Stress/strain distribution in a simple single layered NbTi wounded superconducting sample coil was measured using Fibre Bragg Grating sensors at low temperature (4.2 K) and at high background magnetic field (8 T) excited by electrical potential. Ten gratings with different spatial period were fabricated at various positions along a single mode fibre (SMF). The grating location in the SMF sensing array was then attached at the measuring points on a SSC using stycast 2850 FT©. The change in the current density/ background magnetic field induces a stress in the SSC was then read out with a FS5100 Bragg meter. Experimental results showed that the FBG sensor array was highly repeatable with error of ± 0.008µs for high external magnetic field and high current. Also the maximum stress exhibited by the SSC at 900 A, 8T and at 4.2 K was measured to be 28 MPa which is well below to the young's modulus of the copper material which is ~ 130 GPa at 4.2 K This ensures that the SSC operates linearly well within the elastic limit for the applied current and magnetic field. In this paper, authors report the behaviour of each wound of the single layered SSC and its corresponding Lorentz force. The FBG sensing principle is validated by conducting various modes of SSC excitation.
Index Terms- Stress Measurement, Bragg Gratings, Optical Sensors, Superconducting coils.
INTRODUCTION
Superconducting (SC) magnets are used worldwide for many applications. It is estimated by CONECTUS, "the Consortium of European Companies determined to Use Superconductivity", that the global market for the superconductivity will increase to 5.5 billion euro in 2016 from present 5.1 Billion euro in 2012 [1]. SC magnets are used in large scale applications like International thermonuclear experimental reactors (ITER) which is built to serve the future power requirements. Apart from ITER, power cables, current limiters, transformers, motors/ generators, Nuclear Magnetic Resonance (NMR) spectrometer, Magnetic Resonance Imaging (MRI), magnetic levitation systems, magnetic bearings and cavities for accelerators are few more applications which depend on SC magnets. In addition the electronic applications like high frequency sensor coils for NMR, microwave filter for wireless communications, resonators for oscillators and other passive microwave devices, far infrared Bolometers, microwave and x-ray detectors, SC detectors, squids, and SC Josephson's contacts are some of the other systems that require optimally designed SC magnets for their better operations.
For more than 30 years the Institute for Technical Physics (ITEP) of the Karlsruhe Institute for Technology, campus north (KIT-CN) has been engaged in the field of superconducting high field magnets. The highlights of our efforts are the world record of 20.1 T for a superconducting magnet system achieved in 1987 [2] and the world's first 750 MHz [3] and 800 MHz NMR magnet systems built in 1991 and 1995, respectively. In 2009, along with KIT -CN, Brucker BioSpin GmbH installed its 1000 MHz NMR Magnet in France. This cooperation plans the further development of a 1200 MHZ NMR Magnet in the near future [4].
In order to develop high field magnets, it is essential to ensure that the mechanical support structure is good enough to withstand the mechanical stresses. High fields can induce large Lorentz force which leads to sudden coil movements. This small displacement in the loosely wounded SSC may initiate the quench because of the frictional heat. Moreover large Lorentz forces can damage the pressure sensitive Nb3Sn and new high temperature superconductors (HTS). In addition, cracking of resins and the fabrication process can develop stresses which are to be taken into account when developing such a high field magnets [5].
Considerable theoretical works have been carried out to understand quality of the mechanical support structures and its associated complex physical phenomenon like magnitude of the Lorentz force, local stresses along the coil, hot spot and quench. Many numerical / simulation methods have been developed to investigate the stress distributions in simple solenoids [11-14]. But this can only give an idea about the stress states which completely depends upon the good assumptions. To ensure the mechanical stabilities in the high field magnets they are usually fabricated using a complex composite structure. Hence, it is practically very difficult to estimate the stress states in a complex high field SSC using those two and three dimensional models. Some developed methods like Global-local analysis model and others advocate that they can give information about the local stress states in every material involved in SSC [15-19]. Even though theoretical analyses seem to be very promising, they lack experimental validation. Also, several assumptions are made for the modeling of the SC magnets in order to simplify the computer simulation which takes it away from the practical system. So it is essential to have an experimental system to study the actual stress states of SSC operated in a practical working environment.
The major limitation in validating the theoretical analyses with experiments on the SC magnets is the unavailability of a suitable sensor that can be integrated effectively during assembly of the SC magnets for accurate and reliable measurements. The sensor technology currently available cannot be used to measure the temperature and stress distribution in a SC magnet [15]. Commercially available sensors need penetration of the electrical cabling inside the SC magnet which may interfere with the magnet performance. Moreover, to measure the temperature and stress distribution, more sensors are required to be installed and this makes the sensing system more complex and costly.
