real-Scale REBCO Magnet Aimed at Its Application to Maglev,” IEEE Trans. Appl. Supercond., Vol. 27, 3600205, 2017. [3] Mizuno, K., Sugino M., Tanaka M. and Ogata M., “Development of a Real-scale REBCO Coil for the Demonstration of a Magnetomotive Force of 700 kA,” Quarterly Report of RTRI, Vol. 58, N0. 4, 2017. [4] Tsuchishima H., Suzuki E. and Terai Y., “Development of New Superconducting Magnets for Yamanashi Test Line,” RTRI Report, Vol. 8, No. 10, pp.17-22, 1994 (in Japanese). [5] Mizuno K., Sugino M. and Ogata M., “Experimental Production and Evaluation of Racetrack Coils for On-board REBCO Magnet,” RTRI Report, Vol.29，No.11，pp.11-16, 2015 (in Japanese). [6] SEINO H., “Study of a Frictional Heating Phenomenon Inside the Superconducting Coil and Development to Reduce the Frictional Heating,” RTRI Report, Vol. 20, No. 8, pp. 5-11, 2006 (in Japanese). [7] V. J. Toplosky and R. P. Walsh, “Thermal and Mechanical Properties of Poly‐Dicyclopentadiene (DCPD) at Cryogenic Temperatures,” Adv. Cryo. Eng., Vol. 52, pp. 219-224, 2006.

a. Non-excited condition

b. Excited condition Fig. 9 Temperature and voltage trends during continuous vibration

Acknowledgement

This work was financially supported by the Japanese Ministry of Land, Infrastructure, Transport and Tourism.

The authors would like to thank M. Takeuchi and N. Kishi from RIMTEC CO. for their technical cooperation in the resin filling process using DCP (Dicyclopentadiene) resin.

References

[1] Nagashima K., Ogata M., Mizuno K., Arai Y., Hasega-wa H. and Sasakawa T., “Study on Component of Superconducting Magnet for Maglev Using High-tem-perature Superconducting Wire Based on Rare Earth Barium Copper Oxide,” RTRI Report, Vol.25，No.3，pp.17-22, 2011 (in Japanese).

[2] Mizuno K., Sugino M., Tanaka M. and Ogata M., “Ex-perimental Production of a Real-Scale REBCO Mag-net Aimed at Its Application to Maglev,” IEEE Trans. Appl. Supercond., Vol. 27, 3600205, 2017.

[3] Mizuno K., Sugino M., Tanaka M. and Ogata M., “De-velopment of a Real-scale REBCO Coil for the Demon-stration of a Magnetomotive Force of 700 kA,” Quar-terly Report of RTRI, Vol. 58, N0. 4, 2017.

[4] Tsuchishima H., Suzuki E. and Terai Y., “Development of New Superconducting Magnets for Yamanashi Test Line,” RTRI Report, Vol. 8, No. 10, pp.17-22, 1994 (in Japanese).

[5] Mizuno K., Sugino M. and Ogata M., “Experimental Production and Evaluation of Racetrack Coils for On-board REBCO Magnet,” RTRI Report, Vol.29，No.11，pp.11-16, 2015 (in Japanese).

[6] SEINO H., “Study of a Frictional Heating Phenomenon Inside the Superconducting Coil and Development to Reduce the Frictional Heating,” RTRI Report, Vol. 20, No. 8, pp. 5-11, 2006 (in Japanese).

[7] V. J. Toplosky and R. P. Walsh, “Thermal and Mechani-cal Properties of Poly-Dicyclopentadiene (DCPD) at Cryogenic Temperatures,” Adv. Cryo. Eng., Vol. 52, pp. 219-224, 2006.

Authors

　　　　　

Katsutoshi MIZUNOAssistant Senior Researcher, CryogenicSystems Laboratory, Maglev SystemsTechnology DivisionResearch Areas: Superconducting Technology

　　　　　

Minoru TANAKA Dr. Eng.Senior Researcher, Cryogenic SystemsLaboratory, Maglev Systems TechnologyDivisionResearch Areas: Electrical Engineering, Superconducting Technology

　　　　　

Masafumi OGATA Dr. Eng.Senior Chief Researcher, Laboratory Head,Cryogenic Systems Laboratory, MaglevSystems Technology DivisionResearch Areas: Superconducting Technology

Documents

Mechanical Vibration Tests on Real-scale REBCO Coil