Fusion Engineering and Design 58–59 (2001) 253–257

Stress and strain measurement of the large helical deviceduring coil excitation

A. Nishimura *, H. Tamura, S. Imagawa, T. Satow, S. Satoh, O. Motojima,and the LHD group

National Institute for Fusion Science, 322-6 Oroshi, Toki, Gifu 509-5292, Japan

Abstract

The large helical device (LHD), which has a large superconducting magnet system, has been constructed and themagnetic field at the plasma axis reached to 2.9 T in the third cycle operation in 1999. To carry out the strainmeasurement without temperature rise by eddy current, slow ramp rate of the magnetic field was employed and thedata acquisition system worked continuously during the coil excitation. The results obtained in the experimentsshowed that the deformation behavior of the cryogenic support structure could be explained qualitatively and it wasconfirmed that the FEM analysis gave good results in comparing with the stresses measured. Also, it is clarified thatthe strain measurement will give valuable information on the deformation and the stress condition even at cryogenictemperature, in high vacuum and under high magnetic field, and it is possible to evaluate the soundness of thecryogenic structure. © 2001 Elsevier Science B.V. All rights reserved.

Keywords: Strain measurement; Superconducting magnet; Fusion device

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1. Introduction

The large helical device (LHD) has one pair ofhelical coils and three pairs of poloidal coils. Allthese coils are superconducting, and the helicalcoils are expected to generate huge electromag-netic force of over 10 MN/m when the magneticfield at magnetic axis is 4 T [1–3]. To sustain thehuge electromagnetic force, a large cryogenic sup-port structure was constructed using 316 stainless

steel of 100 mm thickness [4]. During the thirdcycle operation in 1999, the maximum magneticfield of 2.9 T was achieved at magnetic axis andthe plasma experiments were performed. Duringthe coil excitation, stress and strain measurementswere conducted continuously to evaluate thesoundness of the cryogenic support structure.

In this report, the results of the strain measure-ment on the inner and outer equators are pre-sented and the deformation behavior of thecryogenic support structure is discussed focusedon the welding structure. In addition, the stressmeasured is averaged and compared with thenumerical results by FEM, then the relationship isinvestigated.

* Corresponding author. Tel.: +81-572-58-2118; fax: +81-572-58-2616.

E-mail address: nishi-a@lhd.nifs.ac.jp (A. Nishimura).

0920-3796/01/$ - see front matter © 2001 Elsevier Science B.V. All rights reserved.

PII: S0920 -3796 (01 )00454 -9

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2. Strain measurement

The strain gages used in the LHD were newlydeveloped and have a gage length of 5 mm, anelectric resistance of 350 �, a base diameter of 20mm and a gage factor of �2.0 [5]. There arethree resistance gages on one base. Two gagesmake a right angle and the direction of the thirdgage is inclined at 45 ° to others. To cancel theapparent strain induced by fluctuating magneticfield, a Wheatstone bridge circuit consisting ofactive and dummy gages was constructed near theactive gage. Much effort to reduce the electricnoise was attempted, such as finely twisted gageleads and cables that were specially designed forthis purpose [6,7].

The cryogenic support structure consists of 10sectors and one sector covers 36 ° of the centerangle. The top and bottom halves were weldedindependently to the toroidal direction and thenthey were welded on the inner and outer equatorsin the mid-plane. The strain gages were attachedon the crossing position of the toroidal weldingand the equator welding lines as shown in Fig. 1.HSNE 3X09 and 3X12 show the strain in thetoroidal direction, 3X11 and 3X14 are those inthe poloidal direction, and 3X10 and 3X13 arethose in 45 ° direction to the torus. HTE 3X17and 3X19 are thermo-sensors (Cernox) locatedunder IV-U coil frame and on the outer equator,respectively. X in the tag number indicates thesector number. Each sector has four cooling chan-nels and the cooling was carried out by two-phasehelium continuously during the coil excitation.

Fig. 2. Change in magnetic field and temperature excited to2.915 T.

3. Results and discussion

The variation in magnetic field at magnetic axisunder c1−d mode (the plasma major radius is3.6 m) is shown in Fig. 2 together with thetemperature change of HTE 3117 and 3219. Themagnetic field was increased up to 2.6 T at therate of 0.1 T/min, then a step excitation wasperformed and 2.915 T at magnetic axis wasachieved. This magnetic field is the maximum fieldthat the LHD generated up to now. Since theunstable voltage due to normal zone propagationwas observed at 2.915 T, the coil currents werereduced rapidly. On the ramp-up and ramp-downprocesses, the temperature rose clearly, but re-duced during the step excitation. Since there is noelectric break in the cryogenic support structure,the temperature rise is caused by the eddy current.

The strain change in the poloidal direction dur-ing the excitation is shown in Fig. 3. The unit ofstrain is 10−6 and described in the figure. Thevertical axis shows the square of the magneticfield corresponding to the electromagnetic force.The strain on the inner equator shifted to negativedirection on the ramp up process and came nearto a certain line during the step excitation becauseof temperature decrease as shown in Fig. 2. Theinitial shift is caused by the apparent strain gener-ated by the temperature rise of the active gage.On the other hand, the strain on the outer equa-tor varied rather linearly because of the smalltemperature rise.Fig. 1. Cross sectional view of Sector 1.