For more than 15 years Fiber Bragg gratings (FBG) sensors were used extensively used in temperature and stress measurement in structural health monitoring [16]. For last five years, researchers all around the world attempting to use FBG for temperature and strain/stress measurement at cryogenic temperatures and in superconducting applications [17].
Schultz et al. [18] uses the Michelson interferometer method to detect hot spot (quench) in the CICC SC Magnets. They implemented the Fiber Optic sensors (FOS) in the TPX (Tokomak Physics Experiment) in Princeton Plasma Physics (PPP) Laboratory in United States. This sensor works on the principle of measuring optical path length (ΔL) and change in the refractive index (Δn) of the glass fiber. This sensing system measures the integrated temperature along its length which can protect the magnet during quenching. With this method local temperature distribution measurement will be complicated.
Pourrahimi [19] in 1995 reported coupling of laser light from one end to the other end of the fiber. This was the first demonstration of "beginning-to-end" feasibility of a fiber optic sensor in a medium-size, superconducting CICC. Schultz et al. [18] reported that the fibers survive during the winding process of SC magnet fabrication. Fibers were inserted into Quench long length experiment (QUELL) dummy coil and into the QUELL superconducting coil by Hitachi. The coils were 120-133 m long. The inner turn winding radius was 25 cm, while the crossover minimum radius was about 20 cm. It was concluded that the fiber survived during the winding process. All the above works give the integrated temperature/ stress measurement.
Ramalingam et al. [20] in 2006 reported the possibility of using FBG sensors in Cable in conduit Conductors for distributed temperature and stress/strain measurement. Later Lakta et al [21] demonstrated the operation of fiber Bragg grating sensor arrays for quench detection and localization in super conducting coils. Daou et al. [22] tested the FBG interrogation system described above in pulsed magnetic fields at the Hochfeld-Magnetlabor Dresden to measure the global stresses in a multilayered pulsed magnet. Schwartz et al [23] reported the possibility of integrating the FBG sensors into HTS superconducting magnets as co-wound insulation for quench detection.
In all the above referred literatures the authors either used FBG sensing system to identify the quench or study the global stress effects in a whole magnet system. But it is also very essential to know the stress/ strain distribution in a whole superconductor and at each single winding to understand the basic science involved and to estimate the behavior of the coil. This study could help to understand and to validate the operation of the FBG sensors and its sensing characteristics along with sample coil behavior. It also gives an idea for the magnet designer, the design and technology requirements to adapt FBG sensors to detect mechanical stress and conductor movement in or along a SC coil and to develop an optimized coil for the given application.
For this purpose the authors has developed a single layered simple NbTi sample coil in which the FBG sensor array's has been attached at specified locations and the local stress / strain distribution was measured. The initial test results which give test response of the sensors, the issues related to sensor designing and the installation technique has been reported in the previous publication [24]. In this paper the authors are aimed to study the behaviour of each wound of the single layered SSC more in detail and its corresponding Lorentz force for various background magnetic fields and applied current. Also FBG measuring technique has been validated by charging the background magnet with various ramping speed, ramping pattern and conducting various modes of SSC excitation tests.
FBG Principle
Fibre Bragg Gratings principle is well documented which works on the principle of wavelength reflection due to the change in the grating length [16]. The general measurement scheme and set up is shown in fig.1.
Fig.1. General Measurement scheme of Fibre Bragg Gratings
Gratings with different spatial period are arranged at various positions along a single mode fibre attached on the coil. In principle coil temperature and stress will vary the gratings' periods, which can be read out with a tunable laser in a wavelength division multiplexing (WDM) scheme. The spectral position of the reflections may be correlated with the spatial position of the gratings, and the shift of the gratings' maximum reflection indicates the change of the gratings' periods, which in turn measures temperature or stress.
Sample coil fabrication
The sample coil was prepared by wounding the niobium- titanium (NbTi) superconducting wire helically onto G10 glass fibre reinforced plastic coil former of 90 mm diameter shown in Fig.2 a. All conductors were provided with spacers to prevent transverse currents between neighboring windings. To prevent conductor movements, the NbTi conductor was fixed on the coil former with stycast 2850FT. Copper blocks were screwed to the ends of the G10 coil former for current feeding. Voltage taps were attached to the sample well away from the location of current leads to avoid the effects resulting from current redistribution at the ends of superconductor.
Fig.2. Sample coil
Fig. 2 (a) shows the scheme of the sensor design for SC Magnet stress/ strain measurements and its installed location. Fig 2 (b) shows that only the sensor is attached on the SC sample coil and the SMF region without any sensing element is left free. This is to ensure that the sensor exactly senses the local point stress. Further details of sensor design and installation has been discussed in the previous publication. [24]. Table 1 gives the specification the test sample coil.
TABLE I Sample coil specification
Parameters
Specifications
Sample
NbTi - F846
Sample coil dimension
Length = 80 mm
Diameter = 90 mm
Wall Thickness = 10 mm
No. of filaments
846
Diameter of the filament
0.065 mm
Length of conductor
1800 mm
Conductor dimension
2.46 mm * 5.20 mm
Number of layer
Single layer
Copper to non-copper ratio
4
RRR
70
Signal Interrogation and processing
The block diagram of the interrogation unit used in this study is shown in fig.3. Light from the tunable laser was split into two by a 50/50 fibre coupler and optical circulator. Half of the light was guided to a 10-FBG-sensor array while the other half to a National Institute of Standards and Technology traceable wavelength gas cell. This gas cell covers the wavelength range from 1520 nm to 1570 nm. When the wavelength of light emitted by the laser is continuously swept from 1520 nm to 1570 nm, reflections from FBGs are obtained at the photo detector at different instants. This happens because light reflected from each grating left the laser source at different times. In this way, the exact instant at which the reflection from a given FBG is obtained depends on its wavelength. Time can therefore be used for measuring wavelength. For absolute wavelength accuracy, on each laser sweep, the spectrum of a gas cell is also gathered. By comparing time synchronized spectra from both gas-cell and FBGs it is possible to monitor absolute Bragg wavelength changes as small as 1 pm.
Fig.3. Signal detection scheme
TABLE II Detection unit Specification
Technical parameter
Specification
Resolution
0.5 pm
Absolute accuracy
± 2.0 pm
Repeatability
±1.0 pm
Optical output power
10 dBm
Line width
125 kHz
Optical Isolation
45 dB
On each laser sweep the spectra of the FBGs as well as the one of the Gas-Cell is acquired and digitalized using tens of thousands of data points. All the points above a defined threshold are analyzed in order to establish if they correspond to a FBG signal or not (noise). A centroid method is then used to determine the central wavelength of the FBGs.
Test Facility
The stress/ strain distribution measurements shown in this publication are carried out with the high field Magnet facility JUMBO available at Institute of Technical Physics, Karlsruhe Institute for Technology (North Campus) which was commissioned in 1978 with experiments to test transient quench behaviours of superconducting solenoid systems[35]. This JUMBO magnet system is situated in a wide necked bath cryostat with a LN2 shield and liquid helium (LHe) volume of about 200 litres. At present two magnet configurations are in operation using coils wound with the customary round wires. The first configuration produces a field of 10 T using an NbTi solenoid wound wet with epoxy resin and a niobium tin (Nb3Sn) coil wound in a wind and reaction (W&R) technique. In a second configuration 15 T are achieved by adding an insert coil manufactured in W&R technique with an internal tin wire. The coils are serially connected at an operating current of 275 A. JUMBO operates in a power supply mode without quench detectors. An internal shunt resistor network protects the coils at quench. [25]. Operation details and scheme of high field magnet JUMBO testing facility has been discussed in [24].
Experimental Procedure
The Sample test SC coil was mounted concentrically inside a background magnetic field. The magnet system was placed in a cryostat and cooled down from room temperature to 4.2 K using liquid helium. The sensors were connected to the interrogation system via a feed-through at the top of the cryostat. It is known that the Lorentz force in a sample coil can be related as
(2)
(3)
(4)
is Lorentz stress, is diameter of the sample coil, is the applied current, is the cross sectional area of the coil, is the external magnetic field. Therefore there are two possibilities to apply the stress/ strain in the sample coil. One way is to change the applied current, I (t) and other way is to vary the applied magnetic field. The variation of the applied current and the magnetic field can be done either by continuous pattern or by step pattern. Hence the coil energization was conducted by increasing the applied current in step and continuous mode at constant background magnetic field and vice versa. Finally the applied current and background magnetic field has been varied simultaneously. The Bragg wavelength shift was recorded by using Bragg meter. The recorded Bragg wavelength shift was then converted to corresponding strain. The coil energization sequence is listed in Table III in four different cases.