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Fig. 3. Relation between the square of magnetic field andstrain in poloidal direction (c1−d mode).

Fig. 5. Relation between the square of magnetic field andstrain in poloidal direction. (c1−d mode, ramp rate; 0.02T/min).

To reduce the effect of eddy current, the lowerramp rate of 0.02 T/min was adopted and thecoils were excited up to 2.85 T at magnetic axisunder c1−d mode. The profile of the magneticfield variation and the temperature change areshown in Fig. 4. By applying the lower ramp rate,the temperature change on both equators wasreduced to almost negligible, and it was recog-nized that the two-phase helium could remove theheat by the small eddy current under the lowerramp rate. The change in strain against the squareof the magnetic field is shown in Fig. 5. In thisfigure, the straight lines describing the relationbetween the square of magnetic field and strainare the same as those shown in Fig. 3. On theouter equator, the strains in three directions werechanged almost linearly. However, the strains on

the inner equator showed non-linear behavior,drawing a reversible hysteresis curve and notstraight lines. Since all strains varied back to theinitial values after the coil excitation, it is clearthat the deformation of the cryogenic structurewas gone and recovered. To reduce the weldingdeformation, a metal touched area was induced inthe weld groove as shown in Fig. 6. The straingage was attached on the cross point of weld lines

Fig. 6. Schematic illustration of weld joint and strain gagelocation.

Fig. 4. Change in magnetic field and temperature under thelower ramp rate.

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Fig. 7. Summary of measured stress on equators. (c1−d, at2.90 T).

shape of the ports and the ribs. From these re-sults, it is found that the inner equator ispushed to the center of the device and pulled toup and down directions and that the outerequator is pushed to the outside of the majorradius and pulled upward and downward.

To investigate the relationship between themeasured stress and the estimated stress byFEM, the stresses in the poloidal direction ob-tained in the experiment were averaged and thenumerical results were modified taking accountof the differences of the stress concentration, theplate thickness and the magnetic field [7]. Theresults are shown in Fig. 8. All the data areplotted near the one to one correspondence lineand the averaged stress is in good agreementwith the estimated one. This means that theglobal stress can be estimated by the FEM anal-ysis and the support structure works well as ex-pected. When the 4 T operation is performedunder the standard mode of R=3.75 m, theaverage stress on the outer equator is expectedto reach �85 MPa, because the stress becomeslarger by a factor of the square of the magneticfield. This stress is small enough, even consider-ing the stress concentration of �3.0, in com-parison with the yield stress at 4.2 K of over630 MPa.

in poloidal and toroidal directions, and thecompressive electromagnetic force acted in thetoroidal direction on the inner equator and themetal touched area was compressed with theforce as is discussed later. When the compress-ing process and releasing process are not thesame, it results in generating the non-linearstrain behavior and making hysteresis. In addi-tion, the inner horizontal port is not installed ateach sector and the ligament between horizontalports is not the same. Those factors would af-fect the deformation behavior of the cryogenicstructure.

The results of stress evaluation on the equa-tors at 2.90 T under c1−d mode are shownin Fig. 7. The stresses were evaluated usingYoung’s modulus of 200 GPa and Poisson’s ra-tio of 0.33. Fig. 7 describes the mid-plane of thesupport structure and the helical coil position.Solid part of the inner and outer circles showthe ligament and dotted part indicate the hori-zontal ports. A pair of figures shows the stressesat each position; the upper figure indicates thestress in the toroidal direction and the lowerfigure is the poloidal direction stress. The differ-ence of the stress among the sectors is consid-ered to come from the difference of the size and

Fig. 8. Relation between averaged stress measured in theexperiment and estimated stress by FEM.

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4. Conclusion

To measure the stress of the cryogenic supportstructure and evaluate the soundness of the struc-ture, the strain measurement system was devel-oped and installed in the LHD. During the thirdoperation, the maximum magnetic field of 2.9 T atmagnetic axis was created and the long termstrain measurement was carried out successfully.The main results are summarized as follows: (1)The temperature rise by the eddy current wasclarified. (2) The support structure works well tosustain the huge electromagnetic force. (3) Thereversible strain hysteresis curve would be causedon the compression process of the metal touchedarea in the weld groove. (4) The averaged stressagrees well with the numerical result by FEM.

References

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[3] M. Fujiwara, et al., Overview of long pulse operation inthe large helical device, Nucl. Fus. 40 (2000) 1157–1165.

[4] S. Imagawa et al., Design and Construction of CryogenicSupporting Structures for LHD, Proc. 20th SOFT (1998)779–782.

[5] A. Nishimura et al., Strain Measurement in FluctuatingMagnetic Field and during Cold thermal Cycles, Proc. 15thInt. Conf. Magnet Technology (1998) 1275–1278.

[6] A. Nishimura et al., Mechanical Deformation of the LargeHelical Device during Cooling-down and Excitation Tests,Proc. 20th SOFT, (1998) 869–872.

[7] A. Nishimura, et al., Temperature rise and strain behaviorof large helical device during coil excitation, Adv. Cryo-genic Eng. 45 (2000) 745–752.