TABLE III Coil ENERGIZATION SEQUENCE
Case 1: Constant external Magnetic field
External
Field [T]
Current
[A]
Ramp
type
Step
interval
Ramp
Up
(RU)
Speed
[A/s]
Ramp
Down
(RD)
Speed
[A/s]
1
150-900
step
150
3
3
2
150-900
step
150
3
3
4
150-900
step
150
3
3
8
150-900
step
150
3
3
Case II: Constant applied current
Current
[A]
External
Field [T]
Ramp
type
Step
interval
Ramp
Up
(RU)
Speed
[mT/s]
Ramp
Down
(RD)
Speed
[mT/s]
300
1-8
step
1,2,4,8
18.5
14
600
1-8
step
1,2,4,8
18.5
14
900
1-8
step
1,2,4,8
18.5
14
Case III Constant current and varying magnetic field by varying ramp type and ramp speed.
Current
External magnetic
field
Ramp
type
Step interval
Ramp
Up
(RU)
Speed
[mT/s]
Ramp
Up
(RU)
Speed
[mT/s]
600
0-8
step
1,2,4,8
18.5
14
600
0-8
continuous
18
14
600
0-8
continuous
9.5
9
600
0-8
Triangle
18
14.8
Case IV: Simultaneous variation in both external magnetic field and current
Setting
Ramp up
Ramp down
Ramp
type
Parameter
Reach first
5,75 T, 900A
19 mT/s , 3A/s
14mT/s , 3A/s
continuous
Current
7.5 T, 900A
19mT/s, 2,25 A/s
14mT/s, 2,25 A/s
continuous
Current
Evaluation Procedure
The strain in the sample coil can be calculated with the recorded Bragg wavelength shift.
(5)
The stress in the sample coil can be calculated rewriting equation 3 as
(6)
Where r = radius of the sample coil (45 mm)
jcoil = of SC Current density (150 - 900 in steps of 150) A
Bext = External Field of JUMBO magnet system (1, 2, 4, 8) T
Equation 3 explains that the applied current and the field will be linear to the stress developed in the coil. Hence FBG measuring principle can also be validated by proving the linearity in the current and field to the stress in the sample.
Results and discussion
Case 1 & II: Constant background magnetic field for varying applied current and vice versa
The SC sample coil was energized and de-energized in the sequence shown in table III (case 1). Fig. 4 shows the wavelength shift for the applied current which varies in steps from 150 A to 900 A in time for a fixed magnetic field of 1 T.
Fig.4. Wavelength shift of all 12 sensors for applied current (150-900 A) and for magnetic field of 1 T.
The maximum wavelength shift of 11 pm was sensed which can be translated to nearly 9 µ strain by using equation 5. It should be also noted that sensor S1 exhibit a very small wavelength shifts compared to the other sensors. This is because this sensor is attached in the location where the sample SC wire was soldered using a soldering material on top of the coil former. This soldering may not allow the sensor to sense the actual strain caused by the applied current and magnetic field. Sensor 2 was also attached in the same conductor and so the measured strain from this sensor can also have the effect from soldering. Hence for further analysis sensors S1and S2 will be omitted.
Figs. 5 show the mean strain distribution measured by S3- S10 at locations 350 mm and 1400 mm for different magnetic field and the applied current respectively. It has been found that the strain response of all individual sensors for varying magnetic field and for varying applied current varies linearly.
Fig.5. Mean strain distributions measured by S10 located at the distance of 1400 mm for varying B and Jcoil
Fig. 6 (A) shows the average strain of all sensors keeping the sample coil current constant, varying the magnetic field and Fig 6 (B) shows the average strain of all sensors keeping the external magnetic field constant and varying the sample coil current The different operation pattern like step variation continuous variation, different ramping rate of the sample coil has always exhibited the same strain. This behaviour of the FBG sensor array proves that the sensor has a good repeatability and reproducibility. Also the strain exhibited by the sample coil is purely dependent on the Lorentz force in the coil and not from the displacement of the coil which is key information for a magnet designer.
Fig 6. (A) Average strain for fixed magnetic field and varying coil current and (B) for fixed coil current and varying magnetic field
Averaged strain values for constant magnetic field and for constant applied currents cases are showed in table IV and table V. From the above tables, the accuracy/ error in the measurement could be estimated. The error rate at lower magnetic field and applied current is relatively large in the order of ± 4 µs when compared to the higher field and applied current which is estimated to be ± 0.008 µs. At lower fields and currents the noise signals are more dominating as the signal from the strain is relatively low. But as the SC sample operated at high field and the current, then the error seems to be in Nano strain which is very negligible. For example, the values from 8T, 900 A shows more or less the same values in both a cases. This ensures again the sensors are highly repeatable and reproducible.
TABLE IV Averaged Strain for case I
B [T]
300 A/s
600 A/s
900A/s
1
2,25E-06
4,90E-06
7,62E-06
2
5,13E-06
1,03E-05
1,56E-05
4
9,91E-06
2,01E-05
3,02E-05
8
2,00E-05
4,03E-05
6,10E-05
TABLE V Averaged Strain for case II
I [A/s]
1T
2T
4T
8T
300
1,57E-06
3,11E-06
6,22E-06
1,25E-05
600
5,14E-06
1,02E-05
2,04E-05
4,07E-05
900
7,84E-06
1,55E-05
3,02E-05
6,12E-05
Case III Constant current and varying magnetic field by varying ramp type and ramp speed.
To validate the sensor and to ensure the stress states developed in the SC sample coil for various modes of operation, the coil was then energized and de-energized in the sequence shown in table III (case III).
Fig 7. Average strain for various ramp type and speed
Figure 7 shows the bar diagram of the sensor response for the above specified sequence of SC coil operation. Irrespective of the type of ramp and the speed of ramp the SC sample coil always experience the same stress. This also means that the sensor survives for the amount of Lorentz force exhibited by the SC coil and the sensor array was highly repeatable and stable in its operation.
Case IV: Simultaneous variation in both external magnetic field and current
Finally, the SC sample coil was then excited by varying the background magnetic field and the applied current simultaneously to study the stress behavior of the sample coil and the response of the FBG sensor array. The excitation was done according to table III (case IV). The excitation of external magnetic field and the applied current was started at the same time During the first run the applied current reaches the set current of 900 A before the magnetic field can reach its set field of 8 T. The magnetic field could reach only 5.75 T The response of the sensor array is shown in figure 8.
Fig8: Simultaneous excitation of Current and magnetic field (Run 1)
Fig 9: Simultaneous excitation of Current and magnetic field (Run 2)
For the second run, the ramping speed of applied current was reduced to 2.25 A/s from 3A/s which was used in the first run. Figure 10 shows the sensor response of the second run. In this run also the applied current reaches first the set current but the external magnetic field rise nearly matches the speed of applied current. In figure 8, it could be observed that the strain rise was sharp shoot and very fast. Whereas from figure 9 the strain rise was very smooth and slow. This kind of operation can help the magnets to take the strain slowly and thus avoiding the sudden stress rise which could lead the magnet to quench.
Fig 10. Average strain for fixed magnetic field and varying coil current
Fig.10 shows the stress and strain relation of the tested sample coil. The young's modulus of the copper material at 4.2 K has been found to be ~ 130 Gpa [26]. The maximum stress exhibited by the sample coil at 900 A, 8T and at 4.2 K was measured to be 28 Mpa which can be seen clearly from the figure 15. This stress level is comparably negligibly small. This clearly gives information that the sample coil operates well below the linear region of the stress-Strain curve. In other words, the superconducting coil composite material does not enter into the proportional limit of the stress-strain curve and also ensures that the sample SC coil operates well within the elastic limit for the applied current and magnetic field.
Conclusion
A sample coil was fabricated and a wavelength division multiplexed FBG sensor array with 10 sensors was attached in sample SC coil using stycast. The Sensor attached sample SC coil was then installed in a JUMBO testing facility available at High Field Laboratory, ITEP, KIT (north campus). The experiments were conducted by increasing the applied current keeping magnetic field constant, varying the magnetic field and keeping the current constant, with different ramping patterns and speeds and finally varying the magnetic field and the applied current simultaneously. The Bragg wavelength shift was recorded by using Bragg meter. The recorded Bragg wavelength shift was then converted to corresponding strain. As expected the change in the strain increased for the increasing magnetic field and critical current. The maximum strain observed was about 60 µ strain. The strain observed in all cases of operation coincides well with each other. The estimated error was nearly ± 4 µs at lower fields and currents but error getting negligibly small in the order of 8 ns when the SC sample operated at high field and at high current. This implies that the FBG sensors show good repeatability. Also as expected the experimental results exhibit a linear relationship between the stress, coil current and for the magnetic field which validate the reliability of the FBG sensing array. Hence the FBG sensing principle can be utilized to investigate more physical phenomenon related to SC coil design.
